M.Sc.Thesis-Reda Ragab-2008

Zagazig University
Faculty of Engineering
Mechanical Power Engineering Department
Numerical Simulation for the Impact of Wet
Compression on the Performance and Erosion
of an Axial Compressor
A thesis
Submitted in Partial Fulfillment for the Requirements of the
Degree of Master of Science in Mechanical Power Engineering
by
Reda Mohammed Gad Ragab
Supervisors
Prof. Dr. Ahmed Fayez Abdel Azim
Asocc. Prof. Hafez El-Salmawy
Dr. Mohammed Gobran
Mechanical Power Engineering Department
Faculty of Engineering
Zagazig University
Zagazig, Egypt
2008

Approval Sheet
"Numerical Simulation for the Impact of Wet
Compression on the Performance and Erosion
of an Axial Compressor"
A thesis
Submitted in Partial Fulfillment for the Requirements of the
Degree of Master of Science in Mechanical Power Engineering
by
Reda Mohammed Gad Ragab
Approved by
Examiners: Signature
1- Prof. Dr. Mohammed Mostafa El-Telbany
Mechanical Power Engineering Department.
Faculty of Engineering.
Helwan University
2- Prof. Dr. Ahmed Fayez Abdel Azim (Supervisor)
Zagazig University
3- Prof. Dr. Mohammed Mahrous Shamloul
Zagazig University
Zagazig
2008

iii
Acknowledgments
Thanks to Allah who gave me the patience to complete this work. I would like
to express my deep appreciation to my supervisors Prof. Dr. Ahmed Fayez Abdel
Azim, Dr. Hafez Elsalmawy, and Dr. Mohammed Gobran for their guidance and
support through the work on this thesis.
I would also like to thank Dr. Tarek Khass and all engineers in mechanical
power department.
I would like to express my deep appreciation to my parents, brothers, and wife
for their constant encouragement, support, Doaa and patience.

iv
Abstract
The compressor of the gas turbine set consumes around 50 %-60 % of the
power generated by its turbine. Reducing the power consumed by the compressor
increases the net power produced by a gas turbine set. This power gain is attributed
to the redistribution of the power flow within the set. Therefore, this power
increase does not accompanied with increase in thermal or mechanical stresses
within the set. One of the most common technologies for the augmentation of the
gas turbine power is wet compression. Wet compression can be achieved by
introducing liquid droplets into the compressor. Droplets evaporation during
compression process has what could be called micro-inter-cooling effect. This
leads to a reduction in the compressor consumed power.
In this study a numerical model is developed to study the effect of wet
compression on the performance of axial compressors. A commercial CFD code,
FLUENT, is used to solve the governing equations in a three dimensional, unsteady,
and turbulent flow simulation of a three stage axial flow compressor. Liquid
droplets are introduced as a dispersed phase and are tracked in a Lagrangian frame
to simulate the wet compression process. The model accounts for droplet-flow,
droplet-droplet, and droplet-wall interaction. Turbulence phenomenon is treated
using the RNG k turbulence model. The effect of turbulence on the dispersion
of droplets is taken into account using a stochastic model.
The flow field is solved in the dry case and the compressor performance is
analyzed in terms of; variation of air properties, characteristics of the operating
point, and consumed specific power. Performance change due to wet compression
is calculated. Parametric study has been performed to find out the effect of
important parameters on the compressor performance. These parameters include;
the injected coolant mass flow rate as a ratio of the dry air mass flow rate (injection
ratio), the droplet size, and the effect of droplet-droplet interaction.

v
Although water is commonly used for wet compression, methanol has been
considered in this work. This is due to its advantages over water. These advantages
include; non corrosive effect, lower erosion impact, higher volatility, and combined
use for both inlet duct cooling /wet compression and a supplementary fuel to the gas
turbine. The later is making advantage of the nature of methanol as a renewable
fuel.
Regarding the effect of injection ratio, it is found that increasing the injection
ratio causes a reduction in temperature in both axial and radial directions which in
turn causes a reduction in specific power. Air pressure, velocity, and flow angles
distribution within the compressor are slightly changed in both axial and radial
directions. Inlet air mass flow and discharge pressure are both increased, yet the
increase in discharge pressure is small. Regarding the effect of droplet size on the
performance of the compressor, it is found that increasing the injected droplet
diameter has an adverse effect on droplet evaporation rate and hence on specific
power. Its effect is exactly in contrary to that of injection ratio. It can be stated that
increasing the droplet size reduces the benefit of wet compression. Regarding the
effect of droplet-droplet interaction, high tendency of agglomeration is detected and
small droplets tend to increase in size especially at rear stages. Droplet
agglomeration increases as a result of higher loading ratio.

vi
Contents
Title Page
ACKNOWLEDGMENTS ……………………………………………………… iii
ABSTRACT…………………………………………....………..…….………...... iv
CONTENTS………………………..……………………………………..……..... vi
LIST OF TABLES……………………………………………….…….………… viii
LIST OF FIGURES……………………………………..…………….………..... ix
NOMENCLATURE……………………………………..…………….…………. xiv
CHAPTER (1): INTRODUCTION
1.1 BACKGROUND…….……………………………………..…….…….. 1
1.2 EVAPORATIVE COOLING METHODS……….……………….…... 4
1.2.1 Evaporative Cooling Theory………………………....………… 4
1.2.2 Wetted-Honeycomb Evaporative Cooler…………………..…. 5
1.2.3 Inlet Fogging……………………………………….………….... 6
1.3 INLET AIR CHILLING…………..…………………………………..… 7
1.4 LIQUEFIED GAS VAPORIZERS…………..……………….……....… 8
1.5 HYBRID SYSTEMS……..………………………………..…………….. 8
1.6 WET COMPRESSION / OVERSPRAY COOLING.............................. 9
1.7 OBJECTIVES AND METHODOLOGY ……………………..……... 15
CHAPTER (2): LITERATURE REVIEW
2.1 INTRODUCTION……………………………………………...………… 16
2.2 WET COMPRESSION ………………………………………..………… 17
2.3 DROPLET EVAPORATION ……………………………………..…..… 24
2.4 DROPLET INTERACTION …………………………………………..… 26
2.5 EROSION ……………………………………….……………………… 29
2.6 TWO PHASE PREDICTION APPROACHES…………………...…...… 31
2.7 NUMERICAL SIMULATION OF AXIAL COMPRESSORS..........……33
2.8 BLADE ROW INTERACTION…………………………………….….… 36
2.9 DISCUSSION OF PREVIOUS WORK ……………………………. 43

vii
CHAPTER (3): LITERATURE REVIEW
3.1 INTRODUCTION……………………………………………………..… 46
3.2 GOVERNING EQUATIONS ………………………………………….. 46
3.2.1 Carrier Phase Governing Equations ……………………….… 47
3.2.2 Auxiliary Equations……………………………………….. 50
3.2.3 Dispersed Phase Governing Equations……………………..… 50
3.3 SUB-MODELS…………………………………………….……….…… 53
3.3.1 Turbulence Modeling……………………………………....... 54
3.3.2 Near-Wall Treatment for Turbulent Flows…………..…..….. 58
3.3.3 Coupling Between Dispersed and Carrier Phase…………..… 60
3.3.4 Turbulent Dispersion of Droplets…………………………….. 62
3.3.5 Droplet Evaporation Model………………………………….. 63
3.3.6 Droplet Collision Model…………………………………..…… 65
3.3.7 Droplet Breakup Model………………….……………………. 66
3.3.8 Droplet-Wall Interaction Model………………….…………… 67
3.4 NUMERICAL SOLUTION…………………………………..….….…… 69
3.5 PHYSICAL MODEL………………………………………..….….. 72
3.6 COMPUTATIONAL MODEL…………………………..……….….…… 75
3.7 MESH GENERATION………………………………….……...……… 75
3.8 NUMERICAL CALCULATIONS...…………………………..……… 77
CHAPTER (4): RESULTS AND DISCUSSION
4.1 INTRODUCTION…………………………………….……....………… 83
4.2 DRY PERFORMANCE ………………...……………………………… 84
4.3 WET BASE CASE…………………………..…………………………… 93
4.4 PARAMETRIC STUDY………………………………………………… 105
4.5 COMPARISON WITH EXPERIMENTAL WORK…………………. 126
CHAPTER (5): SUMMARY AND CONCLUSIONS
5.1 SUMMARY……………………………………………....…………...… 129
5.2 CONCLUSIONS ………………………………………….…….……… 130
5.3 RECOMMENDATIONS FOR FUTURE WORK………………..…… 132
REFERENCES ………………………………………………………….….…… 133
APPENDIX (A) ………………………………………….……………….……… 140

viii
List of Tables
Table Title Page
1.1 Inlet Air Cooling Techniques………….………………………………….. 3
2.1 Axial Compressor Simulation Models……………………………………. 33
2.2 Levels of Blade Row Interaction Modeling Complexity………………… 38
3.1 Values of the constants in the RNG k model……………..….............. 56
3.2 Comparison of a Spring Mass System to a Distorting Droplet…………… 66
3.3 Constants for the TAB model……………………..……………………... 67
3.4 Section Coordinates of Blades in Percentage of Chord…………..………. 73
3.5 Compressor Blade Data………...…………………………………………. 74
3.6 Boundary Conditions……………………………………………………… 79
3.7 Geometrical Modifications for Unsteady Calculations………………..….. 80
4.1 Summary of Dry Case Average Results at Operating Point …….……….. 85
4.2 Values of the Parameters Considered in the Base Case………..…………. 93
4.3 Summary of Wet Compression Results Compared with Dry Results…….. 103
4.4 Test Matrix Parameters Values…………………………………………… 105
4.5 Summary Results of Injection Ratio Variation…………………………. 114
4.6 Summary Results of Droplet Diameter Variation…………...……………. 121

ix
List of Figures
Figure Title Page
1.1 Change in Compressor Operating Point at High Ambient Temperature….. 2
1.2 T-S Diagram on a Hot Day …………………………………….................. 2
1.3 Psychrometric Chart………………………………………………………. 5
1.4 Effect of Evaporative Cooler on Available Output- 85 % Effectiveness. 5
1.5 Traditional Evaporative Cooler Section.………………….…………...... 6
1.6 Typical Fogging System Diagram ……………………………………… 7
1.7 Mechanical Chilling Schematic for Turbine Inlet Air Cooling ………….. 8
1.8 Wet Compression ( High Fogging) System Layout……….……………… 10
1.9 Ambient Temperature Effect on The Power Gains for Combustion
Turbines………………………………………………………………… 11
1.10 Limits of Operation with Wet Compression……………………..………. 13
2.1 Limits for Splashing and Deposition of Droplets (Mundo et al., 1995)…. 27
2.2 Schematics of: (A) The Major Physical Phenomena Governing Film Flow
(B) The Various Impingement Regimes Identified in the Spray-Film
Interaction Model. (Stanton and Rutland, 1998)…….…….……….. 28
2.3 Velocity Vector and Locus of Water Droplet Inside the Compressor
(Utamura et al., 1999)……………………………………….……………. 30
2.4 Droplet Trajectories in a Spray …………………….………………..…… 31
2.5 Distribution of Droplet Parcels in a Spray Field.……………..………….. 32
2.6 Unsteady Blade Row Interaction Mechanisms……………………..…….. 37
3.1 Types of The External Forces Exerted on The Droplet……..………..…… 51
3.2 Universal Laws of The Wall (Fluent, 2006)……………………….…….. 58
3.3 Near-Wall Treatments in FLUENT………………………………...…….. 58
3.4 Outcomes of Collision…………………………………………………….. 65

x
3.5 "Wall-Jet'' Boundary Condition for the Discrete Phase………………….. 68
3.6 Flow Chart of the Solution Procedure………………………………...….. 70
3.7 Coupled Discrete Phase Calculations……………………………………... 71
3.8 NACA Eight-Stage Axial Flow Compressor…………..………………… 72
3.9 Schematic of The Compressor…………………………………………… 72
3.10 The Computational Domain ………………………..……………………. 75
3.11 First Rotor Surface Mesh…………………………………………………. 76
3.12 First Rotor Mesh. (Zoomed)………………………………………………. 76
3.13 Grid of The First Three Stages of the Compressor (Repeated)...………… 77
3.14 Pressure Coefficient at Second Stator Mid-Span for Three Mesh
Densities…………………………………………………………………... 78
3.15 Averaged Static Pressure Variation at Domain Mid-Span for Three
Meshes.......................................................................................................... 78
3.16 Convergence History of Area-Weighted Average of Total Temperature at
Domain Exit………………….…………………………………........… 82
3.17 Convergence History of Area-Weighted Average of Total Pressure at
Domain Exit…………………………………….………………………… 82
4.1 Dry Compressor Characteristics at Design Speed (Relative to the dry
Operating Point.)....................................................................................... 84
4.2 Meridional Variation of Static Pressure (PS) and Total Pressure (PO) at
Mid-Span………....…………….................................................................. 87
4.3 Meridional Variation of Static Temperature (Ts) and Total Temperature
(TO) at Mid-Span……………...........................................................……... 87
4.4 Meridional Variation of Absolute Velocity Magnitude at Mid-Span……. 88
4.5 Meridional Variation of Absolute Mach Number at Mid-Span. ………… 88
4.6 Spawise Variation of Total Pressure at Exit of Each Blade Row Referred
to That at the Compressor Inlet………………………….……………….. 89
4.7 Spanwise Variation of Total Temperature at Exit of Each Blade Row
Referred to That at the Compressor Inlet ……………….……………….. 89

xi
4.8 Spanwise Variation of Static Temperature at Exit of Each Blade Row....... 90
4.9 Spanwise Varaiation of Static Pressure at Exit of Each Blade Row…....… 90
4.10 Contours of Static Pressure at the Whole Compressor (3D View)………. 91
4.11 Contours of Static Pressure at a Radial Section (R=6 in) for Three
Passages (Repeated)………………….………….........................……… 91
4.12 Contours of Static Pressure at Different Axial Locations along the
compressor ………………………….....................……….…………….. 92
4.13 Droplet Tracks Through The Domain Colored with Droplet Diameter
(Base Case: 5µm Initial Diameter, 1% Injection Ratio)……..…………..
95
4.14 Mean Droplet Diameter at Exit of Stages (at Sampling Planes)………….. 95
4.15 Droplet Diameter Distribution at Exit of Each Stage ..........……………… 96
4.16 Mean Droplet Temperature at Exit of Each Stage.……….………………. 97
4.17 Meridional Variation of (Evaporated) Mean Methanol Mass Fraction on a
Mid-Span Surface….....………………………………………………… 97
4.18 Spanwise Variation of (Evaporated) Mean Methanol Mass Fraction at
Exit of Each Stage........................................................................................ 98
4.19 Contours of Methanol Mass Fraction at Exit of Each Stage.........………... 98
4.20 Meridional Variation of Mean Static Temperature on a Mid-Span Surface 100
4.21 Spanwise Variation of Mean Static Temperature at Exit of Each Stage..... 100
4.22 Meridional Variation of Mean Static Pressure on a Mid-Span Surface..... 101
4.23 Spanwise Variation of Mean Static Pressure at Exit of Each Stage……… 101
4.24 Meridional Variation of Mean Velocity Magnitude on a Mid-Span
Surface........................................................................................................ 102
4.25 Spanwise Variation of Absolute Velocity Angle at Inlet of Each
Stator….......................................................................................………… 102
4.26 Compressor Operating Point Variation in Wet Compression……………. 104
4.27 Mean Droplet Diameter for Different Injection Ratios…………….……. 106
4.28 Mean Droplet Temperature for Different Injection Ratios……..……….. 106
4.29 Droplet Diameter Distribution at Exit of Each Stage for Different
Injection Ratios …………………………………………………………… 107

xii
4.30 Meridional Variation of (Evaporated) Mean Methanol Mass Fraction on a
Mid-Span Surface for Various Injection Ratios….....…………………….. 108
4.31 Spanwise Variation of (Evaporated) Mean Methanol Mass Fraction at
Exit of Third Stage for Various Injection Ratios………...………………. 108
4.32 Meridional Variation of Mean Static Temperature on a Mid-Span Surface
for Various Injection Ratios……...…….……………………………...... 110
4.33 Spanwise Variation of Mean Static Temperature at Exit of Third Stage
for Various Injection Ratios…………………………………………….. 110
4.34 Meridional Variation of Mean Static Pressure on a Mid-Span Surface for
Various Injection Ratios………………………………………………… 111
4.35 Spanwise Variation of Mean Static Pressure at Exit of Third Stage for
Various Injection Ratios…………………..……………………………… 111
Surface for Various Injection Ratios..…………………………………….. 112
4.37 Spanwise Variation of Velocity Angle at Inlet of Third Stator for Various
Injection Ratios………...…………….............……………………………
112
4.38 Effect of Varying Injection Ratio on Performance of the Compressor…… 114
4.39 Effect of Varying Injection Ratio on the Operating Point............................ 114
4.40 Mean Droplet Diameter Variation for Three Initial Diameters…………… 115
4.41 Mean Droplet Temperature for Different Diameters……………………… 115
4.42 Meridional Variation of Mean Methanol Mass Fraction on a Mid-Span
Surface for Various Diameters…….……………………………………… 116
4.43 Spanwise Variation of Mean Methanol Mass Fraction at Exit of Third
Stage for Various Diameters……………………………………………… 116
for Various Diameters..………………..………………………………….. 118
4.45 Spanwise Variation of Mean Static Temperature at Exit of Third Stage
for Various Diameters…………………………………………………….. 118
4.46 Meridional Variation of Mean Static Pressure on a Mid-Span Surface for
Various Diameters………………………………………………………… 119

xiii
4.47 Spanwise Variation of Mean Static Pressure at Exit of Third Stage for
Surface for Various Diameters..………………………………………….. 120
4.49 Spanwise Variation of Mean Velocity Angle at Inlet of Third Stator for
4.50 Spanwise Variation of Mean Velocity Angle at Inlet of First Stator for
4.51 Effect of Varying Injected Droplet Size on Performance of the
Compressor………………………………………………………………... 122
4.52 Effect of Varying Injected Droplet Size on the Operating Point................. 122
4.53 Droplet Tracks Through the Domain Colored with Droplet Diameter
without Collision (5µm Initial Diameter, 1% Injection Ratio, No
Collision) …………………...…………………………………………….. 124
4.54 Mean Droplet Diameter at Exit of Stages with and without Collision...…. 124
4.55 Droplet Diameter Distribution at Exit of Each Stage with and without
collision in the Base Case (5 µm, 1 %)…...........................….…………… 125
with and without Collision………………………………………………... 126
4.57 Compressor-Discharge Temperature for Different Water and Alcohol
Injection Rates (Baron et al., 1948)........................................................
127
4.58 Compressor-Discharge Radial Temperature Variation for Different Water
injection rates (Baron et al., 1948) ………………………………………..
128

xiv
Nomenclature
Symbol Definition
A Area [m2
].
Cd Aerodynamic drag coefficient.
mC Moment Coefficient
C Vapor concentration [kg/m3
], Specific heat [J/kg.K].
D, d Diameter [m], Mass diffusion coefficient [m2
/s].
E Total energy [J/kg]
e Unit vector.
F Force [N].
h Specific enthalpy [J/kg], Convective heat transfer coefficient [W/m2
.K]
fgh Latent heat [J/kg]
K Thermal conductivity, [W/m.K].
k Turbulence Kinetic Energy [m2
/sec2
].
ck Mass transfer coefficient [m/s].
L Length, [m].
m Mass, [kg].
m Mass flow rate, [kg/sec].
N Number, rotational speed [rpm].
uN Nusselt number
P Pressure, [Pa].
Prt Turbulent Prandtl number.
Re Reynolds number.
R, r Radius, [m].
fS Force source term from the interaction with the dispersed phase, [N/m3
].
hS Energy source term from the dispersed phase, [W/m3
].
jS Source term of the th
J species, [Kg/m3
.s].
mS Mass source term from the dispersed phase, [Kg/m3
.s].

xv
Sh Sherwood number.
Sc Schmidt number.
T Temperature, [K]., Torque [N.m]
t Time [s].
u Velocity parallel to the wall [m/s].
u, v, w Fluid fluctuating Velocities [m/s]

u Dimensionless velocity.
V Velocity, [m/sec].
We Weber number.
y The normal distance to the wall [m], Non-dimensional droplet distortion.

y Dimensionless wall distance.
jY Mass fraction of the th
J species in the mixture.
Z Radial direction.
ε Effectiveness of evaporative cooler, Turbulent dissipation rate [m2
/sec3
]
μ Absolute viscosity, [Pa.s].
ν Kinematic viscosity, [m2
/sec].
ρ Density, [kg/m3
].
τ Shear stress, [N/m2
], Time scale, [s].
 Droplet surface tension, [N/m].
 Droplet impingement angle [deg.].
 Droplet leave angle [deg.].
 Compressor pressure ratio
ω,  Angular velocity of the rotating frame, [rad/sec].
 Random number.
Subscripts:
a Ambient, absolute, Air.
B Buoyancy.
Crit Critical.
D droplet, discharge of compressor
DB Dry bulb
eff Effective.

xvi
I Inlet, term number, tensor index (1, 2, 3).
inlet Inlet of Compressor
j Term number, tensor index (1, 2, 3).
k Tensor index (1, 2, 3).
l Vector tensor.
Max Maximum
o Total conditions, reference, operating point.
P droplet, at constant pressure.
R Radial, relative, rotor, rotation.
Ref Reference.
S Surface.
T Turbulent
w Wall.
WB Wet bulb
x Component in x-direction.
Y Component in y-direction.
Z Component in z-direction.
 carrier phase
Abbreviations:
AMF Air Mass Flow
B.L. Boundary Layer Mesh
DSM Domain Scaling Method
OEM Original Equipment Manufacturer
O.P. Operating Point
S.P. Specific Power

1
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND
A major disadvantage of the gas turbine based power plants is their sensitivity
to the ambient conditions. The ambient pressure can vary significantly with
elevation, but it does not usually exhibits large variation at a certain location.
Regarding humidity, the inlet mass flow rate decreases as the humidity increases.
This is because the density of water vapor is less than that of the air. Consequently,
as humidity increases the gas turbine output power decreases. However the effect
of the variation in ambient humidity is small on the gas turbine performance. Out
of all factors, the ambient temperature is the one that influences the gas turbine
engine performance significantly. Temperature exhibits significant variation over
the year. The increase of the ambient temperature decreases the air density (i.e.
mass flow rate) and consequently increases the compressor specific work. This
leads to a decrease in the engine net output power.
Changes in the ambient conditions influence the compressor operating point.
Referring to Fig. (1.1), when the compressor inlet temperature increases the
compressor operating corrected speed as well as the ratio ( 13 TT ) decreases. This
causes the operating point to move left and down, as shown in the figure, resulting
in a decrease in both pressure ratio and corrected mass flow rate. Also Fig. (1.2)
indicates that, for constant maximum temperature, the turbine exhaust temperature
and consequently the heat rate increases (thermal efficiency decreases) as the
ambient temperature increases. In addition to these, the compressor discharge
temperature increases, and the compressor discharge pressure decreases.
Consequently, the net area representing the net specific work is further decreased.

Chapter (1) Introduction
2
On average, drop by 0.5 to 0.9 % in the output power happens for every 1 Co
increase in the ambient temperature. In heavy duty gas turbines, power output loss
of approximately 20% can be experienced when ambient temperature reaches 35°C
(Bhargava and Meher-Homji, 2002). This is coupled with a heat rate increase of
about 5 %.
The compressor is the most engine component sensitive to the changes in the
ambient temperature. It consumes about 50 % to 60 % of the turbine output power
(Zheng et al., 2002). Therefore, efforts should be directed toward decreasing the
compressor consumed power. This will lead to an increase in the net output power
of gas turbine. Cooling of the inlet air to the gas turbine compressor is one of the
techniques to reduce the compression work and thereby increases the net output
power. The net output power can further increase by letting water droplets to get
into the compressor. Due to the large latent heat of water, when it evaporates
within the blade path, a thermodynamic intercooling effect is achieved. The
resulting adiabatic process causes the air temperature to drop. Since it takes less
energy to compress relatively cooler air, reduction in compressor work will be
S
Constant Firing
Temperature
Lower
Pressure
Hot day
T
Fig. 1.2 T-S Diagram on a hot
day
P2
P1
Fig. (1.2) T-S Diagram on a Hot DayFig. (1.1) Change in Operating Point
at High Ambient Temperature
(Meher-Homji and Mee , 2000)
Increasing
(T3/T1)
T
N
Lines of
(T3/T1)
Running
Line

P
Tm
Normal
Hot

3
Hot
achieved and hence an increase in net output power of the gas turbine will be
accomplished. This process is known as "wet compression".
Several air cooling techniques that are commercially available for gas turbine
power augmentation are illustrated in Table (1.1). These techniques can be divided
into the following four major categories:
• Evaporative Cooling Methods: These include wetted media and fogging
techniques.
• Inlet Air Chilling (Using Chillers): These include the use of either mechanical or
absorption chillers to cool the inlet air. These could be combined with thermal
storage to manage energy consumed by the chillers with the variation in the inlet air
temperature.
• LNG or LPG vapourisation: This technique is based on utilizing the cooling
effect resulting from the vaporization of either LNG (Liquefied Natural Gas) or
LPG (Liquefied Petroleum Gas).
• Hybrid systems: A hybrid system could be a combination of any two of the
aforementioned techniques, with consideration to the limitations of each technique.
Table (1.1) Inlet Air Cooling Techniques
Wetted Media
Fogging
Wet compression/Overspray
SwirlFlash® Technology
Evaporative Methods
Mechanical
Chillers
Absorption
Chillers
Direct Chillers
Thermal Energy Storage
Inlet Air Chilling LNG or LPG Vaporization Hybrid Systems
Inlet Air Cooling Techniques

4
It is important to mention that wet compression can be achieved by using any
of the aforementioned techniques. For example, in case of using evaporative
cooling technique, wet compression can be achieved if there is an overspray beyond
that necessary for inlet air cooling. On the other hand, in case of chiller cooling wet
compression can be achieved if cooling went below the wet bulb temperature of the
incoming air.
1.2 EVAPORATIVE COOLING METHODS
1.2.1 Evaporative Cooling Theory
Evaporative cooling process works on the principle of reducing the
temperature of an air stream through evaporation of injected water spray. The
energy for evaporation is drawn from the air stream. The result is cooler and more
humid air as shown schematically on the Psychrometric chart, Fig. (1.3). The
minimum temperature that can be achieved is limited by the wet-bulb temperature.
Practically, this level of cooling is difficult to achieve. The actual temperature is
usually higher than the wet-bulb temperature depending on both the equipment
design and atmospheric conditions. The equipment performance is expressed in
terms of effectiveness  which is defined as follows:
WBDB
DBDB
TT
TT
21
21


 (1.1)
Where
DBT1 = Entering air dry bulb temperature.
DBT2 = Leaving air dry bulb temperature.
WBT2 = Leaving air wet bulb temperature.
Typical evaporative cooler effectiveness is in the range from 85 % to 90 %
(Jones and Jacobes, 2002) depending on the contact area between the air and water
as well as the water droplet size. The exact increase in power available from a

5
particular gas turbine, as a result of air cooling, depends on the machine
specifications and site altitude, as well as on the ambient temperature and humidity,
as illustrated in Fig. (1.4).
1.2.2 Wetted-Honeycomb Evaporative Cooler
It was the first technique to be used for turbine inlet air cooling. In this
technique, the inlet air is exposed to a film of water in a wetted media. A honey-
comb-like medium is one of the most commonly used, as shown in Fig. (1.5).
Water splashes down on a distribution pad and then it seeps into the media. At the
same time air is passing through the media. The extent of cooling is limited by the
wet bulb temperature and it is therefore dependent on the weather with the greatest
cooling benefit is realized when employed in warm, dry climates. The effectiveness
of a traditional wetted-honeycomb cooler is somewhat low and is typically 85%
(Craig and Daniel, 2003). It is one of the lowest capital and operating cost and
requires low water quality. On the other hand, it causes a high inlet pressure drop
that degrades the engine output and efficiency and consumes large amounts of
water.
Fig. (1.3) Psychrometric Chart Fig. (1.4) Effect of Evaporative Cooler
on Available Output - 85% Effectiveness
(Jones and Jacobes, 2002)

6
1.2.3 Inlet Fogging
Fogging is a method of air cooling where demineralized water is converted
into a fog by means of high-pressure pumps and special atomizing nozzles
operating at )21070(  gbar . This fog then provides cooling when it evaporates in
the air at the inlet duct of the gas turbine. This technique allows 100 %
effectiveness to be obtained at the gas turbine inlet and thereby gives the lowest
possible temperature. Droplet size is a critical factor for the efficiency of the inlet
air fogging process. Smaller droplets, in the range of 5 to 10 microns, have the
advantages of remaining airborne, higher evaporation rate and less likely to cause
erosion. A typical inlet fogging system is shown in Fig. (1.6). It consists of a high-
pressure pump skid, a nozzle array located in the intake duct after the filters, and a
PLC based control system integrated with a weather station. The advantages of the
fogging system include:
 Inlet pressure drop is lower than that of evaporative media.
 Potential for higher effectiveness than evaporative media (~ 95 %).
On the other hand, this technique suffers from shortcomings. These include:
 Requires demineralized water and stainless steels for all wetted parts.
 Higher parasitic load than evaporative media for high-pressure systems
DISTRIBUTION
Fig. (1.5) Traditional Evaporative Cooler Section
(Craig and Daniel, 2003)

7
1.3 INLET AIR CHILLING
The two basic categories of inlet chilling systems are direct chillers and
thermal energy storage. Thermal energy storage systems take the advantage of off-
peak power periods to store thermal energy in the form of ice (or chilled water) to
perform inlet chilling during periods of peak power demand. Direct chilling
systems use mechanical or absorption chilling. In these systems, inlet air is drawn
across cooling coils, in which either chilled water or refrigerant is circulated.
Accordingly, air is cooled to the desired temperature. Mechanical chillers, as
shown in Fig. (1.7), could be driven by either electric motors or steam turbines.
Absorption chiller requires thermal energy (steam or hot water) as a primary source
of energy. On the other hand it requires much less electric energy than the
mechanical chillers.
As with evaporative cooling, the actual temperature reduction from a cooling
coil is a function of equipment design and ambient conditions. Unlike evaporative
coolers cooling coils are able to lower the inlet dry-bulb temperature below the
DEMIN
WATER SUPPLY
Fig. (1.6) Typical Fogging System Diagram
(Craig and Daniel, 2003)
)

8
ambient wet-bulb temperature. The main disadvantage of inlet chilling systems is
that it consumes higher power than that needed in case of evaporative techniques.
1.4 LIQIFIED GAS VAPORIZERS
When liquefied natural gases (LNG) or liquefied petroleum gases (LPG) are
used as fuels, they need to be vaporized before entering to the gas turbine
combustor. Gas turbine inlet air can be used for providing the necessary heat for
vaporization. A reduction of 5.6°C in inlet air temperature is typical for this system
(Jones and Jacobes, 2002). Because the fuel needs to be vaporized anyway, using
this technique is considered as energy recovery into useable power.
1.5 HYBRID SYSTEMS
Hybrid systems incorporate some combination of previous technologies.
The hybrid system is optimized for a specific plant based on the power demand,
electricity prices and availability of thermal energy.
Fig. (1.7) Mechanical Chilling Schematic for Turbine
Inlet Air Cooling (Craig and Daniel, 2003)
)
Centrifugal Chilling Unit

9
1.6 WET COMPRESSION /OVERSPRAY COOLING
Early experiments on the continuous injection for large volumes of water (or
any other coolant) into a compressor inlet, which is now referred to as wet
compression, began in the early 1940's. Wet compression is a process in which
small water droplets are, intentionally, injected into the compressor inlet air in a
proportion higher than that required to fully saturate the air. The large amount of
latent heat of water when it evaporates within the blade path has a thermodynamic
intercooling effect. The resulting adiabatic process causes the air temperature to
drop. Since it takes less energy to compress relatively cooler air, there is savings in
compressor work. As mentioned before, the compressor consumes about ½ to ⅔ of
the turbine power so any saving in the compressor work will be directly reflected on
the total gas turbine output power.
Some notes must be marked when speaking about wet compression
1. Wet compression is not haphazardly spraying water into the compressor
inlet; care must be taken as there is an expensive and high precision turbine
downstream. The system must be properly integrated with the turbine and
turbine controls.
2. The technology of wet compression is often confused with that of fogging;
however in reality they are significantly different. A fogging system inject a
small amount of water to cool the air (just close to saturation), whereas a wet
compression system may inject four times the quantity injected in case of
fogging into the compressor inlet. The “excess” moisture is absorbed by the
air in subsequent compressor stages. This means that wet compression takes
the evaporative cooling effect into the compressor.
3. Wet compression system could be complementary to other turbine inlet air
cooling techniques like evaporative cooling, fogging, or chilling.

11
1.6.1 System Description
The wet compression system, shown in Fig. (1.8), consists of the following
major components:
1. A nozzle rack: a grid of nozzle arrays installed in the air intake and located
relatively close to the compressor inlet (to avoid droplet agglomeration).
2. A pump skid: to deliver the high pressure demineralized water to the nozzles.
3. Stainless steel tubing: to deliver water from the pumps to the nozzle arrays.
4. Local control unit: governs the pump skid and exchanges signals with the
engine core controller.
1.6.2 Advantages of Wet Compression over Other Power Augmentation
Technologies
Power gains from all inlet cooling technologies are limited by ambient
conditions. Evaporative cooling (media-based and fogging) systems must have a
temperature difference between the dry-bulb and wet-bulb temperatures in order for
power gains to be achieved. With Wet Compression, gains are not limited due to
increased ambient conditions. Figure (1.9) shows typical percent power gains for
Fig. (1.8) Wet Compression (High fogging) System Layout
(Cataldi et al., 2005)

11
combustion turbines, with traditional evaporative cooling, and with wet
compression. It can be seen that wet compression gives a constant increase in
power regardless of the ambient conditions. Note that wet compression is typically
not utilized in temperatures below 7 Co
.
1.6.3 Challenges to Wet Compression Technology
Wet compression is a very promising technology for power augmentation but
it has some issues which have to be considered to ensure engine protection, safety
of operation and maximum benefit. These issues of particular importance are
described together with their solutions:
a) Foreign Object Damage [FOD] Considerations
With the presence of a large number of nozzles in the air stream, FOD has
high tendency to occur. The danger comes from loosening of the nozzles or
damage of the grid structure due to flow induced vibration. Regarding the
Fig. (1.9) Ambient Temperature Effect on the power Gains for Combustion
Turbines (Shepherd and Faster, 2003)
Delta T (F) Between Dry-Bulb & Wet-Bulb
PowerGains

12
loosening of the nozzles, lock wiring of the nozzles provides a line of defense.
Flow induced vibrations and poor pressure distribution may cause failure on the
structure but with conservative design, this risk can be eliminated.
b) Ice formation in the first compressor blade row.
Because of the flow acceleration within the inlet guide vanes of the
compressor, water may condense from the air stream and ice can be formed. Air
inlet cooling exacerbates this problem as it reduces the temperature at the
compressor inlet and increases the water content of the flow. Therefore, wet
compression operation is limited to a certain minimum ambient wet-bulb tem-
perature at which the system must be turned-off. Several original equipment
manufacturers (OEMs) publish a combination of relative humidity and temperatures
at which anti-icing measures are turned on. Figure (1.10) shows the corresponding
limiting curve in terms of ambient temperature and relative humidity for the GT24/
GT26 engines.
c) Induced distortion of the temperature profile at the compressor inlet.
Temperature distortion is a phenomenon where the compressor inlet
temperature differs significantly from one side to the other. As a result, the “cold”
section of the compressor runs at high aerodynamic speed and produces a high
pressure ratio as expected for a low inlet temperature. The “warm” section of the
compressor runs at a reduced aerodynamic speed but has to achieve the increased
pressure ratio prescribed by the low temperature section. Thus, the surge margin in
the “warm” section is reduced (Chaker et al., 2002, part A). Accordingly, inlet
temperature distortion ( ITD ) can be caused by the following reasons:
 Malfunctions of inlet cooling systems, such as blocked nozzles.
 Poor aerodynamic design of the fogging system or the air intake.
 Operating wet compression system as a standalone system at low water
mass flow for extended periods of time.
 Velocity profile at inlet section.

13
The following equation provides a criterion for ITD at an aero-derivative
machine. Different machines would have different criteria.
   
03.0
,
60min,60max,max





faceavg
avgavg
avg T
TT
T
T
ITD
oo
(1.2)
where,
Maximum area weighted average total temperature (K) in the
warmest 60o
sector of the annulus.
=max,avgT
Minimum area weighted average total temperature (K) in the coldest
60o
sector of the annulus.
=min,avgT
Average area weighted average total temperature (K) over the full
face of the annulus.
=faceavgT ,
Local temperatures within the sectors must be within 20% of the face average.
Figure (1.10) shows the corresponding limiting curve of the G24/G26 family of
engines. The cooling potential ( tamb −tamb,wetbulb) at each ambient condition is also
represented in the diagram by means of dashed lines.
Fig. (1.10) Limits of Operation with Wet Compression
(Cataldi et al., 2005)

14
d) Axial compressor fouling
When good quality demineralized water is used and inlet ducts and silencers
are clean, no problems of deposits have been noted. In fact, operator experience
indicates that there is a washing effect from the fog itself. It is possible that using
fog on a nearly continuous basis for power augmentation, results in a continuous
washing effect which may result in savings of on-line wash costs.
e) Compressor blade erosion due to impingement of water droplets
Erosion resulting from water droplets impacting compressor blades has been a
concern with any system that introduces water droplets at the inlet to compressor.
One of the major advantages of wet compression systems over inlet fogging
systems is the placement of the nozzles near the compressor inlet. The potential for
droplet agglomeration and coalescence on objects within the duct are minimized.
Since the application of this technology is recent, tremendous progress has been
made in understanding the concerns with this system and steps to be taken to assure
satisfactory system performance. The GT-24 wet compression system (Sanjeev
Jolly, 2003) has been operational for more than one year for about 16 hours a day.
A borescope inspection performed during a recent outage did not show excessive
erosion compared with that normally found during scheduled maintenance.
f) Compressor casing distortion due to non-uniform water distribution
The casing temperature distribution did not appear to be impacted by wet
compression and there is no limiting factor for this. But in some cases, rubbing of
compressor blades occurred with the casing in case of higher coolant mass flow
rates.
g) Electro-static charge build-up on the compressor rotor
A grounding brush is usually installed to eliminate the possibility of electro-
static charge build-up on the rotor. This is a very important procedure if the coolant
used in wet compression is combustible like Methyl Alcohol.

15
1.7 OBJECTIVES AND METHODOLOGY OF THE PRESENT WORK.
The present work aims at numerically investigate the effect of wet
compression on the performance of a multistage axial flow compressor. This work
also explores the advantages of using Methanol as an evaporative media in wet
compression. This is attributed to its advantages as biofuel, non corrosive, volatile
and low density liquid. These characteristics offer the advantages of the dual use of
Methanol as an evaporating media for wet compression and as a primary fuel for the
gas turbine. Methanol which injected for wet compression is very lean to be used
for combustion in the gas turbine. It could be supplemented by any gaseous or
liquid fuel in the combustor of the gas turbine. Considering the advantages of
methanol as bio- and renewable fuel, additional environmental gain will be
achieved when Methanol is used.
Also Methanol is non corrosive compared with the use of water in wet
compression. Furthermore, its density is less than that of water, which ensures less
erosion due to less collision impact when the droplets impinge the compressor
blades. Add to these the high volatility of Methanol offers the chance of using it at
relatively low pressure ratio compressors.
This thesis consists of five chapters including this introductory chapter. The
next chapter presents a survey and analysis for the previous work related to the
subject. A discussion of the previous work at the end of that chapter will route and
clarify the scope of the present work. Chapter (3) presents the different aspects of
the mathematical and numerical model considered. The case studied will be
described at the end of that chapter. The obtained results will be presented and
discussed in Chapter (4). A summary of this work, the main findings, and
suggestions for the future work will be presented in Chapter (5). Necessary details
about modeling turbomachines in FLUENT are included in the appendix.

16
CHAPTER 2
LITERATURE REVIEW
2.1 INTRODUCTION
Water injection into gas turbine compressor inlets has been studied and
applied since the forties. Early studies were done by Wilcox (1950) and Hensley
(1952). Wet compression was described in detail in several text books on gas
turbines written in the 50s. Water injection was used in the older jet engines to
boost take-off thrust when aircraft were operating on hot days or from high altitude
airports. The power gain came mainly from the cooling of the intake air (i.e., lower
inlet temperature) and from the intercooling effect in the compressor. Recently,
with the advancement in high-pressure water fogging technology, wet compression
has gained popularity in the industrial gas turbine and is being applied in the power
and cogeneration industries.
Wet compression is a complex process deals with many phenomena. It
includes gas compression, droplet evaporation and droplet interactions. The
occurrence of these phenomena in a multistage axial compressor increases the
complexity of the problem. In wet compression, interaction between the droplets
and the air flow inside the compressor is taking place. This could lead into changes
in the air flow pattern inside the compressor which in turn will affect the
compressor performance. Not only this, but also droplet-droplet interaction affects
the droplet behavior inside the compressor. This is attributed to either droplet
agglomeration or droplet shuttering due to droplet collision. This will have an
impact on the compressor performance as a result of the change in the droplet
trajectory and evaporation rate. Accordingly, wet compression can be characterized
as a two phase flow problem. In the following sections, a review of the previous

Chapter (2) Literature Review
17
work about wet compression and its related topics as well as the axial compressor
simulation will be presented.
2.2 WET COMPRESSION
Baron et al. (1948), have conducted an experimental investigation of thrust
augmentation of an axial-flow turbojet engine by means of water-alcohol injection
at the compressor inlet at sea-level conditions. The exhaust nozzle was adjusted to
fix the exhaust temperature during the investigation. The engine performance was
determined at constant rotor speed and exhaust-gas temperature for various
mixtures and flow rates. The thrust augmentation by injection of water and alcohol
at the compressor inlet was limited by centrifugal separation of the injected liquid
and air in the compressor. Although the maximum thrust augmentation was
obtained at the highest water flow (6.7 % of air flow), this injection rate was
considered injurious to the engine. It caused localized hot spots in the turbine and
large radial temperature distortion. This causes rubbing of the compressor blades
on the casing. An injected water flow of 5.4 % leads to thrust augmentation of 4.15
% at a rotor speed of 7635 rpm, an exhaust gas temperature of 925 K , and an inlet
air temperature of 304 K . The injection of alcohol, at constant water injection rate,
resulted in a marked decrease in fuel flow, in addition to thrust augmentation.
Large decrease in compressor discharge temperature was observed for all water and
alcohol flows. The air mass flow and the compressor discharge pressure increased
slightly. Based on these results, they concluded that water-alcohol injection at the
compressor inlet can be used to the best advantage only when the engine inlet air
temperature is high enough and the initial relative humidity is low enough to
provide considerable evaporation of the injected liquid before compression.
Wilcox and Trout (1950) conducted a thermodynamic model to calculate the
thrust augmentation of a turbojet engine resulting from the injection of water at the
compressor inlet. This model was carried out for various amounts of water injected.
The effects of variation of flight Mach number, altitude, ambient-air temperature,

18
ambient relative humidity, compressor pressure ratio, and inlet-diffuser efficiency
are taken into account. For a typical turbojet engine, the maximum theoretical ratio
of augmented to normal thrust was 1.29. The ratio of augmented liquid
consumption to normal fuel flow for these conditions, assuming complete
evaporation, was 5.01. Both the augmented thrust ratio and the augmented liquid
ratio increased rapidly as the flight Mach number was increased and decreased as
the altitude was increased. Although the thrust augmentation possible from
saturating the compressor-inlet air is very low at flight speeds, appreciable gains in
thrust are possible at high flight Mach number. At standard sea-level atmospheric
temperature, the relative humidity of the atmosphere had a small effect on the
augmented thrust ratio for all flight speeds investigated. At sea-level and zero flight
Mach number conditions, the augmented thrust ratio increased as the atmospheric
temperature increased. Water injection therefore tends to overcome the loss in take-
off thrust normally occurring at high ambient temperatures. For very high
atmospheric relative humidities, the ambient temperature had only a small effect on
the augmented thrust ratio.
Hensley (1952) has evaluated the theoretical performance of a gas turbine with
inlet water injection of an axial-flow compressor operating at compressor pressure
ratios of 4, 8, and 16. He assumed continuous saturation throughout the
compression process. The assumption of choked turbine nozzles and a compression
efficiency at any point in the compressor depend on the evaporative cooling prior to
that point were used. Based on these assumptions, the changes in mass flow,
compressor pressure ratio, compressor work, and overall compressor efficiency
with water injection were determined. The analysis indicates that the compressor
work per unit mass of turbine gas flow is lower with inlet water injection than
without. This is valid even at low altitudes, high Mach numbers as well as high
compressor pressure ratios. Accordingly, engine output per unit mass of turbine gas
flow is greater with injection than without. Hensley’s calculations show that the
inlet temperature for some of flight conditions considered is below the freezing
point, which necessitates the addition of a nonfreezing liquid to the injected water.

19
Hill (1963) presented an analysis of the thermodynamic effects of inlet coolant
injection on axial compressor performance, in comparison with tests on turboshaft
engines. His results showed that the evaporation of the coolant inside the
compressor implies a continuous cooling of the air. This leads to a reduction in the
compression work for a given pressure ratio, and a change in the stage work
distribution. These effects lead to large augmentation of the shaft power of the
turbine engine, especially when the compressor inlet temperature is high. He also
reported an increase in compressor airflow at a given speed and pressure ratio. This
is coupled with unload of the first few stages and load the last stages more heavily.
The maximum desirable ratio of coolant to air flow may be limited by combustion
efficiency, stall, or blade rub. The results showed good agreement with
experimental results.
Ludorf et al. (1995) has extended an existing one dimensional stagewise
compressor stability analysis program to incorporate a model of humidity and
droplet evaporation. The modified program shows the extent of stage re-matching
when ingesting modest amounts of water. The water distribution through the flow
is assumed to be homogenous. The stage interactions of an aircraft engine
compressor are investigated for different environmental operating conditions. The
effects of humidity on stage loading are small while the evaporation of water causes
significant shift of the operating point. No experimental validation was performed
in this work.
Utamura et al. (1998) proposed and examined the possibilities of a new
technology, Moisture Air Turbine (MAT) cycle, of increasing the output of a gas
turbine by introducing a fine water spray into the incoming air to the compressor.
They considered the isentropic work for moist air with phase change. The
theoretical work decline was 6.8% with regard to 1% water spray by mass. They
also verified their results with an experiment using 15 MW axial flow compressor.
According to their measurement, 4% reduction in compressor work is achieved at 1
% water injection by mass. Following this, Utamura et al. (1999) had developed a

21
special spray nozzle to generate water droplets with a sauter mean diameter of 10
μm. Their calculation showed that droplets with that diameter is not seen to collide
with rotor blades and provides maximum evaporation efficiency. Experiments, on a
115 MW simple cycle commercial gas turbine, showed that injection of spray water
of 1 % to air mass flow rate would increase output power by about 10 % and
thermal efficiency by 3 % compared with that in hot summer days. The magnitude
of power increase becomes higher as ambient temperature is higher and humidity is
lower. Given the temperature profile through the compressor stages, they performed
quasi-steady heat and mass transfer calculations in terms of single water droplet.
The life time of the droplet was found to increase as the diameter increases.
The most complicated model was developed by Loebig et al. (1998). They
constructed a three dimensional aero thermal analysis model to aid in the design of
optimum water/methanol injection system, for maximum evaporation of the
multicomponet-droplets, with minimal impingement on the casing. Their model
was built on the basis of the stream line curvature method to study the 3D
compressor flow field. The model also includes computations for 3D droplet
trajectories, evaporation characteristics, and droplet impingement locations on both
the hub and casing surfaces of the compressor. The motion of the droplet is
described by the 3D Lagrangian equations. The model does not take into account
the droplet interaction with the blade. They found that the three-dimensional flow
field strongly influences droplets evaporation characteristics. The evaporation of
the droplet is mainly due to convection and it is a strong function of the droplet
Reynolds number. Computations showed that droplets with initial diameters greater
than 50 microns will impinge on the casing. Maximum air temperature reduction
and complete evaporation will be achieved for small droplets (less than 20
microns). These small size droplets are also found to well track the flow and don’t
impinge on the casing.
Horlock (2001) developed a one-dimensional model to illustrate the effect of
water injection on compressor off-design performance. His model was based on the

21
assumption of known amount of evaporation within the compressor. He used the
perturbation method, assuming small perturbations of design performance. His
analysis showed that, wet compression pushes the operating points of the
evaporating stages away from design and up their temperature rise characteristics.
Wet compression also leads the later evaporating stages in the compressor to
approach their stalling points.
Chaker et. al. (2002-a, b, c) presented the results of extensive experimental
and theoretical studies of nearly 500 inlet fogging systems on gas turbines. Their
studies covered the underlying theory of droplet thermodynamics and heat transfer
and provided practical points relating to the implementation of inlet fogging to gas
turbine engines. They provided experimental data on different nozzles and
recommended a standardized nozzle testing method for gas turbine inlet air fogging.
Bhargava and Meher-Homji (2002) presented a comprehensive parametric
study on the effect of the inlet fogging (both evaporative and overspray) on various
gas turbines. A commercial program was used to evaluate the thermodynamic
performance at different operating conditions (such as changes in ambient
temperature, ambient relative humidity, as well as inlet evaporative and overspray
fogging). The results showed that the aero derivative gas turbines, in comparison to
the heavy-duty industrial machines, have higher performance improvement due to
inlet fogging effects. More recently, Bhargava et al. (2006) expanded their analysis
to combined cycle power plants (CCPs). Their results showed that high pressure
fogging is effective also in case of CCPs.
White and Meacock (2004) examined the impact of evaporative process on
compressor operation, focusing on cases with substantial overspray. They used a
simple numerical method for the computation of wet compression processes, based
on a combination of droplet evaporation and mean-line calculations. They applied
the method to“generic” compressor geometry in order to investigate the behavior
that results from evaporative cooling. Their work was restricted to small droplets of

22
5µm diameters, which follow the gas-phase velocity with negligible slip. For this
condition, higher evaporation rate with minimum erosion probability was achieved.
This was for water injection rate varies from 1 to 10 % of the air mass flow. Mean-
line compressor calculations showed that water injection shifts the characteristics to
higher mass flow and pressure ratio. Individual compressor stages will operate off-
design, with front stages moving toward choke and rear stages toward stall. This
has the effect of lowering the aerodynamic efficiency and narrowing the efficiency
peak. Based on these results, they suggested that some redesign of the compressor
would be necessary to achieve the full benefits that are possible with water-
injection cycles.
More recently, Meacock and White (2006) have developed their computer
program and extended their mean-line calculations to study the effects of water
injection in two shafts industrial gas turbines. Preliminary results showed similar
trends to that predicted for single-shaft machines. The LP compressor in particular
operates at severely off-design conditions. The predicted overall performance of a
three-shafts machine shows a substantial power boost and a marginal increase in
thermal efficiency.
Kang et al. (2005) has provided thermodynamic and aerodynamic analysis on
wet compression in a centrifugal compressor of a micro turbine. They coupled the
meanline performance analysis of the centrifugal compressor with the
thermodynamic equation of wet compression to get the meanline performance of
wet compression. They aimed at investigating the impeller exit flow angle
deviation due to wet compression and its effect on the matching of impeller and
vaned diffuser. The most influencing parameter in his study was the evaporation
rate of water droplets. They found that, the exit flow angle decreases as evaporation
rate increases. They also related the change in exit flow angle 2 to water/air mass
flow rate, X, through the following correlation:
4
2 43473000 (2.1)

23
El-Salmawy and Gobran (2005) developed a detailed model to study the
impact of controlling inlet conditions on gas turbines performance. The inlet
conditions are controlled either by evaporative cooling, as well as mechanical or
absorption chillers. The effect of wet compression has been modeled in addition to
the variation of the specific heat and gas composition over the cycle. A simplified
two zones combustor model has been considered too. Making benefit of the
developed model, they conducted a case study to evaluate the impact of controlling
inlet conditions to "Cairo South II" combined cycle power plant. Their results
showed that the improvement in the output power and heat rate are primarily
attributed to wet compression, pressure ratio recovery and increase in air mass flow.
The case study of Cairo South II plant showed that substantial energy, economical
and environmental advantages can be achieved when inlet conditions to the plant
are controlled. Also evaporative cooling is more attractive than chiller cooling.
Roumeliotis and Mathioudakis (2006) examined the effect of water injection at
the compressor inlet or between stages, on its operation. They used wet
compression model together with an engine performance model. It consists of a
one-dimensional stage stacking model, coupled with a droplet evaporation model.
The effect of water injection on overall performance and individual stage operation
was examined. The possibility to evaluate the effect on various parameters such as
power, thermal efficiency, surge margin, as well as the progression of droplets
through the stages was demonstrated. The results showed that, the surge margin
reduces even with low injection quantities. Water injection causes significant stage
rematching, leading the compressor toward stall. Also performance enhancement is
greater as the injection point moves towards the compressor inlet.
Bhargava et al. (2007-І, ІІ, and ІІІ ) presented a comprehensive review on the
current understanding of the analytical and experimental aspects of inlet and
overspray fogging (wet compression) technology as applied to gas turbines.
Practical aspects including climatic and psychrometric aspects of high-pressure inlet
evaporative fogging is also provided. Discussion of analytical and experimental

24
results relating to droplet dynamics, factors affecting droplet size, characteristics of
commonly used fogging nozzle, and experimental findings are presented. They
reported that most machines operate with an overspray level not exceeding 2 % of
the air mass flow, where the limiting amount of injected water is machine specific.
2.3 DROPLET EVAPORATION
Droplet evaporation (Aweny, 2003) involves simultaneous heat and mass
transfer processes. The heat required for evaporation is transferred to the droplet
surface by conduction and convection from the surrounding gas. The vapor is
transferred by convection and diffusion into the gas stream. The overall rate of
evaporation depends on the pressure, temperature, transport properties of the gas,
the velocity of the droplets relative to that of the surrounding gas, and the loading
ratio. For single droplet, evaporation can be theoretically illustrated by considering
the case of a droplet that is suddenly immersed in a gas at higher temperature.
Initially, almost all of the heat supplied to the droplet serves to raise its temperature.
This period is known as the heat up period. Eventually, this stage ends when the
droplet stabilizes at its wet bulb temperature.
Based on experimental measurements, after an initial transition period (heat up
period), steady state evaporation is soon established. All the heat transferred to the
droplet is used to provide the latent heat of vaporization of the droplet. The droplet
diameter, during the steady-state period, decreases with time according to the
following relationship:
tDDo  22
(2.2)
This is called the " 2
D law" of droplet evaporation. The term  is known as
the evaporation constant. From the " 2
D law ", it is clear that the initial droplet size
has a major effect on the rate of droplet volume diminish.

25
Regarding the evaporation of a droplet in a cloud of droplets, Milburn (1957)
had studied the mass and heat transfer process within finite clouds of water droplets.
He developed a simple nonlinear differential equation to govern the propagation of
vapor concentration, temperature, and droplet size in space and time. He applied a
linearized form of this equation to spherical clouds in order to describe the initial
stages of cloud evaporation.
Kouska et al. (1978) solved the modified Maxwell equation for droplet clouds
to evaluate the evaporation rate of mono disperse water droplets. They also
considered the change in the surrounding air conditions caused by droplet
evaporation. When the number concentrations of droplet clouds are sufficiently
low, the results of the numerical calculation for droplet clouds agree well with those
of a single water droplet. When the number concentration of droplets is high, the
droplet clouds become stable. The equilibrated system, where a water droplet cloud
is steadily mixed with unsaturated air, was also analyzed.
Smolik and Vitovec (1984) analyzed the quasistationary evaporation of a
water droplet into a multicomponent gaseous mixture containing a heavier
component besides air. They solved the generalized Maxwell-Stefan equations
numerically. Numerical examples demonstrated the possibility of condensation of
the heavier component on the surface of evaporating droplet as a result of
supersaturation. Their model takes into account the coupling effects of heat and
mass transfer.
Ferron and Soderholm (1987) estimated numerically the evaporation time of a
pure water droplet in air with a well defined temperature and relative humidity. The
mass transfer at the droplet surface was described by diffusional equations for the
mass and heat transfer. For air at 20 o
C, they calculated the life time from the
following equation:
RH
d
t ae


1
2300 41.1
(2.3)

26
Where t is the life time of the droplet in seconds, aed is the aerodynamic
diameter of the initial droplet in centimeters, and RH is the air relative humidity.
Miller et al. (1998) evaluated a variety of liquid droplet evaporation models.
They considered both classical equilibrium and non-equilibrium formulations. All
the models perform nearly identically for low evaporation rates at gas temperatures
significantly lower than the boiling temperature. For gas temperatures at and above
the boiling point, large deviations were found between the various models. The
simulated results also revealed that non-equilibrium effects become significant
when the initial droplet diameter is lower than 50 µm.
2.4 DROPLET INTERACTION
It includes droplet-wall interaction. The outcome of droplet interactions plays
an important role in droplet dynamics. The major dimensionless groups governing
droplet impact include (Mundo et al., 1995):
Reynolds number

 oovd
Re (2.4)
Ohnesorge number
od
Oh


 (2.5)
Weber number

 oovd
OhWe  2
Re).( (2.6)
and Surface roughness
o
t
t
d
R
S  (2.7)
Where  ,  and  are liquid density, viscosity, and surface tension for the fluid-air
interface, respectively. Also, od is the initial droplet diameter and tR is the mean
roughness height of the wall surface. Droplet initial velocity normal to the surface
is represented by ov .

27
Mundo et al. (1995) have performed experimental studies of liquid spray
droplets impinging on a flat surface. They aimed to formulate an empirical model
describing the deposition and the splashing processes. Monodisperse droplets,
produced by a vibrating orifice generator were directed towards a rotating disk and
the impingement was visualized using an illumination synchronized with the droplet
frequency. A rubber lib was used on the rotating disk to remove any film from
previous depositions. The test matrix involved different initial droplet diameters,
velocities, impingement angles, viscosities, and surface tensions. The liquids used
to establish the different viscosities and surface tensions were ethanol, water and a
mixture of water-sucrose-ethanol. One major result from the visualization is a
correlation of the deposition-splashing boundary, in terms of Reynolds number (Re)
and Ohnesorge number (Oh), in the form
25.1
Re.Oh . A value of K exceeding
57.7 leads to incipient splashing. Whereas K less than 57.7 leads to complete
deposition of the liquid, as illustrated in Fig. (2.1).
Splashing region
K increase
Fig. (2.1) Limits for Splashing and Deposition
of Primary Droplets ( Mundo et al., 1995)

28
Stanton and Rutland (1998) have developed and validated a multi-
dimensional, fuel film model to help account for the fuel distribution during
combustion in internal combustion engines. Spray-wall interaction and spray-film
interaction are also incorporated into the model. The fuel film model simulates thin
fuel film flow on solid surfaces. This is achieved by solving the continuity,
momentum, and energy equations for the two-dimensional film that flows over a
three-dimensional surface. The major physical processes considered in the model
are shown in Fig (2.2, a). In order to adequately represent the drop interaction
process, impingement regimes and post impingement behavior have been modeled.
The regimes modeled for spray-film interaction are; stick, rebound, spread, and
splash as shown in Fig.(2.2, b). The fuel film model is validated through
comparison with experimental data. The model provided a predictive means of
determining spray-wall interactions with the eventual formation of liquid films that
can be used for multi-dimensional simulations.
Weiss (2005) studied the impingement of coarse sprays on vertical walls with
and without an additionally supplied wall film. The main outcome of wall
interaction for the coarse spray is splashing. It is found to be suppressed with
increasing the wall film thickness. The splashed droplets form a secondary spray
Fig. (2.2) Schematics of : (a) The Major Physical Phenomena Governing Film
Flow (b) The Various Impingement Regimes Identified in the Spray-Film
Interaction Model. (Stanton and Rutland, 1998)
(a) (b)

29
hit the primary spray in a cross stream configuration after ejection from the wall.
This inter-droplet collision plays an important role in the impingement dynamics
and on the quantity of liquid deposited on the wall. The collision outcome was
simulated tacking into account droplet coalescence and secondary breakup due to
stretching separation.
2.5 EROSION
Erosion of compressor blades due to liquid droplets impingement is the main
problem of wet compression technique. Erosion probability increases from large
droplets which possess higher momentum and separate from air stream to impinge
blades. Accordingly, droplet size is the main factor affecting the droplet path and
hence erosion. Another factor affecting the droplet path within the compressor is
the injected liquid density. Dense liquid droplets have higher momentum and tend
to separate and impinge on blades causing erosion.
Many preliminary studies about erosion have been conducted. Performance
monitoring of wet compression systems for long term operation has also been
investigated. All assured that wet compression is a safe technique in view of blade
erosion provided using small droplet diameters and relatively low density liquids.
Utamura et al. (1999) conducted a numerical analysis to determine the
condition at which the water droplet avoid collision with rotor blades in view of
blade erosion. Two dimensional potential flow field along gas path was solved
using computational fluid dynamics (CFD) model. Given the velocity of water
droplet at the exit of inlet guide vane, the locus of the water droplet in the flow field
and the velocity vector at each point on the locus were calculated. Calculations are
performed by solving Newton's equation of motion for a representative water
droplet of a given diameter. Figure (2.3) shows the calculation results. Due to the
dominancy of inertia effect, the droplet of the diameter 100 µm has the velocity
vector not much away from its initial velocity vector. On the contrary, the velocity
vector of the droplet with the diameter of 20 µm or below almost coincides with

31
that of air. The lower graph displays the locus of the water droplet within the flow
path. It is apparent that 10 µm water droplet is not seen to collide against rotor
blade.
Fig. (2.3) Velocity Vector and Locus of Water Droplet Inside
the Compressor (Utamura et al., 1999)
Sanjeev Jolly (2003) presented the performance effects of applying wet
compression to an advanced frame combustion turbine, the Alstom GT-24, for
many years. His work also addresses the relative changes in compressor and
turbine operating conditions and how these affect component life. The GT-24 wet
compression system has been operational for more than one year for about 16 hours
a day. A borescope inspection performed during a recent outage did not show
erosion to be manageable within normally scheduled maintenance.
Bhargava et al. (2007-Part ІІІ) focused their study on operational experience
and reviewed the work pursued by gas turbine OEMs in the field of wet
compression. They reported that previous CFD studies showed that relatively small
water droplets (less than 15-20 microns) will tend to follow the air stream and hence
cause no erosion. They also reported that the operational experience showed that
wet compression systems have not resulted in excessive erosion problems.

31
2.6 TWO PHASE PREDICTION APPROACHES
There are two main approaches (Crowe et al., 1998) used to predict the two-
phase flow, namely the Lagrangian and the Eulerian approaches.
2.6.1 Lagrangian Approach
The Lagrangian approach can deal with the dilute and dense two- phase flow.
The dilute flow is the case when the droplets motion is controlled by the droplet
fluid interaction, body forces, and particle-wall collision. The dense flow is the
case when the droplet-droplet interaction controls the dynamics of the droplets but it
is also influenced by the hydrodynamic and body forces as well as droplet-wall
interaction. There are two main methods to implement the Lagrangian approach;
the trajectory method, and the discrete element method. In the trajectory
method, the carrier phase is almost steady. The flow field is subdivided into a set of
computational cells as shown in Fig. (2.4). The inlet stream of the dispersed phase
is discretized into a series of representing starting trajectories.
More details can be known by descretizing the starting conditions according to
a size distribution as well. But more detail requires more trajectories and this will
increase the needed computational time. After the termination of all trajectories
calculations, the properties of the dispersed phase in each computational cell can be
determined. Each property can be determined by carrying out a summation over all
the trajectories, which traverse the computational cell.
Fig. (2.4) Droplet Trajectories in a Spray (Crowe et al., 1998)

32
Fig. (2.5) Distribution of Droplet Parcels in a Spray Field
(Crowe et. al, 1998)
Regarding the discrete element method, it is recommended when the flow is
unsteady and/or dense (droplet-droplet collision is important). In this method
calculation for each individual droplet is performed. Accordingly, the properties
such as motion, position, and temperature of individual droplets or representative
droplets are tracked with time. The tracking of all droplets, which can be presented
in the domain, may not be computationally feasible. Therefore a smaller number of
computational droplets are chosen to represent the actual droplets, where each of
them represents a number of physical droplets. It has been found that the required
number of representative droplets to accurately simulate the dispersed phase is not
excessive. The computational droplet is regarded as a parcel of physical droplets,
which have the same properties as the represented computational droplet, as shown
in Fig. (2.5). The equation of droplet motion takes into account the droplet-droplet
interaction. The droplet displacement can be calculated by integrating the equation
of motion with respect to time. In the same time the droplet temperature, diameter
and other properties can be calculated. During each time step, there may be droplet-
droplet collisions that alter the trajectories and change the distribution of the parcels
in each computational cell. This is treated using a suitable collision model.
2.6.2 Eulerian Approach.
The Eulerian approach (Lee et al., 2002) considers the dispersed phase to be a
continuous fluid interpenetrating and interacting with the fluid phase. This
approach is commonly used for dense particulate flows since it is convenient to
model the inter-particle stresses using spatial gradients of the volume fraction. This

33
requires solving extra continuity and momentum equations for the dispersed phase
with separate boundary conditions. The resulting governing equations of the
dispersed phase are quite similar to Navier-Stokes equations for the carrier phase.
The interaction between the two phases takes place through mass, momentum, and
heat exchange mechanisms.
2.7 NUMERICAL SIMULATION OF AXIAL COMPRESSORS
There have been many approaches to predict the overall performance
multistage axial flow compressors with a good degree of confidence. All of which
can be categorized into the following three approaches: one-dimensional mean-line
models, two-dimensional through flow models and three-dimensional
computational fluid dynamics (CFD) models, as shown in Table (2.1). It is possible
to mix some elements of the above models, creating quasi-one-dimensional, two-
dimensional and three-dimensional models. The term ‘quasi’ is used to indicate
that some three-dimensional effects are included within the correlation set utilized.
Perhaps, the simplest model of compressor simulation is the zero-dimensional
model or simply the thermodynamic model. This model is not included in the
above classification because it is important only from the thermodynamic point of
view and don’t produce any aerodynamic information about the compressor. In this
model, the compressor is simulated as a closed box where its performance is
governed by isentropic relations. In the following, a brief review is presented for
the most common models used to simulate compressors.
Table (2.1) Axial Compressor Simulation Models.
Numerical Simulation
of Axial Compressors
One-dimensional
Mean line))
Models
Two-dimensional
(Through flow)
Models
Three-dimensional
CFD
Models

34
2.7.1 Quasi-One-Dimensional Models
It is often termed mean-line methods, where a radial mean height is usually
selected for the position of the single calculation streamline. There are different
methods to quantify the aerodynamic conditions across a blade row. In order to
account for the three-dimensional flow effects within each stage, a highly empirical
approach is necessary. For this reason, the success of the prediction is heavily
dependent upon the quality of the correlations used within the model. Although this
type of flow analysis represents a gross simplification of a complex three-
dimensional system, which can now be modeled more accurately by many of
today’s computational fluid dynamics (CFD) packages, it does offer the advantages
of simple input requirements and fast convergence times.
Expansion of the model to simulate multistage machines is possible. This can
be done by stacking the pressure and temperature ratios of each blade row to give
an overall performance prediction. This stage-stacking procedure starts at the inlet
and works through each blade row, using the exit conditions from the previous row
as inlet conditions for the next row.
Considering this model Horlock (2001) and White and Meacock (2004) have
used a droplet evaporation model to illustrate the effect of water injection on
compressor off-design performance. White et al. (2002), have also used this
prediction model and employed it within an optimization program. The developed
program was used in restagering the variable stator vanes in a multistage
compressor to obtain the optimum compressor performance during off-design
operation. Its good results, encourages the use of such model as a cost effective
tool for quick and reasonably accurate solutions.
Other one-dimensional models (Lindau and O’Brien, 1993; Adam and
Leonard, 2005) used different methods to quantify the aerodynamic conditions
across a blade row. The model is based on mass, momentum, and energy balances
applied to a one-dimensional discretization of the compressor. The computational

35
domain is the compressor flow path, using a row-by-row, quasi-one-dimensional
representation of the machine at mid-span. The basic Euler equations have been
extended by including source terms expressing the blade-flow interactions. The
source terms are determined using the velocity triangles for each blade row, at mid-
span. The losses and deviations undergone by the fluid in each blade row are
supplied by correlations. Due to generality of source terms approach, this model
could be extended to combustion chambers and turbines, to simulate the operation
of a whole gas turbine engine. Water ingestion, blade fouling or cooling devices
may also be introduced.
2.7. 2 Two-Dimensional Models
The two-dimensional models are usually termed as the through flow or
streamline curvature models. In these models, the flow is considered in the
meridional plane, assuming the flow in the circumferential direction is steady. This
type of model is most often used to design the blade geometry given the desired
pressure and temperature rise. A secondary role is for performance prediction when
the blade geometry and some information about the blade performance are given. A
number of radial stations from hub to tip are selected for analysis at each blade row
through the compressor.
Loebig et al. (1998) constructed a three dimensional aero thermal analysis
code to aid in the design of optimum water/methanol injection system. Their code
was built on the basis of the stream line curvature method. It was aimed to study
the 3D compressor flow field and combines it with the computations of 3D droplet
trajectories, evaporation characteristics, and droplet impingement locations on both
the hub and casing.
Petrovic et al. (2000) have performed flow calculation and performance
prediction of a multistage axial flow turbine. They considered compressible steady
state inviscid through-flow code. The aim was to optimize the hub and casing
geometry and inlet and exit flow parameters for each blade row.

36
2.7.3 Three-Dimensional Models
Solution of the compressible Navier–Stokes equations in Reynolds averaged
form, is the most rigorous method used to predict the three-dimensional flow field
within a compressor. Obviously, this type of modeling is the best approach to
predict all aspects of the flow. Yet it does come with the penalty of very high
computational requirements. For this reason, a full three-dimensional analysis is
usually applied only in the final stages of the design process. Therefore, the quasi-
one-dimensional and two-dimensional methods remain important tools. Where they
can supply the more rigorous three-dimensional model with early estimates for the
flow parameters and suitable boundary conditions.
With the great advance in the modern computer capabilities and numerical
schemes for computational fluid dynamics (CFD), 3-D models became an
achievable task. Many researchers used 3-D models in their analysis to obtain
detailed solutions for all flow aspects as will be discussed in the next section. The
present study will rely on this model.
2.8 BLADE ROW INTERACTION
Most turbomachines include many stages to do more work than could be
accomplished with a single blade row. Moreover, the flow is often characterized by
unsteady, viscous and may be transonic. Unsteady interaction effects play a
significant rule in the performance of such multistage turbomachines, especially
when the adjacent blade rows are placed closely for compact design.
Experimental data from jet-engine tests have indicated that unsteady blade row
interaction effects can have a significant impact on the performance of compressors.
Modern compressors can experience three types of unsteady flow mechanism
associated with the interaction between adjacent blade rows, as shown
schematically for a turbine cascade in Fig. (2.6). The first interaction mechanism is
referred to as potential-flow interaction. It results from the variations in the

37
velocity potential or pressure fields (or propagating pressure waves) associated with
the blades in adjacent rows. This type of interaction is of important concern when
the axial spacing between adjacent blade rows is small or the flow Mach number is
high. The second interaction mechanism is wake interaction. It is the effect on the
downstream blade row due to the vortical waves shed by one or more upstream
rows. The third interaction mechanism is called shock wave interaction. It is
caused by the shock system in a given blade row extending into the passage of an
adjacent blade row.
Fig. (2.6) Unsteady Blade Row Interaction Mechanisms
(Turbine Cascade)
The different blade row interaction mechanisms require different levels of
viscous flow modeling complexity to capture the physics associated with a given
flow field. There are several methods (Dorney, 1997; Chima, 1998) for predicting
the flow field, losses, and performance quantities associated with axial compressor
stages. These methods include: (1) the steady single blade row (SSBR) method, (2)
the steady coupled blade row (SCBR) method, (3) the loosely coupled blade row
(LCBR) method, and (4) the fully coupled blade row (FCBR) method. These
methods are ordered in the direction of increasing modeling complexity and are
shown in Table (2.2). These methods are discussed in the following sections.

38
Table (2.2) Levels of Blade Row Interaction Modeling Complexity
2.8.1 Steady Single Blade Row (SSBR) Method
It is the least sophisticated modeling method for multiple blade row
geometries. In SSBR simulations, each blade row is solved in isolation, i.e. in
absence of any interaction effects. Successive blade rows are analyzed from inlet to
exit, using average flow properties from the exit of one blade row as inlet boundary
condition for the next. This method is simple and has been used by many
researchers to model multistage turbomachines (Chima, 1987; Davis et al., 1988).
Yet it introduces many modeling challenges. First, since blade rows are often
closely spaced, it is unclear how far to extend the computational grid for each blade
row, and whether it is reasonable to overlap grids. Second, many numerical
boundary conditions are not well-behaved when applied too close to a blade. Third,
average flow properties are not well-defined. Since flow properties are related
nonlinearly, it is impossible to define an average state that maintains all the original
properties of the three-dimensional flow. Fourth, for subsonic flow, the inlet
velocity profile and mass flow develop as part of the solution. Although it may be
possible to match the overall mass flow by iterating on the imposed back pressure,
it is generally not possible to match the spanwise distributions of properties between
the blade rows. Finally, the method ignores physical processes such as wake
mixing, acoustic interaction, and other unsteady effects that may be important in
real turbomachinery.
Interaction
Modeling
Level
Steady Single
Blade Row
(SSBR)
Steady Coupled
Blade Row
(SCBR)
Loosely Coupled
Blade Row
(LCBR)
Fully Coupled
Blade Row
(FCBR)

39
2.8.2 Steady Coupled Blade Row (SCBR) Method
SCBR method is the second level in modeling complexity of the blade row
interaction. In SCBR simulations, all blade rows are solved simultaneously. They
are exchanging spanwise distributions of averaged flow quantities at a common grid
interface plane between the blade rows. So that the name “Averaging-Plane” is
generally used to express this method, referring to the averaging process occurs at
the interface plane. There are many methods for obtaining average flow variables at
the averaging-plane. The most famous method is known as “mixed-out” averages
from which the name “mixing-plane” model is derived. Averaging-Plane methods
(SCBR) have been used by many researchers (e.g. Chima, 1998; Prasad, 2005). In
spite of the possibility of some missing physics in this analysis, the output of this
method has shown excellent agreement with experiments.
Chima (1998) has used a modified averaging-plane approach to analyze the
flow in a two-stage turbine. He used the characteristic boundary conditions to
exchange information between the blade rows. Comparison with experiments
showed that the use of characteristic boundary conditions ensures that information
propagates correctly between the blade rows. It also allows close spacing between
the blade rows without forcing the flow to be axisymmetric, as in conventional
numerical boundary conditions. This property overcomes a main limitation of the
averaging-plane codes.
2.8.3 Unsteady Loosely Coupled Blade Row (LCBR) Method
It is also known as “Average-Passage” method. It is a rigorous means of
modeling unsteady blade row interaction using a steady analysis. In this method,
unsteady boundary conditions are specified at the inlet and exit of each blade row to
account for the interaction mechanisms. The inter-blade-row boundary conditions
are periodically updated to couple the unsteady flow effects from the upstream and
downstream blade rows. The LCBR method has been shown to be computationally

41
efficient (Dorney et at., 1995), while retaining a significant amount of the unsteady
flow physics. Because of its complexity it has not been widely used.
2.8.4 Unsteady Fully Coupled Blade Row (FCBR) Method
In the unsteady fully coupled blade row (FCBR) technique the flow fields of
multiple blade rows are solved simultaneously. The relative position of one or
more of the of the blade rows is varied to simulate the blade motion. FCBR
solution techniques presumably avoid all modeling issues and can accurately predict
the unsteady flow phenomena in compressor stages (within the limits of turbulence
and transition modeling). FCBR solution is usually used to validate other steady
solutions. But this method is very expensive computationally, and finally still
requires averaging at the end to produce useful results.
To consider fully unsteady rotor/stator interactions with reduced costs, the
computational domain can be limited to a minimum number of blade passages per
row. For unequal pitch configurations, where the number of blades in one row is
not a multiple of the other, small numbers of blade passage cannot generally be
selected. In this case, different methods can be used to retrieve the space and time
flow periodicity on a minimum number of blade passages. They are gathered into
three categories: (1) methods that use relations to derive time-lagged boundary
conditions in the gap region (Hah, 1997), (2) methods that account for the space-
time periodicity by a transformation of coordinates, and (3) methods that remove
the time periodicity constraint by scaling one blade row geometry in order to
retrieve equal pitch distances on both sides of each rotor/stator interface. This is
called here as Domain Scaling Method (DSM) (Hildebrandt et al., 2005; Dorney
and Sharma, 1997).
The first two methods are complex to generalize to multistage rotor/stator
configurations. To remove these constraints, the computational domain may be
scaled to yield identical pitch distances on both sides of each rotor/stator interface.
This pitch wise scaling requires another scaling in the axial dimensions to maintain

41
a constant solidity and therefore a compensation of the blade loading (space/chord
ratio). The space and time flow periodicity are then uncoupled and the unsteady
flow field may be resolved on a reduced number of blade passages per row. This
can be done without having to consider any time periodicity in the boundary
treatment.
Dorney and Sharma (1997) presented and compared between the previous
methods namely FCBR, SCBR, SSBR, and LCBR. The analysis has been evaluated
in terms of accuracy and efficiency. The modeled case was a transonic compressor
stage containing 76 IGVs (Inlet Guide Vanes) and 40 rotor blades. In numerical
simulations, the compressor is modeled using 2 IGVs and 1 rotor blade. Thus, the
number of IGVs in the first row was increased to 80 and the size of the airfoils was
reduced by a factor of 76/80 to maintain the same blockage (space/chord ratio).
FCBR simulation have been time-averaged and chosen to serve as the base line
results. The SCBR and the LCBR techniques provided a reasonable representation
of the FCBR results. The SSBR method significantly under predicted the IGV loss
and over predicted the stage efficiency in case of passage shocks.
Aube and Hirsch (2001) investigated the effect of unsteady loss sources
generated in rotor/stator interactions on the performance a 1-1/2 axial turbine stage.
Two levels of approximation were used, quasi-steady and full unsteady. The quasi-
steady approximation is performed using the "mixing-plane model" while the
unsteady one is performed using the "sliding grid" model. The results of the two
models compare well with the experimental results and allow capturing of the main
flow structure of the turbine passage. Only the fully unsteady (fully coupled)
calculation resolves the complex loss mechanisms encountered mainly in the rotor
and downstream stator components. These unsteady interactions are observed
through time variations of the entropy, absolute flow angle and static pressure.
The main difference between a full-unsteady simulation and the mixing-plane
solution is the lack of all unsteady effects in the later. This returns to the absence of

42
the so called “Deterministic Stress Terms”, DST, as a result of averaging process in
the case of the mixing plane. For this reason and to improve the efficiency of the
mixing-plane model in predicting unsteady effects, Stridh and Eriksson (2005)
incorporated these DST to the conventional mixing-plane model. The objective was
to enable it to approximately model the unsteady effects of neighboring blade rows.
They used the linearized harmonic approach, applied to rotor/stator interaction by
Chen (2000), to predict the DST. They applied their linearized technique to a 3D,
1-1/2 stage transonic fan and compared the results with the full unsteady and
conventional mixing-plane results. This method makes it possible to evaluate
unsteady effects, such as time dependent blade loads due to wake interaction. It is
also indicated that when the steady flow is continuously updated by the DST, the
surge line can be approached in the compressor map, i.e. it is possible to obtain a
numerical estimation closer to the surge line in comparison to the conventional
steady computation.
Adami et al. (2001) developed a full 3-D unstructured solver and applied it to
the simulation of the 3-D VKI annular turbine stage. The peculiar aspect of their
work, compared to the previous work, was given by the completely hyprid-
unstructured nature of the approach. This feature allows an easy and flexible mesh
generation and refinement, especially for more complex geometries. The higher
CPU and memory demand, often encountered with this type of grids, had been
overcome by the use of the parallel computations. The results compare favorably
with a set of time average calculations and the available experimental data. As a
result their unsteady Euler approach allows a realistic description of the flow pattern
especially when phenomena, such as shock interaction, blade loads and flow
distribution, are not physically accounted for by steady state computations.
Hildebrandt et al. (2005) have conducted a steady and unsteady flow
simulation of a 1.5-stage low speed research compressor. They used a one-equation
turbulence model, Spalart Allmaras, with a semi-empirical transition. The steady
analysis were performed with the mixing plane model using the real geometry,

M.Sc.Thesis-Reda Ragab-2008

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