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This is to certify that the
thesis entitled

THE DESIGN AND OPTIMIZATION OF AN AUTOMOBILE
COOLING FAN

presented by

EMMETT DEMPSEY

has been accepted towards fulfillment
of the requirements for the

MS. degree in MECHANICAL ENGINEERING

 

 

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08/25/06

Date

 

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5/08 K:iProj/Acc&Pres/CIRCIDateDue.indd

THE DESIGN AND OPTIMIZATION OF AN AUTOMOBILE COOLING FAN
By

_ Emmett Dempsey

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Mechanical Engineering

2006

ABSTRACT
THE DESIGN AND OPTIMIZATION OF AN AUTOMOBILE COOLING FAN
By Emmett Dempsey

The goal of this investigation was to design a fan for automotive cooling
applications. Modern automobiles have several heat exchangers within the engine
compartment that are stacked together to form the radiator. A cooling fan was required to
produce a sufﬁcient, uniform cooling ﬂow of air through the stack, having high
efﬁciency, low weight and cost, and optimum mechanical properties in a high
temperature (393 K) environment. Given the inlet conditions, an initial 1-D design was
performed. 2-D blade contours were then designed using the inverse design method and.
an inviscid ﬂow assumption. The 2-D inviscid designs were then analyzed using Navier-
Stokes software. 3-D meshes were created by stacking the 2-D blade contours and
analyzed using two software packages: TRAF3D and CFX. To improve the performance
of each blade, a 3D optimization was performed using the TRAF3D Navier-Stokes

software and the addition of circumferential lean.

ACKNOWLEDGEMENTS

Firstly, I would like to thank my professors Dr. Mueller and Dr. Engeda in the
mechanical engineering department at Michigan State University. Not only have they
provided me with academic guidance, but also with several opportunities to expand my
personal horizons, including co—authoring conference papers and studying at the Von
Karman Institute in Belgium.

I would also like to thank Prof. Van den Braembussche at the Von Karman
Institute for his wise guidance and supervision on the compressor design project. Dr. Z.
Alsalihi, J. Prinsier, and T. Verstraete also provided me with all of the technical
assistance and advice necessary to complete the project. I could not have made such a
smooth transition to the available computer operating systems or understand the software
without their help.

My friends at the VKI, especially Giorgio, Javi, and Marco made my time at the
VKI very enjoyable and an experience that I will never forget. Although I am happy to
be ﬁnishing the diploma course, I wish that my time with them would never end. They
became my European family.

Finally, I would like to thank my family and friends in Michigan for all of the
encouragement they have given me. From encouraging me to study at Michigan State

University to supporting me in Belgium, they have always been here for me.

iii

TABLE OF CONTENTS

1. LIST OF TABLES ................................................................................. v
2. LIST OF FIGURES ........................................................................................................ vi
3. LIST OF SYMBOLS ............................................................................ viii
4. THE DESIGN AND OPTIMIZATION OF AN AUTOMOBILE COOLING FAN ...... 1
4.1 Introduction .............................................................................. l

4.2 Method .................................................................................... 2

4.2.1 1-Dimensional Design ...................................................... 2

4.2.2 2-Dimensional Design ....................................................... 3

4.2.3 3-Dimensiona1 Stacking of 2-Dimensional Grids ...................... 13

4.2.4 3—Dimensional Grid Generation Using CFX Turbogrid ............... 15
4.3 Results ................................................................................... 17
4.3.1 2-Dimensional Inverse Design ............................................ 17
4.3.2 2-Dimensional Analysis: TRAF2D ....................................... 23

4.3.3 3-Dimensional Analysis: TRAF3D and CFX ........................... 25
4.3.4 3-Dimensional Optimization ............................................... 37

4.4 Conclusions ............................................................................. 51

5. APPENDICES ..................................................................................... 53
6. TABLES .......................................................................................... 58
7. REFERENCES ................................................................................... 59

iv

LIST OF TABLES

Required data ..................................................................... 58
Values for constant AP .......................................................... 58
Values for actual blade .......................................................... 58

10

11

12

13

14

15

l6

l7

l8

19

20

21

LIST OF FIGURES

INVC example of a blade made too thin and velocity distribution .......... 6

INVC example of a blade made too thick and velocity distribution... . .....7

Stacked airfoil contours ............................................................ 9
TRAF grid parameters ............................................................ 10
Tip section mesh .................................................................. 12
Hub section mesh .................................................................. 12
Mid section mesh .................................................................. 13
Stacked blade sections ............................................................ 14
Full fan .............................................................................. 15
CFX hub mesh ..................................................................... 16
CFX tip mesh ...................................................................... 17
Final hub contour and velocity distribution .................................... 18
Initial tip contour and velocity distribution .................................... 20
Final tip contour and velocity distribution ..................................... 21
Final mid contour and velocity distribution .................................... 22
Viscous to inviscid velocity distribution comparison: hub .................. 23
Viscous to inviscid velocity distribution comparison: mid .................. 24
Viscous to inviscid velocity distribution comparison: tip .................... 24
TRAF3D convergence history ................................................... 26
CFX convergence history ........................................................ 26
Efﬁciency across the blade span ................................................ 28

vi

 

22

23

24

25

26

27

28

29

3O

31

32

33

34

35

36

37

38

39

4O

41

42

Static pressure across the blade span ........................................... 29
Static temperature across the blade span ....................................... 30
Total temperature across the blade span ....................................... 31

Total pressure across the blade span ............................................ 32
Absolute Mach number across the blade span ................................. 33
Relative Mach number across the blade span ................................. 34
Absolute ﬂow angle across the blade span .................................... 36
Axial velocity across the blade span ............................................ 37
Absolute tangential velocity across the blade span ........................... 38
Relative ﬂow angles across the blade span .................................... 39
Radial velocity across the blade span .......................................... 4O
TRAF3D Result: Mach number at hub section ................................ 41

CFX Result: Mach number at hub section ..................................... 42
TRAF3D Result: Mach number at mid section ............................... 43
CFX Result: Mach number at mid section ..................................... 44
TRAF3D Result: Mach number at tip section ................................. 45
TRAF3D Result: Mach number at tip section ................................. 46
Performance Map .................................................................. 47
Blade stacking with addition of circumferential lean ........................ 49
Efﬁciencies with addition of blade lean ........................................ 50
Relative ﬂow angles with addition of blade lean .............................. 51

vii

LIST OF SYMBOLS

c ......................... Chord (meters)

f ......................... Vertex Angle of Triangle r-z-y (degrees)

In ........................ Mass Flow Rate (kilograms per second)

I ......................... radius (meters)

t ......................... Pitch (meters)

x ........................ Axial Coordinate (meters)

y ......................... Circumferential Coordinate (meters)

2 ......................... Radial Coordinate (meters)

H ......................... Enthalpy (Joules per kilogram)

P ......................... Pressure (Pascals)

T ........................ Temperature (Kelvin)

U ........................ Rotational Velocity (meters per second)

V ........................ Velocity in Absolute System (meters per second)
W ........................ Velocity in Relative System (meters per second)
Z ......................... Number of Blades

0t ......................... Flow Angle in Absolute System (degrees)

[3 ......................... Flow Angle in Relative System (degrees)

11 ......................... Polytropic Compression Efﬁciency (unitless)
A ......................... Stagger Angle (degrees)

p ......................... Density (kilograms per cubic meter)

5 ......................... Solidity (unitless)

viii

(D ........................ Rotational Speed (revolutions per minute)

subscripts

ax ........................ Axial Component

hub ...................... Hub Blade Section

is ......................... Isentropic

mid ...................... Middle Blade Section

tan ....................... Tangential Component

tip ........................ Tip Blade Section

S ......................... Static Quantity

0 ......................... Total Quantity

1 ......................... Inlet Station, Upstream of the Blade
2 ......................... Exit Station, Downstream of the Blade

ix

THE DESIGN AND OPTIMIZATION OF AN AUTOMOBILE COOLING FAN

4.1 Introduction

 

Automobile engines produce heat from several different sources, including
internal combustion and friction of the moving parts. Cooling fluids are necessary to
remove the heat from the engine block, air conditioning system, engine oil, and
turbocharger, and maintain a sufﬁciently low operating temperature for both the engine
and passengers. The cooling ﬂuids pass through a radiator stack where the heat is
exchanged with ambient air. In order to provide the cooling ﬂow through the radiator
stack, a fan is required. Besides the basic pressure rise and mass flow requirements, the
fan also needs to have high efﬁciency, low weight and cost, good mechanical properties
in the operating conditions, lOng life, and provide a uniform ﬂow. The goal of this
project was to design a fan to meet all of these requirements.

The design process consisted of several important steps. The ﬁrst step was to
create an initial l-Dimensional design based on the given thermodynamic requirements.
This step yielded the flow velocities and angles necessary for the 2-Dimensional design.
In the second step, a 2-Dimensional, inviscid blade contour was designed using the
inverse design method at three different radial locations on the fan blade. A viscous 2-
Dimensional analysis was then performed and compared to the inviscid results. The
contours were then stacked into a complete blade and analyzed with a 3-Dimensional
Navier-Stokes ﬂow solver. To validate these results, the results from another ﬂow solver
were employed. Next, the 3—Dimensional blade shape was optimized aerodynamically
and mechanically with the addition of circumferential lean. Finally, the performance

space for the optimized blade was determined. Similar work has been done by K. K.

Pehlivan], who redesigned a fan using the inverse design method and performed a CFX

analysis of the original blade design.
4.2 Method
4.2.1 l-Dimensional Design

The goal of the 1-D design was to determine from the speciﬁed data what the inlet
and outlet flow velocities and angles are required to be for the single-stage, shrouded fan
without inlet guide vanes. The requirements provided by Valeo2 are shown in Table 1.
Knowing these values and using air as the working ﬂuid, all geometrical values were
determined using equations 7-10 in Appendix 5c. By assuming a polytropic compression
efﬁciency of n = 0.7 and using the thermodynamic equations 11-13, the outlet ﬂow
angles were determined. Inlet ﬂow angles were calculated knowing the RPM, radius, and
inlet ﬂow. Therefore, the total ﬂow turning (AB) from inlet to outlet was known, as were
the absolute and relative velocities at inlet and outlet.

Initially, there was a design philosophy for constant static pressure rise across the
blade. This proved impractical, because no amount of turning at the hub section could
produce the necessary pressure rise for the given rotational Speed. As seen in Table 2, the
maximum pressure rise attainable at the hub section is 187.8 Pa at a ﬂow turning of 70.22
degrees. Also, the tip required only 1.08 degrees of turning to achieve the necessary
pressure rise. This can be attributed to the larger radius at the tip section than the hub
section. In other words, the tip section work is done mostly by the rotational U velocity
component while the hub section work requires more AB to do the same amount of work

(see equation 11). To make up for the lack of pressure rise at the hub section, the middle

and tip sections were designed for more pressure rise, while the hub section was unloaded
slightly to reduce the turning. The actual blade data can be seen in Table 3.

4.2.2 2—Dimensional Design

 

The purpose of creating the 2-D blade contour designs at three different radii
(hub, middle, and tip) was to create a basic frame from which the complete, 3-D blade
would be created. The 2-D design method implemented was an inverse, inviscid method.
Unlike the traditional design method, the inverse design method involves starting with a
prescribed velocity distribution on suction and pressure sides and computing a 2-D blade
contour geometry. The programs used were INVC, INVCPL and INVC-MOD. INVC-
MOD was used to modify either the actual or required velocity distribution. INVC was
used to analyze (l iteration) or converge (multiple iterations) to the required velocity
distribution. INVCPL was used to visualize the blade contour and velocity distribution.

The INVC code required an initial blade geometry as a base design, which

theoretically could have been any blade. A NACA65 blade was chosen to start with due
to its already favorable characteristics. Input parameters included t/c, A, and [31. After an

initial analysis of the blade, a velocity ﬁle was automatically created. The velocity at
discrete points along the blade chord for both pressure and suction side were stored in
this ﬁle for independent modiﬁcation using INVC-MOD. After modiﬁcation, a required
velocity ﬁle was created, and INVC was used to determine the physical blade shape for
the required velocity distribution.

This design method had several difﬁcult aspects. One aspect was to specify a
velocity distribution that actually corresponded to a physically-possible blade geometry.

Many distributions that appeared optimum were found to be impossible physically. The

criteria that needed to be satisﬁed for a physical blade were: positive blade thickness
everywhere, a completely enclosed (continuous) contour, and a higher average velocity in

the channel between blades than the velocities upstream and downstream of the blade

3
[CW .

Another consideration was to create a blade with the necessary turning.

Increasing the area between the suction side and pressure side velocity distributions

corresponded to an increase in blade loading and ﬂow turning. Therefore, B2 was very

sensitive, changing with each modiﬁcation of velocity. The target [32 values (from the 1-

D design phase) were each a challenging target to locate and maintain during velocity
modiﬁcations.

A third consideration was to create an acceptable blade shape. The so-called
“controlled-diffusion” blade shape was selected as the target shape. The name comes
from the fact that the deceleration of the ﬂow on the suction side is controlled. The
diffusion should be controlled because a steep flow deceleration can cause separation. In
the separated region, the ﬂow no longer follows the blade surface, so the blade does not
turn the ﬂow, and therefore no pressure rise can occur. If there is no reattachment
following the separation, the ﬂow will remain separated for the remaining length of the
blade. Therefore, separation near the leading edge is worse than separation near the
trailing edge. Besides avoiding steep decelerations, the controlled-diffusion blade
removes unnecessary positive accelerations on the suction side, because extra
acceleration has to be compensated for with extra deceleration. Although the suction side
was the most critical side for controlling diffusion, attention was also paid to the pressure

side deceleration.

The ﬁnal consideration of the inverse design method is that the blade created
should have an appropriate thickness and overall shape. Higher designed velocities on
the blade surfaces translate to more flow blockage in the channel, resulting in thicker
blades. A blade that is too thin would break or deform on impact with any of a number of
small particles and airborne objects that are present in the air near the streets and roads
where the fan would see usage. Figure 1 shows a tip-section design which was too thin,
along with its velocity distribution. Besides the fact that it is too thin, the very high peak
in non—dimensional velocity at the leading edge (W/W. ~ 15.0) is very undesirable. On
the other hand, a blade that is too thick adds unnecessary weight and material cost to the
fan design. The stresses due to the centrifugal force on blades with varying contour
thickness across the span would also be higher than constant thickness blades, possibly
lowering the lifespan of the blades. An example of a thick blade and its velocity
distribution is seen in Figure 2. Considering all aspects of the inverse design method and

understanding their inter-relatedness only came with practice.

x’C-=4.676 EL=77.9

Figure la

B1=81.221 B2=80.852 ITER=1

W/VV l

15-?

12.

 

 

 

9.0

 

6-0

 

 

 

 

 

 

 

 

 

Figure lb

 

T/C=1.431 EL=57.5

 

Figure 28

1 B1=70.220 B2=44.092 ITER=100

W/W
2.0

 

 

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Figure 2b

Due to the fact that the 2-D design process used an inviscid code, each blade
section was analyzed using the 2-D Navier-Stokes(N.S.) ﬂow solver software TRAF2D.
Preparing for and performing the analyses required several steps including: data transfer,
inviscid grid generation, viscous grid generation, ﬂow calculations, and post-processing.

Step one for analyzing the flow of each blade section was transferring the blade
data from the form that was produced by INVC to a form suitable for the NS. ﬂow
solver. Again, a small program was written to re-order the blade coordinates from the
INVC.OUT ﬁle and print them into an airfoil.dat ﬁle. Bearing in mind that the output
from INVC included dimensionless coordinates of a blade section with (x = 0, y = 0) the
location of the leading edge, some modiﬁcations needed to be made to the coordinates.
The program ruota_prof was used to scale the blade coordinates to the correct
dimensions. Then a program called ﬁt.exe was used to locate the center of gravity of the
section. Using ruota_prof and the coordinates of the center of gravity, the blade was
translated in space to have the point (0, 0) located at the center of gravity of the section.
The reason for the translation is that (0, 0) is the stacking point for the 3-D geometry to
be performed after the 2-D geometry; for rotors the center of gravity is the logical
stacking point with respect to the stresses due to centrifugal force.

The modiﬁed sections were then plotted using TECPLOT so that a visual
inspection of the blade contours could be performed (Figure 3). On both the middle and
tip sections there was a small discontinuity at the leading edge slightly toward the
pressure side. Since there was a relatively large concentration of points near the leading

edge of both sections, the points where the discontinuities were located were adjusted to

make a continuous curve without signiﬁcantly altering the blade shape. The result was a

smoother surface at the microscopic level of the pressure side of each of the two blade

 

 

 

CODIOUI'S.
Stacked 20 Aldous
(b —
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E89 _
C -
.9 -
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9? _
’- l l 1 l l l l l l t 1 J l l I l l I l l 1 l l l i
- 0.02 - 0.01 0 0.01 0.02

Axial Direction (m)

Figure 3
The next step was to create an inviscid mesh (grid) for the ﬂow around each
section using the program jerryh_tec. An H-mesh was chosen because it is more suited to
the geometry of compressor blades than the C—mesh, which is typically used more for
blades with rounded leading edges such as turbine blades. Keeping in mind that
eventually the blade sections would be stacked together for the 3-D analysis, the node
distribution was maintained constant from one section to the next. This was necessary

because the grid stacking program interpolates between sections to form the intermediate

mesh and therefore requires that the same number of nodes be present on a given surface
at each radial position. The nodal distribution was speciﬁed for 6 surfaces: inlet lower
(ninl in Figure 4), inlet upper (ninu), suction side (nss), pressure side (nps), wake lower
(nw), and wake upper. In addition, the number of points across the blade channel was
speciﬁed (ny). An example of the different parameters is shown for a turbine blade in

Figure 4.

 

Figure 4

10

The initial mesh generation work was done on the tip section. Because of its
extremely high stagger angle (78.5 degrees), it posed the biggest challenge for generating
an optimum mesh. The ﬁrst grid with default values was severely non-orthogonal and
full of negative volumes at the leading edge. However, orthogonality was drastically
improved by changing the nodal distribution on the surfaces mentioned previously. The
number of nodes was increased on the inlet upper surface and wake lower surface and
decreased everywhere else. The number of negative volumes thus decreased but did not
disappear completely. The remaining negative volumes were eliminated by stretching the
cells around the leading edge. The ﬁnal tip mesh is shown in Figure 5. Hub and middle
section meshes were deﬁned using the same nodal distribution as the tip section (for the
3-D grid stacking and analysis to come later). For these two sections, the grid
orthogonality was made much easier by the lower stagger angles of these sections than
the tip. By the end of the grid optimization, each mesh was well converged with a
residual on the order of 106. The ﬁnal hub and mid section meshes are shown in Figures

6 and 7, respectively.

11

.hs)
8

r3.) _. _'. _'_. _.
O on CD Is Ix)

Tangential Direction (in axial chord Iengt
N)
N)

Tangential Direction (in axial chord lengths)

 

QDTIp Mesh

 

 

 

 

- o 5
Axial Direction (in axial chord lengths)
Figure 5

2D Hub Mesh

Ll

 

 

 

 

 

 

 

‘Il‘

 

 

1 l 1 l l 1

o 2
Axial Direction (in axial chord lengths)

Figure 6

12

2D Middle Mesh

 

l .
IH It
I ll
' ill
{in
l

I
II!
I

Tangential Direction (in axial chord lengths)

or
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J I I l

o 5
Axial Direction (in axial chord lengths)

Figure 7

The viscous mesh was created based on the inviscid mesh using tomh_tec.
Starting with the viscous grid, a new number of points across the channel was speciﬁed
as well as a stretching factor to compress the grid near the blade surfaces and periodic
boundaries. Again, the number of points in the tangential direction across the channel
was required to be the same from section to section for mesh stacking. The meshes were
then each ready for an individual 2D ﬂow analysis.
4.2.3 3-Dimensional Stacking of 2-Dimensional Grids

The stacking process had already been started thanks to the earlier considerations
of the stacking point (0, 0) and the continuous number and location of nodes/cells relating
each blade section to the others. Still, a new minor modiﬁcation was needed. Ideally, the
inlet and outlet planes of the ﬁnal, stacked blade would be straight, radial planes, so each

inlet and wake axial length was calculated and adjusted to meet that criterion. After the

13

mesh ﬁles were ready to be stacked, the number of cells in the radial direction, the
number of blades Z, and the contour of the end-walls in the meridional plane were
speciﬁed. The hub end-wall contour was taken as a straight line at the constant radius of
the hub section, while the shroud end-wall contour was taken as a straight line at the
constant radius of the shroud section. An individual blade after stacking is shown in

Figure 8, and the full fan is shown in Figure 9.

Radially-Stacked 2D Blade Sections
Shroud

      

Leading
Edge ‘

u»...

Figure 8

14

 

 

 

 

 

Figure 9
4.2.4 3-Dimensional Grid Generation UsingCFX Turbogrid
Similar to the grid generation for the TRAF software, the CFX grids required inlet
ﬁles specifying the 2-D contour shapes, as well as the hub and shroud contours in the
meridional plane. The difference was that the TRAF input contour coordinates were all
taken on a constant-radius plane and thus required only two coordinates: an axial
coordinate and a circumferential coordinate. Instead, CFX Turbogrid required the axial

coordinate, a “horizontal” coordinate, and a “vertical” coordinate. The transformations
shown in equations 14-17 were used. Each section’s center of gravity point (xmp = O,
yTRAF = 0) was deﬁned as the point (f = 0, chx = r, ycpx = 0) in the CFX system.

Again, a program was written to store the new coordinates into a proﬁlecurve ﬁle to be

read by the CFX Turbogrid program.

15

Unlike the TRAF mesh sections, the CFX mesh sections were interpolated from
two meshes: the tip section mesh and the hub section mesh. The combination of H and I
type meshes proved to ﬁt well to the tip section mesh, so it was used for the entire blade.
To remove negative volumes and improve orthogonality, control points were created and
moved accordingly. Figures 10 and 11 show the hub and tip mesh sections, respectively.
The small Spheres located at some nodes were the control points. Areas that were
especially non-orthogonal, such as the tip section wake and inlet meshes, required many
control points and modiﬁcations. Intermediate meshes were then interpolated
automatically, and each resulting mesh section (10 total) was modiﬁed with control

points where negative volumes occurred.

CFX"

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16

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4.3 Results
4.3.1 2-Dimensional Inverse Design

The hub section was the most critical and time-consuming section to design,
because it would eventually serve as the basis for the other sections to be designed from.
Very small changes in the velocity proﬁle were often enough to change a blade from a

close-to-optimum design to an unusable one. The target blade shape and performance

were eventually met with the design shown in Figure 12.

17

 

T/C=1.431 EL=60.8

 

Figure 123

B 1:70.220 B2=48.725 ITER=100

W/W
2.0

 

 

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l

 

 

0.8

 

 

 

 

 

 

 

 

 

0.0 0.2 0.4 0.6 0.8 1.0 1.2
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Figure 12b

18

After the target design was achieved for the hub section, the middle section was
designed based on the hub section by modifying the camber and stagger. A program was
created to take coordinates of the hub section at zero stagger and scale the y-component
(normal to chord line) of each point by a certain factor of its original value. The program
then automatically wrote the new coordinates to a text ﬁle that could be read by INVC.
The re-staggering was implemented directly in the INVC ﬁle. The scale factor used for
the middle section was 70% of the hub camber while the factor for the tip section was
55%. The scaling served to not only change the camber angle, but also the thickness of
the sections, providing a favorable evolution of blade thickness from hub to tip. The
middle and tip sections were then analyzed using INVC, and a velocity peak was found at
the leading edge of the tip section (Figure 13). A few modiﬁcations with INVC-MOD
removed the peak and established the controlled diffusion velocity proﬁle and ﬁnal tip
contour shape, seen in Figure 14. The ﬁnal middle (reference section) contour is shown

in Figure 15.

19

um; A. .4"

 

 

 

T/C=3.333 EL=78.5

 

Figure 13a

B1=81.221 B2=80.049 ITER=1

W/VVI
2.01

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Figure 13b

20

T/C=3.333 EL=78.5

 

Figure 14a

31:81.22] B2=79.373 ITER=100

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 14b

21

T/C=1.906 EL=75.4

 

 

 

Figure 153

B 1:77.807 B2=73.565 ITER=100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

W/VVI

2.0

1.6

DQ‘BI‘EI‘B—w
l 2 T 434341
W
o 8 ‘ﬁ’%
K WWW v u v v E 117352;?
0.41
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2
S/C
Figure 15b

22

 

4.3.2 2-Dimensional Analysis: TRAF2D

The purpose of creating a TRAF2D solution for each section was to see if the
blade sections performed the same as the inviscid design predicted when viscosity was
added. The comparisons of blade surface velocity distributions can be seen in Figures
16-18. The hub surface velocities compare well with the designed velocities, as do the
middle section’s velocities. However, near the trailing edge of the middle section suction
side there is a velocity plateau, signifying that the flow has separated from the surface
and is providing no pressure rise in that region. The tip section’s proﬁle does not match
the inviscid design very well at the leading edge, which is an issue of incidence. Because
the area between the velocity curves is smaller for the viscous solution than the inviscid

design, the work being done by the blade on the ﬂow is less than speciﬁed.

1.2 ~ “ - V INVC

1.1

0.9
0.8
.— 0.7
0.5
0.4
0.3
0.2
0.1

‘W‘P—htI-IIYI I I I
\

N.s. ‘ - 1.,

Ir
r’/
f

L I I
:3»

_
“x
l i H

[1%“L‘1-L‘T-IWPLUI

 

04411:.riirlrli-IJ

0.5 0.75 1
SIChord
Figure 16

O
.0
m
U"!

23

III'

1.3
1.2
11

1
(19
(18

1—

E 0.7
3 0.5

0.5
0.4
0.3 r-
0.2 I-
0.1 F

 

0

 

_.
-_ I'LLLLILLLL’I ll Ill I

 

IIII YYTIIII Iv

 

- r] +HI PIW‘II y-lu‘. ITS—H 111.! .
,1

0.11lllll#l L'llillllllLtllll.llllLl IllLl‘ll‘ L
(12 (13 (14 (15 (16 (17 (18 (19 1

/‘
/
/// \\
/

 

SIChord

Figure 17

‘ l

'l

\ j,
3‘ II.
N.S. I:

\‘ \‘N K ;/ I.

A _H _______ 7 _,,, r— J I ll ‘

\I l

A .. ~ I I

INVC ‘

I l l I 1 l 1 I 1 L J

 

0.25 0.5
SIChord

Figure 18

24

The Mach number plots provide a good idea of what the flow is doing in the inlet,
channel, and wake. In each plot there is a good indication of where the leading edge
stagnation point is, characterized by a zone of low velocity. On the suction side, the
acceleration followed by deceleration can also be clearly seen.

4.3.3 3-Dimensional Analysis: TRAF3D and CFX

The 3-D analysis was done using the TRAF3D and CFX software packages. The
TRAF3D convergence history is shown in Figure 19, and the CFX convergence is shown
in Figure 20. A stable solution was reached by 800 iterations for both computations. The
seemingly discontinuous drop in logarithms of RMS at 200 iterations results from the
solver switching from the course grid to the ﬁne grid. The required mass ﬂow rate of
0.84 kg/s was achieved with both solvers but at different pressure ratios. The TRAF3D
solution yielded a static pressure rise of 78.547 Pa while the CFX solution gave 118 Pa.
The values were averaged in the circumferential direction at the inlet plane, taken at 25%
of the hub section axial chord upstream of the leading edge, and at the outlet plane, taken
at 25% of the hub section axial chord length downstream of the trailing edge. The
TRAF3D values are presented in Appendix 5a and the CFX values are presented in

Appendix 5b.

25

Logarithm of RMS

 

 

 

 

 

 

 

 

 

 

200 400 600 800
Iterations
Figure 19
5°."
~91 .
.607
«8 .
2
a: .592"
”58’ .
E
E 5°;
869 .
O
A I-
.59.”
(%l _ L
; x
Q)
,- l l l l l l l l J_ l l J I
200 400 600 800
Iterations
Figure 20

26

The efﬁciency was higher in the CFX result than in the TRAF3D result, as shown
in Figure 21. In this ﬁgure and the following ﬁgures, the circumferentially mass-
averaged values are plotted across the span of the blade. The deﬁnition of efﬁciency
shown in equation 13 was employed. In the 1-D design, an efﬁciency of 70% was
assumed. While a higher average efﬁciency was observed for the CFX solution (77%), a
lower average efﬁciency was observed for the TRAF3D solution (49%). The main
reason for the discrepancy is the fact that the static pressure rise was not as large for the
TRAF3D solution as the CFX solution (Figure 22) due to hub and Shroud end-walls
rotating farther upstream for the TRAF3D solution. In the TRAF3D case, the energy
from the rotating inlet walls was transferred into a temperature rise (Figures 23 and 24)
and pre-swirl instead of a pressure rise. There was an averaged total temperature increase
of 0.409 K, which seems insigniﬁcant but is enough in such a low pressure—rise machine

to reﬂect a reduction in efﬁciency. The total pressure rise can be seen in Figure 25.

27

.0 .0 9
.5. 0*: on

Non-dimensional Span

.0
I\>

 

3D Results

 

 

 

0.4 0.5
Efficiency

Figure 21

28

.0 .0 .0
A O"! 0‘.)

Non-dimensional Span

.0
M

SD Results

 

 

 

* L1 1951730 ()qu CFX Oulbl
L L '
- l l
_ k I
_CF)llnloI I TRAFSDInH I
__ l I
_ L I
_ I I
.— l l
_ l I
- a
— J
b..r._.J.I...|...I.. “MIMI-14A
1.0126 1.0128 1.013 1.0132 1.0134 1.0136 1.0138

Static Pressure (bar)

Figure 22

29

.0 o .0
.ts tn 0:)
I

Non-dimensional Span

9
I\ )

 

CFX Into} JCFX 001M

392

II
II

 

394

3D Results

TRAHDJIIM

TRAF3D Oulbl

14L I

1 396 398

l

J_

Static Temperature (K)

Figure 23

30

l
400

l

.44
402

9 .0 .0
.1; Ch 00

Non-dimensional Span

.0
Ix)

 

CF)! Inlet

3D Results

CF)! Outlet TRAF'JD Inlet
RAFBD Outlet

 

 

 

# I l I l I l l 1 J

 

 

394 396 398 400 402
Total Temperature (K)
Figure 24

31

3D Results
1 ,gﬂlnbl TRAF3D l_nlet _ A _

 

 

 

 

 

 

 

I I TRAFSDOUIIOI
_ I I
0-8 P | 'crxomm
9 ~ l l
0') ~ I I
a 0.6 l- I I
c
o - I
'6 _
c I
(D r I
$0.4 l— I I
l I- ’
é " I l
0.2 - l I
" |
_ I I
OI, Z l l l l l I l l l l I l l l l I
1.013 1.014 1.015 1.016 1.017

Total Pressure (bar)
Figure 25
As well as producing a relatively low pressure rise, the fan operates at a very low
mach number. The absolute and relative mach numbers are plotted in Figures 26 and 27,
respectively. There is a good agreement between the relative mach numbers predicted by
CFX and TRAF3D in the channel, but near the walls the effects of the rotating inlet are

evident for the TRAF3D case.

32

3D Results

 
   
 

TRAFSD Oulbl

.0
on
I

.0
m

 

Non-dimensional Span
O
is

 

.0
to

 

 

 

0.04
Absolute Mach Number

Figure 26

33

0.06

3D Results

 

 

 

1 TRAFSDInlel CFX Outbl fFXInlet
_ THABD 0mm 1
" /
0.8 - /
c _
<5 ..
8
” /
E 0.6 L /
.9 i
g ~ /
E 0.4 e /
1E" /
g F
2 _ /
02 - /
- / /
_ _._ _~- 1/.4.I..4I...1
8.02 0.04 0.06 0.08 0.1 0. 12

Relative Mach Number

Figure 27

The evolution of absolute flow angles across the span of the blade are shown in
Figure 28. The absolute flow angle is zero at the inlet, matching the uniform inlet ﬂow
speciﬁed. The effect of the rotating tip shroud is apparent in both the inlet and outlet
absolute angles from the TRAF3D solution. Also, near both the hub and shroud walls the
axial velocity is zero (Figure 29), but the absolute tangential velocity (Figure 30) is the
same as the rotating walls (no-slip condition). Therefore, the absolute angles approach a
negative inﬁnite angle asymptotically near the hub and tip. These absolute outlet angles
are closer to zero (more axial ﬂow) than the 1-D design, which is a result of lowering the

required pressure rise to get the required mass ﬂow rate. The relative outlet flow angle

34

(Figure 3]) increases almost linearly across the center of the span as expected due to the
increase of rotor tangential velocity (U) with increasing radius. A signiﬁcant area of
relative ﬂow angles is from about 90% span to the tip. Here, the difference in flow
angles becomes negligible and then increasingly negative with radius, indicating that the
ﬂow is not turning correctly in the tip region. Compared to the 1D design, the calculated
inlet relative ﬂow angles are lower while the outlet relative flow angles are higher.
Therefore the difference in outlet and inlet angles is lower than the 1D design, signifying
that the blade is unloaded. This is correct, since the imposed static pressure rise was
lower for both flow solvers than the 215 Pa in the 1-D design. The inlet angle near the tip
decreases with increasing radius because ﬂow has gained a tangential component before
entering the blade passage due to the rotating shroud end-wall. The relative outlet angle
increases more steeply near the tip than at mid-span as the axial velocity decreases in the

boundary layer.

35

30 Results

 

.0 so .0
.13 0‘) CD

Non-dimensional Span

.0
no

 

 

 

 

 

 

-60 -4o -éo
Absolute Flow Angles (deg)

Figure 28

36

.0 .0 .0
A 0‘) (I)
I T l

Non-dimensional Span

.0
to
l

 

  

3D Results

 

_ —
' ‘— f
q

1 I . . . t I . .
2o 15 10
Absolute Tangential Velocity (mls)

Figure 29

37

" -~ —TR—i Dlnlel
on couch f3

3D Results

 

.0 .0 .0
A CD CI)
l l l l I I

Non-dimensional Span

.0
to
I

 

 

 

    

TRAF3D Oulbl

 

 

 

 

6 8
Axial Velocity (mls)

Figure 30

38

3D Results
1 — TRAF30 Inlet

    

CFX Outlet I

.0 .0 .0
J}. 0') CD

Non-dimensional Span

:0
Ix)

 

so — 55 7o 75 80
Relative Flow Angles (deg)

Figure 31

Another parameter worth noting is the radial velocity component. While no radial
velocity was taken into account in the 1-D design, there is, never-the-less a very small
radial component resulting from the TRAF3D calculation. While this component is
probably too small to have a signiﬁcant effect on the performance of the design, it should
at least be noted that it is present and that the assumption used in the 1-D design that it is
non—existent is not completely correct. The radial velocity distributions can be seen in
Figure 32. The highest negative radial velocities can be found close to the mid—section of

the blade. In addition, there is an increase toward hub and tip of the highest velocities.

39

3D Results

1 — w v
.- K?
/ )
’ CF” ""°'/ /CFx Outbt
08 _ TRAFSD Inlet / /
c / /
8 l/
U) - TRAPSD Outlet
‘8 0'5 " /
.9 _ 1
8 ‘ / \
°’ ' t
E 0.4 — \
'0
e ’ \
o r—
z _ \ \
o2 - \ \
_ \
\ \
l- l
O l l L l l l l I. l l l I l l 1 LI 1 l I l l l L E. Jr

 

 

4.2 -1 -0.8 -o.5 -o.4 -o.2 o 0.2
Radial Velocity (mls)

Figure 32

Blade—to-blade mach number plots are shown in Figures 34-38. There is a good
visualization of the acceleration on the suction side, deceleration on the pressure side, and
stagnation points at leading and trailing edges. The relative velocity vectors also follow
the blades well at each section for both solvers. The vectors are less tangent to the
leading edge for the TRAF3D solution than the CFX solution, again because of the
longer rotating inlet used in the TRAF3D computations.

A performance map was created using the TRAF3D solver by imposing different

static outlet pressures on the blade. The efﬁciency, mass ﬂow rate, and pressure rise are

plotted in Figure 39.

4O

 

Figure 33

41

 

 

M1eal_1el

0.08783
0.079047
0.070284
0.081481
0.052898
: 0.043915
g 0.035132
i 0.028349
‘ 0.017588
0.008783
0

  
 

 

 

 

 

—8.783e-02

(Tubo Plotter 828 Surface)
"if-6.587802

Mach Number

0. 00081.00

 

13.171 .11 I :1 rrmm’

r'fI

@339

Figure 34

42

 

M1eal_1el

0.1 1 5
0.1085
0.102
0.0955
0.089
0.0825
0.076
0.0695
0.063
0.0565
0.05

 

 

 

 

 

Figure 35

43

Mach Number
(Turbo Plotter 828 Surface)

*‘1.150e-01

/ {ﬁrm
1 1 : “11"?3'

}— 9.375e-02

1'-
r.
:-.-.
"1.-
IL.
l;.'_.

7.250e-02

 

 

5.125e-02

 

3.000e-02

 

 

 

 

Figure 36

  
    

GFXSQ’

 

Figure 37

45

 

 

Mreal_1el

0.155
0.1455
0.136
-- 0.1285
-- 0.117
:9; 0.1075
' 0.098
0.0885
0.079
0.0695
0.06

IUJ

 

 

 

 

 

   

Mach Number
(Tubo Plotter BZB Surface)

—1.SSOe-01

.:_'_—- 1.3126-01

1.075e-01

 

 

 

. -_--..... ‘...".

8.375e—02

u
4 »-‘Ulrmm~dﬁl¢mwm ' - -

..‘WW “1

 

6.000e-02

9~N34*4w~&r-v-Li- p544”.

1
1.
E7

.' “.WH‘TL’Q'w-in-‘v .. u

Figure 38

46

 

Performance Map

 

 

 

 

 

 

 

160 _ 7 _ , z, 7 .. 7 , 7* 7' 71 '7 ,7, “F 0.55
1 ,
.. 7.1.48.7. 7 *7 ' 7 7 7 “’5“
Q: 140 A -2 -* t- ‘ 7 0.53
.3 130 ..-7. 7. ﬂ 1 i W . 'L‘ 0.52
r: >'
120 4 ,,,,,,, a -_/ ,- _ — —— — + 0.51 o
g TRAF3D n w ' g
gms~ar~~" '7"75§
2 .0.-- - 4 - ~0-49ﬁ
n. 1 *
.2 90 d___ _A A _+ A 7 ¥ 147* , , *7 77' 77777 " ‘ T— 0.48
.5 80 A?“ _ __ __ L -k a .7. l, 7 A ‘ W‘ 7; “771— “ ‘ " ' F 0.47
(D 1 , '
70 4 -~ — ~~~ 7 i -— , ’ 0'46
60 1 4 1 1' 0.45
o 0 2 0.4 0.6 0 8 1
Mass Flow Rate (kg/s)
Figure 39

4.3.4 3-Dimensional Optimization

The 3-D Optimization was performed by adding lean in the circumferential
direction. No axial sweep was added to the blades since that would extend the blade in
the axial direction and require more space in the engine compartment. Eleven blade
sections over the span and a new TRAF3D mesh were generated for the optimization to
provide a smoothly curved blade. The hub section and next two radial sections were
stacked radially, and then a circular arc was deﬁned from the center of mass of the third
section to a set circumferential location of the tip section center of mass. The center of
mass of each of the intermediate sections fell on the arc. By increasing circumferential

component of tip lean in the direction normal to the pressure side, the goal is to force the

47

work done by the middle and hub sections to increase while decreasing the work done by
the tip section. In this way, the least efﬁcient part of the blade would do the least amount
of work. An example of a blade with a tip lean of 0.09 meters is shown in Figure 40.
The efﬁciencies tend to increase with tip lean, as is shown across the span for several
lean conditions in Figure 41. The efﬁciency increases with lean, especially near the tip
section. The drop in efﬁciency at approximately 25% of the blade span corresponds to
the place on the blade where the stacking changes from radial to leaned. The acute angle

formed on the pressure side becomes more acute with increasing lean, and acute angles
become sources of losses during stacking4. The blade turning, decreases near the tip with
increasing lean (Figure 42) while turning increases near the hub section in accordance
with predictions from a past Von Karman Institute lecture series4. The comparison of

Figures 41 and 42 conﬁrm that increasing the lean optimizes the performance of the
blade. While the blade turning actually decreases near the tip with increasing lean, the
efﬁciency near the tip actually increases due to the ﬂow work being redistributed toward

more efﬁcient parts of the blade.

48

3D BladeWIth Tlp Lean = 0.09 m

3.... 974w

 

Figure 40

49

3D Lean Results

9 o .0
.1; tn oo

Non-dimensional Span

O
Ix)

 

 

 

0.4 0.8 ' 0.8
TRAF3D Elliciency

Figure 41

50

3D T1p Lean Values

      
  

 

 

 

 

 

 

L

0.8 -
C ..
(0 ..
Q
U) .-
6 0.6 -
C
o _
.5 ,.
C
w .—
..E. 0.4 l— / _
T? _ 0.04 Outlet/
C / 5T
2 ' _.-'

021 0.08 Inlet 1111111111

' —0.041nlet---

40.00 Inlet
O -__'"”'1"|l'lllllllllllllllllll
55 60 65 70 75 80 85

Relative Flow Angles (deg)
Figure 42

4.4 Conclusions

An axial cooling fan was designed for application in an automobile heat
exchanging system. From the inlet conditions and constraints an initial l-Dimensional
design was performed, yielding ﬂow angles for the blades and important initial
thermodynamic values. 2-Dimensional blade sections were then designed using an
inverse, inviscid method. The 2—Dimensional sections were then analyzed with a Navier-
Stokes ﬂow solver for comparison to the inviscid designs. The sections were then

stacked and analyzed using two different 3-Dimensional Navier-Stokes solvers, and the

51

results were compared. Finally, several circumferential lean values were added to the
stacking and the blades were again analyzed with a 3—Dimensional ﬂow solver.

For highest efﬁciency and pressure rise, the hub and shroud should not extend
much farther than the leading edge of the blades. Otherwise, a pre-swirl is imparted on
the flow near the walls due to the no-slip condition and the energy is converted to
temperature rise instead of pressure rise. However, even with different rotating inlet wall
lengths, the results from TRAF3D and CFX compared well at the designed mass ﬂow.
The difference in static pressure rise between the two solutions could be attributed to
several possible sources. First, the results of CFX were averaged by mass only, while the
results from TRAF3D were averaged by mass, momentum, and energy. Therefore the
TRAF3D solution may be more accurate since it takes into account mixing losses from
the wake. Another possible source is the turbulence model used. CFX uses a k-u) model
while TRAF3D uses a Baldwin-Lomax scheme. Also, the mesh quality can affect all
results. A less-than-optimum grid for either solver could produce errors in the results.

Adding circumferential lean to the blade increases the overall efﬁciency of the
blade but generally decreases the static pressure rise and mass ﬂow rate. The reason for
the increase in efﬁciency is that lean increases the work done by the most efﬁcient parts
of the blade (near the middle where endwall losses are low) and decreases the work done
by the lesser efﬁcient parts of the blade. A decrease in efﬁciency is observed at the
location on the span where the stacking changes from radial to leaned, due to an
accumulation of losses in the acute angle formed there on the pressure side. Using a
completely leaned blade (without any radial stacking) could eliminate this zone of low

efﬁciency, and would be a good candidate for future work.

52

APPENDICES

Appendix 5a
---------- TRAF3D Results-—---------—--

MASS Averaged values for section : 1

 

mass ﬂow = 0.840431333

mach averaged = 2.72347685E-02
ro averaged = 0.897607207

vx averaged = 10.4376307

vt averaged = -0.487607330

vr averaged = -0.366480708
Speed averaged = 10.4554386

vxr averaged = 10.4376307

vtr averaged = 37.1336327
vrr averaged = -O.366480708
p averaged = 101277.773
pe averaged = 101277.938
pt averaged = 101332.500
ptr averaged = 101977.234
pte averaged = 101332.523

t averaged = 393.140564

tt averaged = 393.201324

e averaged = 282139.000
alfa averaged = -2.32546568
delta averaged: -2.01091361
beta averaged = 74.3002319
vx(real) averaged (total
mass/(rho_av*tot_area))= 9.99389458

MASS Averaged values based on conservation of mass,
tangential and radial momentum and total energy (see VKI CN l41/T U)
VALUES after 3 iterations!

Paver = 101281.617 (Pa)
Poaver = 101326.633 (Pa)
Roaver = 0.897612512 (kg/m"3)

53

Alpha = -3.55518794 (deg)
Vmaver = 9.99383450 (m/s)
Vuaver = -0.620911360 (m/s)
Taver = 393.151398 (K)
Ttaver = 393.201324 (K)

MASS Averaged values for section : 2

 

mass ﬂow = 0.835089684

mach averaged = 3.06479130E-02

ro averaged = 0.897414207

vx averaged = 10.2742290

vt averaged = -5.46047258

vr averaged = 0770395339

Speed averaged = 11.6606188

vxr averaged = 102742290

vtr averaged = 31 .8020630

vrr averaged = -0.770395339

p averaged = 101356.117

pe averaged = 101355.828

pt averaged = 101423.719

ptr averaged = 101885.602

pte averaged = 101423.320

t averaged = 393.529510

tt averaged = 393.604218

8 averaged = 282433.312

alfa averaged = -26.8656254

delta averaged: 428820038

beta averaged = 72.0960083

vx(real) averaged (total mass/(rho__av*tot_area))= 9.99052143
Re2 aver.(based on Lref)= 9041 .45020
Re2 aver.(based on chord): 21946.2656

MASS Averaged values based on conservation of mass,
tangential and radial momentum

and total energy (see VKI CN 141/T U)

VALUES after 3 iterations!

Paver = 101356.250 (Pa)
Poaver = 101415.289 (Pa)
Roaver = 0.897389829 (kg/m"3)

54

Alpha = -29.4281540 (deg)

Vmaver = 9.99079323 (m/s)

Vuaver = -5.63598680 (m/s)

Taver = 393.538757 (K)

Ttaver = 393.604218 (K)

mass ﬂow error = -6.35580812E—03
tot. press. rat. =1.00089598

 

efﬁciency = 0.487949
Appendix 5b
----------- CFX Results--------

--Mass Averaged Values at position 1--

rhol =0.897656 kg*m-3
Mrell = 0.0988336

M1 = 0.0275811

P1 = 101268 Pa

T1 = 392.942 K

Vaxl = 10.6613 m*s-1
Uavel = 37.6941 m*s-l
Vradl = 0.186534 m*s-1
Vtanl = -0.08334 m*s-1

--Mass Averaged Values at position 2--

rhol = 0.898800 kg*m-3
Mrell = 0.0872737

M1 = 0.0288309

P1 = 101386 Pa

T1 = 393.116 K

Vaxl = 10.1308 m*s—1
Uavel = 33.0955 m*s-l
Vradl = 0.268073 m*s—1
Vtanl = -4.94675 m*s-l

efﬁciency = 0.772147

55

Appendix 5c
--------- Equations----------
Velocity Trigonometry:
V=U+W
U = r * (1)
Vax = V * Cos(0t)
Vtan = V * Sin(0t)

W... = w * C0803)

Wtan 7" W * 391(9)
Blade Geometry:

rtip = Utip / (2*1t:*(n/60)

r1111b = [rtip - m / (9”‘TI*V1,ax)]”2

t = (2*1t*r) / Z

cax = c * CosOv)
Thermodynamics:

AH = U * £3an = U * Vax * (132—13.)

AP = AH * p

11 = (AP/P) / (U * AVtan)
Coordinate Transformation:

xCFX = xTRAF

56

(1)
(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

f=yTRAF/r (15)

ycrx = r * Sin(f) (16)

chx = r * Cos<0 <17)

57

Table 1 Required Data

TABLES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m(rpm)= 2500 Chub (m): 0.04
Utip(m/S)= 50 Cmid(m)= 0.05
T011K): 393.15 ctip(m)= 0,04
Po1(Pa)= 101300 V1(m/s)= 7.72145
Xhub (deg)= 60.8 at (deg) = 0
Amid(deg)= 75.3 m(kg/s)= 0.84
ktip(deg)= 78.5 AP (Pa): 215
Z: 9

Table 2 Values for Constant AP

r (m) U (m/s) A13 (deg) AP (Pa)
0.190985932 50 1.084448404 215
0.136499886 35.73559 3.560140908 215
0.082013841 21.47117 70.22043191 187.816
Table 3 Values for Actual Blade

r(m) U (m/s) AB (deg) AP (Pa)
0.190985932 50 1.848218104 328.5753
0.136499886 35.73559 4.477440272 249.3758
0082013841 21.47117 21.49543191 156.2893

 

 

 

 

 

58

 

REFERENCES

IPehlivan, K. K., “Inverse Design and Optimization of an Axial Cooling Blower,” Von
Karman Institute Stagiere Report 2000-25. August 2000.

2Foss, J ., Henner, M., Moreau, 8., Neal, D., “Evaluating CFD Models of Axial Fans by
Comparisons with Phase-Averaged Exeriments,” SAE 2001, OlVTMS-89.

3Van den Braembussche, R. A., “Inverse Design Methods for Axial and Radial
Turbomachines,” Von Karman Institute Preprint 1994-35, May 1994.

4VKI LS 1999-02, “The Exploitation of 3-Dimensional Flow in Turbomachinery
Design,” Turbomachinery Blade Design Systems, Von Karman Institute 1999.

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