modeling of a cooling airflow

5/26/2018 Modeling of a Cooling Airflow

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Modeling of a Cooling Airflowin an Electric Motor

D A N I E L A A N D E R L

Master of Science ThesisStockholm, Sweden 2011


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Modeling of a Cooling Airflowin an Electric Motor

D A N I E L A A N D E R L

Masters Thesis in Numerical Analysis (30 ECTScredits)

at the Scientific Computing Master Programme

Royal Institute of Technology year 2011

Supervisor at CSC was Jesper OppelstrupExaminer was Michael Hanke

TRITA-CSC-E 2011:083

ISRN-KTH/CSC/E--11/083--SE

ISSN-1653-5715

Royal Institute of Technology

School of Computer Science and Communication

KTHCSC

SE-100 44Stockholm, Sweden

URL: www.kth.se/csc


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Abstract

An electric motor converts electrical to mechanical energyand provides the rotational torque which is converted intolinear motion. In some applications the duty is cyclic andthe motor is used for both providing driving and breakingtorque. In many applications today, the power to weightrequirements are continuously increasing which means thatthe cooling is crucial. One of the major design elementsin the cooling system of an electric motor is the fan. Un-fortunately the current fan exceeds the noise constraints.The thesis analyses the fan in terms of noise productionand performance, and proposes an improved fan design.

The computation of the airflow is done with the softwareCOMSOL. In the beginning different design guidelines andnoise sources of a fan in general are summarized. Subse-quently the concrete simulation procedure in COMSOL isdescribed. After these basic issues are discussed, the dif-ferent noise sources, namely the broad-band and the tonalnoise, are investigated for the current fan and the improvedfan design. The analysis of different design-space param-eters is also done in terms of performance of the fan, i.e.the actual transported airflow together with the producedpressure difference. In the end, the results of these studiesare summarized and the most improved fan design is the

outcome of this.


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Referat

Modellering av en luftstrm fr att kyla en

elektrisk motor

En elektrisk motor producerar mycket vrme och kylnin-gen av en sdan motor blir hgst viktig. Fr att tillse ettluftflde som uppfyller nedkylningskraven roterar en flktmed motorn. Olyckligtvis uppfyller inte, typiskt sett, ettsdant system krav pbuller. Detta arbete analyserar flk-ten utifrn dess genererade buller och kapacitet och freslren frbttrad flktdesign. Berkningen av luftfldet utfrsmed mjukvaran COMSOL. Till en brjan sammanfattasversiktligt olika riktlinjer fr flktdesign och bullerkllorfrn flkten. Nstfljande del beskriver det konkreta frlop-pet av simuleringen i COMSOL. Efter att dessa grundlg-gande frgor diskuterats utreds de olika bullerkllorna, speci-fikt bandbredd och tonljud, fr flkten och den frbttradedesignen. Analys av olika geometriska parametrar utfrsutifrn flktkapaciteten, alltsdet frflyttade luftfldet till-sammans med det genererade tryckskillnaderna. Till slutsammanfattas resultaten av dessa studier. Resultatet avdetta blir att en frbttrad design pvisas.


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Contents

List of Figures

List of Tables

1 Fans 1

1.1 Different types of fans . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Ideal fan design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Fan characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.1 Fan curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.2 Fan laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Application to straight radial blades . . . . . . . . . . . . . . . . . . 71.5 Generation of fan noise . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5.1 Theory for noise radiation . . . . . . . . . . . . . . . . . . . . 81.5.2 Fan noise sources . . . . . . . . . . . . . . . . . . . . . . . . . 101.5.3 Unsteady blade forces . . . . . . . . . . . . . . . . . . . . . . 111.5.4 Influence of outlet grille . . . . . . . . . . . . . . . . . . . . . 12

2 COMSOL 13

2.1 CFD module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Design of Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Slice of fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Building geometries in COMSOL . . . . . . . . . . . . . . . . 15

2.3 Application case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.1 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.2 Boundary layers . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.3 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 192.3.5 Convergence issues . . . . . . . . . . . . . . . . . . . . . . . . 192.3.6 Rotating reference frame . . . . . . . . . . . . . . . . . . . . . 202.3.7 Inconsistent Stabilization . . . . . . . . . . . . . . . . . . . . 21

2.4 Mesh-converged solution . . . . . . . . . . . . . . . . . . . . . . . . . 232.5 Cluster Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Approach for broad-band noise 29


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3.1 Basic idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Original geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.1 Important parameters . . . . . . . . . . . . . . . . . . . . . . 313.3.2 Observations and Changes . . . . . . . . . . . . . . . . . . . . 31

3.4 Geometry variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.4.1 Height of inter-blade channel inlet . . . . . . . . . . . . . . . 393.4.2 Distance between ring and blade . . . . . . . . . . . . . . . . 413.4.3 Outer blade radius . . . . . . . . . . . . . . . . . . . . . . . . 413.4.4 Angle of blade end back . . . . . . . . . . . . . . . . . . . . . 443.4.5 Radius for rounding of ring edge . . . . . . . . . . . . . . . . 49

4 Fan performance 534.1 Model set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2 Fan curve from simulation . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Influence of different parameter changes . . . . . . . . . . . . . . . . 57

4.3.1 Height of inter-blade channel inlet . . . . . . . . . . . . . . . 574.3.2 Distance between ring and blade . . . . . . . . . . . . . . . . 574.3.3 Outer blade radius . . . . . . . . . . . . . . . . . . . . . . . . 584.3.4 Angle of blade end back . . . . . . . . . . . . . . . . . . . . . 594.3.5 Radius for rounding of ring edge . . . . . . . . . . . . . . . . 60

5 Tonal Noise 63

5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 Blade spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6 Results 67

6.1 Shortened motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1.1 Number of blades . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Bibliography 75


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List of Figures

1.1 Different types of fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Open self-ventilated electric motor . . . . . . . . . . . . . . . . . . . . . 21.3 Sketch of inter-blade channel geometry . . . . . . . . . . . . . . . . . . . 41.4 Analogy electricity and flow system . . . . . . . . . . . . . . . . . . . . . 51.5 Sketch of fan and system curve . . . . . . . . . . . . . . . . . . . . . . . 61.6 System curve from ABB measurements . . . . . . . . . . . . . . . . . . 61.7 Sketch of curved blades and lift principle . . . . . . . . . . . . . . . . . 81.8 Variable explanation for Lighthill analogy . . . . . . . . . . . . . . . . . 91.9 Summary of aeroacoustic fan noise sources [8] . . . . . . . . . . . . . . . 10

2.1 Principle of slice domain of blade wheel . . . . . . . . . . . . . . . . . . 142.2 Steps to build geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Cylinder with additional edges . . . . . . . . . . . . . . . . . . . . . . . 162.4 Sketch of different boundary layers . . . . . . . . . . . . . . . . . . . . . 172.5 Sketch of wall lift-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.6 Sketch of boundary layer mesh . . . . . . . . . . . . . . . . . . . . . . . 182.7 Sketch of rotating reference frame . . . . . . . . . . . . . . . . . . . . . 202.8 Static pressure on the stator inlet for different stabilization . . . . . . . 222.9 Turbulent kinetic energy for different stabilization . . . . . . . . . . . . 232.10 Meshes with different resolutions . . . . . . . . . . . . . . . . . . . . . . 242.11 Static pressure in z x-plane for different meshes . . . . . . . . . . . . . . 252.12 Static pressure in z x-plane for refined mesh . . . . . . . . . . . . . . . . 252.13 Turbulent kinetic energy in z x-plane for different meshes . . . . . . . . . 26

3.1 Sketch of cross section area in inter-blade channel . . . . . . . . . . . . . 313.2 Static pressure inz x-plane for original and improved geometry . . . . . 333.3 Radial velocity inz x-plane for original and improved geometry . . . . . 343.4 Tangential velocity inz x-plane for original and improved geometry . . . 353.5 Turbulent kinetic energy in z x-plane for original and improved geometry 363.6 Radial velocity on azimuthal planes for original and improved geometry 373.7 Sketch of design-space parameters to sweep . . . . . . . . . . . . . . . . 383.8 Radial velocities for different inter-blade inflow heights . . . . . . . . . . 403.9 Turbulent kinetic energy for different ring-blade distances . . . . . . . . 41


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3.10 Maximum turbulent kinetic energy for different outer blade radii . . . . 42

3.11 Tangential velocity for different outer blade radii . . . . . . . . . . . . . 433.12 Sketch of secondary flows . . . . . . . . . . . . . . . . . . . . . . . . . . 433.13 Sketch of blade back end angle variation . . . . . . . . . . . . . . . . . . 443.14 Static pressure in z x-plane for different blade end angles . . . . . . . . . 453.15 Turbulent kinetic energy in z x-plane for different blade end angles . . . 463.16 Static pressure in y z-plane for different blade end angles . . . . . . . . . 473.17 Turbulent kinetic energy in yz-plane for different blade end angles . . . 483.18 Radial velocity inz x-plane for different ring edge diameters . . . . . . . 50

4.1 Sketch of different inlets . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.2 Sketch of two different measurement set-ups . . . . . . . . . . . . . . . . 55

4.3 Fan curve for original geometry . . . . . . . . . . . . . . . . . . . . . . . 564.4 Fan curve for improved geometry . . . . . . . . . . . . . . . . . . . . . . 564.5 Dependency between pressure difference and blade-ring distance . . . . 584.6 Dependency between pressure difference and outer blade radius . . . . . 594.7 Dependency between pressure difference and blade end angle . . . . . . 604.8 Dependency between pressure difference and ring edge diameter . . . . . 61

5.1 Blade spacing for original and regular blade wheel . . . . . . . . . . . . 645.2 Blade spacing for minimization with different initial conditions . . . . . 655.3 Best spacing out of15.000 only slightly irregular spacings . . . . . . . . 66

6.1 Shortened motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.2 Results inxz -planes for shortened motor . . . . . . . . . . . . . . . . . . 706.3 Radial velocity on azimuthal planes for different blade numbers . . . . . 71


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List of Tables

2.1 Variable values for different meshes . . . . . . . . . . . . . . . . . . . . . 24

3.1 Surface areas for different inlets . . . . . . . . . . . . . . . . . . . . . . . 303.2 Radial velocities for different azimuthal planes and geometries . . . . . . 373.3 Radial velocities at azimuthal planes for different inter-blade inlet heights 403.4 Variable values for different blade end angles . . . . . . . . . . . . . . . 493.5 Variable values for different ring edge diameters . . . . . . . . . . . . . . 50

4.1 Measurements of velocity through inlets with1.05ms1 at4500rpm. . . 54

6.1 Radial velocities for different azimuthal planes and blade numbers . . . 71


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Chapter 1

Fans

1.1 Different types of fans

Fans are used in many different application areas and show therefore a huge varietyin design. They range from turbomachines to ceiling fans, which of course results

in totally different geometric appearances. But fans can be roughly grouped by twomain classes:

Axial fans suck in the air axially and blow it out axially again, as sketched infigure 1.1(a). This means the fluid flows in and out parallel to the rotation axis.In the fan wheel the fluid is accelerated around the rotation axis to achieve thenecessary pressure difference.

The other group of fans are the radial or centrifugal fans, see figure 1.1(b).There the fluid also enters axially but leaves the fan wheel in radial direction. Thefluid is also accelerated, or decelerated for turbines, around the axis and in additiondeflected from axial to radial direction.

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CHAPTER 1. FANS

(a) Axial fan (b) Radial fan

Figure 1.1. Different types of fans

The fan in this thesis is a radial fan. The considered fan delivers the coolingairflow for an electric motor and is placed at the end of the motor and rotates withthe same speed as the rotor. This is called an open self-ventilated motor.

The air flows axially into the inlet and through the channels in the motor andis deflected within the fan in order to leave the motor radial through the outlets.

In figure 1.2 the position of the fan is visualized at the back of the motor and theairflow is denoted by arrows.

Figure 1.2. Open self-ventilated electric motor

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1.2. IDEAL FAN DESIGN

1.2 Ideal fan design

The cross sections in a fan channel from the inflow to the outflow should be equaleverywhere since the air passing the fan channels can mostly be assumed as incom-pressible. In case of very high velocities, the air will be slightly compressed withincreasing radius. Therefore, the outflow cross section can be even smaller than thecross section at the inflow position. So if there is a bottleneck for the airflow goingthrough a fan, this should be right at the outlet. In order to ensure this, a conicshroud or ring can be used. A rough estimate which should be fulfilled is

w2w1

d1d2

(1.1)

wherew denotes the radial velocity and d the radius of the blade wheel at the inletposition 1 and the outlet position 2, see also figure 1.3. This formula can be foundin [6].

In figure 1.3 the schematic view of a blade wheel is shown. The dashed linesdenote different cross sections at different positions. By applying equation 1.1 andassuming the flow to be incompressible a geometrical rule for figure 1.3(c) can beshown:

w1h1d1 w2h2d2 (1.2)w1d1< w2d2 (1.3)

h2< h1 (1.4)

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CHAPTER 1. FANS

(a) 3D view

(b) Top view (c) Side view

Figure 1.3. Sketch of inter-blade channel geometry

A basic property of a radial fan is that the flow will be redirected twice, whichmakes the flow field more complicated [11]. First, when entering the fan, the flowwill receive a tangential velocity component due to the rotating blades. In a perfectfan the flow will be guided smoothly through this deflection and the blades have acurvature with an appropriate angle to care for this. The second redirection occurswhen the flow changes direction from axial to radial in order to leave the fan throughthe radial outlets. This should again happen smoothly, i.e. without separation, andis therefore realized with curved blade channels.

A further aspect is the space between the blade back and the shroud or ring.This space should be as small as possible, since the fluid takes always the easiestway and would again flow back (from high to low pressure) into the motor if thereis a too big gap. To prevent this effect, the ring should be as close as possible tothe blade.

In order to guide the flow into the blade wheel without too much separationalready in the beginning, the inflow should be designed like a nozzle. This canbe achieved by avoiding sharp edges near the blade wheel inlet and perhaps evenbig, curved geometries around the inner edge of the ring. In figure 1.3(c) such anattempt of forming the ring is already sketched.

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1.3. FAN CHARACTERISTICS

1.3 Fan characteristics

1.3.1 Fan curves

To evaluate a fan with respect to its ability to transport an air volume, fan curvesare used. A fan curve from a specific fan together with a system curve of the cooledmotor yield an operating point. This operating point yields the airflow that isdelivered by the fan to the system.

To make things clearer one can think about a circuit, where the fan is the source

that produces the pressure differenceP =P1P0to overcome the resistance of thesystem. Instead of a current an airflow [Q] = m3s1 is circulating. The illustrationof this analogy is shown in figure 1.4.

Figure 1.4. Analogy electricity and flow system

In figure 1.5 a fan curve together with a system curve is sketched. The Q-axisranges over different airflows and the P-axis shows the pressure difference. Thefan curve itself is the dashed line and cuts the coordinate system twice. The cutwith the Q-axis gives the maximum airflow through the fan. Here the fan is atmaximum kinetic energy [5]. The cut with the P-axis denotes the shut-off point.

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CHAPTER 1. FANS

Figure 1.5. Sketch of fan and system curve

0 0.5 1 1.50

500

1000

1500

2000

2500

3000

3500

4000

4500

Q in m3/s

dPi

n

Pa

Figure 1.6. System curve from ABB measurements

The system in our application is the set of channels and other conduits throughthe motor from the inflow from free air to the outflow again to free air. Thesystem curve is determined by the flow resistances in the flow paths and is given infigure 1.6.

The fan curve can be measured if a prototype is available and is therefore pro-vided by the fan manufacturer. The fan curve can also be computed by using CFDsoftware. This is done in this thesis.

The resulting intersection points are very useful to compare different fan designs

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1.4. APPLICATION TO STRAIGHT RADIAL BLADES

with respect to their performance.

1.3.2 Fan laws

A guideline for effects of different variable changes between geometrically similarfans is provided by fan laws. Such laws have a solid theoretical background andhave also been determined experimentally [10].

By looking at two geometrically similar fans with constant speed and air densityone can conclude parameter influences. The two different diameters, D1 and D2,can be related with other parameters in the following way:

P1P2

=

D1D2

2(1.5)

Q1Q2

=

D1D2

3(1.6)

Pdenotes the pressure and Q is the airflow through the different fans.The first law can be easily explained in terms of the centrifugal force. It grows

in radial direction with the square of the distance to the rotation axis. This forceis then balanced with the pressure, which is zero close to the rotation axis andincreases in outwards direction,

P

r =r2 (1.7)

For further fan laws see [10].

1.4 Application to straight radial blades

The main issue of our fan is that it has to work independently of the direction ofrotation as the application requires bi-directional operation. This means that it hasto operate in both rotation directions and therefore does not allow any asymmetryregarding the blade design. This yields a quite poor fan since it is not possible togenerate the pressure additionally by lift. In figure 1.7(b) the principle of lift anddrag is shown. A good fan has blades which are inclined so that they have a properangle of attack as in figure 1.7(b) to deliver pressure also due to lift. This kind ofcurved blades are sketched in figure 1.7(a) and are the basic concept for a workingfan.

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CHAPTER 1. FANS

(a) Curved blades (b) Lift

Figure 1.7. Sketch of curved blades and lift principle

Nevertheless, the guidelines to design an efficient fan can be applied also to thisrestricted geometry.

First of all the channels created by the blade should have the same cross sectionindependent from the radial position or even decrease with increasing radius. Thisis something that can be done also for purely radial fans. The smooth guidingthrough the channel around the 90 curve to prevent separation can also be donefor this special case. Both design issues can be resolved by adapting and curvingthe ring in order to meet this demands.

A problem arises from the 90 angle at the blade wheel beginning. The flowhas to adapt to the tangential velocity component at the fan inflow without anyguidance. This induces for sure separation and turbulence.

In order to achieve a convenient inflow again the ring has to be adapted. Herea rounding of the edge helps the flow to enter the blade wheel smoothly.

1.5 Generation of fan noise

1.5.1 Theory for noise radiation

In this thesis, only aerodynamically generated fan noise is considered, since this isthe dominating noise source for high rotational speeds as in the electric motor. Thenoise coming from vibrations and the motor itself can therefore be neglected.

In the Lighthill analogy the fluctuating density = 0 is assumed to bean acoustic field with small amplitudes which is created by fluctuating velocities insmall turbulent regions, the source regions. The related acoustical wave equation is

2

t2 a20

2

xixi=

2Tijxixj

(1.8)

Tij =cicj ij+ (p a0)ij (1.9)

where Tij denotes the Lighthill stress tensor, ij is the shear stress tensor, cis thefluid flow velocity and a0the speed of sound.

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1.5. GENERATION OF FAN NOISE

In a resting medium which surrounds the source region together with a rigid surface,

the inhomogeneous wave equation 1.8 can be written for the radiation into a farfield in form of the Ffowcs Williams and Hawkins equation:

(xi, t) = 1

4

2

xixj

V

Tijr|C|

tr

dV(i) (1.10)

14

xi

S

fir|C|

tr

dS(i) (1.11)

14

xi

Vc

0bir|C|

tr

dV(i) + 1

4

2

xixj

Vc

0WiWj

r|C|tr

dV(i) (1.12)

fidenotes the force that acts on the flow due to the rigid surface, e.g. the fan blade.Cis the Doppler-factor

Ci= 1 rir

Wia0

(1.13)

andri= xi yiis the distance between the observer and the source, see figure 1.8.Wi andbi denote the velocity and the acceleration of the rigid surface respectively,which is denoted by Sand encloses the volume Vc. i are the coordinates of thesource relative to the reference system which is moving with the rigid surface, see [3].

Figure 1.8. Variable explanation for Lighthill analogy

The subscripttr denotes the retarded time which is the moment of sound emis-

sion at the source. All terms in squared brackets with this subscript relate to thistime. The relation between the time of emission at the source and reception ofsound at the observer position is

tr =t 1a0|xi yi(i, tr)| (1.14)

This can be found in [3].The Ffowcs Williams and Hawkins equation describes the aeroacoustic sources

for a surface flow which moves relative to a rigid surface. The first term denotes theLighthill integral for an unbounded flow. This sound generated by volume forces is

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CHAPTER 1. FANS

called quadrupole noise and becomes important at blade tip speeds where the Mach

number is exceeding 0.8. This is not the case in the herein described application.The second term describes the sound radiation due to solid surface-flow inter-

action which is called dipole noise. This is the main noise contribution for thisapplication. It contains the force that acts on the flow due to the rigid surfacewhich is in a fan, for example, the blade.

The last two terms account for the monopole radiation. They contain the inte-gral over the velocity and the acceleration of the rigid surface and describe thereforethe noise production by the displacement due to the movement of the rigid surface.Since every blade in a fan has a certain thickness which displaces fluid, the resultingnoise is often called blade thickness noise [8].

To sum up, the only source which contributes to fan noise crucially is the dipole

source, which arise from the forces that originate from the interaction of the tur-bulent flow and the rigid boundaries, e.g. blades, casing or ring. In figure 1.9 anoverview about the three noise generation mechanisms is given and it can be di-rectly seen that all actual noise sources are deviated from the dipole source. In thefollowing the different mechanisms are described more detailed.

Figure 1.9. Summary of aeroacoustic fan noise sources [8]

1.5.2 Fan noise sources

As summarized above, the main cause of fan noise comes from the forces of theturbulent flow on the surfaces of the fan. These forces can be periodic, e.g. due tothe rotation of the fan and the resulting blade passing frequency. These yield the

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1.5. GENERATION OF FAN NOISE

discrete components in the sound field, the tonal noise. The surface-turbulent flow-

interaction with a random nature is responsible for the broad-band components ofthe noise.

1.5.3 Unsteady blade forces

According to [8] the noise component related to steady blade forces, the so calledGutin-noise, is negligible compared to the noise generated by unsteady blade forces.This noise occurs when the blades travel in a uniform unsteady flow field. Therefore,the focus is on the unsteady blade forces.

Non-uniform inflow field

These unsteady blade forces arise from a non-uniform inflow field, which can begenerated by upstream wakes due to duct bends and corners or inhomogeneities ofthe incoming airflow in general. The length scales of these flow distortions haveto be of the same order of magnitude as the blade spacing to effect the soundradiation [8]. Since the flow in the electric motor has to pass coils, curves andedges, inhomogeneity of inflow is hard to avoid.

Since the goal is to avoid this source of turbulence generation and thereforenoise radiation, the inflow should be guided smoothly around the 90curve it hasto perform as already described above.

Turbulent boundary layer

Even when the inflow is completely steady without any inhomogeneities a turbulentboundary layer on the blades will evolve. This yields random forces on the fan bladesurfaces.

The noise which comes from the turbulent boundary layer, is mostly dominatedby the noise which comes from inlet homogeneities. So, the boundary layer noisegives a lower bound for the broadband noise of the fan [3].

Tip clearance flow

This flow is driven by the pressure difference between the leading side of a bladeand the trailing side. This pressure difference produces secondary flows [8]. If thepressure difference becomes large due to high rotating velocity, this flow plays amajor role in noise generation. Vortices will be shed from the blade tip and hitagainst the casing or any outlet construction respectively. To decrease this noise, areduction in diameter will help since it decreases the velocity at the blade tip andincreases the distance from the outlet. How much decrease is possible without losingto much efficiency can be estimated by applying the fan laws given in section 1.3.2.

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CHAPTER 1. FANS

1.5.4 Influence of outlet grille

A grille is placed at the outlet for safety reasons. Due to space restrictions, thismesh-like grille is quite close to the fan blade tips. This gives good reason toassume that the wakes which are produced by interaction of the mesh and theoutflow interact again with the blades and therefore contribute to the net noise.

Measurements with the actual fan did not show any influence when they werecarried out with and without the grille. But when checking data from real fanswith backward curved blades an influence was measured as an increase in the levelof blade passing tones. An explanation for this phenomenon could be that the flowproduced by straight radial blades is already badly stalled. This means that theflow separates in form of vortices which produce a lot of noise when proceeding

towards the outlet. So wakes produced by the mesh had no additional influence [2].So herein, the influence of the outlet grille can be neglected. For a better fanwheel, they may become important.

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Chapter 2

COMSOL

2.1 CFD module

The herein used version of COMSOL is 4.1.0.88. For the simulation of a turbulent

flow, COMSOL offers as physics under Fluid Flow Single-Phase Flow, the Tur-bulent Flowapplication case. Different turbulence models are available, namely thek model, a Low Reynolds numberk model and a Spalart-Allmarasmodel.

The equations which are solved are theReynolds Averaged Navier-Stokes (RANS)equations. Those can be treated incompressible, which means the density is treatedas a constant or compressible for small Mach numbers. In the compressible casethe fully compressible equations are solved. Applications withM a > 0.3, i.e. notsmall Mach numbers, are not supported within the Single-Phase Flow physics sincealso the energy equation has to be solved, other boundary conditions have to beemployed and stabilization techniques have to be adjusted.

The computation can be done stationary or time-dependent and several stabi-

lization techniques are offered. For stabilization techniques in this application seesection 2.3.7. Solving is done in the stationary mode here since the time-dependentsolver would take far too much time and would not give any benefit due to theset-up of the problem. The time-dependent solver would be interesting for thecomputation of the full fan with the real, non-symmetric outlet configuration.

For the meshing, the element size can be calibrated for fluid dynamics. This isa good choice, since the mesh sizes for general physics are much coarser by default.

There exists also aRotating Machineryapproach for the single-phase flow. Thisis not appropriate in the herein application, since the domain must be divided intoa rotating and a non-rotating part which is not the case here.

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CHAPTER 2. COMSOL

2.2 Design of Geometries

2.2.1 Slice of fan

To build the whole model of the fan together with the motor will for sure resultin a far too big and complicated geometry with too many degrees of freedom forany available machine. Therefore, cutting out a slice or wedge of the fan, whichcontains only one blade is a proper approach. In the original geometry there are 13blades. This yields a domain with an angle of 360/13. Due to symmetry, periodicboundary conditions can be applied at the two cut planes. This pretends a full bladewheel with symmetrically placed blades. Only 1/13part of elements is needed forthe discretization, which allows to carry out the simulation within an acceptabletime span.

In figure 2.1(a) and 2.1(b) the principle is visualized. The slice will contain allimportant, but simplified, parts like the outlet and the entry of the inflow channelsfrom the motor. They are marked in figure 2.1(a). For a detailed description ofwhich simplifications are made, see section 3.2. Also the windings are modeled.They do not appear in the drawing of the original geometry 2.1(b). Neverthelessthey are an important part of the flow domain.

(a) Simulation domain as slice (b) Original geometry of motor

Figure 2.1. Principle of slice domain of blade wheel

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2.2. DESIGN OF GEOMETRIES

2.2.2 Building geometries in COMSOL

In order to build the slice with one blade, first the full 360of the geometry are built.This was done by using almost only primitives like cylinders and cones. Workingplanes together with Bezier curves are also very useful. They can be extruded androtated to build more advanced rotational symmetric geometries, see [4]. To connectsingle parts, boolean operations were used. The blade itself is only built once.

The last step is, to intersect the built geometry with a wedge that has the rightangle at the cusp, namely 360/13, see figure 2.2. It is important that this cusp hasno sharp edge, because this will give an error when intersecting with the geometry.

(a) 360 (b) intersection with wedge (c) final geometry

Figure 2.2. Steps to build geometry

In general, the geometry should be as easy to vary in its shape as possible.Therefore, the dimensions for the variables, which should be easy to change later,are stored as Parameters under Global Definitions. This makes quick geometrysweeps possible.

There are some tricks which simplify the modeling procedure a lot. Sometimes if

trying to build some shapes with boolean operations, it helps to increase the Defaultrelative repair tolerance. This will prevent from errors and avoid too small gaps.In general, small gaps, sharp edges and small surfaces, which do not contribute tothe geometry but developed as artifacts while building, must be avoided. Thoseartifacts will later cause troubles in the meshing procedure, since COMSOL triesto mesh every surface separately. Another problem occurs due to the concept, howCOMSOL builds cylinders, cones or spheres. There will always be an additional edgeintroduced at 0, 90, 180and 270, see figure 2.3. This produces in the resultinggeometry more surfaces than really needed, which complicates the meshing. Toavoid this, every geometric primitive has to be rotated by 45.

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CHAPTER 2. COMSOL

Figure 2.3. Cylinder with additional edges

2.3 Application case

Once the geometry is ready, the application mode has to be set up. Since theproblem is highly turbulent, the k model was chosen as turbulence model. Thevelocities are still under subsonic scales, so the computation is done incompressible.

M a= vmax

a =116

340 0.3 (2.1)

Although many adjustments have to be considered for the computation, in the endthe default solver settings are used, which worked very well.

2.3.1 Meshing

A very important task is to provide a good mesh which resolves critical areas prop-

erly, but does not waste elements in regions where no resolution is needed. At theinlet slices, for example, there should be at least two elements along the short sidedirection, to allow the flow to pass into the domain. For any flow that involves dif-fusion for the narrow regions at least five elements have to be used. Otherwise thereis no chance that any velocity profile can develop. But since the flow is stronglyturbulent and therefore involves the gradients of the mean flow, it should be evenmore resolved. Close to the moving wall, boundary layer meshes with small elementsizes have to be introduced. Otherwise the steep velocity gradient near the wall isnot correctly reflected. This gradient comes from the shape of the turbulent velocityprofile in the boundary layer, which differs from the laminar one, see figure 2.4.

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2.3. APPLICATION CASE

(a) laminar (b) turbulent

Figure 2.4. Sketch of different boundary layers

The first point in wall-normal direction in the flow domain has to be withinthis boundary layer. Otherwise, the wall functions are not predicting correctly.The variable accounting for the fact if the first mesh point is in the turbulentboundary layer, is the wall lift-offw, see figure 2.5. It must be chosen sufficientlysmall. To know if the wall lift-off is small enough it has to be compared locallywith the corresponding domain dimension. The perfect wall lift-off in viscous units+w =uw/with the friction velocity u =C

1/4

kin COMSOL is 11.06, see [4].

It denotes the distance from the wall, where the turbulent boundary layer changesfrom the viscous sublayer to the region where the logarithmic law applies. But alsoa wall lift-off below 100 can be sufficient depending on the corresponding dimension.

Figure 2.5. Sketch of wall lift-off

2.3.2 Boundary layers

To achieve sufficiently small wall lift-off, boundary layer meshes are needed. Theycan be generated automatically in COMSOL. The generation principle for theboundary layer mesh for one surface is visualized in figure 2.6. The triangles atthe boundary surface are extruded to prisms with increasing height in wall-normaldirection. This boundary layer mesh is then continued with normal tetrahedral

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CHAPTER 2. COMSOL

elements in the rest of the domain. Although COMSOL handles this on its own,

there are some points which should be considered.

Figure 2.6. Sketch of boundary layer mesh

The set of faces where boundary layers should be applied must not include avertex with more than three incoming edges. Otherwise COMSOL will give an errormessage. Also the angle, where the transition from surfaces with boundary layersto those without takes place, must not be too large. If so, the automatic meshing

will not work. Another issue is the distance between two parallel faces which shouldbe covered with boundary layers. Here the distance must be large enough so thatthe boundary layers do not intersect with each other or with the opposite wall. Agood choice to avoid errors arising from this restriction is to choose fewer layers. Ingeneral around five layers are sufficient.

Badly shaped elements with a too large aspect ratio cause convergence difficul-ties. Elements in a boundary layer are good candidates for bad elements. Therefore,to achieve convergence also with boundary layers some additional settings in theBoundary Layer Propertiesshould be adapted. As already mentioned, decreasingthe number of boundary layers to around five is probably a good idea. The bound-ary layer elements should not grow more than 50% in wall normal direction. This

would mean a growth factor of1.5which is very large. Also, the transition from thelast boundary element to the first regular element should be smooth in terms of thewall normal size. Here a growth rate of 50% yields good results. To achieve this,the Boundary layer stretching factorand the Thickness adjustment factorhave tobe adapted.

If there are still convergence problems with boundary layers, a computationwithout boundary layers should be taken as initial condition for the boundary layercomputation. This can be set in the solver under Dependent Variables. Also startingwith fewer boundary layers and a really smooth transition in wall normal directionwill help.

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2.3.3 Initial conditions

Attention should be paid to the initial conditions since they can decide if a com-putation converges or not. Just keeping the default which is zero for all variableswill probably give an error right in the beginning of the computation. Choosingthem as close as possible to the solution will enormously increase the convergencespeed. So if any pre-simulation on the same domain is available, take this as initialcondition. If not take the velocities arising from the rotation or from the inlet flowas initial value and set any pressure different from zero as initial value.

2.3.4 Boundary conditions

The boundary conditions for the inflow are prescribed velocities. The velocities arechosen according to the total airflow and the distribution of the airflow is basedon measurements. Note that the inflow has to rotate in the same way as the wallwhich it is surrounded by. So for the inflow at the stator it is not sufficient to

just define the normal velocity but a complete flow field has to be defined. For aturbulent flow also the Turbulent intensityand the Turbulence length scalehave tobe adapted. The turbulent intensity is typically 5% and the scale should reflect thesmallest dimension in the inflow geometry, i.e. the short side of the slit.

The outflow condition is zero pressure without any stresses. This should notdisturb the upstream flow too much.

Since the domain is designed as a slice, cyclic boundary conditions are needed.COMSOL has already an advanced built in case for this, namely the Periodic FlowConditionwhich can be easily applied.

For the walls one has to distinguish between moving and still-standing walls. Inboth cases wall functions are used. The velocity for the moving wall can be definedas a velocity field in terms of the global coordinate system.

For the extended outlet slip boundary conditions are applied which are onlysupposed to guide the flow out without any friction and disturbances.

2.3.5 Convergence issues

If convergence cannot be achieved with the default settings it may be a good ideato enable Isotropic diffusionunder Inconsistent Stabilization. This will help if theviscosity is too low which will be the case for air. Also doubling the number ofiterations in the solver settings can help to get a converged solution and it does notaffect the accuracy as long as the solution converges.

Refining critical areas is also a strategy to achieve convergence. To figure outthe problematic areas one can increase the tolerance by a factor of two for examplewhich will probably yield at least a solution. Subsequently refining the critical areasand decreasing the tolerance again will yield a converged solution. Just increasingthe tolerance will not yield a correct solution since the residuals will be far too big.

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CHAPTER 2. COMSOL

2.3.6 Rotating reference frame

The approach to use a rotating or non-inertial reference frame is typical in appli-cations where rotating parts are involved and the exact flow around the actuallymoving part is of interest. By using this reference frame the flow around the movingpart can be modeled as steady-state problem although it is unsteady when viewedfrom the fixed frame, see [1].

Using a non-inertial reference frame means that forces which are arising fromthe rotation have to be taken into account. All actually still standing parts, suchas the stator, have to rotate in the opposite direction as the rotating parts wouldactually rotate.

Assuming a positive rotational velocity which is defined by the rpm number,

which denotes revolutions per minute, as

= 2rpm

60 (2.2)

The rotor is rotating counterclockwise with the velocity

vrotate =

yx0

(2.3)

Therefore, the stator has to rotate withvrotate.

Figure 2.7. Sketch of rotating reference frame

One additional force is the Coriolis force which deflects a moving particle to theright direction if the reference system, as assumed herein rotates counter-clockwise.This force can be written as

2 v= 2

00

uvw

=

2v2u

0

(2.4)

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The second force which acts on a particle is the centripetal force

r=

00

00

xyz

=

2x2y

0

(2.5)

There is no pre-defined machinery in COMSOL to change between differentreference frames. For this reason a Volume Forcehas to be added which accounts

for the centripetal and the Coriolis forces. This has to be done for the whole domain.The moving wall in the model includes all faces belonging to the stator which arestill standing in reality.

In the post-processing, the velocities must be corrected to transform the com-putation back into the static reference frame for the observer. The static pressureis invariant under the change of reference frame.

Note that the moving walls have to be resolved accurately, otherwise the rotationvelocity will not be correct and strange pressure gradients close to the wall will showup.

2.3.7 Inconsistent Stabilization

In order to achieve a converged solution in the beginning Inconsistent Stabilizationwas enabled for both the Navier-Stokes and the turbulence equations. The stabi-lization method used in COMSOL is isotropic diffusion. Therefore, an additionalterm is added to the viscosity coefficient. Since this is a change in the used equationsystem, not the original problem is solved. For this reason Inconsistent Stabilizationshould be avoided.

As the model became more correct and the meshing improved also the computa-

tion without Inconsistent Stabilization converged, if using the stabilized solution asinitial value. This changed the solution a lot. The net pressure difference changesand also the flow in the domain looks different and therefore all variables changedfrom only slightly to completely.

The pressure distribution at the inlet on the stator, which looked quite strangefor the stabilized case, became more reasonable and the high pressure gradient alongthe inflow edge vanished almost completely which can be seen in figure 2.8. Thepressure difference over the whole domain became higher. But since this happenedfor every computation to almost the same extent, the comparison of different fandesigns with respect to pressure differences stays almost the same.

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CHAPTER 2. COMSOL

(a) With Inconsistent Stabilization (b) Without

Figure 2.8. Static pressure on the stator inlet for different stabilization

Also the streamlines changed a lot. For the computation without InconsistentStabilization the re-circulation area in the stator is much stronger developed. Thisseems physical since air has a very low viscosity. The flow around the blade changedtoo when looking at the streamlines.

The turbulent kinetic energy changed the most which can be observed in fig-

ure 2.9. For the computation where the Inconsistent Stabilization was used, a highvalue can be observed near the inlet on the stator. But as the pressure gradient, alsothis values disappeared by switching off the Inconsistent Stabilization. The maindifference for the turbulent kinetic energy between the two computations is the over-all range. For the case with stabilization the maximum value is kmax= 74.6m2s2,however for the correct computationkmax = 803.1m2s2 can be found. This is morethan one order of magnitude larger and has to be taken into account. This can beexplained in terms of viscosity. The additional terms in the stabilization makethe flow much more viscous and therefore decrease the magnitude of the turbulentfluctuations.

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2.4. MESH-CONVERGED SOLUTION

(a) With Inconsistent Stabilization (b) Without

Figure 2.9. Turbulent kinetic energy for different stabilization

The conclusions for the further work are that for correct investigations, the sim-ulation should be run without the Inconsistent Stabilization. This takes of coursea bit longer since the stabilized solution has to be used as initial condition for thefinal, not stabilized, computation. Although the comparisons between different de-

signs in terms of the net pressure are not really changing with the used stabilizationtechnique, also here the correct solutions should be used.

2.4 Mesh-converged solution

By definition, a mesh-converged solution means, to make the mesh twice as fine ineach spatial dimension and run the simulation again. If the solution for the originaland the refined mesh are identical, or nearly so, the solution can be assumed to bemesh-converged, see [4].For this purpose, the mesh which is used to compute the solutions, the workingmesh, was refined by halving every spatial direction. The result can be seen infigure 2.10.

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CHAPTER 2. COMSOL

(a) working mesh (b) refined mesh

Figure 2.10. Meshes with different resolutions

The finer mesh contains3.154.750tetrahedral elements, which is five times morethan the amount of elements in the working mesh. This mesh contains 641.470elements. The refinement was done uniformly on the whole mesh. Since critical

parts of the domain are already well resolved by the working mesh, those areas areeven twice as fine in the bigger mesh.Looking at the two solutions with respect to the important variables gave the

following results:

P kmax vradial,max vtangent,max Pmax

working mesh 5022Pa 803m2s2 98ms1 126ms1 1.1601 104Parefined mesh 5088Pa 968m2s2 107ms1 134ms1 1.3967 104Pachange rate 1.3% 20.5% 9.2% 6.3% 20.4%

Table 2.1. Variable values for different meshes

One can see in this table that the changes for the maximum static pressure andmaximum turbulent kinetic energy are quite big. Looking closer to the solutionson both meshes explains this phenomena. In figure 2.11 a cut exactly throughthe middle of the domain was made. One can see, that the position of the lowpressure spot is not changing. Only the magnitude is increasing, which confirmsthe importance of this steep pressure gradient and its physical correctness. Since itis even more stressed in the solution on the refined mesh, there is no danger that it

just arises from numerical errors.

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2.4. MESH-CONVERGED SOLUTION

(a) working mesh, centered (b) refined mesh, centered

Figure 2.11. Static pressure in zx-plane for different meshes

(a) leading side (b) trailing side

Figure 2.12. Static pressure in zx-plane for refined mesh

Investigating the trailing and leading side of the blade respectively, see fig-ure 2.12, and comparing the general appearance of the pressure distribution to the

one on the working mesh in figure 3.2(a) and 3.2(c), the same pattern can be ob-served. This confirms the correctness of the solution on the working mesh. Againthe intensity is higher on the refined mesh.

The pressure difference Pin table 2.1 is only slightly increasing. This stressesthe mesh-convergence of the working mesh in terms of measuring the pressure dif-ference and therefore in terms of the performance of the fan. A change of1.3% isneglibible. So the higher intensity of static pressure in the overall pressure distri-bution does not effect the net pressure difference achieved by the fan.

The change in radial and tangential velocity in table 2.1 is right under the 10%border, so in terms of mesh-convergence absolutly acceptable. Looking at those

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CHAPTER 2. COMSOL

velocities on both sides of the blade, there is no difference between the solution on

the working mesh and the refined mesh observable. So in terms of velocity, theassumed solution on the working mesh is mesh-converged.

The maximum value for the turbulent kinetic energy changes seriously whengoing to the finer grid. In figure 2.13 the effect of finer meshing on k can be seen.The basic position of the spots stay the same, but the intensity of the spot on theblade back at the inlet changes a lot, around50%. The other spot close to the outletstays with the same values. Since the big changes occur at the same position wherealso the static pressure changes a lot, the problems at this position are confirmedand even stressed.

(a) working mesh, centered (b) refined mesh, centered

Figure 2.13. Turbulent kinetic energy in zx-plane for different meshes

Summing up the observations regarding mesh-convergence, one can say that interms of pressure difference and velocities the solution on the working mesh is mesh-converged. For the static pressure distribution and the turbulent kinetic energy theregion close to the ring edge should be even more resolved. But the tendency of thesevariables there, already shows up in the working mesh. One should pay attentionto the region close to the ring edge and must not neglect the effects there, when thering shape is varied for the design optimization.

2.5 Cluster Computing

The computations are done on the ABB research cluster. The used node has eightprocessors (Intel Xeon x5677) with 12 MB cache and a memory size of 128 GB.Solving with the described settings, occupies all eight cores and approximately sixGB, i.e. 4.7%, of the complete memory. This is the maximum use of resources dur-ing the activity of the segregated solver. For the herein built models, the numberof degrees of freedom is about one million. For both computations with stabiliza-

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2.5. CLUSTER COMPUTING

tion and without, circa 60 iterations are needed to achieve convergence and the

computation time varies from three to four hours.Spreading parameter sweeps over the nodes of the cluster was not done, since

the number of CFD licenses is limited.

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Chapter 3

Approach for broad-band noise

3.1 Basic idea

The basic idea to reduce the broad-band noise is, to decrease the losses due toturbulence within the blade wheel. By reducing those, the fan will become moreefficient and, even more important, the broad-band noise will be reduced. Thelosses are produced by vortex shedding and separation within the blade channels.The goal here is to redesign the blade channels to avoid turbulence production forreasons which are closer described in section 1.5.2.

The first step is therefore, to develop a more efficient fan. Therefore the guide-lines, described in section 1.2, are used to reshape the current fan. Once the fanis more efficient compared to the old one, a fine-tuning with respect to severaldesign-space parameters can be made. This will help to optimize the new shape.This optimization is done with respect to both important fan properties, namelyperformance or efficiency and turbulence production. The latter is the importantproperty when it comes to noise production.

In general one can say that the lower losses due to turbulence, the less noisewill be produced by the fan. This basic principle was explained by Mats bom, anexpert in Engineering Acoustic at KTH, in a personal conversation on February 1,2011.

3.2 Original geometry

To design a computational domain which is appropriate in terms of meshing andnot too detailed, several simplifications were made. Those simplifications reducethe number of discretization points to an acceptable number.

The biggest simplification was done with respect to the coil. In reality this isa very complex geometry and varies from motor to motor slightly. In the compu-tational domain this is only modeled as a block, neglecting all the small coolingchannels through it. The dimensions and distances were constructed based on datafrom ABB.

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CHAPTER 3. APPROACH FOR BROAD-BAND NOISE

Another issue is that the stator has to be symmetric, to run a steady state

simulation in the rotating reference system. Assume the reference frame to rotatewith the wheel. Everything which is not rotating with the wheel, has to look thesame from every position of the blade wheel.

So the outlet has to be modeled with the correct outflow area but rotationallysymmetric which is done with a smooth extension. This is of course different fromthe original geometry but the best thing to do here. The outflow area is the sameas for the real motor. The whole outlet was also put a bit downstream, i.e. awayfrom the computational domain, to minimize the influence of the outflow boundarycondition on the solution around the blade.

Also the cooling channels on the stator must be made axisymmetric. Thereforeit has a slit shape along the outer radius of the motor with the correct surface area,

according to the data from ABB in table 3.1.Everything which is rotating can be modeled non-symmetric. So the inflow on

the rotor is modeled as one big hole, although there are more holes with differentsizes in the real motor. The surface area is correct according to table 3.1.

The balance ring on the rotor also underlies a simplification. The wings on it,which differ from motor to motor and are completely irregular in general, are meltedtogether as a block with roughly the same volume as all of them together.

The inflow between rotor and stator is modeled as a slit, like in the real geometry.The ring edge is modeled as round as possible like in the real motor but probably

with slightly different curvature. Since it is quite hard to estimate the exact distancebetween blade back and ring it is set to a realistic number, namely 4mm.

The blade was modeled with the same length and height as in the real motor,but the curvature at the tip will probably not exactly match, since it is hard todetermine the exact shape and also to model it exactly with the correct curvature.

Regarding the blade wheel some simplifications were necessary because it is farto detailed and impossible to mesh with all its teeth around the boundary. Theywere neglected together with the small increase in height at the boundary of thewheel. The step from the wheel down to the outlet is modeled.

total slice

stator back 9474mm2 728.8mm2

air gap 1562mm2 120.2mm2

rotor 9316mm2 716.6mm2

Table 3.1. Surface areas for different inlets

The most important change in the geometry had to be made in order to get onlya slice out of it. The slice is built as the fan would contain 13 equally spaced bladeswhich is not the case in the real geometry. The distances between the blades varyin order to eliminate tonal noise, see chapter 5.

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3.3. IMPROVEMENTS

3.3 Improvements

After setting up the described model in order to simulate the original geometry, thesolution on this domain gave several hints on which parts should be changed.

3.3.1 Important parameters

The parameter which was investigated closer in terms of turbulence and thereforenoise production is the turbulent kinetic energy k. kis associated with the vorticesin a turbulent flow and is the mean of the turbulence normal stresses:

k=1

2

(u)2 + (v)2 + (w)2

(3.1)

But also the pressure distribution and the radial and tangential velocities areevaluated.

In terms of performance the most important variable is the pressure differencebetween the inlets and the outlet. This difference is strongly influenced by theturbulence production since pressure drops are produced and therefore losses. Soalso for the performance of the fan, turbulence in the blade channel has to bereduced as much as possible.

3.3.2 Observations and Changes

Regarding the cross section issue, it turned out that shifting the bottle neck to the

outlet works very well. The ratio between the cross section areas at radius d2 andradiusd1is

A1A2

= 1.5 (3.2)

A visualization for the cross section is sketched in figure 3.1. sis the position inthe inter-blade channel and h(s)denotes the height at every position. This heightshould be adapted so that the cross section at different positions, which is denotedby dashed lines, has the right surface area according to equation 3.2.

(a) original shape (b) modified shape

Figure 3.1. Sketch of cross section area in inter-blade channel

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Looking at the solution for the original geometry gives rise to fundamental changes

in the design. To investigate the results, the variable values at the leading side andat the trailing side of the blade are studied.

The static pressure distribution for the original geometry can be seen in fig-ure 3.2(a) and 3.2(c). The high pressure gradient close to the ring edge makes achange there very reasonable. Opening the inflow to the blade channel and alsoa rounding of this edge might be a good idea. In figure 3.2(b) and 3.2(d) thesechanges were made.

In the original geometry the low pressure at the inflow to the blade channel is,due to Bernoullip + v2/2 =constant, coupled with the high velocities there. Thisis caused by the narrow cross section area at this position. In the improved geometrythe pressure at this position increased, so the pressure gradient there decreases.

On the leading side, in figure 3.2(a), it can be observed that the pressure rightunder the ring is very low, so the air flows around the ring edge very quickly. Inthe improved geometry the radius for the curvature of the ring edge increased andtherefore the pressure became a bit more balanced there since the way around thecorner is now longer and the velocity therefore slower, see figure 3.2(b).

For both designs the pressure increases smoothly along the blade surface in radialdirection, which can be seen in figure 3.2(c) and 3.2(d) and which is physical. Bylooking at the pressure distribution around the blade, it can be observed that thepressure at the leading side of the blade is much higher than the pressure at thetrailing side, which also confirms the physics of the model.

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3.3. IMPROVEMENTS

(a) Original geometry, leading side (b) Improved geometry, leading side

(c) Original geometry, trailing side (d) Improved geometry, trailing side

Figure 3.2. Static pressure in zx-plane for original and improved geometry

Another interesting variable one should look at, is the radial velocity. In fig-ure 3.3(c) it can be seen that the radial velocity is quite high at the inlet to theblade channel compared to the complete channel. This occurs due to the smallcross section there which gives rise to a further improvement, namely bending upthe the ring edge. To place the bottle neck in terms of cross section area right at the

inlet of the blade channel, as it is done in the original geometry, is in general not agood idea for fans as described already in chapter 1.2. In figure 3.3(d) the inflow tothe blade channel is widened, which results in an equally distributed radial velocityalong the blade. Needless to say that this is much better, since also the maximumradial velocity decreased from 87ms1 to77ms1 in the region close to the blade.

On the leading sides, figure 3.3(a) and figure 3.3(b), it can be seen that theradial velocity at the tip of the blade also decreases, due to the more uniform flowaround the blade for the improved geometry from 97ms1 to 76ms1. It is ingeneral very good to decrease the radial speed close to the outlet with respect tonoise production.

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Directly on the ring the radial flow for the improved design was decelerated too,

due to the longer way around the corner with increased radius.



Figure 3.3. Radial velocity in zx-plane for original and improved geometry

The maximum tangential velocity which has to be expected is given by the bladetip speed

vt= r= r 471 1s

(3.3)

The radii for the two cases are ro = 0.2465m and ri = 0.23m for the orig-inal geometry and the improved one respectively. So the tangential velocitiesvo = 116.2ms

1 and vi = 108.4ms1 should be observable at the tips, which isthe case in the figure 3.4(c) for the original geometry and in figure 3.4(b) for theimproved geometry respectively. Additionally the tangential velocity increases uni-formly along the blade side as expected.

As explained above the tangential velocity for the improved geometry has a lowermaximum due to the radius reduction. But even proportionally to the maximum

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3.3. IMPROVEMENTS

speed, the tangential velocity close to the outlet is lower for the improved geometry,

see figures 3.4(a) - 3.4(d). This means that the flow leaves the blade channel in theimproved geometry with a higher radial component and therefore less swirl.

The tangential velocity distribution on both sides of the blade is more balancedfor the improved geometry. In figure 3.4(b) and 3.4(d) it can be seen that themaximum varies between 108ms1 and 113ms1 for the leading and the trailingside. For the original geometry the maximum speed ranges between107ms1 and116ms1, compare to figure 3.4(a) and 3.4(c) respectively.



Figure 3.4. Tangential velocity in zx-plane for original and improved geometry

Looking at the turbulent kinetic energy, which can be taken as a measurementfor turbulences in the flow, one can observe that the spots with the maximum valuesoccur almost at the same positions in both geometries. But the maximum valuesfor k decreased a lot from the original geometry. This arises from the much morebalanced flow in the improved geometry in terms of pressure and velocities. Lookingat the whole domain, the maximum k decreased from 803m2s2 to 555m2s2.

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Figures 3.5(a) - 3.5(d) show that the center of the k spot moved slightly away

from the outlet for the improved geometry. Less turbulence close to the outlet mayhave positive influence on the noise production. This effect comes probably from themore equally distributed velocity profiles at the outlet for the improved geometry.

In figure 3.5(a) and 3.5(b) one can see that the turbulent spot moved more onthe back side of the blade in the improved geometry. This happened because thebottleneck at the inflow area is not longer existent, which places the k spot underthe ring edge in figure 3.5(a) and 3.5(c).



Figure 3.5. Turbulent kinetic energy inzx-plane for original and improved geometry

Another point of view is, to look at the azimuthal planes. Those are parallelto the outlet and placed in radial direction at the position of the inner and outerradius of the fan blade, see figure 3.6.

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3.3. IMPROVEMENTS

(a) Original geometry (b) Improved geometry

Figure 3.6. Radial velocity on azimuthal planes for original and improved geometry

In the original geometry the planes are placed at d1= 15.5cmandd2= 24.65cm.In the improved geometry this positions are d1 = 14.9cm and d2 = 23cm. Bothdomains were evaluated at those planes with respect to the radial velocity. Itsmean value and the maximum value can be seen in table 3.2 for the four describedplanes.

original geometry improved geometry

vradial vradial,max vradial vradial,max

d1 36.15ms1 88.64ms1 22.98ms1 82.47ms1

d2 18.52ms1 95.60ms1 32.74ms1 74.14ms1

Table 3.2. Radial velocities for different azimuthal planes and geometries

The values in the table again confirm the already mentioned bottleneck for theoriginal geometry at the inner radius. The radial mean velocity here is much biggerthan the mean velocity at the d2-position. In the improved geometry those meanvelocities are much more the same and the bottleneck is even shifted to the d2-

position, which is reasonable as explained in section 1.2.The maximum values for the radial velocity are much higher for the original

geometry. As already mentioned before, in the improved geometry the radial veloc-ity is more balanced within the blade channel. So even if the radial mean velocityfor the improved geometry at position d2 is higher than for the original one, themaximum value is smaller. This is an improvement, since the high maximum valuereflects the fact that there is locally a high velocity close to the outlet. This isprobably quite bad for the noise production.

Evaluating the values in the table with respect to equation 1.1 yields also infor-mation about the two designs. Forw1 and w2 the mean values at position d1 and

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d2 can be inserted accordingly. Doing this yields that equation 1.1 is fulfilled for

the improved geometry, but not for the original one.

3.4 Geometry variation

In the analysis of the improved geometry above, a lot of geometric parametersseem interesting for further investigations. Their impact on turbulence productionand performance will be analyzed in the following. In figure 3.7 those geometricparameters are visualized.

Figure 3.7. Sketch of design-space parameters to sweep

1. Height of inter-blade channel inlet

As already mentioned, the bottleneck in cross section area should be shiftedtowards the outlet. Therefore the height of the inter-blade channel at theouter radius is fixed and the cross section area calculated. This area will be

multiplied by a factor greater than one and yields the cross section area at theinlet of the inter-blade channel. With this number, the height of the blade atthis position is computed.

2. Distance between ring and blade

This distance is mostly important in terms of performance. The flow willalways go from high pressure to low pressure, so it will use the space which isthere to travel, from the high pressure area near the outlet, back to the lowpressure in the free space between motor and fan. There is also a leakage fromthe leading to the trailing side due to the pressure difference. So a big gap

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3.4. GEOMETRY VARIATION

here will decrease the performance. But also in terms of turbulence this gap

plays an important role, since the air in this gap is between the fast rotatingblade and the still standing ring. This results in high turbulent kinetic energywhich can be seen in figure 3.5(b). Ifkincreases or decreases with the distancewill be investigated.

3. Outer blade radius

The outer radius determines mainly the length of the blade and will thereforehave a major influence on the performance. This can be already seen whenhaving a look to the fan laws in section 1.3.2. Of course the simulations shouldconfirm those laws. But also in terms of noise production this parameter isimportant since it will also determine the maximum tip speed, which influencesthe noise a lot.

4. Inner blade radius

The inner radius is basically bounded from below, since it must not becomesmaller than the cross section area for the inflow allows. But it should bechosen as small as possible with this constraint. The reasons are that thedifference between d1 and d2 determines the blade length and therefore theperformance and additionally a small inner radius keeps the ring edge awayfrom the coil. The minimum distance between coil and ring is according toABB 15mm.

5. Angle of blade end back

This angle is important due to turbulence production. As written above thespot for k lies exactly at the back of the blade end, see e.g. figure 3.5(d).So inclining this edge could cause a difference in turbulence production whichwill effect both, noise and performance.

6. Radius for rounding of ring edge

The smoother the flow can travel into the blade channel the less separationand therefore turbulence production will take place. Therefore different radiihere should be considered. The radius is restricted from above since it shouldnot take away too much place and decrease the distance between coil and ringbelow the mentioned constraint.

3.4.1 Height of inter-blade channel inlet

The height at the position of the inner blade radius was computed with two differentfactors for the cross section area. For one setting, the opening to the channels iswide and the factor is A1/A2 = 1.5. This turned out to be a very good defaultsetting and is used for all following computations. The other factor which waschosen is A1/A2 = 1.2, so inlet and outlet of the blade channels vary only a bit.

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This set-up is only used in order to compare it to the previous one. In figure 3.8

the two resulting geometries can be seen.

(a) A1/A2 = 1.2 (b) A1/A2 = 1.5

Figure 3.8. Radial velocities for different inter-blade inflow heights

The radial velocity profile is not changing fundamentally between both set-ups.Looking at the mean and maximum value for the radial velocity, as in section 3.3.2at the azimuthal planes, yields also almost the same values for the mean velocities,see table 3.3. Especially, the value at positiond2is similar for both set-ups, which

means that both geometries have the same outflow velocity. But the maximumvalues for the radial velocity are much higher for the smaller factor. This meansthat the higher factor, i.e. the larger inlet area, provides a more balanced flow.Nevertheless, both set-ups fulfill equation 1.1, which the original geometry doesnot.

A1/A2= 1.2 A1/A2= 1.5

vradial vradial,max vradial vradial,max

d1 28.48ms1 89.46ms1 22.98ms1 82.47ms1

d2 32.72ms1 87.57ms1 32.74ms1 74.14ms1

Table 3.3. Radial velocities at azimuthal planes for different inter-blade inlet heights

Also for the turbulent kinetic energy a similar observation can be made. Forthe smaller inlet height, the maximum value for k increased from 555m2s2 to759m2s2, which is a large change. The same increased intensity can be observedfor the minimum of the static pressure distribution under the ring. Here the valuedecreased from1.13 104Pato1.40 104Pa.

For the turbulence production, which involves noise production, the increasedheight for the inter-blade channel yields far better results and is therefore chosen

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as the default height for the following investigations.

3.4.2 Distance between ring and blade

With respect to turbulence production, the distance between ring and blade seemsto play an important role. Therefore, several simulations with different distances arecomputed. In figure 3.9 the turbulent kinetic energy k is shown with two differentdistances. For the bigger distance a region with high k developed in the spacebetween blade and ring. This spot even affects the area near to the outlet. In

contrary, in the model without this big distance, there is no turbulent kinematicviscosity in this area at all.

(a) 1 mm distance (b) 4 mm distance

Figure 3.9. Turbulent kinetic energy for different ring-blade distances

So in terms of turbulence and therefore noise production it can be concluded

that a smaller distance has a positive effect.

3.4.3 Outer blade radius

To see how the outer radius of the fan wheel influences the turbulence production,the simulation was done with different values for d2. The rpm number and theairflow stay constant. Looking at the maximum turbulent kinetic energy, a decreaseofk with increasing radius can be observed, see figure 3.10.

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21 21.5 22 22.5 23 23.5 24 24.5 25500

505

510

515

520

525

530

maximumk

inm

2/s2

radius in mm

rpm = 4500; Q = 1.05 m3/s

data from simulations

linear approximation

Figure 3.10. Maximum turbulent kinetic energy for different outer blade radii

This can be explained by the change of the azimuthal cross section. The crosssection in the model is always computed at the tip of the blade and is then extruded

over the complete blade channel length, see figure 3.1. When the outer radiusbecomes smaller, the total cross section becomes smaller everywhere. So the velocitygradient in vertical direction in the blade channel increases for smaller radius. Thiscauses the higher values for k. The position of the turbulent spot stays the samefor all diameters.

Looking at the radial velocity, there is no clear tendency for increase or decrease.It is insensitive to the outer diameter. But what changes naturally is the tangentialvelocity. In figure 3.11 one can see its increase which has the same slope as theanalytically computed tip speed, which is plotted as a line and computed withequation 3.3.

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21.5 22 22.5 23 23.5 24 24.5100

105

110

115

120

125

maximumt

angentialvelocityinm/s

radius in mm

rpm = 4500; Q = 1.05 m3/s

data from simulations

analytic computation

Figure 3.11. Tangential velocity for different outer blade radii

The values for the maximum tangential velocities are larger than the computedtip speed. This is caused by secondary flows that evolve in the inter-blade channels,see figure 3.12.

Figure 3.12. Sketch of secondary flows

From the above observations one can conclude that althoughkdecreases slightlywith increasing outer radius, the tangential velocity grows. This is probably effect-ing the noise production a lot more. In addition the distance between blade tipand outlet which is gained by decreasing d2 can be used to apply further damp-ing techniques like additional vanes or filling the free space with damping material.Already without applying anything, the free space acts naturally as diffuser andwill decelerate the flow towards the outlet. This happens naturally since the areatowards the outlet increases due to increasing radius.

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3.4.4 Angle of blade end back

The variation of the angle of the blade end back is interesting with respect toturbulence since the low pressure spot and high values for turbulent kinetic energyoccur there. From investigations on the outer radius it can be concluded, that aradius of 22cm is enough to achieve the needed pressure difference. A distance of4mmbetween blade back and ring is compatible with manufacturing tolerances andyields even together with the small radius enough pressure difference. So the anglesweep was carried out with this set-up.

Figure 3.13. Sketch of blade back end angle variation

The results for three extreme angles can be seen below in figure 3.14 and 3.15.As in the analysis in section 3.3, the plane on the leading side is visualized. Thetrailing side will not give different results, so to show one side is enough. It can beobserved that there is no real shift of the spot position. It stays basically at thesame place relative to the geometry change.

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(a) = -28

(b) = 0

(c) = 28

Figure 3.14. Static pressure in zx-plane for different blade end angles

The static pressure becomes significantly lower for both inclinations. It decreasesroughly200Pa. But in general, the pressure distribution at the leading side is notchanging much.

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(a) = -28

(b) = 0

(c) = 28

Figure 3.15. Turbulent kinetic energy in zx-plane for different blade end angles

The maximum for the turbulent kinetic energy decreases on the leading side ifthe angle is negative, see figure 3.15(a). For the positive angle in figure 3.15(c) themaximumk value increases slightly. This will not influence the overall turbulenceproduction, which will be explained below more detailed.

Further investigations are made by looking on the domain in a different way. Infigure 3.16 and 3.17 a cut through the domain in the yz -plane is shown. This meansalmost parallel to the outlet and the plane is placed at the position just before thering. This is done because with this view the behavior of the static pressure and kover the whole channel width is visualized.

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(a) = -28

(b) = 0

(c) = 28

Figure 3.16. Static pressure in yz-plane for different blade end angles

By looking at the static pressure in figure 3.16 one can see that the pressuredistribution stays basically the same, independent of the inclination angle. For thepositive angle the pressure is more balanced since the maximum spot spreads a bitand moves slightly away from the position right under the ring. Also the minimumvalue increases.

For the negative angle and the straight end, the pressure minima are almost thesame, namely1.0925 104Paand1.0947 104Pa respectively. For the positiveangle it increased to9878Pa.

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(a) = -28

(b) = 0

(c) = 28

Figure 3.17. Turbulent kinetic energy in yz-plane for different blade end angles

Also the turbulence production for the positive angle is more balanced for thepositive angle, see figure 3.17. The spot is more spread and the maximum value fork is 453m2s2. For the decreased angle this value is higher, namely 502m2s2 and

the maximum spot is much more concentrated to the bottom of the flow channel.An explanation therefore is that for a higher blade end, the redirection of the

air flow from axial to radial happens already earlier in the flow field and before theentry to the actual blade channel. So in the blade channel itself, the redirectionhas already taken place and therefore less turbulence develops. In contrary for thedecreased angle, the redirection of the flow happens quite late and therefore the flowentering the blade channel still has to accelerate in radial direction. This results inmore turbulence in the blade channel.

This observations are committed by the maxima for the whole domain. Thosevalues can be found in table 3.4.

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kmax Pmax

-28 547.82m2s2 1.0947 104Pa-14 525.19m2s2 1.1553 104Pa0 522.98m2s2 1.1718 104Pa

14 530.45m2s2 1.1413 104Pa28 527.83m2s2 1.0871 104Pa

Table 3.4. Variable values for different blade end angles

Lowering the angle, yields a clear tendency for k to increase compared to thestraight back. This is in terms of turbulence production of course not good. Butwhen looking at the maxima for k for increasing angle, a tendency for k cannotbe determined. So increasing the angle will not influence, or even decrease, theturbulence production, though decreasing the angle will result in more turbulence.

Since, according to the maximum values for the pressure, the pressure spot in-tensity changes for positive and negative angles, it is a good idea to change the angle.And since the pressure gradient decreased for the positive angle, see figure 3.16(c),a positive angle is even better.

To sum up, a change in the blade back angle will not affect the flow too muchin terms of turbulence even though a positive angle could reduce turbulence. Inaddition, the angle has an influence on the performance, which should be considered.This is analyzed in section 4.3.4

3.4.5 Radius for rounding of ring edge

To investigate the influence of different roundings of the ring edge, its radius isvaried. The results for this geometric change can be seen in figure 3.18. The ringwith 2cm diameter is the standard set-up for the previous simulations. The radiuswas increased as far as possible to keep the required distance between ring andwindings. The biggest possible ring diameter was 3cm. To achieve this, the innerradius of the blade wheel was decreased in order to gain some space to increase thering edge diameter. But the radius is still big enough to have a non-restricting inletin terms of cross section area.

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(a) Ring diameter 2cm (b) Ring diameter 2.5cm

(c) Ring diameter 3cm

Figure 3.18. Radial velocity in zx-plane for different ring edge diameters

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