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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
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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)
Mechanical Power Engineering Department.
Faculty of Engineering.
Zagazig University
3- Prof. Dr. Mohammed Mahrous Shamloul
Mechanical Power Engineering Department.
Faculty of Engineering.
Zagazig University
Zagazig
2008
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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.
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
4.36 Meridional Variation of Mean Velocity Magnitude on a Mid-Span
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
4.44 Meridional Variation of Mean Static Temperature on a Mid-Span Surface
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
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4.47 Spanwise Variation of Mean Static Pressure at Exit of Third Stage for
Various Diameters………………………………………………………… 119
4.48 Meridional Variation of Mean Velocity Magnitude on a Mid-Span
Surface for Various Diameters..………………………………………….. 120
4.49 Spanwise Variation of Mean Velocity Angle at Inlet of Third Stator for
Various Diameters………………………………………………………… 120
4.50 Spanwise Variation of Mean Velocity Angle at Inlet of First Stator for
Various Diameters………………………………………………………… 121
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
4.56 Meridional Variation of Mean Static Temperature on a Mid-Span Surface
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
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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/sec
2].
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 thJ species, [Kg/m3.s].
mS Mass source term from the dispersed phase, [Kg/m3.s].
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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 thJ species in the mixture.
Z Radial direction.
ε Effectiveness of evaporative cooler, Turbulent dissipation rate [m2/sec
3]
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.
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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
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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.
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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 Day
Fig. (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
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Chapter (1) Introduction
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
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Chapter (1) Introduction
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
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Chapter (1) Introduction
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)
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Chapter (1) Introduction
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)
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Chapter (1) Introduction
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)
)
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Chapter (1) Introduction
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
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Chapter (1) Introduction
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.
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Chapter (1) Introduction
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)
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Chapter (1) Introduction
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
Pow
er G
ains
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Chapter (1) Introduction
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.
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Chapter (1) Introduction
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
TITD
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)
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Chapter (1) Introduction
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.
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Chapter (1) Introduction
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.
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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
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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,
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Chapter (2) Literature Review
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.
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Chapter (2) Literature Review
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
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Chapter (2) Literature Review
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
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Chapter (2) Literature Review
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
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Chapter (2) Literature Review
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)
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Chapter (2) Literature Review
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
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Chapter (2) Literature Review
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 " 2D law" of droplet evaporation. The term is known as
the evaporation constant. From the " 2D law ", it is clear that the initial droplet size
has a major effect on the rate of droplet volume diminish.
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Chapter (2) Literature Review
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
dt ae
1
2300 41.1
(2.3)
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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
oovdRe (2.4)
Ohnesorge number od
Oh
(2.5)
Weber number
oovdOhWe 2Re).( (2.6)
and Surface roughness o
t
td
RS (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 .
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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 25.1Re.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)
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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)
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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
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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.
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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)
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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
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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
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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
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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.
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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
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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.
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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)
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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
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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
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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
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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,
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while the unsteady analysis were performed using the sliding grid domain scaling
technique. The blade count was 45:43:45 (IGV, Rotor, Stator) favors an unsteady
sliding grid calculation. For these unsteady calculations the number of IGVs and
Stators was decreased to 43, while scaling the axial chord accordingly in order to
maintain a constant solidity and therefore a compensation of the blade loading
(blade pitch/blade chord length). Apart from these slight geometrical changes,
necessary purely for numerical reasons, the unsteady and steady configurations
were identical.
2.9 DISCUSSION OF PREVIOUS WORK AND SCOPE OF THE CURRENT
WORK
From the previous studies, all the researchers confirmed the benefits of wet
compression in reducing the compressor work and hence increase the total output of
the gas turbine unit. Considering the previous work, the following remarks are
found:
Because wet compression process is a complex phenomenon, no attempt was
made to study the problem comprehensively from its all aspects. All the
models were restricted to zero- and one-dimensional models except that of
Loebig et al. (1998) who used a quasi-three dimensional model with some
simplifications.
Injected water quantity was limited to small values (about 1.5 %) in most
studies.
Injected droplet diameters in all previous investigations were restricted to
small values (about 10 microns). Only droplets with such size can be
completely evaporated within the compressor and follow the air stream. This
makes wet compression process a safe process and far from causing erosion.
This was confirmed by long term operation and investigation where no
evidence for erosion was detected.
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Compressor work reduction is a strong function of compressor pressure ratio
which necessitates the use of a large multistage compressor.
The amount of evaporation achieved within the compressor depends mainly
on the axial length of the compressor and initial droplet diameter. Longer
compressors achieve longer residence time of water droplets and hence more
evaporation.
The effect of droplet-droplet interaction and its expected effect on droplets
agglomeration is not included in any previous work. Also the effect of
droplet-blade interaction is not included in any previous work.
Little experimental work is available and this reduces the chance of
validating computational models.
From the previous remarks, the scope of the present study is as follows:
A three dimensional numerical model will be used to describe the wet
compression process in more detail. A CFD model will be used to
simulate the multistage compressor and track the droplets in
Lagrangian frame to simulate wet compression process.
The discrete element method will be used to solve the droplet
trajectories in a Lagrangian frame. Using the discrete element method
enables the consideration of droplet-droplet and droplet-blade
interactions.
The Fully Coupled Blade Row (FCBR) technique (Sliding Grid) will
be used to solve the blade row interaction in this multistage
compressor simulation. The FCBR technique necessitates making
some geometrical modifications to unify the pitch on both sides of the
sliding interface, so that the Domain Scaling Method (DSM) will be
used for this purpose.
Page 61
Chapter (2) Literature Review
45
The three-dimensional model used in the current study along with the
other models (FCBR and discrete element method) are unsteady and
very computationally demanding. For this reason, only the first three
stages of a multistage compressor will be simulated.
Water is commonly used in wet compression. On the other hand
water has corrosive as well as erosive effects as it impacts the moving
surfaces in the compressor. To avoid these shortcomings in this work,
Methanol droplets will be used instead. This benefit from Methanol
as non corrosive liquid. It also has less erosion effect due to its lower
density compared with water such that the impact momentum on the
moving surface is less. Methanol has higher volatility which enables
achieving the effect of wet compression even in short and low
pressure ratio compressors. Last but not least, using methanol will
have a dual use where it provides wet compression effect as well as
being used as a primary fuel to the gas turbine. The last important
advantage is taking into consideration the advantage of methanol as a
renewable bio-fuel.
Page 62
46
CHAPTER 3
NUMERICAL SIMULATION OF WET
COMPRESSION PROCESS
3.1 INTRODUCTION
The approach adopted in this work is the computational one. This enables to
identify with great details the impact of wet compression on the flow field inside a
multistage axial compressor. The evaporating media considered in this work is
Methyl-Alcohol. This attributed to the advantages of Methyl-Alcohol in
comparison to water. These advantages include; high volatility, low density; non-
corrosive, and renewable fuel. These advantages enable using Methyl-Alcohol in
short compressor. Furthermore it offers less erosion as well as corrosion in
comparison with using water droplets.
In this chapter the numerical study is conducted to simulate the wet
compression of Methyl-Alcohol droplets in a three axial flow compressor. The
unsteady, viscous, and 3D governing equations representing the flow field are
described as well as the discrete phase governing equations. In addition, sub-
models and auxiliary equations are introduced. These sub-models include;
turbulence model (RNG k ), droplet collision, droplet evaporation and the droplet
breakup models. The coupling between the carrier phase and the dispersed phase is
considered to be two-way coupling, which is also explained herein. Moreover the
computational model and grid setup are explained. FLUENT 6.3.26 software
provided by FLUENT Inc. is used to simulate the problem under consideration.
3.2 GOVERNING EQUATIONS
The equations governing the carrier phase, as well as those for the dispersed
phase are presented in this section. The equations of the carrier and the dispersed
phases are coupled in two-way coupling. This is done by taking into consideration
Page 63
Numerical Simulation Chapter (3)
47
the effect of the dispersed phase on the carrier phase in form of source terms, which
appear in the carrier phase governing equations. On the other hand, the effects of
the carrier phase on the dispersed phase appear in the dispersed phase equations.
3.2.1 Carrier Phase Governing Equations
Air, which is the carrier phase, is treated as a perfect gas mixture composed of
four species: Oxygen, Nitrogen, Methyl-Alcohol vapor (zero concentration in dry
case) and Water vapor. The basic equations are conservation of mass, conservation
of momentum, conservation of energy, and conservation of species. In addition to
these basic equations, there are some other auxiliary equations. The basic equations
are expressed in a fixed frame of reference. Accordingly they are based on the
absolute velocity formulation over the whole domain. These differential equations,
for laminar flows, are expressed as follows:
3.2.1.1 Mass conservation equation
The mass conservation equation for unsteady flow is given as (FLUENT, 2006)
mi
i
SVxt
)(
(3.1)
Where;
iV : velocity in the thi direction
ix : coordinate in the thi direction
: air density.
mS : mass source term from the dispersed phase
i : a tensor indicating 1, 2, 3.
The relative velocity irV , in the rotating frame can be obtained by:
kjjkiiir xeVV , (3.2)
Page 64
Numerical Simulation Chapter (3)
48
Where;
j : the angular velocity for the rotating frame in the j direction
kx : coordinates in the rotating frame in the k direction.
ikj ,, : tensors indicating 1, 2, 3.
jkie : the permutation symbol given by:
0
1
1
jkie
If ikj ,, are in a repeating order as 1, 2, 3.
If ikj ,, are in different repeating order.
If any two of ikj ,, are equal.
Species conservation equation.
The conservation equation of the thj species for unsteady flow can be written as
j
j
j
i
ji
i
jS
xi
YD
xV
xt
)( (3.3)
where
j : is the mass fraction of the thj species in the mixture.
jD : is the diffusion coefficient of the thj species in the mixture.
jS : is the source term for this species.
3.2.1.2 Momentum conservation equation
The conservation of momentum equation in the thi direction for unsteady flow
can be written as follows (FLUENT, 2006):
f
j
ij
i
jji
j
i Sxx
pgVV
xt
V
)(
)( (3.4)
Where p is the static pressure, and ij is the viscous stress tensor given by
l
lij
i
j
j
iij
x
V
x
V
x
V
32 (3.5)
Page 65
Numerical Simulation Chapter (3)
49
where
: is the absolute viscosity.
lji ,, : are tensor indices indicating 1, 2, 3.
jiif
jiifij
0
1
g and fS are the gravitational body force and the source term which represents
external body forces (that arise from interaction with the dispersed phase),
respectively.
3.2.1.3 Energy conservation equation
The unsteady equation of conservation of energy is given as (FLUENT, 2006)
hiji
j
ij
ii
i
i
SVJhx
TK
xpEV
xt
E
)()(
)(
(3.6)
Where
E : is the total energy of the air.
K : is the air thermal conductivity.
hS : is heat source term form the dispersed phase
iJ : is the diffusion flux of thj species in the thi direction
The first three terms in the right-hand side of equation (3.6) represent the
energy transfer due to conduction, species diffusion, and thermal energy created by
viscous shear, respectively. The air total energy E is given by
2
2
iVphE
(3.7)
where sensible enthalpy h is defined for ideal gases as
j
jj hh (3.8)
Where
jh is the specific enthalpy,
T
T
jpj
ref
dTch , ( refT =298.15 K)
Page 66
Numerical Simulation Chapter (3)
51
3.2.2 Auxiliary Equations
The density of an ideal gas is computed through the equation of state. The air
viscosity is computed according to the Sutherland viscosity law (FLUENT, 2006).
Sutherland’s law is expressed as follows:
ST
ST
T
T
0
2/3
0
0 (3.9)
For air at moderate temperatures and pressures, sPa.10*7894.1 5
0
,
KT 11.2730 , KS 56.110 .
The mixture's specific heat capacity is computed as a mass fraction average of
the pure species heat capacities:
iP
i
iP CYC , (3.10)
The mixture's thermal conductivity is computed based on a simple mass
fraction average of the pure species conductivities:
i
i
i KYK (3.11)
3.2.3 Dispersed Phase Governing Equations
The governing equations representing the droplet motion through the moving
stream of a compressible flow is introduced herein. The solution of these equations
is carried out based on the Lagrangian approach.
3.2.3.1 Droplet motion
The trajectory of a droplet can be obtained by integrating its equation of
motion which results from the force balance on the droplet. From Newton’s second
law of motion the droplet equation of motion per unit mass of droplet is written as
Page 67
Numerical Simulation Chapter (3)
51
Fdt
Vd p
(3.12)
where pV
is the droplet velocity vector, and F
is the sum of all external
forces exerted on a unit mass of the droplet. Figure (3.1) shows different types of
these forces. The force term in the right hand side of equation (3.12) depends on
the droplet relative Reynolds number eR , as well as on the local acceleration,
pressure gradient, and shear gradient of the flow field. In the following sections the
external forces acting on a single droplet are discussed.
a) Drag Force
The drag force is one of the most dominant forces affecting the droplet motion.
It is expressed as follows:
24
182
eD
pp
D
RC
dF
(3.13)
External Forces F
Force due
to rotating
R.F.
Drag
force
Gravity
and
buoyancy.
Lift
forces.
Thermophoretic
force.
Unsteady
forces.
Pressure
gradient
force.
Saffman. Magnus. Virtual
mass.
Basset.
Fig.(3.1) Types of the External Forces Exerted on the Droplet
(FLUENT, 2006)
Page 68
Numerical Simulation Chapter (3)
52
where, p is the droplet material density, pd is the instantaneous droplet diameter
(updated each time step to account for evaporation ), DC is the drag coefficient ,
and eR is the relative Reynolds number which is defined as follows:
VVdR
pp
e
(3.14)
The droplet drag coefficient DC depends on the droplet shape and orientation,
as well as the flow parameters such as turbulence level, Mach number, and the
relative Reynolds number. FLUENT provides a method that determines the droplet
drag coefficient ( DC ) dynamically, accounting for variations in the droplet shape for
unsteady models involving discrete phase droplet breakup. This method is the
dynamic drag law. The dynamic drag law takes into account the distortion of the
droplet shape as it moves through the gas especially when the Weber number is
large. This distortion in droplet shape, from the spherical, causes the drag
coefficient to change dynamically from that of the sphere. In the extreme case, the
droplet shape will approach that of a disk with a drag coefficient of 1.52 (FLUENT,
2006). The dynamic drag model linearly varies the drag between that of a sphere
and that of a disk. The drag coefficient is calculated as follows:
)632.21(, yCC Spheredd (3.15)
where y is the droplet distortion, as determined by the solution of
dt
dy
r
Cy
r
C
r
u
C
C
dt
yd
l
ld
l
k
l
g
b
F
232
2
2
2
(3.16)
which is obtained from the TAB model for spray breakup, described later. In the
limit of no distortion ( y =0), the drag coefficient of a sphere will be obtained as
follows:
1000
6
11
24
1000424.0
32
,ee
e
e
Sphered RRR
R
C (3.17)
Page 69
Numerical Simulation Chapter (3)
53
While at maximum distortion ( y =1) the drag coefficient corresponding to a disk
will be used.
b) Force due to rotating frame
For rotation defined about the x -axis, the forces on the droplets in the y and
z directions can be written respectively as (FLUENT, 2006):
z
p
pz
p
y VVyF
21 2 (3.18)
y
p
py
p
z VVzF
21 2 (3.19)
where; pypz VV , are the droplet velocity components in z and y directions
respectively, is the angular speed of the rotating frame.
Other forces can be neglected due to their minor impact compared with the
aforementioned two forces.
The droplet velocity is obtained by integrating equation (3.12). The trajectory
of a droplet is then obtained by integrating the following relation:
p
pV
dt
xd
(3.20)
Both equations (3.12) and (3.20) are solved in each coordinate direction to
determine the velocity and position of the traced droplet at any given time.
3.3 SUB-MODELS
In addition to the governing equations described previously, there are other
sub-models. These sub-models govern the phenomena associated with wet
compression and will be described in the following sections.
Page 70
Numerical Simulation Chapter (3)
54
3.3.1Turbulence Modeling
The turbulence model has a great effect on the droplet trajectory. In turbulent
flows, the Discrete Random Walk (DRW) is used to present the effect of turbulence
fluctuating velocity on the droplet movement using a stochastic model as will be
detailed. The fluctuating velocities are randomly drawn from a Gaussian random
distribution of the turbulent kinetic energy. Consequently, the turbulence model
affects the droplet trajectory through the value of the turbulent kinetic energy.
It is an unfortunate fact that no single model is universally accepted as being
superior for all class of problems. The turbulence model selection needs to be
coupled with the selection of a near-wall treatment. Those decisions are closely
related to the development of an appropriate computational grid. There are many
factors which must be considered when selecting a turbulence model. The most
obvious factors are the physics of the flow, the level of accuracy required, and the
available computational resources. The flow field in this study is solved using the
commercial code FLUENT 6.3.26. The available turbulence models in this version
of FLUENT are:
1. The Spalart-Allmaras one equation model.
2. The standard k model and its variants ( RNG and Realizable k ).
3. The standard k model and its variants.
4. The Reynolds stress model (RSM).
5. Large Eddy Simulation (LES) model.
These models are arranged in terms of accuracy and hence, computational
resources. The RSM is the most elaborate turbulence that FLUENT provides but it
is extremely computationally expensive, therefore it is not used in this study. The
standard k model falls in the category of the two equation turbulence models
based on an isotropic eddy-viscosity concept. As such, it is more universal than
other low-order turbulence models. Robustness, economy, and reasonable accuracy
Page 71
Numerical Simulation Chapter (3)
55
for a wide range of turbulent flows explain its popularity in industrial flow and heat
transfer simulations.
The RNG k model also belongs to the k family of models. There is a
major difference between the RNG k and the standard k models. The RNG
k model has an additional term in the equation. This significantly improves
the accuracy for rapidly strained flows. So that the RNG k model shows better
performance than the standard k model in the prediction of turbomachinery
flow and heat transfer as examined by El-batsh (2002). As a consequence the
turbulence model used in this study is the RNG k model.
The RNG-based k- turbulence model is derived from the instantaneous
Navier-Stokes equations, using a mathematical technique called renormalization
group (RNG) methods. The analytical derivation results in a model with constants
different from those in the standard k model, and additional terms and functions
in the transport equations for k and . The scale elimination procedure in RNG
theory results in a differential equation for turbulent viscosity as follows:
dC
kd
172.1
3
2
(3.21)
Where
=
eff and C 100
Equation (3.21) is integrated to obtain an accurate description of how the effective
turbulent transport varies with the effective Reynolds number (or eddy scale). This
allows the model to better handle low-Reynolds-number and near-wall flows. In
the high-Reynolds-number limit, Equation (3.21) gives
2kCt (3.22)
Page 72
Numerical Simulation Chapter (3)
56
The RNG theory provides the transport equations for k and , respectively as:
Mbk
j
effk
ji
i GGx
k
xx
kV
t
k
)()( (3.23)
R
kCGCG
kC
xxV
xtbk
j
effk
j
i
i
2
231
)( (3.24)
where;
kG : generation of k due to mean velocity gradients.
bG : generation of k due to buoyancy.
M : contribution of compressibility.
k , : the inverse effective Prandtle numbers for k and respectively. They are
calculated using the following formula derived analytically by RNG theory as:
effoo
3679.06321.0
3929.2
3929.2
3929.1
3929.1 (3.25)
Where
o = 1.0. In the high-Reynolds number limit )0.1/( eff , k = 1.393.
R in the equation is given by:
k
CR
o2
3
3
1
)/1(
(3.26)
where /Sk , 38.4o , 012.0 .
The model constants 1C and 2C in equation (3.24) have values derived analytically
by the RNG theory. Table (3.1) shows the values of the constants used in the RNG
k model. More details can be found in FLUENT manual (FLUENT, 2006).
Table (3.1) Values of the Constants in the
RNG k Model
1C 2C C
1.42 1.68 0.0845
Page 73
Numerical Simulation Chapter (3)
57
3.3.2 Near-Wall Treatment for Turbulent Flows
Turbulent flow is largely affected by the presence of walls. The mean velocity
field is affected through the no-slip condition that has to be satisfied at the wall.
Turbulence is also changed by the wall presence. Very close to the wall, viscous
damping reduces the tangential velocity fluctuations while kinematic blocking
reduces the normal fluctuations. Toward the outer part of the near wall region,
turbulence is rapidly augmented by the production of turbulent kinetic energy due to
the Reynolds stresses and large gradient of the mean velocity. Many experiments
have shown that the near wall region can be subdivided into three layers. In the
innermost layer called the viscous sub-layer, where the flow is almost laminar like.
Viscosity plays a dominant rule in momentum and heat transfer. In the outer layer
called the fully turbulent layer, turbulence plays the major rule. Finally, there is an
intermediate region between the viscous sub-layer and the fully turbulent layer
called buffer layer, where the effects of viscosity and turbulence are equally
important.
In the near-wall region, the velocity has a universal distribution, Fig. (3.2).
According to numerous measurements, the viscous sub-layer and the fully-turbulent
region can be represented as functions between the dimensionless wall distance y
and dimensionless velocity u , (Fluent, 2006).
Viscous sub-layer: 50 yyu (3.27)
Fully-turbulent region: ycyK
uc
70ln1
(3.28)
Where:
yuy
u
uu t
t
,
And;
cK : is the Von Karman constant ( = 0.4187).
c : is an empirical constant ( = 5.0 ).
Page 74
Numerical Simulation Chapter (3)
58
tu : is the wall friction velocity ( /w ).
u : is the velocity parallel to the wall.
w : is the wall shear stress.
y : is the normal distance to the wall.
1 10 100 1000 10000
DIMENSIONLESS WALL DISTANCE y+
0
10
20
30
DIM
EN
SIO
NL
ES
S V
EL
OC
ITY
u+
fully turbulent layer
u+ = 1/k lny+ + C+
viscous sublayer
u+ = y+
Fig. (3.2 ) Universal Laws of The wall
(FLUENT, 2006).
Fig.(3.3) Near-Wall Treatments in
FLUENT
There are two approaches for modeling the near-wall region. The first one
approach referred to as the wall function approach. In this approach semi-empirical
formulas are used to bridge the viscosity-affected region between the wall and the
fully-turbulent region. The use of wall functions obviates the need to modify the
turbulence models to account for the presence of the wall. The other approach may
be called the near wall modeling approach or the enhanced wall treatment. In this
approach, the turbulence model is modified to enable the viscosity-affected region
to be resolved with a mesh all the way to the wall, including the viscous sublayer.
The near-wall mesh must be fine enough to be able to resolve the laminar sublayer
(typically y 1). This demand imposes too large computational requirement.
Page 75
Numerical Simulation Chapter (3)
59
These two approaches are shown schematically in Fig. (3.3). It is apparent
that the wall functions approach is a cost effective alternative to the enhanced wall
treatment and it will be used in this simulation.
FLUENT offers two choices of wall function approaches. Standard wall
functions and non-equilibrium wall functions. Non-equilibrium wall functions are
used in this study as they are modified to account for the severe pressure gradients.
Because of the capability to partly account for the effects of pressure gradients and
departure from equilibrium, the non-equilibrium wall functions are recommended
for use in complex flows involving separation, reattachment, and impingement,
where the mean flow and turbulence is subjected to severe pressure gradients and
change rapidly. In this flow, improvements can be obtained, particularly in the
prediction of wall shear (skin-friction coefficient) and heat transfer (Nusselt or
Stanton number). More details about turbulence modeling and near wall treatment
can be found in FLUENT user's guides (FLUENT, 2006).
The log-law for mean velocity sensitized to pressure gradients, as formulated
in Non-equilibrium wall functions approach, is expressed as follows:
ykCEIn
k
kCU
w
21
41
21
41
1~
(3.29)
Where
2
2
1~ vv
v
v y
kk
yy
y
yIn
kk
y
dx
dpUU (3.30)
and vy is the physical viscous sub-layer thickness, and is computed from
21
41
P
vv
kC
yy
(3.31)
Where 225.11
vy .
Page 76
Numerical Simulation Chapter (3)
61
3.3.3 Coupling between Dispersed and Carrier Phase
In two-phase flow systems, the terms one-way coupling and two-way coupling
are often used to represent the effect of droplet phase on the fluid flow. In one-way
coupling, the droplet phase has no effect on the fluid flow. In the two-way
coupling, dynamic interactions between the droplets and the fluid are considered.
The evaporation of the droplet changes the temperature field of the carrier phase
which in turn affects the evaporation rate. Therefore, mutual effects exist between
the dilute dispersed droplets and the air and the two-way coupling will be
considered to account for the interaction effects.
As the trajectory of a droplet is computed, the heat, mass, and momentum
gained or lost by the droplet stream that follows that trajectory are calculated.
These quantities can then be incorporated in the subsequent carrier phase
calculations. Thus, while the carrier phase always impacts the discrete phase, the
effect of the discrete phase trajectories on the continuum can also be incorporated.
This two-way coupling is accomplished by alternately solving the discrete and
carrier phase equations until the solutions in both phases have stopped changing.
The momentum transfer from the carrier phase to the discrete phase is
computed by examining the change in momentum of a droplet as it passes through
each control volume. This momentum change is computed as follows (FLUENT,
2006):
tmFVVd
RCS PotherP
PP
eDf
)(
24
182
( 3.32)
where
Pm = mass flow rate of the droplets
t = time step
otherF = interaction forces other than drag
Page 77
Numerical Simulation Chapter (3)
61
The heat transfer from the carrier phase to the discrete phase is computed by
examining the change in thermal energy of a droplet as it passes through each
control volume in the model. The heat exchange is computed as follows:
dTCmdTCmHmmSinP
ref
in
outP
ref
outoutin
T
T
PP
T
T
PPlatrefPPh (3.33)
where
inPm = mass of the droplet on cell entry (kg)
outPm = mass of the droplet on cell exit (kg)
inPT = temperature of the droplet on cell entry (K)
outPT = temperature of the droplet on cell exit (K)
refT = reference temperature for enthalpy (K)
latrefH = latent heat at reference conditions (J/kg)
The mass transfer from the discrete phase to the carrier phase is computed by
examining the change in mass of a droplet as it passes through each control volume
in the model. The mass exchange is computed simply as follows (FLUENT, 2006):
o
o
P
P
Pm m
m
mS
(3.34)
This mass exchange appears as a source of mass in the carrier phase continuity
equation. The mass sources are included in any subsequent calculations of the
carrier phase flow field.
Page 78
Numerical Simulation Chapter (3)
62
3.3.4 Turbulent Dispersion of Droplets
The dispersion of droplets due to turbulence in the fluid phase is predicted
using the Discrete Random Walk model (DRW) (FLUENT, 2006). In this model
the instantaneous values of the fluid velocities u , v , and w appearing in the
equations of motion of the droplet are given by:
www , vvv , uuu (3.35)
where u , v and w are the fluid average velocities and u , v , and w are the
fluid fluctuating velocities. By calculating the trajectories in this manner for a
sufficient number of representative droplets, the random effects of turbulence on
droplet dispersion can be accounted for. In the discrete random walk (DRW)
model, the interaction of a droplet with a succession of discrete fluid phase
turbulent eddies is simulated in a stochastic manner. Each eddy is characterized by
a Gaussian distributed random velocity fluctuation, u , v , and w
a time scale, e
The values of u , v and w which prevail during the lifetime of the fluid eddy
are sampled by assuming that they obey a Gaussian probability distribution such:
2uu , 2vv ,
2ww (3.36)
Where
is a normally distributed random number, and the remainder of the right-hand
side is the local RMS value of the velocity fluctuations. Since the kinetic energy of
turbulence is known at each point in the flow, these values of the RMS fluctuating
components can be defined (for RNG k and assuming isotropy) as:
32222 kwvu (3.37)
Page 79
Numerical Simulation Chapter (3)
63
The value of the random number is applied for the characteristic life time of
the eddy given by
ke 3.0 (3.38)
The droplet is assumed to interact with the fluid phase eddy over this eddy life time.
When the eddy life time is reached, a new value of the instantaneous velocity is
obtained applying a new value of . The values u , v w and 2u , 2v , 2w are
updated whenever migration into a neighboring cell occurs.
3.3.5 Droplet Evaporation Model
The droplets can get heating or cooling from the carrier phase. After the
droplet is evaporated due to either high temperature or low moisture partial
pressure, the vapor diffuses into the main flow. The droplet temperature is
calculated according to a heat balance that relates the sensible heat change in the
droplet to the convective and latent heat transfer between the droplet and the carrier
phase (radiation is neglected) (FLUENT, 2006):
fgP
PPP
PP hdt
dmTThA
dt
dTCm )( (3.39)
where
Pm : mass of the droplet (kg)
PC : droplet specific heat (J/kg.k)
PT : droplet temperature (k)
T : local temperature of the carrier phase (k)
h : convective heat transfer coefficient (W/m2.k)
PA : droplet surface area (m2)
dt
dmP : evaporation rate (kg/s)
fgh : latent heat (J/kg)
Page 80
Numerical Simulation Chapter (3)
64
The convective heat transfer coefficient h is evaluated using the following
correlation (Ranz and Marshall , 1952 ):
3/12/16.00.2 reP
u PRK
hdN
(3.40)
where
uN : Nusselt number
K : thermal conductivity of the carrier phase (W/m.k)
rP : Prandtl number of the carrier phase ( kCP )
The evaporation rate dt
dmP is governed by gradient diffusion and the corresponding
mass change rate of the droplet can be given as follows:
)( ,, isicP
P CCkAdt
dm (3.41)
where
ck : the mass transfer coefficient (m/s)
siC , : vapor concentration at the droplet surface (kg/m3)
,iC : vapor concentration in the bulk gas (kg/m3)
The value of ck can be calculated from the Sherwood number correlation:
3/12/1
,
6.00.2 ScRD
dkSh e
mi
Pc (3.42)
where
Sh : Sherwood number
Sc : Schmidt number ( miD , )
miD , : mass diffusion coefficient of the vapor in the bulk flow (m2/s)
The vapor concentration at the droplet surface siC , is evaluated by assuming
that the flow over the droplet surface is saturated at the droplet temperature. The
concentration of vapor in the bulk flow, is obtained by solving the transport
equation of species i .
Page 81
Numerical Simulation Chapter (3)
65
3.3.6 Droplet Collision Model
When two parcels of droplets collide, the collision algorithm determines the
type of collision. Only coalescence and bouncing outcomes are considered in the
current collision model (O'Rourke, 1981), where Weber number is low. The
probability of each outcome is calculated from the collisional Weber number ( cWe )
and a fit to experimental observations as follows:
DUWe rel
c
2
(3.43)
where relU is the relative velocity between two parcels, D is the arithmetic mean
diameter of the two parcels, and is the droplet surface tension.
The outcome of the collision must be determined. In general, the outcome
tends to be coalescence if the droplets collide head-on, and bouncing (or grazing) if
the collision is more oblique as shown in Fig. (3.4).
Fig.(3.4) Outcomes of Collision
The probability of coalescence can be related to the offset of the collector
droplet center and the trajectory of the smaller droplet. The critical offset is a
function of the collisional Weber number and the relative radii of the collector and
the smaller droplet. The critical offset is calculated by using the expression
We
frrbcrit
4.2,0.1min)( 21 (3.44)
where f is a function of 21 rr , defined as
Page 82
Numerical Simulation Chapter (3)
66
2
1
2
2
1
3
2
1
2
1 7.24.2r
r
r
r
r
r
r
rf (3.45)
The value of the actual collision parameter,b , is Yrr )( 21 where Y is a
random number between 0 and 1. The calculated value of b is compared to critb , and
if critbb , the result of the collision is coalescence. The properties of the coalesced
droplets are found from the basic conservation laws. In the case of a grazing
collision, the new velocities are calculated based on conservation of momentum and
kinetic energy.
3.3.7 Droplet Breakup Model
The classic Taylor analogy breakup (TAB) model is used for calculating
droplet breakup. This model is based on Taylor's analogy (Fluent, 2006) between
an oscillating and distorting droplet and a spring mass system. Table (3.2)
illustrates the analogous components.
Table (3.2) Comparison of a Spring-Mass System to a Distorting Droplet
Spring-Mass System Distorting Droplet
restoring force of spring surface tension forces
external force droplet drag force
damping force droplet viscosity forces
The resulting TAB model equation set, which governs the oscillating and
distorting droplet, can be solved to determine the droplet oscillation and distortion
at any given time. When the droplet oscillations grow to a critical value the
"parent'' droplet will break up into a number of smaller "child'' droplets. The
equation governing a damped, forced oscillator is as follows:
dt
dy
r
Cy
r
C
r
u
C
C
dt
yd
l
ld
l
k
l
g
b
F
232
2
2
2
(3.46)
Page 83
Numerical Simulation Chapter (3)
67
Where
y = the dimensionless droplet distortion ( rCxy b )
x = the displacement of the droplet equator from its spherical position
bC = 0.5 at breakup
r = is the undisturbed droplet radius
l = the discrete phase density
g = carrier phase density
u = is the relative velocity of the droplet.
= droplet surface tension.
l = droplet viscosity
The droplet is assumed to break up if the distortion is equal to the droplet
radius, i.e., the north and south poles of the droplet meet at the droplet center. This
breakup requirement is given as 1y . For under-damped droplets, the equation
governing y can easily be determined from Equation (3.46) if the relative velocity
is assumed to be constant and breakup will not occur ( y will never exceed unity).
In case of breakup, equations determine the produced droplet sizes and velocities
can be deduced (FLUENT, 2006). The model constants have been chosen to match
experiments and is shown in Table (3.3).
Table (3.3) Constants for the TAB Model
KC dC FC
8 5 1/3
3.3.8 Droplet-Wall Interaction Model
Droplet-wall interaction represents an important part of the droplet trajectory
calculations in wall-bounded flows. There are two models in FLUENT suitable for
droplet-wall interaction namely; wall-film model and wall-jet model. The wall-film
model is very suitable in the case under concern but it is not stable in 3D
Page 84
Numerical Simulation Chapter (3)
68
calculations. It gives wrong values of temperatures at film cells. Hence, the model
available for droplet-wall interaction in FLUENT is the wall-jet model. This model
is considered in this work. The direction and velocity of the droplet particles are
given by the resulting momentum flux, which is a function of the impingement
angle, and Weber number as shown in Fig. (3.5).
Fig. (3.5) "Wall-Jet'' Boundary Condition for the Discrete Phase
The "wall-jet" type boundary condition assumes an analogy with an inviscid
jet impacting a solid wall. Equation (3.47) represents the analytical solution for an
axisymmetric impingement assuming an empirical function for the sheet height ( H )
as a function of the angle that the drop leaves the impingement ( )
1
)( eHH (3.47)
where H is the sheet height at and is a constant determined from
conservation of mass and momentum. The probability that a drop leaves the
impingement point at an angle between and is given by integrating the
expression for )(H
eP 11ln (3.48)
where P is a random number between 0 and 1.
Page 85
Numerical Simulation Chapter (3)
69
The expression for is given by Naber and Reitz (1988) as follows:
2
11
1)sin(
e
e
(3.49)
3.4 NUMERICAL SOLUTION
The previous models for fluid flow and heat transfer are solved in this study
using the commercial code Fluent 6.3.26. This code is a general purpose computer
program for modeling fluid flow, heat transfer and chemical reactions. Fluent solve
the governing differential equations for the conservation of mass, momentum,
energy, species and turbulence using a control-volume-based technique that consists
of:
1. Division of the domain into discrete control volumes using an arbitrary
computational grid.
2. Integration of the governing equations on the individual control volumes to
construct algebraic equations for the discrete dependent variables such as
velocities, pressure, temperature, and conserved scalars.
3. Linearization of the discretized equations and solution of the resultant linear
equation system to yield updated values of the dependent variables.
The Pressure-Based segregated solver in the Fluent software is selected to
solve the air flow field. Each iteration consists of the steps illustrated in Fig. (3.6)
and outlined below (Fluent, 2006):
1. Fluid properties are initialized and successively updated, based on the current
solution.
2. The momentum equation is solved in turn using current values for pressure
and face mass fluxes, in order to update the velocity field.
3. Since the velocities obtained in Step 2 may not satisfy the continuity equation
locally, an equation for the pressure correction is derived from the continuity
equation and the linearized momentum equations. This pressure correction
Page 86
Numerical Simulation Chapter (3)
71
equation is then solved to obtain the necessary corrections to the pressure and
the face mass fluxes such that continuity is satisfied.
4. Equations for scalar quantities are then solved and convergence is checked
Fig. (3.6) Flow Chart of the Solution Procedure (Fluent, 2006)
Initialization
Update the flow field properties.
Start
Solve the momentum equation and update the
velocity field.
Solve the pressure correction equation and
update velocity, pressure and face mass flux
Solve the energy equation and update
temperature.
Solve the turbulence, other scalar equations.
Converged?
Read the geometry and grid.
Set the boundary conditions.
Stop
No
Yes
Page 87
Numerical Simulation Chapter (3)
71
In a coupled two-phase simulation, FLUENT performs the trajectory
calculation as follows:
1. Solve the carrier phase flow field (prior to introduction of the droplets)
2. Introduce the discrete phase by calculating the droplet trajectories for each
discrete phase injection.
3. Recalculate the carrier phase flow, using the interphase exchange of
momentum, heat, and mass determined during the previous droplet
calculation.
4. Recalculate the discrete phase trajectories in the modified carrier phase flow
field.
5. Repeat the previous two steps until a converged solution is achieved, in
which both the carrier phase flow field and the discrete phase droplet
trajectories are unchanged (within a definite error range) with additional
calculation .
This coupled calculation procedure is illustrated in Fig. (3.7). When the model
includes a high mass and/or momentum loading in the discrete phase, the coupled
procedure must be followed in order to include the important impact of the discrete
phase on the carrier phase flow field.
Fig. (3.7) Coupled Discrete Phase Calculations
Page 88
Numerical Simulation Chapter (3)
72
3.5 PHYSICAL MODEL
The physical model considered in the present work is the first three stages of a
NACA eight-stage axial flow compressor. This compressor was designed,
constructed, and tested by NACA in the 1940s. It may appear very old and lacks of
many recent design optimizations, but it is the only multistage compressor available
in the open literature with nearly sufficient geometrical specifications. It is well
known that the complete geometrical specifications of turbomachines are not
publicly available. Yet it is important to mention that the aim of this work is to
evaluate the impact of wet compression regardless the design details of the
compressor. The aforementioned compressor was selected based on private
communications with Prof. Awatif Hamed at Cencinaty University.
The salient geometrical features of that compressor are presented by Sinnette
et al. (1944) and shown in Fig. (3.8) and (3.9). The compressor essentially consists
of a solid rotor enclosed in a casing of three sections: the bell mouthed inlet, the
cylindrical stator, and the scroll collector. The maximum diameter of the
compressor at the inlet is approximately 20 inches and the over-all length is 42
inches. Compression of the air is accomplished by eight stages proceeded by a row
of inlet guide vanes to reduce the relative velocity at inlet of the first rotor row. The
stator was machined to a constant inside diameter of 14 inches.
Fig. (3.8) NACA Eight-Stage
Axial Flow Compressor Sinnette et al., 1944))
Fig. (3.9) Schematic of the Compressor
7 i
n
Stage 8
R1 S1
Stage 1
3 i
n
Page 89
Numerical Simulation Chapter (3)
73
The untapered rotor and stator blades were designed with the thickness
distribution of the NACA 0009-34 airfoil section and with a maximum camber of
5.4 percent of the chord. Instead of using a standard air foil section for the entrance
guide vanes, the space between the vanes is considered to be a passage and the
vanes were curved to give the desired prerotation to the air. The coordinates of the
blades and the vanes are given in Table (3.4). The stationary blade-tip clearance is
0.015 inch. The blades in the first row have a uniform twist of 11.25o per inch and
all other rotor blades have a uniform twist of 6.25o per inch. The stator blades have
a uniform twist of 5.75o per inch. The inlet guide vanes are not twisted. The
number of blades in each row, the chord, the mean length, and the setting of all
blades are given in Table (3.5). Flow path shape and interstage distances are not
well specified so their dimensions are interpolated from the given data with hub
curves approximated as straight lines.
Table (3.4) Section Coordinates of Blades
in Percentage of Chord.
Rotor and Stator blades
Lower surface Upper surface
Ordinate Station Ordinate Station
0 0 0 0
-0.41 1.47 1.23 1.03
-0.49 2.79 1.96 2.21
-0.54 5.3 3.13 4.64
-0.52 7.9 14.11 7.1
-0.47 10.42 4.94 9.58
-0.33 12.42 6.36 14.58
-0.15 20.39 7.45 19.61
0.27 30.27 8.95 29.73
0.69 40.2 9.68 39.88
1.02 49.96 9.79 50.04
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Numerical Simulation Chapter (3)
74
1.26 59.81 9.23 60.19
1.35 69.7 8.05 70.3
1.2 79.62 6.13 80.38
0.56 89.72 3.31 90.28
0.18 94.84 1.68 95.16
-0.09 100 0.09 100
Table (3.5) Compressor Blade Data.
Blade Angles (deg.) Approximate
Mean
Length (in)
Chord
(in)
Number
of
Blades
Location At Casing At Hub
27 27 3.348 2 35 Inlet Guide
Vanes
70.8 40 2.765 1.35 22 R1
56 42 2.4525 1.35 25 S1
54.7 41 2.2025 1.35 26 R2
53.1 42 1.9525 1.35 27 S2
50.6 40 1.7025 1.35 28 R3
49.6 41 1.515 1.35 29 S3
47.2 39 1.3275 1.35 30 R4
45.6 39 1.1712 1.013 42 S4
45.6 39 1.0775 1.013 43 R5
45.4 40 0.9525 1.013 44 S5
44.1 39 0.8275 1.013 45 R6
42.3 38 0.765 1.013 44 S6
42.1 38 0.67125 1.013 45 R7
39.4 36 0.60875 1.013 46 S7
41.3 36 0.54625 1.013 47 R8
39 36 0.54625 1.013 48 S8
Page 91
Numerical Simulation Chapter (3)
75
3.6 COMPUTATIONAL MODEL
The computational domain in the study includes only the first three stages of
the compressor. Only the first three stages are modeled due to the complexity of the
3D model used in the present work and the limited computer resources.
The blade row is represented by a single blade passage represents a 3-D
periodic sector along the whole compressor. Each sector includes one blade and its
angle is (29
360
). The Domain Scaling Method (DSM) was used to unify the pitch in
to satisfy the circumferential periodicity condition in each block, Fig. (3.10).
3.7 MESH GENERATION
Every compressor stage is discretized using 2 blocks, one for the rotor and the
other for the stator. Each block is a sector, with blade in the middle, represents the
flow volume around the blade and is called the turbo volume. The geometry and
mesh of each block were generated separately using GAMBIT; the preprocessor of
FLUENT package. The First three stages are stacked in one mesh file using
TMERGE, utility software in FLUENT package. GAMBIT generates structured
(mapped), unstructured (paved), and hybrid meshes. The mesh used for the model
Inlet
Casing
Hub R1
S1
Periodic boundaries
Fig. (3.10) The Computational Domain
Page 92
Numerical Simulation Chapter (3)
76
is mainly unstructured except near the blade wall where it takes the form of
structured grid called boundary layer (B.L.).
Two different meshing schemes were used in the present study namely, the
Tet/Hybrid and the Cooper schemes. The Tet/Hyprid scheme is used for meshing
the first rotor only because it is highly staggered and twisted. This scheme allows
creating the mesh with acceptable quality around the highly twisted first rotor. The
cooper scheme is used for meshing the remaining blades. Both schemes are
preceded by grading the blade profile and creating four rows of boundary layer
(B.L). Figures. (3.11) and (3.12) shows the first rotor mesh. In all rows, the blade
pressure and suction sides are graded with 30 grid points in the streamwise
direction. The grid points are clustered toward the leading and trailing edges of the
blade where fine mesh is required. In the spanwise direction, grid is clustered
toward hub and casing walls with number differs slightly form a block to other to
maintain a reasonable aspect ratio. The total number of cells in this simulation is
334,890 cells.
Fig.(3.11) First Rotor Mesh
Fig. (3.12) First Rotor Mesh. (zoomed)
Page 93
Numerical Simulation Chapter (3)
77
3.8 NUMERICAL CALCULATIONS
Domain Descritization: Every stage is descritized using 2 blocks, one for the
rotor and the other for the stator, each of them is generated separately using
GAMBIT which is the preprocessor of FLUENT's package. Each block is a one
blade passage and has a hybrid mesh consists of a structured boundary layer around
the blade followed by an unstructured (paved) mesh allover the passage. The
computational domain is composed of the first three stages of the compressor
stacked and merged in one file using a utility program, TMERGE, available in the
package. Figure (3.13) shows the computational grid repeated circumferentially for
clarification.
Fig. (3.13) Grid of the First Three Stages of the Compressor
( Repeated)
Mesh Sensitivity Analysis: The total number of cells used in the computations
was 334,890 cells. This number of cells is based on recommendations of previous
works in the literature and tested for solution dependency. Three mesh densities of
S3 R3 S2 R2 S1 R1
Inlet
Page 94
Numerical Simulation Chapter (3)
78
225704, 334890, and 417192 cells were examined. Figures (3.14) and (3.15) show
that the last two mesh densities give identical results. This means that a mesh
density of 334,890 cells approaches a mesh independent solution and it will be used
in the subsequent calculations.
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.1 0.105 0.11 0.115 0.12 0.125 0.13
Axail Diastance (m)
Pre
ss
ure
Co
eff
icie
nt
Mesh Size = 417192 Cells
= 334890 Cells
= 225704 Cells
Fig.(3.14) Pressure Coefficient at Second Stator Mid-Span
for Three Meshes
95
110
125
140
155
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Sta
tic
Pre
ss
ure
(K
pa
)
Mesh Size = 417192 Cells
= 334890 Cells
= 225704 Cells
Fig.(3.15) Averaged Static Pressure Variation at Domain Mid-Span
for Three Meshes
Page 95
Numerical Simulation Chapter (3)
79
Boundary Conditions: Along the inlet boundary; total pressure, total
temperature, flow angles, species mass fractions and turbulence parameters are
imposed. Along the exit boundary, static pressure is imposed at the hub radius.
Radial equilibrium is used to compute static pressure radial distribution in 3D
calculations. Rotational periodic boundary conditions are used on both sides of
each blade passage. All walls are considered stationary relative to the motion of the
adjacent fluid zone with no slip boundary conditions. Wall function was considered
for near wall solution. The rotors fluid zones move with 14000 min/rev . Table
(3.6) displays the numerical values of boundary conditions used in the current
simulation.
Table (3.6) Boundary Conditions.
Boundary Type Input Data ( Operating Point)
Pressure Inlet Po1 =101325 Pa , To1 = 310 K, Turbulent Intensity = 5 %
YH2O=0.008, YO2=0.23 , YCH3OH = 0.
Pressure Outlet Ps = 147000 Pa , Radial Equilibrium.
Periodic Rotational periodic.
Rotors Fluid Moving Mesh , Direction =(-1,0,0), N=14000 RPM
Stators Fluid Stationary
Numerical Strategy: The interaction between adjacent blade rows is taken
into account using the sliding mesh technique, available in FLUENT. FLUENT
provides three techniques to solve rotating machinery problems namely; the
multiple reference frame (MRF) model, the mixing plane (MP) model, and the
sliding mesh technique. The first two techniques are not used, despite giving very
reasonable results for air only cases with low cost computations. Only the third
technique is able to solve the wet compression process with its all inherent
phenomena with no limitations except for periodicity condition. The sliding mesh
technique is an unsteady technique which gives accurate results but it is highly
computational demanding. Details of this technique as well as the other two
techniques are found in APPENDIX A.
Page 96
Numerical Simulation Chapter (3)
81
Modifications for Unsteady Calculations: For unsteady calculations, the
domain scaling method (DSM) is used to satisfy the condition of equal pitch
distance on both sides of each rotor/stator sliding interface. In this way, the space
and time flow periodicities of the flow field are uncoupled and the unsteady flow
field can be resolved considering any time periodicity in the boundary treatment. In
the case under concern, the first three stages of the compressor are simulated
simultaneously. The blade counts in each of the six rows are 22, 25, 26, 27, 28, and
29 blades respectively (R1, S1, R2, S2, R3, S3). Blade numbers are increased to 29
blades in each blade row to unify the pitch. This pitchwise scaling was followed by
scaling of the axial chord in order to maintain a constant solidity and therefore a
compensation of the blade loading. The chords of the six blade rows are multiplied
by 22/29, 25/29, 26/29, 27/29, 28/29, and 29/29 respectively. Table (3.7) illustrates
these geometrical modifications.
Table (3.7) Geometrical Modifications for
Unsteady Calculations
Actual
Blade No.
Actual
Chord (in)
Scaled
Blade No.
Scaled Chord
(in)
Scaling
Ratio
R1 22 1.35 29 1.02414 22/29
S1 25 1.35 29 1.16379 25/29
R2 26 1.35 29 1.21034 26/29
S2 27 1.35 29 1.25689 27/29
R3 28 1.35 29 1.30345 28/29
S3 29 1.35 29 1.35 29/29
Time Step Selection: Time step selection is critical in unsteady simulations.
In case for unsteady simulations, it is usually interested in a time-periodic solution,
after the start up phase has passed. This time- periodic solution is expressed as:
)()( NTtt ( N = 1, 2, ….) (3.50)
where
)(t = any flow property at a given point in the flow field, at time t.
T = the period of unsteadiness.
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Numerical Simulation Chapter (3)
81
For rotor-stator simulations, the period (in seconds) is referred to as the blade
passing period (BPP). BPP is the period in which the rotor passes from one stator
blade to the next. For rotating problems, 3D radial cascades, this period can be
calculated by dividing the sector angle of the domain (in radians) by the rotor
speed (in radians per second) as follows:
BPP (3.51)
The time step size is usually taken as a fraction of this period (BPP) for
accurate capturing of unsteady phenomena with a reasonable computing time and
stability of the numerical procedure. In the case under concern, the BPP is
calculated on the basis of 29 blades (which represents a sector of 12.4138 degrees)
and a rotor speed of 14000 rev/min. The BPP is found to be equal to 1.47783 e-4
sec. The time step size is taken as 4e-6 sec (9458.36
1 of the BBP) which represents
the length of time during which the rotor will rotate 0.336 degrees. In this manner
the BPP will be divided into 36.9458 time steps. Accordingly, a complete
revolution of the rotor will take 1071 time steps.
Convergence Monitoring: To determine how the solution changes from one
period to the next, it is needed to compare the solution at some point in the flow
field over two periods. Also, global quantities such as lift, drag, and moment
coefficients on walls and mass flow rate are tracked across boundaries. When the
solution field does not change from one period to the next (if the change is less than
5 %), a time periodic solution has been reached. In the case under concern the
convergence of each unsteady physical solution (time step) can be achieved within
14 numerical sub-iterations with a reduction of the initial residuals larger than 3
orders of magnitude. The unsteady flow field converges to a pattern periodic in
time after about 29 passing-periods which is equivalent to one rotor revolution.
This time-periodic solution is apparent from examining the time-averaged values of
Page 98
Numerical Simulation Chapter (3)
82
mass flow rate at inlet and exit of the domain. Time averaging is carried over three
BPP after the first rotor revolution. The convergence history of area-weighted
average of the total temperature, as well as that of the total pressure at exit of the
domain are shown in Figs (3.16) and (3.17) respectively. It is apparent that the
solution repeats in a time periodic manner which means that a time periodic
solution is obtained.
358.25
358.3
358.35
358.4
358.45
358.5
1500 1550 1600 1650
Time Step
Te
mp
era
tu
re (
K)
159.6
159.65
159.7
159.75
159.8
159.85
159.9
1500 1550 1600 1650
Time Step
P
ressu
re (
KP
a)
Fig. (3.16) Convergence History of
Area-Weighted Average of Total
Temperature at Domain Exit
Fig. (3.17) Convergence History of
Area-Weighted Average of Total
Pressure at Domain Exit
Page 99
83
CHAPTER 4
RESULTS AND DISCUSSION
4.1 INTRODUCTION
Wet compression of methanol droplets in the first three stages of an axial
compressor has been numerically simulated. Simulation is considered to be three
dimensional, viscous, unsteady, and turbulent flow model of the compressor.
Turbulence is modeled using the RNG k model together with the non-
equilibrium wall function approach for the near-wall region. Motion of rotors are
simulated using the sliding grid technique available in the commercial code
FLUENT. The sliding mesh technique necessitates some geometrical modifications
of the compressor blades. These modifications were done using the domain scaling
method. The droplets are solved using the Lagrangian discrete phase model. Two
way-coupling is considered in this model. The droplet breakup and droplet-droplet
interaction are also considered. Turbulence effect on droplet dispersion is taken
into account by considering the stochastic Discrete Random Walk (DRW) model
available in FLUENT. In case of interaction between methanol droplets and any
wall (hub, casing, or blade), the wall-jet model is used to calculate the conditions
after impact.
This chapter includes the results and discussion of the computer experiment
carried out using the aforementioned simulation. This chapter is divided into four
sections. The first section presents the results of the dry performance analysis. The
second section presents the wet base case. The third section presents a parametric
study that evaluates the effect of changing some important parameters (Injection
Ratio and Droplet Size) on the performance of the compressor. The final section is
a comparison with experimental wok.
Page 100
s and DiscussionResult ) 4Chapter (
84
4.2 DRY PERFORMANCE
In this section the solution results for the dry case, without liquid injection, is
displayed. The trend of variables variation may be a sufficient judging point
because the performance of the axial compressors is well documented in many
textbooks.
4.2.1 Characteristics of Dry Compressor.
Compressor performance is determined at a design speed of 14000 min/rev .
To construct this speed line, the static pressure at exit of the domain was varied
gradually. After convergence is achieved in each time step, pressure ratios and
mass flow rates are calculated. The operating point is specified in Table (3.6).
Figure (4.1) shows the dry characteristics of the compressor at the design speed
relative to the operating point. The results of this dry operating point are
summarized in Table (4.1).
0.976
0.984
0.992
1
1.008
0.98 0.99 1 1.01 1.02 1.03
o
/
Omm /
O.P.
Fig. (4.1) Dry Compressor Characteristics at Design Speed
(Relative to the Dry Operating Point)
Page 101
s and DiscussionResult ) 4Chapter (
85
Table (4.1) Summary of Dry Case Average Results
at Operating Point (O.P.)
Par.
Case
Inlet Air Mass
Flow (kg/s)
Total Discharge
Pressure (Pa)
Total Discharge
Temperature(k)
Moment
Coefficient
Dry Case 0.16730 159716 358.34 0.00245147
From Table (4.1) the compressor Specific Power ( ..PS ) (or work) for the dry case
can be calculated as follows:
60
2*
*.*..
N
m
Cconst
m
TPS
inlet
m
inlet
(4.1)
ALV
TCm 25.0
(4.2)
Where mC is the moment coefficient of all rotors around the rotational axis
( axisx ) and the constant is the value used in normalizing the moment about
axisx which is explicitly defined in the reference values panel in FLUENT.
4.2.2 Air Properties Variation through the Compressor.
When comparing numerical solutions of turbomachinery problems, it is often
useful to plot circumferentially-averaged values of variables as a function of either
the spanwise coordinate or the meridional coordinate. Meridional Coordinate is the
normalized coordinate that follows the flow path from inlet to outlet. Spanwise
Coordinate is the normalized coordinate in the spanwise (radial) direction, from hub
to casing. Their values vary from to .
Page 102
s and DiscussionResult ) 4Chapter (
86
The following plots show the variation of circumferentially-averaged values of
some important variables with either meridional direction or spanwise direction.
Meridional variation is always computed at midspan (Spanwise Surface of 0.5
Isovalue). Spanwise variation is computed at certain sections through the
compressor. Figure (4.2) shows the meridional variation of static pressure (Ps) and
total pressure (PO) at mid-span. Approximate locations of each blade row are also
illustrated on the figure. Figure (4.3) shows the meridional variation of static
temperature (TS) and total temperature (TO) at mid-span. Figure (4.4) shows the
meridional variation of absolute velocity magnitude at mid-span. Figure (4.5)
shows the meridional variation of absolute Mach number at mid-span. Figure (4.6)
shows the spawise variation of total pressure ratio at exit of each blade row
(referred to that at inlet). Where R1, S1, R2, S2, R3, and S3 represents the exit of
corresponding blade row where averaging is carried out. Total pressure ratio is the
ratio of the total pressure at the exit of the blade row to that at the inlet of the
compressor. It is a measure of loss in stators. Figure (4.7) shows the spanwise
variation of the total temperature ratio at exit of each blade row referred to that at
inlet. Total temperature ratio is the ratio of total temperature at the exit of the blade
row to that at the inlet to the compressor. It is also a measure of loss in stators.
Figure (4.8) shows the spanwise variation of static temperature at the exit of each
blade row. Figure (4.9) shows the spanwise variation of the static pressure at the
exit of each blade row. Another method to evaluate the actual variation of a certain
variable in any direction is to display the contours of the variable at a certain
surface. This is a good method for illustration, especially in three dimensional
calculations. Figure (4.10) shows the contours of static pressure at the whole
compressor (3D View). The solution domain is reproduced 29 times to complete
the 360 degree. Figure (4.11) shows the contours of static pressure variation in the
axial direction at a radial section (R= 6 in) for three passages. Finally, Fig. (4.12)
shows the contours of static pressure at different axial locations along the
compressor.
Page 103
s and DiscussionResult ) 4Chapter (
87
95
115
135
155
175
0 0.2 0.4 0.6 0.8 1
Non - Dimensional Meridional Distance
Pre
ss
ure
(K
Pa
)Total Pressure
Static PressureR1 S1 R2 S2 R3 S3Inlet Exit
MeridionalS
pan
wis
e
Fig.(4.2) Meridional Variation of Static Pressure (PS) and Total
Pressure (PO) at Mid-Span.
300
310
320
330
340
350
360
370
0 0.2 0.4 0.6 0.8 1
Non - Dimensional Meridional Distance
Te
mp
era
ture
(K
)
Total Temp.
Static Temp.
Fig. ( 4.3) Meridional Variation of Static Temperature (TS) and Total
Temperature (TO) at Mid-Span
Page 104
s and DiscussionResult ) 4Chapter (
88
50
100
150
200
0 0.2 0.4 0.6 0.8 1
Non - Dimensional Meridional Distance
Ab
so
lute
Ve
loc
ity
(m
/s)
Fig.(4.4) Meridional variation of Absolute Velocity Magnitude
at Mid-Span.
0.15
0.3
0.45
0.6
0 0.2 0.4 0.6 0.8 1
Non - Dimensional Meridional Distance
Ab
so
lute
Ma
ch
Nu
mb
er
Fig.(4.5) Meridional Variation of Absolute Mach Number
at Mid-Span.
Page 105
s and DiscussionResult ) 4Chapter (
89
0
0.25
0.5
0.75
1
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Inlet
R1S1R2S2R3S3
Fig.(4.6) Spawise Variation of Total Pressure at Exit of Each Blade Row
Referred to That at the Compressor Inlet .
0
0.25
0.5
0.75
1
1 1.05 1.1 1.15 1.2
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Inlet
R1S1R2S2R3S3
Fig.(4.7) Spanwise Variation of Total Temperature at Exit of Each Blade
Row Referred to That at the Compressor Inlet .
Page 106
s and DiscussionResult ) 4Chapter (
91
0
0.25
0.5
0.75
1
300 310 320 330 340 350 360
Static Temperature (k)
No
n-D
im. S
pa
nw
ise
Dis
tan
ce St1_Dry
St1_Wet
St2_Dry
St2_Wet
St3_Dry
St3_Wet
Fig. (4.8) Spanwise Variation of Static Temperature
at Exit of Each Blade Row
0
0.25
0.5
0.75
1
95 105 115 125 135 145 155
Static Pressure (KPa)
No
n-D
im. S
pa
nw
ise
Dis
tan
ce St1_Dry
St1_Wet
St2_Dry
St2_Wet
St3_Dry
St3_Wet
Fig.(4.9) Spanwise Varaiation of Static Pressure
at exit of Each Blade Row
Page 107
s and DiscussionResult ) 4Chapter (
91
Fig. (4.10) Contours of Static Pressure at the Whole Compressor (3D View)
Fig. (4.11) Contours of Static Pressure at a Radial Section (R=6 in)
for Three Passages (Repeated).
R=
7 in
R=
6 i
n
Page 108
s and DiscussionResult ) 4Chapter (
92
Inlet R1 outlet
S1 outlet R2 outlet
S2 outlet R3 outlet
S3 outlet Exit
Fig.(4.12) Contours of Static Pressure at Different Axial Locations
along the Compressor
Page 109
s and DiscussionResult ) 4Chapter (
93
4.3 WET BASE CASE
A wet base case is studied to indicate the effect of wet compression on
performance. The values of parameters, for this wet base case, are chosen based on
the previous work in the literature and the specifications of the current compressor.
In the base case, methanol liquid droplets were injected at the inlet plane of the first
rotor. A group of ten points, equally distributed from hub to casing, were chosen as
the injection configuration. The injected droplets are of monodispersed with mean
diameter of 5 µm. The mass flow rate of methanol is 0.001647 kg/s which equals to
about 1 % of dry air mass flow rate (which is termed as " injection ratio"). The
injected methanol temperature is 265 K as it is assumed to be cooled before
injection to ensure good atomization. The droplet velocity components are equal to
that of air at inlet to the compressor. Air is considered to be homogenous mixture
of Oxygen, Nitrogen, and water vapor. The initial concentration of methanol in air
is equal to zero. Air inlet total temperature is taken to be 310 K and its absolute
velocity magnitude is 64 m/s. Table (4.2) summarizes the values of the parameters
used in the base case.
Table (4.2) Values of the Parameters Considered in the Base Case.
Parameter Base Case Value (BC)
Inlet air total temperature 310 K
Inlet Relative Humidity 23 %
Inlet air turbulence intensity 5 %
Initial droplet diameter 5 µm
Initial droplet x-velocity 58
Initial droplet y-velocity 31
Initial droplet z-velocity 0
Initial droplet temperature 265 K
Methanol injection rate 0.001647 kg/s
Page 110
s and DiscussionResult ) 4Chapter (
94
After injection, methanol droplets travel with air and evaporate as a result of
heat transfer from air to the droplets. The result is a reduction in air temperature
and successive evaporation and heating of the droplets. Figure (4.13) shows the
dispersion of the droplets through the passage as a result of interaction with the
main flow. The evolution of droplet diameter from inlet to exit of the compressor
indicates that there is a tendency of droplets to agglomerate. The agglomeration is
attributed to the formation of larger droplets as an outcome of droplet collision. To
investigate and analyze the development of droplets properties during compression,
three sampling planes were constructed at the exit of the three stages and termed as
St1, St2, and St3 respectively. Droplets are sampled as they pass through these
planes and their properties are stored over 3 BPP. Properties of the droplets are
then time averaged and displayed to show the development of spray properties
through out the compressor. Figure (4.14) shows the mean droplet diameter at the
sampling planes at the exit of each stage. Droplet evaporation causes the droplet
diameter to decrease but the mean diameter of the droplets tends to increase at the
end of the compressor. This is because the small droplets evaporate early in the
passage while larger droplets, formed from agglomeration, continue in the path.
Figure (4.15) illustrates the droplet diameter distribution at sampling planes.
Figure (4.16) shows the average droplet temperature. It is clear that the mean
droplet temperature increases along the path. This increase in droplet temperature
during evaporation is attributed to the increase in the saturation temperature as a
result of successive compression. Figure (4.17) and (4.18) show the evaporation
characteristics of methanol droplets in the meridional and spanwise directions,
respectively. It is represented in terms of mass fraction of methanol in the mixture
(which results from evaporation). It is apparent from Fig. (4.18) that good mixing
and hence good evaporation is achieved at the first quarter of the span and at the
casing surface. Figure (4.19) shows the same result by displaying the contours of
methanol mass fraction at the exit of stages where St1, St2, and St3 represent the
exit of each stage.
Page 111
s and DiscussionResult ) 4Chapter (
95
Fig. (4.13) Droplet Tracks Through the Domain Colored with Droplet Diameter
(Base Case: 5µm Initial Diameter, 1% Injection Ratio )
0
1
2
3
4
5
1 2 3 4
Stage No. (Exit)
Me
an
Dia
me
ter
(mic
ron
s)
Inlet St1 St2 St3
Fig. (4.14) Mean Droplet Diameter at Exit of Stages
(at Sampling Planes)
Injection Plane
(10 Points)
R1 S1
St1 St2 St3
Exit
3 Sampling Planes (at exit of each stage)
Page 112
s and DiscussionResult ) 4Chapter (
96
Sta
ge
1
Sta
ge
2
Sta
ge
3
Fig. (4.15) Droplet Diameter Distribution
at Exit of Each Stage
Mean = 3.86 µm
Mean = 2.35 µm
Mean = 2.48 µm
Page 113
s and DiscussionResult ) 4Chapter (
97
260
265
270
275
280
285
1 2 3 4
Stage No. (Exit)
Mea
n D
rop
let
Tem
pera
ture
(K
)
Inlet St1 St2 St3
Fig. (4.16) Mean Droplet Temperature at Exit of Each Stage
0
0.0025
0.005
0.0075
0.01
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Mean
Meth
an
ol M
ass F
racti
on
Dry
Wet
Fig.(4.17) Meridional Variation of (Evaporated) Mean Methanol
Mass Fraction on a Mid-Span Surface
Dry
Page 114
s and DiscussionResult ) 4Chapter (
98
0
0.25
0.5
0.75
1
0 0.005 0.01 0.015
Mean Methanol Mass Fraction (Evap.)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Inlet
St1St2St3
Fig. (4.18) Spanwise Variation of (Evaporated) Mean Methanol
Mass Fraction at Exit of Each Stage
St1 Outlet Inlet
St3 Outlet St2 Outlet
Fig. (4.19) Contours of Mean Methanol Mass Fraction
at Exit of Each Stage
Page 115
s and DiscussionResult ) 4Chapter (
99
4.3.1 Changes in Air Properties through the Compressor.
Studying the impact of methanol droplet evaporation on air properties during
compression is important. This is because air properties affect compressor
performance. In order to quantify the trend of the variation of different parameters
along the compressor, circumferentially-averaged values of time averaged
properties are calculated along the meridional and spanwise directions. To show
the effect of evaporation on performance, the wet compression case (Wet) is
compared with the dry case (Dry).
Air temperature is markedly decreased through out the compressor as a result
of droplet evaporation as shown in Figure (4.20) and (4.21). This reduction in
temperature results in a lower discharge temperature and hence lower consumed
work. Figure (4.21) also indicates an increase in the temperature difference
between hub and casing. This difference in temperature may be harmful at large
injection rates as it may cause distortion in the casing of the compressor or rubbing
between the casing and the blade tip as it has been experimentally examined by
Baron et al. (1948).
Air pressure variation is small in both the meridional and spanwise directions,
with tendency to decrease at the front stage and increases near the exit as shown in
Fig. (4.22) and (4.23). This change in pressure build up through out the compressor
(the increase in the unloading of the early stages) is similar to what is found by
Bhargava et al. (2007-Part ІІІ). Air velocity tends to increase slightly with liquid
droplets injection especially at the first stage, as shown in Fig. (4.24). Air velocity
angles tend to increase at the inlet of stators due to wet compression. The
maximum increase in the absolute angle at the stator inlet is one degree, as shown in
Fig. (4.25). In this Figure S1, S2 and S3 represent inlet of the first, second and third
stators respectively.
Page 116
s and DiscussionResult ) 4Chapter (
111
300
310
320
330
340
350
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Sta
tic
Te
mp
era
ture
(K
) Dry
Wet
Fig.(4.20) Meridional Variation of Mean Static Temperature
on a Mid-Span Surface
0
0.25
0.5
0.75
1
300 310 320 330 340 350 360
Mean Static Temperature (k)
No
n-D
im. S
pa
nw
ise
Dis
tan
ce St1_Dry
St1_Wet
St2_Dry
St2_Wet
St3_Dry
St3_Wet
Fig.(4.21) Spanwise Variation of Mean Static Temperature
at Exit of Each Stage
Page 117
s and DiscussionResult ) 4Chapter (
111
90
100
110
120
130
140
150
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Sta
tic
Pre
ss
ure
(K
Pa
)
Dry
Wet
Fig.(4.22) Meridional Variation of Mean Static Pressure
on a Mid-Span Surface
0
0.25
0.5
0.75
1
95 105 115 125 135 145 155
Mean Static Pressure (KPa)
No
n-D
im. S
pa
nw
ise
Dis
tan
ce St1_Dry
St1_Wet
St2_Dry
St2_Wet
St3_Dry
St3_Wet
Fig.(4.23) Spanwise Variation of Mean Static Pressure
at Exit of Each Stage
Page 118
s and DiscussionResult ) 4Chapter (
112
60
80
100
120
140
160
180
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Mea
n V
elo
cit
y M
ag
nit
ud
e (
m/s
) Dry
Wet
Fig.(4.24) Meridional Variation of Mean Velocity Magnitude
on a Mid-Span Surface
0
0.25
0.5
0.75
1
22 24 26 28 30 32 34 36
Velocity Angle (deg)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce
S1_Dry
S1_Wet
S2_Dry
S2_Wet
S3_Dry
S3_Wet
Fig.(4.25) Spanwise Variation of Absolute Velocity Angle
at Inlet of Each Stator
Stators
Page 119
s and DiscussionResult ) 4Chapter (
113
4.3.2 Effect of Wet Compression on Compressor Performance
The effect of methanol injection on the performance of the compressor
compared with the dry case is summarized in Table (4.3). Inlet air mass flow
(AMF), total discharge pressure (Pd), total discharge temperature (Td), and the
moment coefficient of rotors around axisx are all changed due to wet
compression but with different magnitudes. Time averaged values of these
variables are used to investigate the performance change due to wet compression.
Time averaging of these variables occurs after the time periodic solution is obtained
which is achieved here after a complete revolution of the rotor.
Table (4.3) Summary of Wet Compression Case Results
Compared with Dry Case Results
Parameter
Case
Inlet Mass
Flow (kg/s)
Total Discharge
Pressure (Pa)
Total Discharge
Temperature(k)
Moment
Coefficient
Dry Compression 0.16730 159716 358.34 0.00245147
Wet Compression 0.17246 160279 346.54 0.00248654
Change (%) (Relative to Dry Case)
3.08 0.35 -3.29 1.43
The effect of methanol injection can be summarized as follows:
Compressor discharge temperature is decreased by 3.29 % due to wet
compression. This reduction in compressor discharge temperature is
expected to increase for larger compressor with higher pressure ratios.
Compressor discharge total pressure slightly increases by 0.35 %. This
trend well agrees with the experimental study carried by Baron et al. (1948)
on methanol injection in a turbo jet engine.
Inlet air mass flow rate increases by 3.08 % due to wet compression. This
increase in air mass flow is attributed to internal cooling. This results in a
corresponding increase in torque with a value of 1.43 %.
Page 120
s and DiscussionResult ) 4Chapter (
114
Compressor specific power (S.P.) (work) decreases as a result of exit
temperature reduction. The power is calculated by calculating the torque of
the three rotors around the axisx and multiplying it by the angular
velocity. The specific power is then calculated from equation (4.1).
Accordingly, the specific power reduction can be calculated as follows:
Percent Reduction in Compressor S.P. = 604.1100*.).
.)..).
Dry
WetDry
PS
PSPS %
Compressor operating point is shifted up on its characteristics curve. This
shift is a result of the increase in inlet air mass flow and discharge pressure.
This shift also makes the compressor operates under off-design conditions
as shown schematically in Fig (4.26).
Fig. (4.26) Compressor Operating Point Variation
in Wet Compression
Dry /
Drymm /
1.1
1.1
2
Dry Case
Wet Base Case
Page 121
s and DiscussionResult ) 4Chapter (
115
4.4 PARAMETRIC STUDY
To enhance the understanding of the effect of wet compression on compressor
performance, it is important to study the effect of some important parameters. The
most important parameters studied here are; (1) the ratio of injected methanol mass
flow rate to dry air mass flow rate (injection ratio), (2) the injected droplets
diameter, and (3) the effect of droplet agglomeration. The injection ratio and the
initial droplet diameter are varied with respect to the base case values. The effect of
droplet agglomeration is studied by switching off the collision model in the base
case. By switching off the collision model, droplet-droplet interaction (which is
responsible for coalescence) is not taken into account and hence the effect of
agglomeration is evaluated. Table (4.4) shows the different values of the
parameters, which have been considered in the simulation as well as the base case
values for comparison.
Table (4.4) Test Matrix Parameters Values.
Parameter
Case Injection Ratio (%) Droplet Diameter (µm) Droplet Collision
1 0.5 % 3 on
2 (Base Case) 1 % 5 on & off
3 1.5 % 7 on
4.4.1 Effect of Varying Injection Ratio.
Increasing the injected methanol injection ratio affects the evaporation rate of
the droplets. This results in reducing this rate. As shown in Fig. (4.27), the exit
droplet diameter is larger. Also droplet temperature is lower as shown in Fig.
(4.28). It is important to point out that, larger droplet diameters could be the result
of the combined effect of low droplet evaporation rate and droplets agglomeration.
In case of polydispersed droplets a third factor is also happened, which is due to the
evaporation of smaller droplets at higher rate than bigger one. Accordingly, the
Page 122
s and DiscussionResult ) 4Chapter (
116
averaged droplet size of the remaining droplets will shift to larger size due to the
omitting of smaller one, as shown in Fig. (4.29).
Figures (4.30) and (4.31) show the evaporation characteristics of methanol
droplets and it is apparent that at lower injection ratios, complete evaporation is
approached.
0
1
2
3
4
5
1 2 3 4
Stage No. (Exit)
Mean
Dro
ple
t D
iam
ete
r (m
icro
ns)
0.5%1%1.5%
St2 St3St1Inlet
Base Case
Injection Ratio
Fig. (4.27) Mean Droplet Diameter for Different Injection Ratios
265
270
275
280
285
1 2 3 4
Stage No. (Exit)
Mea
n D
rop
let
Tem
pera
ture
(K
)
0.5%1%1.5%
St2 St3St1Inlet
Injection Ratio
Fig. (4.28) Mean Droplet Temperature for Different Injection Ratios
Page 123
117
%.5 1 )aseCase 1% (B %0.5
St1
St2
St3
Fig. (4.29) Droplet Diameter Distribution at Exit of Stages for Different Injection Ratios
Mean =3.43 µm
Mean=2.23 µm
Mean=2.61 µm
Mean=3.86 µm
Mean=2.35 µm
Mean=2.48 µm
Mean=4.15 µm
Mean=2.82 µm
Mean=3.18 µm
Page 124
s and DiscussionResult ) 4Chapter (
118
0
0.0025
0.005
0.0075
0.01
0.0125
0.015
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Me
tha
no
l M
as
s F
rac
tio
n
Dry
0.5%1%
1.5%
Injection Ratio
z
Fig. (4.30) Meridional Variation of (Evaporated) Mean Methanol Mass Fraction
on a Mid- Span Surface for Various Injection Ratios.
0
0.25
0.5
0.75
1
0 0.005 0.01 0.015 0.02
Mean Methanol Mass Fraction (Evap.)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce
Dry
0.5%
1%
1.5%
Injection Ratio
Fig.(4.31) Spanwise Variation of (Evaporated) Mean Methanol Mass Fraction at
Exit of Third Stage for Various Injection Ratios.
Page 125
s and DiscussionResult ) 4Chapter (
119
The effect of injection ratio on air properties has also been evaluated. This is
important due to the impact of the change in air properties on the compressor
performance. For the simulated number of stages, the variation of air properties is
as follows:
Air temperature is decreased through out the compressor, as a result of
increasing injection ratio as shown in Figures (4.32) and (4.33). Figure (4.32)
shows that the temperature reduction is higher in later stages as a result of
higher evaporation rate. This is attributed to higher temperature. Increasing
the injection ratio also enlarges the difference in temperature in the radial
direction and between the hub and the casing as shown in Fig. (4.33). Improper
injection ratios may cause large radial temperature differences, which may
causes rubbing of the compressor blades on the casing (Baron et al., 1948).
Air pressure variation with injection ratio is not considerable. Figure (4.34)
shows that almost no meridional variation of mean static pressure at the mid-
span, while Fig. (4.35) shows a slight increase of discharge pressure in the
spanwise direction.
Air velocity is nearly not changed with increasing the injection ratio. This is
confirmed from Fig. (4.36) in meridional direction.
Air flow angle variation is an important measure of the aerodynamic
performance variation. This is responsible for efficiency of the individual
stages and matching between stages. Unfortunately, the small number of
stages simulated here don't give the chance for large variation in flow angles
even with large injection ratios. Generally, there is a small increase in the
absolute air flow angle at the inlet to the third stator with increasing injection
ratio, as shown in Fig. (4.37). Maximum increase in air flow angle is found at
the position of the span, where maximum evaporation rate is presented (nearly
at the lower third of the span).
Page 126
s and DiscussionResult ) 4Chapter (
111
300
310
320
330
340
350
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Sta
tic
Te
mp
era
ture
(K
)Dry
0.5%
1%
1.5%
Injection Ratio
Fig.(4.32) Meridional Variation of Mean Static Temperature on a Mid-Span
Surface for Various Injection Ratios
0
0.25
0.5
0.75
1
325 330 335 340 345 350 355 360
Mean Static Temperature (K)
No
n-
Dim
. S
pan
wis
e D
ista
nce
Dry
0.5%
1%
1.5%
Injection Ratio
Fig.(4.33) Spanwise Variation of Mean Static Temperature at Exit of Third Stage
for Various Injection Ratios
Page 127
s and DiscussionResult ) 4Chapter (
111
90
100
110
120
130
140
150
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Mean
Sta
tic P
ressu
re (
KP
a) Dry
0.5%
1%
1.5%
Injection Ratio
Fig.(4.34) Meridional Variation of Mean Static Pressure on a Mid-Span
Surface for Various Injection Ratios.
0
0.25
0.5
0.75
1
146 147 148 149 150 151
Mean Static Pressure (KPa)
No
n-
Dim
. S
pan
wis
e D
ista
nce
Dry
0.5%
1%
1.5%
Injection Ratio
Fig.(4.35) Spanwise Variation of Mean Static Pressure at Exit of Third Stage
for Various Injection Ratios
Page 128
s and DiscussionResult ) 4Chapter (
112
60
80
100
120
140
160
180
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Mea
n V
elo
cit
y M
ag
nit
ud
e (
m/s
)Dry
0.5%
1%
1.5%
Injection Ratio
Fig.(4.36) Meridional Variation of Mean Velocity Magnitude on
a Mid-Span Surface for Various Injection Ratios
0
0.25
0.5
0.75
1
27 28 29 30 31 32 33 34
Velocity Angle (deg)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce
Dry0.5%1%1.5%
Injection Ratio
Fig. (4.37) Spanwise Variation of Velocity Angle at Inlet of Third Stator
for Various Injection Ratios.
Page 129
s and DiscussionResult ) 4Chapter (
113
The effect of varying methanol injection rate on the overall performance of
the compressor is summarized in Table (4.5). The change of wet results from that
of dry results are plotted for various injection ratios, as shown in Fig.(4.38). The
impact of varying the injection ratio on the performance of the compressor can be
summarized as follows:
The average discharge total temperature (Td) is markedly decreased by
increasing the injection rate. The reduction approaches 4.11 %, from that of
dry compression, for injection ratio of 1.5 %. This reduction is a result of
droplet vaporization. This leads to work reduction in wet compression. The
discharge temperature is expected to further decrease in larger compressors.
The average discharge total pressure (Pd) increases slightly with increasing the
injection rate. It reaches 0.45 % for injection ratio of 1.5 %.
Compressor specific power (S.P.) decreases as a result of the reduction in
temperature. The reduction of compressor specific power approaches 1.65 %
at injection ratio of 1.5 %. The reduction in S.P. is a strong function of
compressor pressure ratio, as it has been stated by White and Meacock (2004).
Therefore greater reduction in compression work is expected to be achieved for
larger compressors with injection rates not much different from 1.5 %.
Inlet air mass flow rate (AMF) increases by 3.43% with increasing injection
ratio to 1.5 %. This increase in air mass flow rate is a result of density
increase due to lower air temperature. The increased air mass flow rate
together with the injected coolant flow causes larger increase in turbine power.
Compressor Torque (Torq) increases by 1.73 % for injection ratio of 1.5 %.
This slight increase in torque is attributed to the increase in mass flow rate.
The operating point is displaced up and right on the performance map with
increasing injection ratio. This displacement is resulted from the increase in
both the pressure ratio and the mass flow rate, as shown in Fig. (4.39).
Page 130
s and DiscussionResult ) 4Chapter (
114
Table (4.5) Summary Results of Injection Ratio Variation
Injection
Ratio
(%)
inletm
(kg/s)
dP
(Pa)
dT
(K)
mC
(-)
c
(-)
Dry 0.16730 159716 358.34 0.00245147 1.5763
0.5 0.17031 160008 352.6 0.00246798 1.5792
1 (Base Case) 0.17246 160279 346.54 0.00248654 1.5818
1.5 0.17304 160437 343.6 0.00249382 1.5834
-5
-4
-3
-2
-1
0
1
2
3
4
5
0 0.5 1 1.5
Injection Ratio (%)
Ch
an
ge
(%
)
AMF
Torq
Pd
S.P.
Td
Fig. (4.38) Effect of Varying Injection Ratio on Performance
of the Compressor (Relative to the Dry Case)
Fig. (4.39) Effect of Varying Injection Ratio on the Operating Point
Drymm /
Dry /
1.1
1.1
2
Dry
0.5 %
1.0 %
1.5 %
Injection Ratio
Page 131
s and DiscussionResult ) 4Chapter (
115
4.4.2 Effect of Varying Injected Droplet Diameter
Droplet mean diameter decreases due to evaporation as shown in Fig. (4.40).
Figure (4.41) shows the corresponding change in droplet temperature as a result of
evaporation and compression. Complete evaporation is almost reached for the
smallest diameter, 3 micron, as shown in Fig (4.42) and (4.43). It is apparent that
higher evaporation rate, and hence smaller life time, is achieved for smaller
droplets.
0
1
2
3
4
5
6
7
1 2 3 4
Stage No. (Exit)
Mean
Dro
ple
t D
iam
ete
r (m
icro
ns)
d=3 Microns
d=5 Microns
d=7 Microns
St2 St3St1Inlet
Fig. (4.40) Mean Droplet Diameter Variation
for Three Initial Diameters
265
270
275
280
285
1 2 3 4
Stage No. (Exit)
Me
an
Dro
ple
t T
em
pe
ratu
re (
K)
d=3 Microns
d=5 Microns
d=7 Microns
St2 St3St1Inlet
Fig. (4.41) Mean Droplet Temperature for Different Diameters
Page 132
s and DiscussionResult ) 4Chapter (
116
0
0.002
0.004
0.006
0.008
0.01
0 0.2 0.4 0.6 0.8 1
Me
an
Me
tha
no
l M
as
s F
rac
tio
n Dry
d=3 Microns
d=5 Microns
d=7 Microns
Non- Dimensional Meridional Distance
Fig. (4.42) Meridional Variation of Mean Methanol Mass Fraction on
a Mid-Span Surface for Various Diameters
0
0.25
0.5
0.75
1
0 0.005 0.01 0.015
Mean Methanol Mass Fraction (Evap.)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Dry
d=3 Microns
d=5 Microns
d=7 Microns
Fig.(4.43) Spanwise Variation of Mean Methanol Mass Fraction at Exit of
Third Stage for Various Diameters.
Page 133
s and DiscussionResult ) 4Chapter (
117
The effect of varying the injected droplet diameter on air properties can
be summarized as follows:
Air temperature decreases through out the compressor as a result of
decreasing the injected droplet diameter. Figure (4.44) shows the meridional
variation of mean static temperature for various injected droplets diameters.
Figure (4.45) shows the spanwise variation of the static temperature at exit of
third stage. Decreasing the injected droplet diameter increases the distortion
in temperature in the radial direction and between the hub and the casing
surfaces.
Air pressure variation with varying droplet diameter is not considerable.
Figure (4.46) shows the meridional variation of mean static pressure at the
mid-span, while Fig. (4.47) shows its spanwise variation. In the last figure
lower discharge pressure is found for larger droplets.
Air velocity variation with the change in injected droplet diameter, like the
air pressure, is very small. Figure (4.48) shows this clearly in the meridional
direction.
Air flow angle variation with varying the injected diameter is small.
Generally, there is a small increase in the absolute air flow angle at the inlet
to the third stator with decreased droplet diameter, as shown in Fig. (4.49).
This is valid except for the case of 3 micron. In this special case the air
angle variation is very small from that of dry case. This may be attributed to
the fast evaporation rate at front stages of the compressor. This leads to little
variation in later stages. To well understand this effect, air flow angle is
plotted at inlet of first stator as shown in Fig. (4.50). This figure well
clarifies the trend without exceptions.
Page 134
s and DiscussionResult ) 4Chapter (
118
300
310
320
330
340
350
0 0.2 0.4 0.6 0.8 1
Me
an
Sta
tic
Te
mp
era
ture
(K
)Dry
d=3 Microns
d=5 Microns
d=7 Microns
Non- Dimensional Meridional Distance
Fig. (4.44) Meridional Variation of Mean Static Temperature
on a Mid-Span Surface for Various Diameters
0
0.25
0.5
0.75
1
330 335 340 345 350 355 360
Mean Static Temperature (K)
No
n-
Dim
. S
pan
wis
e D
ista
nce
Dry
d=3 Microns
d=5 Microns
d=7 Microns
Fig. (4.45) Spanwise Variation of Mean Static Temperature at Exit of Third
Stage for Various Diameters
Page 135
s and DiscussionResult ) 4Chapter (
119
90
100
110
120
130
140
150
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Sta
tic
Pre
ss
ure
(K
Pa
) Dry
d=3 Micronsd=5 Microns
d=7 Microns
Fig. (4.46) Meridional Variation of Mean Static Pressure on a Mid-Span
Surface for Various Diameters.
0
0.25
0.5
0.75
1
146 147 148 149 150 151
Mean Static Pressure (KPa)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Dry
d=3 Microns
d=5 Microns
d=7 Microns
Fig. (4.47) Spanwise Variation of Mean Static Pressure at Exit of Third Stage for
Various Diameters
Page 136
s and DiscussionResult ) 4Chapter (
121
60
80
100
120
140
160
180
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Ve
loc
ity
Ma
gn
itu
de
(m
/s) Dry
d=3 Microns
d=5 Microns
d=7 Microns
Fig. (4.48) Meridional Variation of Mean Velocity Magnitude on a Mid-Span
Surface for Various Diameters
0
0.25
0.5
0.75
1
27 28 29 30 31 32 33 34
Velocity Angle (deg)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Dry
d=3 Microns
d=5 Microns
d=7 Microns
Fig. (4.49) Spanwise Variation of Velocity Angle at Inlet of Third Stator
for Various Diameters
Page 137
s and DiscussionResult ) 4Chapter (
121
0
0.25
0.5
0.75
1
29 30 31 32 33 34 35 36
Velocity Angle (deg)
No
n-
Dim
. S
pa
nw
ise
Dis
tan
ce Dry
d=3 Microns
d=5 Microns
d=7 Microns
Fig. (4.50) Spanwise Variation of Velocity Angle at Inlet of First Stator
for Various Diameters
The effect of increasing the injected droplet diameter is exactly contrary to the
effect of increasing the injection ratio, as shown in Table (4.6) and Fig. (4.51). It is
apparent that increasing the droplet diameter reduces the effect of wet compression
on the overall parameters. So that, the compression process is assumed to approach
the dry case when injecting relatively larger droplet. This is because large droplets
have a lower evaporation rate and don’t mix well with air due to centrifugal
separation. This reduces the change in air properties which in turn makes a slight
change compressor performance. Also increasing droplet diameter causes the
operating point of the compressor to approach that of dry compression. This is
shown schematically in Fig. (4.52).
Table (4.6) Summary Results of Droplet Diameter Variation
Droplet Diameter
(µm)
inletm
(kg/s)
dP
(Pa)
dT
(K)
mC
(-)
c
(-)
Dry 0.16730 159716 358.34 0.00245147 1.5763
3 0.17365 160436 346.24 0.00249809 1.5834
5 0.17246 160279 346.54 0.00248654 1.5818
7 0.17095 160099 348.71 0.0024755 1.5801
Page 138
s and DiscussionResult ) 4Chapter (
122
-5
-4
-3
-2
-1
0
1
2
3
4
5
1 3 5 7
Droplet Diameter (Microns)
Ch
an
ge
(%
)
AMF
Torq
Pd
S.P.
Td
Fig. (4.51) Effect of Varying Injected Droplet Size on Performance
of the Compressor ( Relative to the Dry Case )
Fig. (4.52) Effect of Varying Injected Droplet Size
on the Operating Point
Drymm /
Dry /
1.1
1.1
2
Dry
d= 7 µm
= 5 µm
= 3 µm
Page 139
s and DiscussionResult ) 4Chapter (
123
4.4.3 Effect of Droplet-Droplet Collision (agglomeration)
Droplet agglomeration is detected especially at rear stages of the compressor
as shown in Fig. (4.13). This is apparent from the droplet color which represents
the diameter. Its effect is some what dangerous, especially when initially injecting
large droplets. The droplets grow in size due to coalescence. These larger droplets
impact the blades causing severe erosion problems and exerting a braking torque
which countering the benefits of evaporation in front stages. In the present study,
agglomeration effect is not that dangerous due to small injection rates and small
initial diameters. Therefore, it is expected that the variation in both droplets and air
properties due to agglomeration is not considerable.
To quantify the effect of agglomeration on the development of the droplet size
through out the compressor, and hence air properties, the coalescence is forbidden
by turning the collision model off. This is valid as the outcome of collision is either
coalescence or grazing. The base case is resolved with the collision model being
deactivated and the results are compared with that where collision is activated.
According to the resulting outputs, the following effects can be identified:
(a) Effect of agglomeration on spray properties.
Figure (4.53) shows the droplets tracks through out the domain in the absence
of collision effect. Carrier evaporation and decrease in diameter is noticed as
agglomeration is deactivated and complete evaporation is achieved. This result is
also noticed from Fig. (4.54) which compares the droplets mean diameter at the end
of each stage in both cases. The actual size distribution of droplets at the sampling
planes is displayed in both cases, as shown in Fig. (4.55).
Page 140
s and DiscussionResult ) 4Chapter (
124
Fig.(4.53) Droplet Tracks Through the Domain Colored with Droplet Diameter
without Collision (5µm Initial Diameter, 1% Injection Ratio, No Collision )
0
1
2
3
4
5
1 2 3 4
Stage No. (Exit)
Me
an
Dia
me
ter
(mic
ron
s)
Collision
No Collision
St2 St3St1Inlet
Fig. (4.54) Mean Droplet Diameter at Exit of Stages
with and without Collision
Page 141
s and DiscussionResult ) 4Chapter (
125
Base Case with Collision Base Case Without Collision
St1
St2
St3
Fig. (4.55) Droplet Diameter Distribution at Exit of Each Stage with and without
Collision in the Base Case (5 µm, 1 % Injection Ratio)
Mean =3.86 µm
Mean =2.35 µm
Mean =2.48 µm
Mean = 3.47 µm
Mean = 1.74 µm
Page 142
s and DiscussionResult ) 4Chapter (
126
(b) Effect of agglomeration on air properties.
For the small liquid mass flow and small injected droplets considered in this
study, agglomeration effect is not dangerous. Its effect on air properties is also not
considerable. Figure (4.56) shows the effect of agglomeration on temperature
distribution through out the compressor. Despite being the most sensitive variable
in this study, temperature is slightly reduced due to agglomeration prevention (no
collision). This slight reduction in temperature is due to higher evaporation rate
which is resulted from smaller diameters of droplets in absence of agglomeration.
All other variables are expected to undergo no change due to agglomeration (under
considered conditions).
300
310
320
330
340
350
0 0.2 0.4 0.6 0.8 1
Non- Dimensional Meridional Distance
Me
an
Sta
tic
Te
mp
era
ture
(K
) Collision
No Collision
Fig. (4.56) Meridional Variation of Mean Static Temperature on
a Mid-Span Surface with and without Collision.
4.5 COMPARISON WITH EXPERIMENTAL WORK
Few experimental work has been carried out by researchers on the
phenomenon of wet compression. The most comprehensive work was carried out
by Baron et al. (1948). They considered a turbojet engine with 11 stages
compressor. They used a mixture of water and Alcohol as an evaporative media.
Page 143
s and DiscussionResult ) 4Chapter (
127
Com
pre
ssor-
dis
ch
arg
e te
mp
eratu
re,
oR
Figure (4.57) shows the change in the compressor discharge temperature with
the quantity of mixture injected. This behavior has the same trend as that found in
this work, which has been presented in Fig. (4.38) for the variable (Td) which
represents the compressor discharge temperature in this work. Also they measured
the radial variation of temperature from the hub to the casing. Figure (4.58) shows
the outcome of these measurements. Increasing the injected coolant mass flow rate
causes an increase in temperature distortion in radial direction. Again this result is
consistent with that has been found in this work, as shown in Fig. (4.33)
Although there is a difference in the compressor specifications and the injected
materials however the results are still indicative for the effect of wet compression
on the compressor performance.
Injected water flow, Ib/s
Fig. (4.57) Compressor-Discharge Temperature for Different Water
and Alcohol Injection Rates (Baron et al., 1948)
Page 144
s and DiscussionResult ) 4Chapter (
128
Radial distance across compressor-discharge annulus from
outside wall, in. ( No injected alcohol flow)
Co
mp
ress
or-
dis
ch
arg
e te
mp
eratu
re,
oR
Fig. (4.58) Compressor-Discharge Radial Temperature Variation for
Different Water injection rates (Baron et al., 1948)
Casi
ng S
urf
ace
Page 145
129
CHAPTER 5
SUMMARY AND CONCLUSIONS
5.1 SUMMARY
A numerical model has been developed to simulate the wet compression
process of methanol droplets in a three stage axial flow compressor. The model is
three dimensional, viscous, turbulent, and unsteady flow model with full coupling
between the droplets and the air flow. The commercial code FLUENT has been
used in the simulation.
The air flow field is solved first to study the dry performance of the
compressor. Dry performance is analyzed in terms of air properties variation along
the compressor, the compressor specific power, and the compressor characteristics.
Methanol droplets are then introduced and the flow field is resolved with droplet
trajectory calculations. The effect of wet compression on the performance of the
compressor is studied. A parametric study is performed to study the effect of some
controlling parameters (injection ratio and droplet size) on the efficiency of wet
compression process and hence on the compressor performance. Also, the
importance of considering droplet collision in prediction has bee highlighted. The
model is considered a guide for subsequent validated numerical models. It is the
first three dimensional model deals with the wet compression process nearly from
its all aspects. Only due to lack of resources and data, the model is limited to this
small number of stages. This in turn limits the range of studied variables which
simplified the analysis and unintentionally avoided the investigation of some
expected problems like blade erosion, surge margin, and stage mismatching. These
limitations have to be removed to full cover the topic of wet compression
comprehensively with its related and expected problems.
Page 146
Summary and Conclusions ) 5Chapter (
131
5.2 CONCLUSIONS
According to the computational study carried out for wet compression using
methanol droplets in axial compressor, the following conclusions can be drawn:
1. Three dimensional, unsteady, turbulent and viscous flow model of a three stage
axial flow compressor has been developed based on the “Fluent” CFD code.
The model accounts for droplet-flow, droplet-droplet, and droplet-wall
interactions. The model considered droplet breakup, turbulent dispersion,
collision and evaporation. This detailed computational model offered a
powerful tool to analyze in details the impact of wet compression on the air flow
characteristics as well as changes in the compressor performance.
2. Although the study is carried out for a short compressor and covers only three
compressor stages, due to the highly computational burden, yet this enabled
assessing the impact of wet compression in much detail. For larger compressor
extensive computational resources are needed.
3. Since the design details of compressors are restricted by each manufacture and
not publicly available, to assess the impact of wet compression on specific
compressor, specific program dedicated to each manufacture is needed. The
developed model enables a powerful tool to simulate any compressor whenever
the detailed data of this compressor is available.
4. Use methanol droplet for wet compression offers four advantages over wet
compression using water droplets.
5. Injecting methanol with a rate of 1 % of the dry air mass flow rate causes
reduction in the compressed air temperature in both axial and radial directions.
The total discharge temperature is decreased by 3.3 % after the third stage. This
reduces the compressor consumed specific power by 1.6 % compared with dry
Page 147
Summary and Conclusions ) 5Chapter (
131
compression. Larger reduction in consumed specific power is expected with
more number of stages.
6. Due to the reduction in the compressed air temperature, air density increases.
On the other hand minor changes in air velocity and air flow angles distribution
through the compressor are happened. This leads to an increase in the air mass
flow rate.
7. Wet compression result in slight increase in the pressure ratio. Considering this
and the increase in the mass flow rate, wet compression results in shifting the
operating point of the compressor toward the surge line.
8. Considering methanol as a polar liquid an electrostatic charge could build up on
the compressor component, when it is used as evaporative coolant in wet
compression. Grounding the compressor is highly recommended to avoid any
spark due to the discharge of the electrostatic charge.
9. Increasing the injected droplet size minimizes the benefits of wet compression
because small droplets have a higher evaporation rate than large droplets. So
that, reduction in discharge temperature and consumed specific power are
inversely proportional to the injected droplet diameter.
10. Maximum droplet size is limited to small values (7 microns) to avoid centrifugal
separation of droplets and minimizes the probability of erosion.
11. Regarding the effect of droplet-droplet collision, it has a great effect on droplet
agglomeration. Agglomeration is detected at the later stages of the compressor
which causes a growth in droplet diameter and increases the probability of
erosion. So that, small droplets have to be injected at inlet of compressor to
avoid large droplet formation at the end.
Page 148
Summary and Conclusions ) 5Chapter (
132
5.3 RECOMMENDATIONS FOR FUTURE WORK
Wet compression is a promising power augmentation technique but it still
needs more research for better understanding and enhancement. All the problems
have to be well studied to reach to a safe and reliable power augmentation
technique. Some research points are recommended for future work. These can be
listed as follows:
Complete performance analysis has to be conducted to study the effect of wet
compression on the gas turbine unit performance.
Using different atomizer models is required to study the effect of atomization
characteristics and mixing on the efficiency of the wet compression process.
The problem of blade erosion requires a lot of experimental and numerical
studies and its effect on the compressor and the gas turbine unit performance
need to be evaluated.
Page 149
133
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A 1
APPENDIX A
MODELING FLOWS IN MOVING ZONES
USING FLUENT
A1 INTRODUCTION
FLUENT solves the equations of fluid flow and heat transfer, by default, in a
stationary (or inertial) reference frame. However, there are many problems where
it is advantageous to solve the equations in a moving (or non-inertial) reference
frame. Such problems typically involve moving parts (such as rotating blades,
impellers, and similar types of moving surfaces), and it is the flow around these
moving parts that is of interest. In most cases, the moving parts render the problem
unsteady when viewed from the stationary frame. With a moving reference frame,
however, the flow around the moving part can (with certain restrictions) is modeled
as a steady-state problem with respect to the moving frame.
FLUENT's moving reference frame modeling capability allows you to model
problems involving moving parts by allowing you to activate moving reference
frames in selected cell zones. When a moving reference frame is activated, the
equations of motion are modified to incorporate the additional acceleration terms
which occur due to the transformation from the stationary to the moving reference
frame. By solving these equations in a steady-state manner, the flow around the
moving parts can be modeled and computational domain can then be made
stationary by using such rotating reference frame.
For simple problems, it may be possible to refer the entire computational
domain to a single moving reference frame. This is known as the single reference
frame (or SRF) approach. The use of the SRF approach is possible, provided the
geometry meets certain requirements. For more complex geometries, it may not be
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possible to use a single reference frame. In such cases, you must break up the
problem into multiple cells zones, with well-defined interfaces between the zones.
The manner in which the interfaces are treated leads to two approximate, steady-
state modeling methods for this class of problem: the multiple reference frame (or
MRF) approach, and the mixing plane approach. These approaches will be
discussed in Sections A3.1 and A3.2. If unsteady interaction between the stationary
and moving parts is important, you can employ the Sliding Mesh approach to
capture the transient behavior of the flow. The sliding meshing model will be
discussed in section A3.3.
A2 EQUATIONS FOR A ROTATING REFERENCE FRAME
Consider a coordinate system which is rotating steadily with angular velocity
relative to a stationary (inertial) reference frame, as illustrated in Fig. (A1). The
origin of the rotating system is located by a position vector or
.
Fig. (A1) Stationary and Rotating Reference Frames
The axis of rotation is defined by a unit direction vector a such that
a
(A1)
The computational domain for the CFD problem is defined with respect to the
rotating frame such that an arbitrary point in the CFD domain is located by a
position vector from the origin of the rotating frame. The fluid velocities can be
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transformed from the stationary frame to the rotating frame using the following
relation:
rr uVV
(A2)
where
rur
(A3)
In the above, rV
is the relative velocity (the velocity viewed from the rotating
frame), V
is the absolute velocity (the velocity viewed from the stationary frame),
and ru
is the "whirl" velocity (the velocity due to the moving frame).
When the equations of motion are solved in the rotating reference frame, the
acceleration of the fluid is augmented by additional terms that appear in the
momentum equations. Moreover, the equations can be formulated in two different
ways:
Expressing the momentum equations using the relative velocities as
dependent variables (known as the relative velocity formulation).
Expressing the momentum equations using the absolute velocities as
dependent variables in the momentum equations (known as the absolute
velocity formulation).
The exact forms of the governing equations for these two formulations are
explained in as follows:
A2.1 Relative Velocity Formulation
For the relative velocity formulation, the governing equations of fluid flow for
a steadily rotating frame can be written as follows:
Conservation of mass:
(A4)
Conservation of momentum:
(A5)
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Conservation of energy:
(A6)
The momentum equation contains two additional acceleration terms: the Coriolis
acceleration ( rV
2 ), and the centripetal acceleration ( r
). In addition, the
viscous stress ( r ) is identical to Equation 3.2 except that relative velocity
derivatives are used. The energy equation is written in terms of the relative internal
energy ( rE ) and the relative total enthalpy ( rH ), also known as the rothalpy. These
variables are defined as:
(A7)
(A8)
A2.2 Absolute Velocity Formulation
For the absolute velocity formulation, the governing equations of fluid flow for
a steadily rotating frame can be written as follows:
Conservation of mass:
(A9)
Conservation of momentum:
(A10)
Conservation of energy:
(A11)
In this formulation, the Coriolis and centripetal accelerations can be collapsed into a
single term ( V
).
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A3 FLOW IN MULTIPLE ROTATING REFERENCE FRAMES
Many problems involve multiple moving parts or contain stationary surfaces
which are not surfaces of revolution (and therefore cannot be used with the Single
Reference Frame modeling approach). For these problems, you must break up the
model into multiple fluid/solid cell zones, with interface boundaries separating the
zones. Zones which contain the moving components can then be solved using the
moving reference frame equations (Section A2), whereas stationary zones can be
solved with the stationary frame equations. The manner in which the equations are
treated at the interface lead to two approaches which are supported in FLUENT:
Multiple Rotating Reference Frames
o Multiple Reference Frame model (MRF)
o Mixing Plane Model (MPM)
Sliding Mesh Model (SMM)
Both the MRF and mixing plane approaches are steady-state approximations,
and differ primarily in the manner in which conditions at the interfaces are treated.
These approaches will be discussed in the sections below. The sliding mesh model
approach is, on the other hand, inherently unsteady due to the motion of the mesh
with time.
A3.1 The Multiple Reference Frame Model (MRF)
The MRF model is, perhaps, the simplest of the two approaches for multiple
zones. It is a steady-state approximation in which individual cell zones move at
different rotational and/or translational speeds. The flow in each moving cell zone is
solved using the moving reference frame equations (see Section A2). If the zone is
stationary, the stationary equations are used. At the interfaces between cell zones, a
local reference frame transformation is performed to enable flow variables in one
zone to be used to calculate fluxes at the boundary of the adjacent zone.
It should be noted that the MRF approach does not account for the relative
motion of a moving zone with respect to adjacent zones (which may be moving or
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stationary); the grid remains fixed for the computation. This is analogous to
freezing the motion of the moving part in a specific position and observing the
instantaneous flow field with the rotor in that position. Hence, the MRF is often
referred to as the "frozen rotor approach."
While the MRF approach is clearly an approximation, it can provide a
reasonable model of the flow for many applications. For example, the MRF model
can be used for turbomachinery applications in which rotor-stator interaction is
relatively weak, and the flow is relatively uncomplicated at the interface. In mixing
tanks, for example, since the impeller-baffle interactions are relatively weak, and
the MRF model can be used. Another potential use of the MRF model is to compute
a flow field that can be used as an initial condition for a transient sliding mesh.
A3.1.1 The MRF Interface Formulation
The MRF formulation that is applied to the interfaces will depend on the
velocity formulation being used. It should be noted that the interface treatment
applies to the velocity and velocity gradients, since these vector quantities change
with a change in reference frame. Scalar quantities, such as temperature, pressure,
density, turbulent kinetic energy, etc., do no require any special treatment, and thus
are passed locally without any change.
Interface Treatment: Relative Velocity Formulation
In FLUENT's implementation of the MRF model, the calculation domain is
divided into subdomains, each of which may be rotating and/or translating with
respect to the laboratory (inertial) frame. The governing equations in each
subdomain are written with respect to that subdomain's reference frame. At the
boundary between two subdomains, the diffusion and other terms in the governing
equations in one subdomain require values for the velocities in the adjacent
subdomain (see Fig. (A2)). FLUENT enforces the continuity of the absolute
velocity, , to provide the correct neighbor values of velocity for the subdomain
under consideration. (This approach differs from the mixing plane approach
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described in Section A3.2, where a circumferential averaging technique is used.)
When the relative velocity formulation is used, velocities in each subdomain are
computed relative to the motion of the subdomain. Velocities and velocity gradients
are converted from a moving reference frame to the absolute inertial frame using
Equation A12.
Fig. (A2) Interface Treatment for the MRF Model
For a translational velocity tV
, we have
(A12)
From Equation A12, the gradient of the absolute velocity vector can be shown to be
(A13)
Note that scalar quantities such as density, static pressure, static temperature,
species mass fractions, etc., are simply obtained locally from adjacent cells.
Interface Treatment: Absolute Velocity Formulation
When the absolute velocity formulation is used, the governing equations in
each subdomain are written with respect to that subdomain's reference frame, but
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the velocities are stored in the absolute frame. Therefore, no special transformation
is required at the interface between two subdomains. Again, scalar quantities are
determined locally from adjacent cells.
A3.2 The Mixing Plane Model (MPM)
The mixing plane model in FLUENT provides an alternative to the multiple
reference frame and sliding mesh models for simulating flow through domains with
one or more regions in relative motion. In the mixing plane approach, each fluid
zone is treated as a steady-state problem. Flow-field data from adjacent zones are
passed as boundary conditions that are spatially averaged or "mixed'' at the mixing
plane interface. This mixing removes any unsteadiness that would arise due to
circumferential variations in the passage-to-passage flow field (e.g., wakes, shock
waves, separated flow), thus yielding a steady-state result. Despite the
simplifications inherent in the mixing plane model, the resulting solutions can
provide reasonable approximations of the time-averaged flow field.
A3.2.1 The Mixing Plane Concept
The essential idea behind the mixing plane concept is that each fluid zone is
solved as a steady-state problem. At some prescribed iteration interval, the flow
data at the mixing plane interface are averaged in the circumferential direction on
both the stator outlet and the rotor inlet boundaries. The FLUENT implementation
uses area-weighted averages. By performing circumferential averages at specified
radial or axial stations, "profiles'' of flow properties can be defined. These profiles--
which will be functions of either the axial or the radial coordinate, depending on the
orientation of the mixing plane--are then used to update boundary conditions along
the two zones of the mixing plane interface. In the examples shown in Fig.(A3) and
(A4), profiles of averaged total pressure ( oP ), direction cosines of the local flow
angles in the radial, tangential, and axial directions ( Ztr ,, ), total temperature
( oT ), turbulence kinetic energy ( k ), and turbulence dissipation rate ( ) are
computed at the rotor exit and used to update boundary conditions at the stator inlet.
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Likewise, a profile of static pressure ( sP ), direction cosines of the local flow angles
in the radial, tangential, and axial directions ( Ztr ,, ), are computed at the stator
inlet and used as a boundary condition on the rotor exit. Passing profiles in the
manner described above assumes specific boundary condition types have been
defined at the mixing plane interface. The coupling of an upstream outlet boundary
zone with a downstream inlet boundary zone is called a "mixing plane pair''.
Fig.(A3) Axial Rotor-Stator Interaction
(Schematic of the Mixing Plane Concept)
Fig.(A4) Radial Rotor-Stator Interaction
(Schematic of the Mixing Plane Concept)
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A3.2.2 FLUENT's Mixing Plane Algorithm
FLUENT's basic mixing plane algorithm can be described as follows:
1. Update the flow field solutions in the stator and rotor domains.
2. Average the flow properties at the stator exit and rotor inlet boundaries,
obtaining profiles for use in updating boundary conditions.
3. Pass the profiles to the boundary condition inputs required for the stator exit and
rotor inlet.
4. Repeat steps 1-3 until convergence.
A3.3 Modeling Flows Using Sliding Meshes
In sliding meshes, the relative motion of stationary and rotating components in
a rotating machine will give rise to unsteady interactions. These interactions are
generally classified as follows:
Potential interactions: flow unsteadiness due to pressure waves which
propagate both upstream and downstream.
Wake interactions: flow unsteadiness due to wakes from upstream blade
rows, convecting downstream.
Shock interactions: for transonic/supersonic flow unsteadiness due to shock
waves striking the downstream blade row.
Where the multiple reference frame (MRF) and mixing plane (MP) models are
models that are applied to steady-state cases, thus neglecting unsteady interactions,
the sliding mesh model cannot neglect unsteady interactions. The sliding mesh
model accounts for the relative motion of stationary and rotating components.
In the case of the sliding mesh, the motion of moving zones is tracked relative
to the stationary frame. Therefore, no moving reference frames are attached to the
computational domain, simplifying the flux transfers across the interfaces.
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A3.3.1 Sliding Mesh Theory
The sliding mesh model allows adjacent grids to slide relative to one another.
In doing so, the grid faces do not need to be aligned on the grid interface. This
situation requires a means of computing the flux across the two non-conformal
interface zones of each grid interface. To compute the interface flux, the
intersection between the interface zones is determined at each new time step. The
resulting intersection produces one interior zone (a zone with fluid cells on both
sides) and one or more periodic zones. If the problem is not periodic, the
intersection produces one interior zone and a pair of wall zones (which will be
empty if the two interface zones intersect entirely).
In the example shown in Fig. (A5), the interface zones are composed of faces
A-B and B-C, and faces D-E and E-F. The intersection of these zones produces the
faces a-d, d-b, b-e, etc. Faces produced in the region where the two cell zones
overlap (d-b, b-e, and e-c) are grouped to form an interior zone, while the remaining
faces (a-d and c-f) are paired up to form a periodic zone. To compute the flux across
the interface into cell IV, for example, face D-E is ignored and faces d-b and b-e are
used instead, bringing information into cell IV from cells I and III, respectively.
Fig. (A5) Two-Dimensional Grid Interface
Page 167
ملخص الرسالة
لذلك فمن أحد . ىالتربين الغاز وحدة القدرة الناتجة من من ٪٦ ٠ - ٪٥ ٠حوالى ضاغطليستهلك ا
.وحدات هى تخفيض شغل الضاغطتلك ال أهم الطرق المسستخدمة فى زيادة القدرة الناتجة من
لاذلك . ىعاادة توزياع القادرة داخال الوحادةمان الوحادة ىلاى وترجع هذه الزياادة فاى القادرة الناتجاة
وي ااد .يسااتلزمها تغيياار فااى التيااميم حيااج أنااد يوجااد زيااادة فااى اىجهااادات الوا ااة علااى التربينااة
التاربين وحادات مان زياادة القادرة الناتجاةأهام الطارق المساتخدمة فاى أحد من "اإلنضغاط الرطب"
حياج ياتم داخل الضاغط مع الهواء -و أى سائل تبريد آخرأ - من الماءخلط كمية يتم وفيد. ىالغاز
ى فاهذا اىنخفاض .الهواءحرارةفى تخفيض درجة أثناء اىنضغاط ملية تبخير السائلاىستفادة من ع
درجة الحرارة ين كس بدوره على شغل الضاغط الذى ينخفض أيضا مسببا زيادة فى القدرة الناتجاة
. من الوحدة
فى هاذه الدراساة تام انشااء نماوذض رياضاى عاددى لدراساة تاةثير عملياة اىنضاغاط الرطا علاى آداء
لحال الم ااد ت (FLUENT)لقاد تام اساتخدام البرناامح الحساابى .ت ادد المراحالمضاغط محاورى
مضطر داخل ضاغط محورى ذو ثالج مراحال، غير مستقر، لزض وريان ثالثى األب ادسالحاكمة ل
عملية اىنضغاط الرط عن طريق حقن وتتبع عادد مان طارات الكحاول الميثيلاى ةمت محاكالقد ت.
ويةخاذ النماوذض فاى اىعتباار التاةثير المتباادل باين القطارات .لدراسة تةثير تبخرها على أداء الضاغط
يستخدم النموذض األسلو ال شوائى . ريش الضاغطوالهواء والقطرات وب ضها الب ض والقطرات و
.ى محاكاة التيادم البينى للقطراتى محاكاة تشتت القطرات نتيجة الحركة المضطربة للهواء وفف
بحسا خواص الهواء ودراسة تغيرهاا لدراسة آداء الضاغط و د تم دراسة السريان فى الحالة الجافة
أخرى ثم أعيد حسا الخواص مرة . المستهلكة فى اىنضغاط النوعية داخل الضاغط وحسا القدرة
و اد تام . ب د حقن القطرات وتتب ها داخل الضااغط لدراساة تاةثير تبخار القطارات علاى آداء الضااغط
كمياة الساائل المحقاون، حجام ) الهاماة رامترياة لتحدياد تاةثير مجموعاة مان المتغياراتاىجراء دراسة ب
ى آداء بالتااالى علااعلااى عمليااة اىنضااغاط الرطاا و (القطاارات المحقونااة، و تااةثير تجمااع القطاارات
.الضاغط المحورى
تاام ىسااتخدام ااد علاى الاارغم ماان شاايوا ىسااتخدام المااء كوساايط للتبريااد فااى اىنضااغاط الرطا ى أنااد
.لكحول عن الماءالتى يتميز بها ا يرجع ذلك ىلى المميزات ال ديدةو. الكحول الميثيلى فى هذه الدراسة
. كمااا أنااد متطاااير يسااهل تبخيااره. طى ريااش الضاااغ يسااب أى ياادأ أو تفكاال فاافااالكحول الميثيلااى
Page 168
كوسيط للتبريد فى اىنضغاط الرط فهاو يساتخدم فاى الو ات ذاتاد كو اود وباىضافة ىلى أند يستخدم
ميزة ىضاافية حياج أناد و اود متجادد مماا ويوفر ىستخدامد كو ود .ىالتربين الغاز مساعد فى وحدات
يكس الدراسة ب دا .بيئيا
.هذا ال مال فقاد تام اساتخالص ب اض اىساتنتاجات فى التى تم الحيول عليهاتائح على الن اواعتماد
ملحوظاا أوضاحت النتاائح انخفاضا فقاد نضاغاط الرطا ىففى ما يخص الدراسة التحليلية فى عملية ا ا
باا ى المتغيارات .نتيجاة لتبخار الكحاول وزيادة كبيرة فى م دل سرياند وذلك فى درجة حرارة الهواء
تةثرا واء وسرعتد و زوايا دخولد على الريش تةثرتكضغط اله وأوضحت الدراسة البرامترية .ثانويا
يزداد اىنخفااض فاى درجاة الحارارة داخال الضااغط زياادة ملحوظاة نوقأند بزيادة كمية السائل المح
غط رياد زياادة فاى كمياة الهاواء الاداخل وضا مارة أخارى تم. وبالتالى تقل القدرة النوعية المستهلكة
.وهماا يتناسابان ماع كمياة الساائل المحقاون بمقدار أ ل الزيادة فى الضغط كانت الخروض للهواء ولكن
التبخيار وبالتاالى لقد وجد أند بزيادة طر القطرات يقال م ادف القطرات المحقونة حجم أما بخيوص
( وخيويااا اىنخفاااض فااى درجااة الحاارارة) التغياار فااى خااواص الهااواء داخاال الضاااغط ريقاال مقاادا
على عكس ماتم ريده فى حالة زيادة كمية وبالتالى تقل الفائدة المرجوة من عملية اىنضغاط الرط
وخيويا بخيوص عملية تجمع القطرات فقد وجد أن هناك ابلية لتجمع القطرات. السائل المحقون
.حجما ربعند المراحل األخيرة فى الضاغط لتتنح طرات أك
تكتس هذة الدراسة أهمية خاية فى مجال اىنضغاط الرط حيج أنها اشاتملت علاى نماوذض ثالثاى
األب اد يةخذ فى اىعتبار التةثير المتبادل باين القطارات والهاواء والقطارات وب ضاها الاب ض كماا أناد
لااك كلااد بخااال علااى مسااار القطاارات داخاال الضاااغط ذ والااريش يةخااذ فااى اىعتبااار تااةثير الحااوائط
وذلاك يفاتا الباا لدراساة تفيايلية للمشااكل . م بال ذلاكدالنماذض الحسابية البسيطة التى كانت تساتخ
ويمهد الطريق ىستخدام الطرق ال ددية فى دراسة أداء المتو ع حدوثها مثل التفكل فى ريش الضاغط
للماء فى اىنضغاط الرطا مماا كما أنها ىشتملت على ىستخدام الكحول الميثيلى كبديل .المحرك ككل
.لد من مميزات سبق ذكرها
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داء األعلى تمثيل حسابى للتأثير اإلنضغاطى الرطب والتآكل لضاغط محورى
رسالة الميكانيكية القوى ضمن متطلبات الحصول على درجة الماجستير فى فى هندسة ةمقدم
المهندسمن رضا دمحم جاد رجب
وى الميكانيكيةهندسة القالمعيد بقسم جامعة الزقازيق -كلية الهندسة
لجنة الحكم والمناقشة التوقيع
د دمحم مصطفى التلبانى.أ
سم هندسة القوى الميكانيكية جام ة حلوان –كلية الهندسة
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(مشرفا ) د أحمد فايز عبدالعظيم.أ
سم هندسة القوى الميكانيكية جام ة الز ازيق –كلية الهندسة
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د دمحم محروس شملول.أ
سم هندسة القوى الميكانيكية جام ة الز ازيق –كلية الهندسة
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الزقازيق جامعة٨٠٠٢
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جامعة الزقازيق ةــة الهندسـكلي
هندسة القوى الميكانيكية قسم
الرطب على األ داء ىلتأثير اإلنضغاطل حسابىتمثيل والتآكل لضاغط محورى
رسالة الميكانيكية القوى ضمن متطلبات الحصول على درجة الماجستير فى هندسة ةمقدم
المهندس من رضا دمحم جاد رجب
هندسة القوى الميكانيكيةالمعيد بقسم جامعة الزقازيق -كلية الهندسة
المشرفون
السيد أحمد فايز عبدالعظيم ./د.أ حافظ عبدالعال السلماوى /.د.م.أ
دمحم حسن جبران/ د هندسة القوى الميكانيكيةقسم
جامعة الزقازيق -كلية الهندسة
الزقازيق٨٠٠٢