DESIGN AND NUMERICAL INVESTIGATIONS OF A COUNTER-ROTATING AXIAL COMPRESSOR
FOR A GEOTHERMAL POWER PLANT APPLICATION
By
Thomas Qualman II

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering – Master of Science
2013

ABSTRACT
DESIGN AND NUMERICAL INVESTIGATIONS OF A COUNTER-ROTATING AXIAL COMPRESSOR
FOR A GEOTHERMAL POWER PLANT APPLICATION
By
Thomas Qualman II
Geothermal provides a steady source of energy unlike other renewable sources,
however, there are non-condensable gases (NCG’s) that need to be removed before the steam
enters the turbine/generator or the efficiency suffers. By utilizing a multistage counter-rotating
axial compressor with integrated composite wound impellers the process of removing NCG’s
could be significantly improved. The novel composite impeller design provides a high level of
corrosion resistance, a good strength to weight ratio, reduced size, and reduced manufacturing
and maintenance costs. This thesis focuses on the design of the first 3 stages of a multistage
counter-rotating axial compressor with integrated composite wound impellers for NCG
removal. Because of the novel technique, an unusual set of constraints required a simplified 1
and 2D design methodology to be developed and investigated through CFD. The results
indicate that by utilizing constant thickness blades with constant shroud radius (to ease
manufacturing difficulties) a total pressure ratio of 1.37 with a total polytropic efficiency of
89.81% could be achieved.

ACKNOWLEDGEMENTS

First, I would really like to thank my thesis advisor, Dr. Mueller, for all the support and
guidance he has given me since our paths first crossed when I was just a lowly undergraduate
student. A special thanks also goes out to Dr. Engeda and Dr. Wichman for both being on my
committee as well as for their encouragement over the years. I would also like to thank my
friend and colleague Blake Gower for all his help.

iii

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................................................ vi
LIST OF FIGURES ............................................................................................................................. vii
KEY TO ABBREVIATIONS.................................................................................................................. ix
CHAPTER 1.0 ................................................................................................................................... 1
1.1 Introduction to Geothermal Power Plants ........................................................................... 1
1.2 Issue of NCG Removal and Current Methods ....................................................................... 3
1.3 Proposed Improvement ........................................................................................................ 4
CHAPTER 2.0 ................................................................................................................................... 7
2.1 Introduction of COSO Application ........................................................................................ 7
2.2 COSO Benchmark Design ...................................................................................................... 9
2.3 Scope of Work ..................................................................................................................... 10
CHAPTER 3.0 ................................................................................................................................. 12
3.1 Introduction of Simple 1D Design ....................................................................................... 12
3.2 Axial Compressor Basics ..................................................................................................... 13
3.3 1D Counter-Rotating Axial Compressor Design Methodology ........................................... 19
CHAPTER 4.0 ................................................................................................................................. 27
4.1 Introduction of Simple 2D Design ....................................................................................... 27
4.2 2D Counter-Rotating Axial Compressor Design Methodology ........................................... 27
CHAPTER 5.0 ................................................................................................................................. 31
5.1 Introduction to CFD ............................................................................................................ 31
5.2 Compressor Modeling for CFD............................................................................................ 31
5.3 Meshing of Fluid Domain .................................................................................................... 32
5.4 Simulation Setup and Post Processing ................................................................................ 33
5.5 Preliminary Results ............................................................................................................. 35
5.6 Results ................................................................................................................................. 37
CHAPTER 6.0 ................................................................................................................................. 51
6.1 Conclusions ......................................................................................................................... 51
6.2 Potential Future Work ........................................................................................................ 52
iv

REFERENCES .................................................................................................................................. 53

v

LIST OF TABLES

Table 1: COSO Design Requirements .............................................................................................. 9
Table 2: System of Equations to be Solved ................................................................................... 23
Table 3: FV Design Mesh Independence Study Results ................................................................ 36
Table 4: COSO Design Mesh Independence Study ....................................................................... 37
Table 5: FV 2D/CFD Comparison ................................................................................................... 38
Table 6: FV v COSO Performance Parameters .............................................................................. 42

vi

LIST OF FIGURES

Figure 1: Typical GPP Setup ............................................................................................................ 2
Figure 2: Plant Net Power Output as Function of NCG Fraction .................................................... 4
Figure 3: A Prototype Wound Impeller with Integrated Magnets in Shroud ................................. 5
Figure 4: Rotor/Counter-Rotor Pair with VFD Assemblies ............................................................. 7
Figure 5: 11 Stage Prototype Installation ....................................................................................... 8
Figure 6: 1st 6 Stages of COSO Benchmark Design ....................................................................... 10
Figure 7: 1D Design Constraint Guide ........................................................................................... 13
Figure 8: Stage Velocity Triangles at Inlet and Outlet .................................................................. 17
Figure 9: IGV Circular Arc Blade Definition ................................................................................... 21
Figure 10: R-CR Circular Arc Blade Definition ............................................................................... 23
Figure 11: R-CR Main Iteration Loop............................................................................................. 25
Figure 12: Fluid Domain of COSO Design ...................................................................................... 34
Figure 13: Fluid Domain of FV Design ........................................................................................... 35
Figure 14: Relative Mach # v. Normalized M ................................................................................ 39
Figure 15: FV Stage 3 Velocity Vectors at 10% Span .................................................................... 40
Figure 16: Relative Mach # at TE v Normalized Span - 2D/CFD .................................................... 41
Figure 17: Relative Mach # v. Normalized M ................................................................................ 43
Figure 18: Total and Local Pressure v. Normalized M .................................................................. 44
Figure 19: Entropy v. Normalized M ............................................................................................. 45
Figure 20: Stage 2 Pressure Rise Coefficient v. Normalized M ..................................................... 46
vii

Figure 21: Stage 3 Pressure Coefficient v. Normalized M ............................................................ 47
Figure 22: FV Stage 3 Velocity and Entropy Plots at 50% Span .................................................... 48
Figure 23: COSO Stage 3 Velocity and Entropy Plots at 50% Span ............................................... 48
Figure 24: Total-to-Total Pressure Ratio of Full Machine ............................................................. 49
Figure 25: 6 Stages of COSO Design and Equivalent 4 Stages of FV Design ................................. 50

viii

KEY TO ABBREVIATIONS

2

A

Cross-Sectional Area (m )

AC

Axial Chord (m)

C

Absolute Velocity (m/s)

CFD

Computational Fluid Dynamics

Cp

Pressure Rise Coefficient

CR1

Counter-Rotor 1

DF

Diffusion Factor

FV

Free Vortex

GPP

Geothermal Power Plant

IGV

Inlet Guide Vane

LE

Leading Edge

LRVP

Liquid Ring Vacuum Pump

M

Mach Number

MW

Molecular Weight (kg/kmol)

N

Rotational Speed (RPM)

NCG

Non-Condensable Gas

P

Pressure (kPa), Power (kW)

R

Mixture Gas Constant (kJ/kg/K)

RANS

Reynolds-Averaged Navier-Stokes

RMS

Root Mean Square

R1

Rotor 1
ix

SST

Shear Stress Transport

T

Temperature

TE

Trailing Edge

U

Blade Speed (m/s)

VFD

Variable Frequency Drive

W

Relative Velocity (m/s)

Z

Number of Blades, Axial Position

a

Speed of Sound (m/s)

c

Blade Chord (m)

cp

Constant Pressure Specific Heat (kJ/kg/K)

cv

Constant Volume Specific Heat (kJ/kg/K)

dH #

de Haller Number

h

Specific Enthalpy (kJ/kg)

mf

Mass Fraction

n

Number of Elements

q

Specific Heat Transfer (kJ/kg)

r

Radius (m)

s

Blade Spacing (m)

w

Specific Work (kJ/kg), Circular Arc Geometric Coordinate (m)

y

Circular Arc Geometric Coordinate (m)

Γ

Temperature Ratio

Δ

Change

Π

Pressure Ratio

α

Absolute Flow Angle (deg)
x

β

Blade Angle, Relative Flow Angle (deg)

γ

Ratio of Specific Heats

ζ

Blade Stagger Angle (deg)

η

Efficiency

ρ

Density (kg/m )

σ

Blade Solidity (c/s)

3

Torque (Nm)
Camber Angle (deg), Flow Coefficient
Loading Coefficient

ω
̃

Angular Velocity (rad/s)
Specific Work (kJ/kg)

̇
̇

Mass Flow Rate (kg/s)
3

Volume Flow Rate (m )

Subscripts
ax

Axial Component

b

Blade

c

Full Multistage Compressor

hub

Hub

i

Discretization Index

in

Inlet

isen

Isentropic

xi

m

Mean Line

out

Outlet

poly

Polytropic

rel

Relative

shroud

Shroud

t

Total Property

tt

Total-to-Total

u

Tangential Component

1

Stage Inlet

2

Stage Outlet

Superscripts
*

Critical Property

xii

CHAPTER 1.0
1.1 Introduction to Geothermal Power Plants
With a rising global population there also comes a rise in energy demand and consumption.
It is predicted that global energy demand will increase by 56% from 2010-2040 (1). In order to
meet these damands, many different sources are available. While the traditional sources (coal,
natural gas, and nuclear) are still going to be a large source of energy generation, the need to
reduce emissions has driven many renewable sources to be utilized as well. Many of the
renewable sources of power are dependent on the cyclic nature of the resource (solar, tidal,
and wind) which can be problematic during peak demand periods. Geothermal, however,
harnesses the energy locked deep within the molten core of the Earth and can provide a
constant source of energy. In the United States, renewable energy sources provided about 12%
of the total energy generated in 2012, and less than 3% of that was from geothermal sources
(2). That is, geothermal provided less than 0.5% of the total energy generated in the U.S. in
2012. This leaves ample room for expansion both in the U.S. and internationally.
Geothermal energy is typically extracted in areas where extremely hot magma has moved
close to the surface. In these locations, it heats the trapped groundwater greatly increasing its
energy content. To extract this energy, geothermal wells are drilled where the hot
water/steam can be collected and the energy harvested. Afterwards the water can be reinjected back into the earth to keep the supply of hot water going. An example of a typical
geothermal power plant (GPP) is shown in Figure 1 (3).

1

Energy Conversion
Plant

Production
Well

Injection Well

Engineered
Fracture
System

Hot Rock

Figure 1: Typical GPP Setup “For interpretation of the references to color in this and all other
figures, the reader is referred to the electronic version of this thesis.”
Depending on the location, the geothermal fluid can vary in temperature and chemical
composition significantly. For this reason there are three main types of GPPs: dry steam, flash
steam, and binary cycle. A dry steam system is used when the geothermal fluid is hot enough
to already be dry steam and can be directly used to run a turbine/generator system. When the
fluid contains saturated steam/liquid water mixture, a flash steam system is used to flash
evaporate the liquid into steam, which is then used to run the turbine/generator system and
the remaining liquid water can be sent to the injection well. A binary cycle is used when the
fluid is not hot enough to produce enough steam effectively and therefore an auxiliary fluid
with a lower boiling point is heated through a heat exchanger by the geothermal fluid and this
auxiliary vapor is then used to run the turbine/generator system.
2

1.2 Issue of NCG Removal and Current Methods
Because most geothermal sources are typically a mix of steam/liquid, flash steam power
plants account for 61% of the installed capacity as well as 63% of the energy produced by GPPs
(4). Aside from containing a mix of steam and liquid water, the geothermal fluid typically also
contains a wide range of other components that exist in the Earth’s crust. These contaminants
are solids and other gases. Most of these are easily separated off in the flash tank but there are
certain non-condensable gases (NCGs) that cannot be easily removed. These are typically
mostly carbon dioxide with smaller amounts of ammonia, nitrogen, methane, hydrogen sulfide,
and hydrogen (5). If neglected, these NCGs reduce the thermodynamic efficiency at which the
turbine can operate. In order to maintain maximum turbine efficiency these NCGs need to
removed. There are several methods currently being used for NCG removal and they are steam
jet ejectors, liquid ring vacuum pumps (LRVPs), radial blowers/centrifugal compressors (turbocompression), reboilers, and hybrid systems. The method or combination of methods used
depends on the amount of NCGs that need to be removed.
The most common method is a steam jet ejector which operates using the Venturi effect.
However, this method has several areas of concern. They require their own supply of steam to
operate which in turn cannot be used to generate electricity. Their capacity is dictated by their
size, so multiple ejectors could be necessary, thereby increasing the required space. They can
only handle relatively small amounts of NCGs (<3%) and can only achieve efficiencies of 10-15%.
A more efficient alternative is NCG removal by turbo-compression, which can easily achieve
efficiencies of 75% or higher. A study comparing the performance of a steam jet ejector and a
turbo-compressor illustrates the difference in performance as seen in Figure 2, which indicates
3

that a turbocompression system is not only more efficient, but more effective over a wider
range of NCG concentrations (6).

Figure 2: Plant Net Power Output as Function of NCG Fraction

1.3 Proposed Improvement
It is clear that turbocompression is the most logical choice in terms of efficiency and
capacity, but this comes at a cost. Installing or converting to this type of system can be both
expensive and require large areas of the plant to house all of the components and auxiliary
systems. The proposed solution is a multi-stage counter-rotating axial compressor with
composite wound impellers (impeller based on patented design by Michigan State University)
(7). The composite impellers provide the compressor with a high strength-to-weight ratio (hub,
blades, and shroud all one piece) and provide excellent corrosion resistance at the same time.
4

Integrating magnets into the outer shroud can remove the need for a strong central shaft for
torque transmission (see Figure 3). This could remove the need for a central shaft all together
(if the bearings could also be adapted to the outer shroud), or the central shaft could be
significantly less bulky if its main purpose is simply to support bearings.

Figure 3: A Prototype Wound Impeller with Integrated Magnets in Shroud
Since the goal is NCG removal and not necessarily maximum pressure ratio, utilizing a multistage counter-rotating axial compressor can reduce the size while maintaining the necessary
compression and flow capacity versus a multi-stage centrifugal setup. By utilizing counterrotation, this allows for much higher work potential versus a conventional axial compressor of a
comparable volume. Another benefit of counter-rotation is that rotational speeds can be
reduced compared to a traditional axial compressor while performing similar work. Also, the
5

need for stators in each stage is no longer there, allowing for the size to be reduced when
compared to a conventional axial compressor where each stage requires its own stator.
The wound impeller design allows for comparatively quick and inexpensive manufacturing
as compared to conventional and current composite manufacturing techniques. Conventional
impellers are expensive to machine from metals while also producing a lot of waste material.
Conventional composite impellers are constructed like the hull of a boat where alternating
layers of fiber and resin are layered into a mold and then cured. This process can be very time
consuming and also costly. The wound impeller is manufactured by CNC where a continuous
fiber that is run through a resin bath is then wound around a set of mandrels that are particular
to that specific impeller design. By utilizing a well thought out pattern, there are a wide range
of potential patterns/designs that are possible using this technique. The main cost involved is
getting the initial mandrels manufactured. After this, impellers are wound, cured, and then the
mandrels can be removed and reused. This can greatly reduce the manufacturing costs while
producing an impeller of superior strength, lighter weight, and higher corrosion resistance.

6

CHAPTER 2.0
2.1 Introduction of COSO Application
Currently, an 11 stage counter-rotating axial compressor prototype with wound impellers
and integrated shroud magnets is being designed, built, and tested at a single flash GPP located
in the COSO volcanic fields in California. In this application, there is an inlet guide vane (IGV)
followed by 5 rotor/counter rotor pairs; a guide vane or impeller each constitutes what is
defined as a stage. This compressor is to be used as a replacement for the plant’s steam jet
ejector system. An example of this setup can be seen in Figure 4, which shows a rotor/counterrotor pair with variable frequency drive (VFD) at the shroud, and in Figure 5, which shows the
complete compressor installation.

Figure 4: Rotor/Counter-Rotor Pair with VFD Assemblies

7

Figure 5: 11 Stage Prototype Installation
The specific application of NCG removal imparts its own set of constraints on the
requirements of the compressor. More specifically, in terms of the working fluid, mass flow
rate ( ̇ ), inlet total pressure ( ) and total temperature ( ), and overall total-to-total pressure
ratio (Π

). In order to simplify the initial analysis, and since the NCGs are comprised mostly

of carbon dioxide, the working fluid was specified to be a mixture of H20 and CO2. The
remaining design specifications, which are mostly geometric, can be found in Table 1.

8

Table 1: COSO Design Requirements
Property
Mixture MW

Units
kg/kmol

Value
24.50

mf-H20

-

0.55

mf-CO2
γ
̇

kg/s

0.45
1.34
2.00

Πtt,c

-

3.75

Pt,in

kPa

8.27

Tt,in
N
IGV rshroud

K
RPM

309.82
8000.00

m

0.26

IGV rhub
Axial Spacing

m
m
-

0.09
0.12
12

Z

2.2 COSO Benchmark Design
Utilizing these baseline parameters, a prototype design was created to enable the COSO
plant to begin testing this technology. This design consisted of an IGV of constant hub and
shroud radii. The IGV was followed by Rotor 1 (R1) with constant hub and decreasing shroud
radius (from 0.26 m to 0.2471 m). This was followed by Counter-Rotor 1 (CR1) which also has a
constant hub radius and a decreasing shroud radius (from 0.2471 m to 0.236 m). After this, the
remaining rotor/counter-rotor pairs maintain a constant shroud radius of 0.236 m and in turn
have increasing hub radii through the rest of the compressor. The rotational speed was kept
constant (though alternating in sign to accommodate for the counter-rotation). This design
makes use of a constant chord (in both the radial sense and for each rotor or counter-rotor)

9

and custom airfoil shape for the blade profiles. A model of the first six stages is shown below in
Figure 6.

Figure 6: 1st 6 Stages of COSO Benchmark Design

2.3 Scope of Work
The main focus of this thesis will be the design of the first 3 stages of a multistage counterrotating axial compressor with wound composite impellers and integrated magnets at the
shroud (referred to as the FV design). In the benchmark design, both R1 and CR1 have
decreasing shroud radii which can unnecessarily add to the difficulty of implementing magnets
into the outer shroud. This also reduces the possible work transfer, by reducing the tip speed
at the impeller outlets, which translates into reduced pressure gains. Also, while the airfoil
shaped blades could be manufactured via the novel wound composite technique, it does
present its own set of challenges such as fiber bunching in some areas (for example, at the
leading/trailing edges) while being thin in other areas. The constant chord design, which causes
10

the axial length at the shroud to be less than at the hub, can also contribute to the issue of fiber
bunching with the current state of this manufacturing technology. With these potentially
problematic areas in mind, basic design goals can be laid out.
The new design must also satisfy the following design requirements:


Constant tip radius



Constant axial length (chord not constant in radial direction)



Constant thickness blades



Circular arc blades



Maximize pressure ratio while maintaining efficiency

This will be accomplished by developing a simple 1D design tool in Microsoft Excel. Then
this will be expanded into a simple 2D design tool also based in Excel. The 2D design results will
then be used as the inputs for creating a 3D CFD model which will be used to validate the
design. The COSO benchmark design will also be imported into CFD and the results used for
comparison against the new design.

11

CHAPTER 3.0
3.1 Introduction of Simple 1D Design
The benefits of first performing a simple 1D design is that in this method only a set of
algebraic equations are needed (versus partial differential equations) which therefore renders
the calculations to be much less complex. When dealing with compressor design, the freedoms
that remain for the designer are finely connected to what is given or specified in the design
problem. This web of connections can easily cause the design to become over constrained if
care is not exercised when deciding what equations can be used where or in which situations.
In order to begin constructing the simple 1D design tool, a basic strategy needs to be
determined which will be used as guide to ensure that the design remains within the scope of
this work as well as making certain that the design does not become over constrained. Figure 7
(below) lays out the basic areas that these constraint issues could originate from and can serve
as a reminder of the areas where extra care needs to be taken.

12

Figure 7: 1D Design Constraint Guide

3.2 Axial Compressor Basics
The goal of a compressor is to increase the pressure of the working fluid by performing
work on the fluid. The work is performed by the rotating blades of the compressor impellers.
To be able to describe and understand what is occurring during this process several sets of
equations are necessary. Several of these are derived using a control volume analysis alongside
basic aero and thermo-dynamic laws. The main thermodynamic laws used are ideal gas law,
the conservation of mass (continuity), the conservation of energy, and the conservation of
momentum. The compressible flow relationships are derived using these laws along with some
clever manipulation. Because the design problem required constant thickness blades on a

13

wound composite impeller traditional loss correlations were foregone in favor of a generalized
loss through specification of an approximate isentropic efficiency for each stage similar to the
method used by Wilcox in (8). The velocity component vector relationships are determined
from geometric and reference frame considerations.
The fluid will be treated as an ideal gas meaning that it follows the ideal gas law, which is
given as:
Equation 1: Ideal Gas Law

The ideal gas law provides a useful relationship between the pressure, temperature, and
density. The pressures and temperatures typically dealt with in compressors are relatively mild
when compared with the values necessary for the ideal gas equation of state to start breaking
down and no longer remain valid. When using the ideal gas law it is also common to assume
constant specific heats (

and ).

The continuity equation simply states that the mass flow rate into a steady state device
(compressors are typically steady state devices) must equal the mass flow rate out of the device
and is shown in Equation 2.
Equation 2: Continuity Equation
̇
Next is the conservation of energy, which can be expressed in its simplified form as:

14

Equation 3: Energy Balance
̃
Where Δ

is the change in specific total enthalpy (can be thought of as the change in energy of

the fluid and is also equal to

), q is the specific heat transfer of the system

(compressors are assumed to be adiabatic, that is q=0), and w is the specific work of the
system. This means that the change of energy of the fluid is simply a function of the work done
on that fluid. By considering the conservation of angular momentum (Equation 4), it is possible
to find another expression for the work.
Equation 4: Conservation of Angular Momentum
̇(

)

If both sides are multiplied by the rotational speed (ω) (where r*ω=U) and then divided by ̇
the expression on the left hand side becomes equal to the specific work. Equating these two
expressions for the specific work gives Euler’s turbomachinery equation shown in Equation 5.
Equation 5: Euler's Turbomachinery Equation
̃
Inspection of this equation indicates that the work input is directly related to the blade speed

(U) and the difference in the tangential velocity of the fluid. The larger the change in Cu, the
more work that is done on the fluid and hence larger pressure gains can be realized.
When dealing with moving fluid properties, there are two versions of each property: the
local or static and the total or stagnation. The total property accounts for the motion of the
15

fluid and the local property is as if the reference frame was traveling with the fluid. The exact
derivations of these are given in (9) and (10) with the equations themselves given below.
Equation 6: Speed of Sound and Critical Speed of Sound
√

√

,

Equation 7: Mach Number and Critical Mach Number

Equation 8: Total Enthalpy

Equation 9: Total Temperature

Equation 10: Ratio of Total to Static Temperature
(

)

(

)

Equation 11: Ratio of Total to Static Pressure
(

)

(

)

(

(

)

)

Equation 12: Total-to-Total Isentropic and Polytropic Efficiencies
(Π )
(Γ )

16

In multistage compressors, aside from the isentropic efficiency, it is typical to also introduce
the concept of the polytropic efficiency as well. The polytropic efficiency accounts for the
energy dissipation within a turbine or compressor whereas the isentropic does not. This is why
the isentropic efficiency is not conducive for comparing components operating under different
conditions. It should be noted that the polytropic efficiency is always going to be larger than
the isentropic efficiency in a compressor. As the polytropic efficiency increases (a reduction in
energy dissipation), the difference between the two efficiencies reduces as demonstrated in
(11).
Another major staple of axial compressor design and analysis are the velocity triangles
which describe the velocity vectors in both the relative and absolute frames of reference.
General velocity triangles for the inlet and outlet of a rotating stage are shown in Figure 8. It is
the absolute components of velocity at the outlet of one stage that are equal to the absolute
components of velocity at the inlet of the following stage.

β

β

α
Cax

α
C

W

C

U

Cu

Cax
Cu

Wu

Wu
U

Figure 8: Stage Velocity Triangles at Inlet and Outlet

17

W

Through inspection of Equation 5 and Figure 8, it should be seen that since the difference in

U between the inlet and outlet is small, the difference in Cu is mostly responsible for the work
input and thus the increase in pressure. Logically then, to maximize pressure ratio the blade
should provide maximum turning to give the largest difference in Cu. However, in reality if the
blades attempt to turn the flow too far, flow separation can begin to occur. Flow separation
can lead to compressor stall and large reductions in efficiency so it is important to ensure that
this does not occur. Over time several factors were devised to use easily determined quantities
to give an indication on when separation and then potentially stall would occur. The simplest
was developed by de Haller in 1953 (12) and is given as:
Equation 13: de Haller Number

The simplistic nature of this factor makes it quick and easy to use as an indicator of the blade
performance, however it is strictly based on the relative flow velocities at the inlet and outlet
and does not account for the geometry at all. Lieblein came up with the Diffusion Factor (DF)
in 1956 (13) which is similar to the dH # but with a slight modification. He included de Haller’s
1D deceleration ratio and added another term to take into account the relative turning of the
flow and its geometry. The relative turning portion is easily identified in the top of the second
term (absolute value sign has been included to account for counter-rotation as suggested by
Petralanda in (14)). The blade geometry is accounted for through the blade solidity (σ) which is
the ratio of the blade chord (c) to the blade spacing (s) (blade spacing is the space between
two blades in a 2D cascade). Typically dH ’ must be larger than 0.7. The DF values of greater
18

than 0.6 typically indicate compressor stall and a sharp drop in efficiency, a value in the range
of 0.35-0.55 should ensure that the flow shouldn’t separate significantly.
Equation 14: Diffusion Factor
[

]

|

|

In order to be able to more directly compare the results of the two compressors of differing
design strategy, a non-dimensional pressure rise coefficient (Cp) has traditionally been
employed. The pressure rise coefficient deals with the rise in static pressure normalized by the
inlet dynamic pressure (dynamic = total - local).
Equation 15: Pressure Rise Coefficient

3.3 1D Counter-Rotating Axial Compressor Design Methodology
Due to the rather unusual set of design specifications, an unconventional design
methodology needed to be developed which could accommodate for this. Since the IGV has
constant hub and shroud radii, and if an isentropic flow is assumed, the given IGV total pressure
and temperature can be considered constant through the IGV. Now the total properties, mass
flow rate, rotor inlet geometry are known. By specifying a constant axial length as well as
circular arc blades, this means that if the blade angles at the inlet and outlet of the rotor are
known then this completely specifies the blade angle throughout. With this information it was

19

possible to step through the rotor satisfying continuity by solving for the requisite hub profile.
This same process was then repeated for CR1. Once both the R1 and CR1 designs have been
deemed satisfactory the focus was shifted back to the IGV where it was “reverse designed”,
that is it was matched to the desired inlet conditions of R1.
The first step that needed to be taken was to discretize the 1D domain (axially). Since the
axial length or axial chord (AC) is constant throughout the compressor, no special care is
required when switching from IGV to R1 or R1 to CR1. Each domain was discretized equally into
n=15 elements or n+1=16 nodes. Therefore the length per element is AC divided by n. The
generalized formula is given in Equation 16
Equation 16: 1-D Discretization

With the spatial discretization completed it was then possible to use this in conjunction with
some trigonometry to determine the blade angle at each axial node. For a circular arc blade,
the inlet and outlet angle are related by the camber angle:
Equation 17: Camber Angle for Circular Arc Blade
(

)

Figure 9 illustrates the circular arc blade under the special condition that

is equal to 90

degrees (with respect to the tangential versus 0 degrees if it was referenced to the axial
direction), which applies to the IGV. Notice that for
⁄ .

20

the stagger angle (ζ) is equal to

AC

c

Flow Direction
Figure 9: IGV Circular Arc Blade Definition
It should be realized that the radius of the circular blade curvature can be determined via
trigonometry:
Equation 18: IGV Blade Radius of Curvature

With

and

it is possible to determine the chord length (c):
Equation 19: Blade Chord Length
( )

Now solving Equation 18 for

and substituting Equation 16 for AC:

21

Equation 20: IGV Discretized Camber Angle
(

)

and finally inserting this into Equation 17 and rearranging results in:
Equation 21: IGV Discretized Blade Angle

While this was a relatively simple process for the IGV (because of the 90 degree inflow and
thus blade angle), it becomes more complex if the specified outlet blade angle is not 90
degrees. This added complexity can readily be seen by comparing Figure 9 and Figure 10.

22

Flow Direction

c

ω

AC

y
c

x

w

c

c

Figure 10: R-CR Circular Arc Blade Definition
There are four important relationships needed to fully determine the blade angle
everywhere and are given in Table 2 (Note there are 4 equations and 4 unknowns).
Table 2: System of Equations to be Solved
Formula
(

Unknowns

)

x, w, rb
x, rb
x, y

(

x, w, y

)

23

In order to avoid the tedious nature of solving these through substitution, use of linear algebra
in the form of coefficient matrix inversion was chosen instead. The important result is shown in
Equation 22, which can then be used in conjunction with Equation 21 to obtain the blade angle
at every location. With the blade angles specified everywhere the aero/thermodynamic design
process could then be started.
Equation 22: R-CR Discretized Camber Angle
(

(

)

To begin the design process, aside from specifying
(recall

)

and

, an initial guess of

) had to be specified. Through the use of the velocity triangle relationships

previously introduced in Figure 8, all of the fluid properties and flow conditions can be
determined at the inlet node. This includes a calculated ̇ which was also specified in the
design constraints. To ensure that continuity is satisfied the initial guess of

needed to be

iterated upon until the mass flows became equal. Now the actual values of the properties have
been determined at the inlet of R1.
The remaining nodes however, cannot be solved in this manner because the area is not
known at the next node. In order to be able to continue it was assumed that
constant throughout the rotor. With this, a
to obtain a value of

at the next node,

would remain

increase factor was initially guessed (in order
) and then later iterated on to satisfy continuity.

This process is illustrated below in Figure 11. There are two small differences between the
treatment of R1 and CR1 that serves to account for the counter rotation. First, the absolute
velocity triangle at R1 outlet is the same as at the inlet of CR1. With
24

,

, and

known at

the CR1 inlet, this fully specifies the relative velocity triangle, and therefore βin is calculated
rather than specified.

Figure 11: R-CR Main Iteration Loop
R1 and CR1 are now fully defined and solved, so now the IGV can be matched to the R1
inlet. Since the IGV is stationary, the blade angle affects the absolute velocity components
rather than the relative velocity components like in the rotating impellers. This can be
expressed as

. Now the IGV blade angles are fully specified throughout, and

the remaining properties can be solved for by iterating on

to satisfy continuity at each node

beginning at the outlet of the IGV and progressing towards the inlet. Excel/Visual Basic macros
25

were used to automate all of the iterative steps for each of the stages. Once the macros were
functioning correctly, the blade angles could be adjusted to find a combination that provides
good pressure rise while keeping parameters like the dH # and the DF within their limits so as
to minimize flow separation, which will decrease the efficiency of the compressor.

26

CHAPTER 4.0
4.1 Introduction of Simple 2D Design
Although the 1D design process is rather crude in terms of its assumptions and
simplifications, it is a vital step of the overall design process for several reasons. First, it serves
to help lock certain design constraints into place to help facilitate a smooth transition to the
more refined and complex design steps. Secondly, because of the simplifications made, the
calculation time is greatly reduced when compared to CFD. This allows for quick baseline
optimization before moving on to more advanced design techniques which, due to their
increased complexity, have increased calculation times.
Despite the usefulness of the 1D design, it is a mean-line calculation and therefore does not
provide enough information to smoothly transition to a 3D design. This is why it is important to
expand the calculations from the mean line to the hub and shroud to better define the
compressor’s geometry. These results will provide the necessary data needed to create a
model for CFD.

4.2 2D Counter-Rotating Axial Compressor Design Methodology
In order to make the transition from 1D to 2D, the assumption that there is no radial
velocity component must be maintained. The rotational motion imparted on the fluid by the
blades causes an inertial force to be generated facing radially outward. The increasing hub
radius also contributes to the generation of this inertial force, and if nothing is done to account

27

for this force, it can introduce a radial velocity component and cause the assumption to become
invalid.
One way to deal with the inertial forces is to balance them with a pressure gradient in a
simple radial equilibrium. By decomposition of the Euler equation of motion for inviscid flow
(in to its cylindrical components) it is possible through several simplifying assumptions to
reduce the radial component to (11):
Equation 23: Simple Radial Equilibrium

To determine the static pressure gradient the Bernoulli Equation was used along with the
assumptions that

and

are constant in radial direction. This was then substituted into

Equation 23 which transforms it into a separable first order ordinary differential equation.
Integration of this new equation results in Equation 24, which is known as the free vortex
condition.
Equation 24: Free Vortex Condition

The free vortex condition provides a method to expand the 1D mean line results to the hub
and shroud. Before this can be applied, the field needs to be discretized radially, adding the
second dimension. Again, 15 elements and 16 nodes were chosen. The elements were
distributed based on the mean radius location, which resulted in more elements between the

28

hub and mean, and fewer elements between the mean and shroud. Each domain has now
been fully discretized into an n x n grid.
Since the 1D mean line results are going to serve as the basis for the 2D calculations, it is
not necessary to first solve for R1 and CR1 before the IGV. Assuming uniform inlet properties
and using the free vortex condition, all properties and flow conditions can be determined at the
first node of the IGV. The remaining IGV nodes are solved similarly as before by iterating

to

satisfy continuity throughout the IGV.
For R1 and CR1, the mean radius at the next node is guess via the

increase factor as

done in the 1D design. The hub radius at this node could then be solved for which then fully
specified the radial discretization at this location. With the radii known, the free vortex
condition was applied to solve for all the fluid properties at off-mean-line nodes. A new value
of the hub radius could be found based on Equation 2. In order to ensure that continuity was
satisfied, the difference between the two values of the hub radius at this axial node was
iterated to zero by changing the

increase factor which fully determines the flow field.

It is typical in multistage axial compressors that the hub/tip ratio of the beginning stages is
small, which causes the hub radius to change drastically from the inlet to the outlet of the
stage. This can cause a radial velocity component to be generated if the hub radius gradient is
too extreme, which would violate one of the main assumptions needed to complete this design
step. In order to prevent this from occurring, the hub contour was smoothed using a cubic
spline.

29

Up until this point, the design process has assumed inviscid flow to aide in simplifying the
calculation process. This is typically a good assumption everywhere except near the hub,
shroud, and blade surfaces where in reality viscous effects lead to boundary layer formation.
This boundary layer effectively reduces the cross-sectional area of the compressor, which
directly affects how much mass flow can fit through (see Equation 2), creating a large
discrepancy between the mass flow of the 1D/2D design compared to the viscous 3D CFD
simulation. A very simple method was used to determine approximately how much, on
average, the boundary layer reduces the cross-sectional area. Through application of boundary
layer theory detailed in Pope (15), the boundary layer thickness on each surface was estimated
at each axial node. A new value of the cross-sectional area was then determined that included
the boundary layer thicknesses. With this area, an approximate, adjusted ̇ was calculated. It
is this value of the mass flow that must be matched to the 2.0 kg/s that was specified. Since the
1D/2D were originally based on the given ̇ it was necessary to go back to the 1D design and
increase the ̇ . Once the adjusted mass flow rate matched the required value, the design was
ready to transition to CFD.

30

CHAPTER 5.0
5.1 Introduction to CFD
In order to gain a more comprehensive understanding of how the compressor design will
perform in reality, a CFD analysis was the next step of the design process. Caution must be
exercised however, because CFD results are highly sensitive to the mesh quality as well as the
simulation setup (physics, boundary conditions, etc.). The CFD analysis was performed with the
ANSYS 14.5 line of software through the use of ANSYS BladeGen, TurboGrid, and CFX modules.
First, BladeGen was used to convert the 2D geometry data into an actual 3D model. Next, the
simulation domain (fluid flow path) was meshed using the TurboGrid. Lastly, the simulation
was setup and ran in CFX utilizing the 2D data to specify the boundary conditions.
ANSYS CFX utilizes a Reynolds-Averaged Navier-Stokes (RANS) solver. This means it employs
Reynolds decomposition to break instantaneous velocities into their time-averaged and
fluctuating quantities, thus allowing for approximate solutions to the Navier-Stokes equations.
The Shear Stress Transport (SST) turbulence model was chosen because it gives highly accurate
predictions of onset and amount of flow separation under adverse pressure gradients (16).

5.2 Compressor Modeling for CFD
In ANSYS it is necessary to model and then mesh each stage individually, and then assemble
these later. Two models were imported to ANSYS, the COSO benchmark model as well as the
2D design-based model. Each of these had to be imported in a different manner due to the
nature of what information was known for each. The COSO benchmark design was imported
31

via blade profile curves at the hub and shroud. For the new design, the model was constructed
by inputting data points to define the annulus, followed by the blade angles at the hub, mean,
and shroud positions.
Notice the decreasing shroud radius of the COSO design compared to that of the FV design.
Recall from Equation 5 that the work transfer is equal to

. If

becomes less at

the outlet due to the decreasing tip radius, then this will reduce the work potential. Also, as
specified in the scope of the project, the FV design uses constant thickness blades while the
COSO design employs a blade profile. By comparison, the profile used in the COSO design is not
drastically different than the constant thickness blades used to reduce manufacturing
difficulties with respect to the wound impeller technique. Since the profile differences are not
extreme, it should be a relatively safe assumption that they should perform similarly, justifying
the tradeoff of a slight decrease in performance for reduced manufacturing difficulty. The CFD
results will be able to validate if this assumption holds or not.

5.3 Meshing of Fluid Domain
Since this is a fluid analysis rather than a structural analysis, a model of the fluid domain
between the blades is actually what is needed. ANSYS has streamlined the process over the
years so that now the 3D compressor models from BladeGen can be linked directly to
TurboGrid. TurboGrid then automatically determines the fluid domain from the model rather
than it having to be set up manually. ANSYS has also greatly improved the meshing capabilities
in recent years. TurboGrid can now automatically generate a relatively high quality mesh very
32

quickly (high quality means more uniform elements with less warped and stretched elements
that would need to be manually corrected using traditional meshing techniques). This
automatic meshing option (ATM Optimized) still provides the user the ability to refine the mesh
in important areas, such as in the boundary layer and at the leading/trailing edges. Once good
parameters have been settled on, it is possible to increase the mesh density through a scaling
factor which makes transitioning to finer meshes for mesh independence studies a quick and
easy process.
Initially, each stage was meshed with a node count in the range of 400-500,000 nodes,
which has shown to be a reasonable mesh size to be able to resolve the potential flow features
that occur in an axial compressor (17). In order to validate these results, a fine mesh of
approximately 1,000,000 nodes per stage was also created.

5.4 Simulation Setup and Post Processing
At this point, the fluid domains of each stage have been successfully meshed. Now the
actual simulation can be setup. The meshes were imported to CFX through CFX-Pre which is
the tool used to fully define the simulation physics models, boundary conditions, and solver
options. The simulations were modeled as steady state with adiabatic walls, and employed the
SST turbulence model. Since each rotor has an equal number of blades, this allows for a
periodic boundary condition to be used to reduce the computational domain to only one fluid
path for each rotor rather than having to simulate an entire rotor (which would greatly increase
the calculation time). Each of the fluid domains that were meshed is shown below in Figure 12
33

and Figure 13. A

and

inlet boundary conditions and an ̇ outlet boundary condition were

chosen since those were specified in the design problem. The time steps chosen varied for the
difference mesh densities. For turbomachines, a good time step is typically in the range of
(the automatic option in CFX-Pre is

) (18). Using this as a guide, the

automatic time step option was used for the coarser of the two meshes, while the lower limit of
was used for the finer of the two meshes. In order to determine when the solver should
stop running, a convergence criterion is used. For a simulation to be considered converged, the
normalized RMS residual values for mass and momentum must all become lower than this
-4

specified value of 3x10 .

Figure 12: Fluid Domain of COSO Design

34

Figure 13: Fluid Domain of FV Design
Once a simulation has converged, the raw data has to be processed in CFD-Post to obtain
usable results. CFD-Post provides some premade templates/macros that can be used to
generate quantities, charts, tables, and plots relevant to turbomachines, but also provides the
freedom for the user to customize the results to their needs.

5.5 Preliminary Results
Before directly comparing the FV design with the benchmark design, it was necessary to
ensure the simulation results were realistic. Again, this was accomplished through a mesh
independence study. Typically a mesh independence study would require more than two
different meshes to determine if the results are mesh-independent or not; however, because
the initial mesh was specified based on prior turbomachinery CFD experience (17), the results

35

were shown to be independent with only one increase in mesh density. The results of this
study are shown in Table 3 and Table 4.
Table 3: FV Design Mesh Independence Study Results
FV
Rotor
̃

Πt

Counter Rotor
̃

Πt

Med Mesh

Fine Mesh

%Difference

kJ/kg

19.13

19.35

1.14

%
%

1.16
87.23
88.93

1.16
88.78
90.02

0.27
1.76
1.22

kJ/kg

22.38

22.86

2.12

%
%

1.18
87.23
88.93

1.19
88.94
90.60

0.43
1.94
1.86

kg/s

2.01

2.03

0.71

Machine
̇
̇

m /s

25.54

25.72

0.70

Πt

-

1.37

1.38

0.48

Γt

%
%

1.10
75.74
89.81

1.10
76.64
90.53

0.05
1.18
0.81

3

36

Table 4: COSO Design Mesh Independence Study
COSO
Rotor
̃

Πt

Counter Rotor
̃

Πt

Med Mesh

Fine Mesh

%Difference

kJ/kg

12.45

12.54

0.72

%
%

1.09
78.80
79.97

1.09
79.38
80.55

0.12
0.73
0.73

kJ/kg

15.48

15.67

1.21

%
%

1.12
79.77
81.41

1.12
80.30
81.94

0.29
0.66
0.65

kg/s

1.97

1.97

0.05

Machine
̇
̇

m /s

24.94

24.96

0.05

Πt

-

1.21

1.21

0.41

Γt

%
%

1.07
58.70
77.30

1.07
59.56
77.96

0.08
1.46
0.85

3

If the results vary by more than a few percent, then this is a good indication that the results
are not mesh-independent. Looking at Table 3 and Table 4, it can be concluded that the results
for both designs are independent of their mesh statistics.

5.6 Results
In order to evaluate the effectiveness of the simple design tool, the 2D results needed to be
compared to the CFD results. Comparisons of some basic performance parameters are given in
Table 5 .

37

Table 5: FV 2D/CFD Comparison
FV
Rotor
̇
̇

Πt
̃

dH #
DF
Counter Rotor
̇
̇

Πt
̃

dH #
DF

2-D

CFD

%Difference

1.98

1.99

0.59

m /s

25.16

25.28

0.46

kJ/kg
-

1.21
26.84
0.86
81.00
81.88
0.71
0.44

1.16
19.13
0.65
87.69
88.92
0.75
0.37

4.19
33.54
27.96
7.93
8.24
6.53
16.99

kg/s

1.98

1.99

0.62

m /s

22.07

22.78

3.16

kJ/kg
-

1.21
27.22
0.82
81.00

1.18
22.38
0.70
87.23

1.87
19.52.
14.66
7.41

-

81.88
0.71
0.45

88.93
0.71
0.44

8.25
0.58
2.23

kg/s
3

3

The strengths and weaknesses of the simplified design approach utilized in this study were
illuminated by comparison of these results. For instance, the method of estimating the average
boundary layer thickness and using this to calculate a new area and thus adjusted mass and
volume flow rates appear to satisfactorily make the transition without the need for a more
complicated profile loss correlation to be implemented. There is a downside of using this
method though, because the bulk of the calculations are based on the unadjusted (larger) ̇
which effectively over predicts the axial velocity component (which carries over into the other

38

velocity components and fluid properties). A good example of this is demonstrated in Figure 14
where the 2D

line is clearly shifted in the direction of higher velocities. Also, recalling

Equation 5 and noting that U should be approximately the same in the 2D and CFD, it is only
logical that the larger

(and in turn

) values would cause the specific work to be over

predicted as well.

Relative Mach # v. Normalized M
0.9
0.8

Mach #

0.7

0.6

FV CFD
FV 2D

0.5
0.4
0.3
0

0.5

1

1.5
Normalized M

2

2.5

3

Figure 14: Relative Mach # v. Normalized M
Since the

was specified in order to account for the losses in the simplified 2D

calculation, it was expected this might be an area with some discrepancies. At first it appears
as though it was conservatively specified as lower than what it would be in reality. However,
the CFD model in its current form has left out the central shaft mounting brackets as seen
previously in Figure 4. This was done purposefully in order to initially avoid having to simulate
39

the full compressor impellers rather than just a single flow path, which greatly reduced the
calculation time at this early stage of development. This is also why no attempt was made to go
back and use the CFD values to recalculate the 2D design at this point.
Both the dH #’s and DF’ were satisfactorily within their design ranges. Recalling that these
parameters were chosen to help ensure that flow separation that could lead to stall and a loss
in efficiency was minimal. It would appear that this was accomplished strictly because of the
high efficiencies achieved in CFD. This isn’t necessarily true though, and can be verified by
inspection of a plot of the velocity vectors near the hub of CR1 shown in Figure 15.

Figure 15: FV Stage 3 Velocity Vectors at 10% Span

40

Figure 16 shows the relative Mach numbers at the trailing edge for 2D and CFD. The effect
of the boundary layer can be seen to reduce

near the hub and shroud (the hub is at span

0 and the shroud is at span 1).

Rel Mach # at TE v Normalized Span - 2D/CFD

1
0.9
M rel 2
FV CFD

0.8
0.7

M rel 3
FV CFD

Span

0.6
0.5

M rel 2
FV 2D

0.4
0.3

M rel 3
FV 2D

0.2
0.1
0

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mach #

Figure 16: Relative Mach # at TE v Normalized Span - 2D/CFD
At this point it should be noted that while this unique design approach required many
techniques and simplifying assumptions that might not be used typically, the results it provided
were more than adequate to smoothly transition from a 1D design into successful 3D design.
With the FV CFD results validated they could then be compared to the COSO benchmark results.

41

Table 6: FV v COSO Performance Parameters
CFD Performance Parameters
FV
COSO
R1
ẽ
kJ/kg
19.13
12.45
kW
38.11
24.72
P
Nm
45.49
29.51

Πt

-

1.16

1.09

Γt

-

1.04

1.03

%

87.69

78.80

%
-

88.92
0.65
1.00
0.75
0.37

79.97
0.54
0.99
0.82
0.32

P

kJ/kg
kW
Nm

22.38
44.60
53.24

15.48
31.03
37.04

Πt

-

1.18

1.12

Γt

%

1.05

1.04

87.23

79.77

88.93
0.70
1.02
0.71
0.44
Machine
kJ/kg
41.52
kW
82.71
Nm
98.72

81.41
0.72
1.14
0.76
0.39

dH #
DF

CR1
ẽ

dH #
DF
ẽ

P

%
-

27.93
55.75
82.52

Πt

-

1.37

1.21

Γt

-

1.10

1.07

%

75.74

58.70

%

89.81

77.30

42

Through inspection of Table 6 it is shown that the FV design out performs the COSO design
in almost every category. The Π for the 3 stage machine is almost double that of the COSO
design. Some of this increased pressure gain is due to the higher blade speeds that come from
keeping the tip radius constant, however because the blade profiles and angles are different,
the increase in performance cannot solely be attributed to the constant tip radius.

Mach # v. Normalized M
0.9
0.8

Mach #

0.7
0.6

FV
COSO

0.5
0.4
0.3
0

0.5

1

1.5
Normalized M

2

2.5

3

Figure 17: Relative Mach # v. Normalized M
Figure 17 shows the area averaged relative Mach number plotted along the streamwise (or
meridional) direction where 0-1 is the IGV, 1-2 is R1, and 2-3 is CR1. The larger the distance
between the peak and valley, the more diffusion that occurs between the blades. This was
validated by the fact the FV values of the dH # were lower (larger change in W from inlet to

43

outlet) than those of the COSO design, as well as the fact that the DF values were higher than
those in the COSO design (where higher values of DF indicate more diffusion).

Pressure v. Normalized M
12

Pressure (kPa)

11

10
Pt FV
9

Pt COSO
P FV

8

P COSO

7
6
0

0.5

1

1.5
Normalized M

2

2.5

3

Figure 18: Total and Local Pressure v. Normalized M
Figure 18 shows the total and local pressures and serves to illustrate the difference in pressure
gain achieved by each design.

44

Entropy v. Normalized M
80
75

s (J/kg/K)

70
65

FV
COSO

60
55
50
0

0.5

1

1.5
Normalized M

2

2.5

3

Figure 19: Entropy v. Normalized M
Referring back to Table 6, it can also be seen that the FV design achieved higher efficiencies
for both stages and thus also for the machine. These values also help to illustrate the
difference between the polytropic and isentropic efficiencies. The isentropic efficiencies for
each stage are similar in magnitude, while for the entire machine it is much lower. The
polytropic efficiencies do not demonstrate this discontinuity between the stages and the
machine and are all of a similar magnitude. It can also be seen that the FV design actually
outperformed the benchmark design in terms of efficiency, which was rather unexpected due
to the lack of a blade profile. Figure 19 reaffirms this finding by illustrating that the COSO
design generated more entropy throughout the compression process.

45

In order to better compare these two machines it was necessary to make use of the nondimensional pressure coefficient,

. This was plotted along the blade surfaces for both R1 and

CR1. These types of charts are called blade loading charts where the bottom portion of the
curve represents the suction side and the top portion the pressure side of the blade.

Stage 2 Pressure Coefficient (Cp) v Normalized M
3
2
1

Cp

0
Cp FV

-1

Cp COSO
-2
-3
-4
0

0.2

0.4
0.6
Normalized M

0.8

1

Figure 20: Stage 2 Pressure Rise Coefficient v. Normalized M
Based on the higher pressure ratios achieve by the FV design, it is only logical that the values of
would generally be higher, which is the case in both Figure 20 and Figure 21.

46

Stage 3 Pressure Coefficient (Cp) v Normalized M
3
2
1

Cp

0

Cp FV

-1

Cp COSO

-2
-3
-4
0

0.2

0.4
0.6
Normalized M

0.8

1

Figure 21: Stage 3 Pressure Coefficient v. Normalized M
For the most part, both of the plots in Figure 20 and Figure 21 are smooth (except at the
leading and trailing edges). However, looking at the plot of

FV (Figure 21), on the suction

side (bottom) immediately after the spike near the leading edge, there is a small disturbance
from a normalized M value of about 0.02 to 0.08. Since this artifact occurs in the FV plot and
not the COSO plot it was posited that this could be caused by the constant thickness blade
profile. In order to investigate this, plots of both velocity vectors and entropy were used
(Figure 22 and Figure 23). It can be seen that there is a tiny separation bubble (notice the
arrowhead facing in the direction opposed to the core flow direction) just after the leading
edge on the suction side of the FV blade which is not present on the COSO blade (18). This is
more clearly illustrated in the entropy plot. This is a side effect of the constant thickness blade

47

profile used in the FV design but is not of major concern because the flow reattaches in just a
short distance and therefore has little influence on the overall performance.

Figure 22: FV Stage 3 Velocity and Entropy Plots at 50% Span

Figure 23: COSO Stage 3 Velocity and Entropy Plots at 50% Span

48

Despite the extremely simplified 1 and 2D design process, the CFD analysis demonstrated
that the design significantly outperformed the benchmark design not only in terms of pressure
ratio, but also in efficiency. This means that it would be possible to reduce the number of
stages needed to achieve the required Π

of 3.75. In fact, assuming the same trend of

performance increase would continue if the whole compressor was redesigned, this pressure
ratio could be achieve in only 7 stages (as shown below in Figure 24 and Figure 25). This would
greatly reduce the initial, maintenance, and operational costs of NCG removal. It would also
reduce the space required to house the system, which would make it easier to replace the
other less efficient and limited methods of NCG removal.

Total-to-Total Pressure Ratio of Full Machine
4.06

Pressure Ratio

3.56
3.06
2.56

COSO

2.06

FV

1.56

1.06
1

2

3

4

5
6
7
8
Stage Number

9

10

11

Figure 24: Total-to-Total Pressure Ratio of Full Machine

49

Figure 25: 6 Stages of COSO Design and Equivalent 4 Stages of FV Design

50

CHAPTER 6.0
6.1 Conclusions
With an increasing demand for energy as well as a need to reduce the negative impacts on
the environment from traditional energy sources, the focus in recent years has been shifting
towards sustainable and renewable techniques to help meet these demands. While other
sources of renewable energy are cyclical or intermittent in their ability to provide power (wind,
solar, tidal), geothermal energy sources are not and can provide a constant source of energy.
One of the main issues affecting current GPP’s performance is the presence of NCG’s in the
working fluid. Current methods of NCG removal are bulky, expensive, and inefficient. The
proposed solution is to use a multistage counter-rotating axial compressor with integrated
composite wound impellers.
The focus was on the development of the first 3 stages of this compressor. The scope of the
design work was chosen in order to demonstrate that an increase in performance as well as a
decrease in manufacturing difficulties, such as fiber bunching, that could occur with utilizing
airfoil blades of constant chord was possible to achieve. A simple 1 and 2D design methodology
was developed and validated though CFD which demonstrated, when compared to the
benchmark design, that it was possible to simplify the design as far as axial compressors are
concerned, while still obtaining good flow characteristics and performance results. The 3 stage
FV design was shown to be able to obtain a Π

of 1.37 and a

the 1.21 and 77.30% of the benchmark design.

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of 89.81% compared to

6.2 Potential Future Work
Since the preliminary design and investigation was an overall success, there are several
areas that could be focused on for refinement. First, the central axle mounting brackets that
were initially neglected to speed up simulation time should be included into the CFD model.
This would provide a more realistically prediction of the compressors performance potential.
Secondly, the design approach should be expanded to design and simulate the full multistage
compressor. Through the addition of the brackets as well as the remaining stages, the
performance capabilities and required number of stages can be more accurately determined.
Lastly, in order to prove or disprove the CFD results, a prototype of the design should be
manufactured and tested.

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53

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