m.sc.thesis-reda ragab-2008

Zagazig University

Faculty of Engineering

Mechanical Power Engineering Department

Numerical Simulation for the Impact of Wet

Compression on the Performance and Erosion

of an Axial Compressor

A thesis

Submitted in Partial Fulfillment for the Requirements of the

Degree of Master of Science in Mechanical Power Engineering

by

Reda Mohammed Gad Ragab

Supervisors

Prof. Dr. Ahmed Fayez Abdel Azim

Asocc. Prof. Hafez El-Salmawy

Dr. Mohammed Gobran

Mechanical Power Engineering Department

Faculty of Engineering

Zagazig University

Zagazig, Egypt

2008

Approval Sheet

"Numerical Simulation for the Impact of Wet

Compression on the Performance and Erosion

of an Axial Compressor"

A thesis

Submitted in Partial Fulfillment for the Requirements of the

Degree of Master of Science in Mechanical Power Engineering

by

Reda Mohammed Gad Ragab

Approved by

Examiners:

Signature

1- Prof. Dr. Mohammed Mostafa El-Telbany

Mechanical Power Engineering Department.

Faculty of Engineering.

Helwan University

2- Prof. Dr. Ahmed Fayez Abdel Azim (Supervisor)



Zagazig University

3- Prof. Dr. Mohammed Mahrous Shamloul



Zagazig University

Zagazig

2008

iii

Acknowledgments

Thanks to Allah who gave me the patience to complete this work. I would like

to express my deep appreciation to my supervisors Prof. Dr. Ahmed Fayez Abdel

Azim, Dr. Hafez Elsalmawy, and Dr. Mohammed Gobran for their guidance and

support through the work on this thesis.

I would also like to thank Dr. Tarek Khass and all engineers in mechanical

power department.

I would like to express my deep appreciation to my parents, brothers, and wife

for their constant encouragement, support, Doaa and patience.

iv

Abstract

The compressor of the gas turbine set consumes around 50 %-60 % of the

power generated by its turbine. Reducing the power consumed by the compressor

increases the net power produced by a gas turbine set. This power gain is attributed

to the redistribution of the power flow within the set. Therefore, this power

increase does not accompanied with increase in thermal or mechanical stresses

within the set. One of the most common technologies for the augmentation of the

gas turbine power is wet compression. Wet compression can be achieved by

introducing liquid droplets into the compressor. Droplets evaporation during

compression process has what could be called micro-inter-cooling effect. This

leads to a reduction in the compressor consumed power.

In this study a numerical model is developed to study the effect of wet

compression on the performance of axial compressors. A commercial CFD code,

FLUENT, is used to solve the governing equations in a three dimensional, unsteady,

and turbulent flow simulation of a three stage axial flow compressor. Liquid

droplets are introduced as a dispersed phase and are tracked in a Lagrangian frame

to simulate the wet compression process. The model accounts for droplet-flow,

droplet-droplet, and droplet-wall interaction. Turbulence phenomenon is treated

using the RNG k turbulence model. The effect of turbulence on the dispersion

of droplets is taken into account using a stochastic model.

The flow field is solved in the dry case and the compressor performance is

analyzed in terms of; variation of air properties, characteristics of the operating

point, and consumed specific power. Performance change due to wet compression

is calculated. Parametric study has been performed to find out the effect of

important parameters on the compressor performance. These parameters include;

the injected coolant mass flow rate as a ratio of the dry air mass flow rate (injection

ratio), the droplet size, and the effect of droplet-droplet interaction.

v

Although water is commonly used for wet compression, methanol has been

considered in this work. This is due to its advantages over water. These advantages

include; non corrosive effect, lower erosion impact, higher volatility, and combined

use for both inlet duct cooling /wet compression and a supplementary fuel to the gas

turbine. The later is making advantage of the nature of methanol as a renewable

fuel.

Regarding the effect of injection ratio, it is found that increasing the injection

ratio causes a reduction in temperature in both axial and radial directions which in

turn causes a reduction in specific power. Air pressure, velocity, and flow angles

distribution within the compressor are slightly changed in both axial and radial

directions. Inlet air mass flow and discharge pressure are both increased, yet the

increase in discharge pressure is small. Regarding the effect of droplet size on the

performance of the compressor, it is found that increasing the injected droplet

diameter has an adverse effect on droplet evaporation rate and hence on specific

power. Its effect is exactly in contrary to that of injection ratio. It can be stated that

increasing the droplet size reduces the benefit of wet compression. Regarding the

effect of droplet-droplet interaction, high tendency of agglomeration is detected and

small droplets tend to increase in size especially at rear stages. Droplet

agglomeration increases as a result of higher loading ratio.

vi

Contents

Title Page

ACKNOWLEDGMENTS ……………………………………………………… iii

ABSTRACT…………………………………………....………..…….………...... iv

CONTENTS………………………..……………………………………..……..... vi

LIST OF TABLES……………………………………………….…….………… viii

LIST OF FIGURES……………………………………..…………….………..... ix

NOMENCLATURE……………………………………..…………….…………. xiv

CHAPTER (1): INTRODUCTION

1.1 BACKGROUND…….……………………………………..…….…….. 1

1.2 EVAPORATIVE COOLING METHODS……….……………….…... 4

1.2.1 Evaporative Cooling Theory………………………....………… 4

1.2.2 Wetted-Honeycomb Evaporative Cooler…………………..…. 5

1.2.3 Inlet Fogging……………………………………….………….... 6

1.3 INLET AIR CHILLING…………..…………………………………..… 7

1.4 LIQUEFIED GAS VAPORIZERS…………..……………….……....… 8

1.5 HYBRID SYSTEMS……..………………………………..…………….. 8

1.6 WET COMPRESSION / OVERSPRAY COOLING.............................. 9

1.7 OBJECTIVES AND METHODOLOGY ……………………..……... 15

CHAPTER (2): LITERATURE REVIEW

2.1 INTRODUCTION……………………………………………...………… 16

2.2 WET COMPRESSION ………………………………………..………… 17

2.3 DROPLET EVAPORATION ……………………………………..…..… 24

2.4 DROPLET INTERACTION …………………………………………..… 26

2.5 EROSION ……………………………………….……………………… 29

2.6 TWO PHASE PREDICTION APPROACHES…………………...…...… 31

2.7 NUMERICAL SIMULATION OF AXIAL COMPRESSORS..........…… 33

2.8 BLADE ROW INTERACTION…………………………………….….… 36

2.9 DISCUSSION OF PREVIOUS WORK ……………………………. 43

vii

CHAPTER (3): LITERATURE REVIEW

3.1 INTRODUCTION……………………………………………………..… 46

3.2 GOVERNING EQUATIONS ………………………………………….. 46

3.2.1 Carrier Phase Governing Equations ……………………….… 47

3.2.2 Auxiliary Equations……………………………………….. 50

3.2.3 Dispersed Phase Governing Equations……………………..… 50

3.3 SUB-MODELS…………………………………………….……….…… 53

3.3.1 Turbulence Modeling……………………………………....... 54

3.3.2 Near-Wall Treatment for Turbulent Flows…………..…..….. 58

3.3.3 Coupling Between Dispersed and Carrier Phase…………..… 60

3.3.4 Turbulent Dispersion of Droplets…………………………….. 62

3.3.5 Droplet Evaporation Model………………………………….. 63

3.3.6 Droplet Collision Model…………………………………..…… 65

3.3.7 Droplet Breakup Model………………….……………………. 66

3.3.8 Droplet-Wall Interaction Model………………….…………… 67

3.4 NUMERICAL SOLUTION…………………………………..….….…… 69

3.5 PHYSICAL MODEL………………………………………..….….. 72

3.6 COMPUTATIONAL MODEL…………………………..……….….…… 75

3.7 MESH GENERATION………………………………….……...……… 75

3.8 NUMERICAL CALCULATIONS...…………………………..……… 77

CHAPTER (4): RESULTS AND DISCUSSION

4.1 INTRODUCTION…………………………………….……....………… 83

4.2 DRY PERFORMANCE ………………...……………………………… 84

4.3 WET BASE CASE…………………………..…………………………… 93

4.4 PARAMETRIC STUDY………………………………………………… 105

4.5 COMPARISON WITH EXPERIMENTAL WORK…………………. 126

CHAPTER (5): SUMMARY AND CONCLUSIONS

5.1 SUMMARY……………………………………………....…………...… 129

5.2 CONCLUSIONS ………………………………………….…….……… 130

5.3 RECOMMENDATIONS FOR FUTURE WORK………………..…… 132

REFERENCES ………………………………………………………….….…… 133

APPENDIX (A) ………………………………………….……………….……… 140

viii

List of Tables

Table Title Page

1.1 Inlet Air Cooling Techniques………….………………………………….. 3

2.1 Axial Compressor Simulation Models……………………………………. 33

2.2 Levels of Blade Row Interaction Modeling Complexity………………… 38

3.1 Values of the constants in the RNG k model……………..….............. 56

3.2 Comparison of a Spring Mass System to a Distorting Droplet…………… 66

3.3 Constants for the TAB model……………………..……………………... 67

3.4 Section Coordinates of Blades in Percentage of Chord…………..………. 73

3.5 Compressor Blade Data………...…………………………………………. 74

3.6 Boundary Conditions……………………………………………………… 79

3.7 Geometrical Modifications for Unsteady Calculations………………..….. 80

4.1 Summary of Dry Case Average Results at Operating Point …….……….. 85

4.2 Values of the Parameters Considered in the Base Case………..…………. 93

4.3 Summary of Wet Compression Results Compared with Dry Results…….. 103

4.4 Test Matrix Parameters Values…………………………………………… 105

4.5 Summary Results of Injection Ratio Variation…………………………. 114

4.6 Summary Results of Droplet Diameter Variation…………...……………. 121

ix

List of Figures

Figure Title Page

1.1 Change in Compressor Operating Point at High Ambient Temperature….. 2

1.2 T-S Diagram on a Hot Day …………………………………….................. 2

1.3 Psychrometric Chart………………………………………………………. 5

1.4 Effect of Evaporative Cooler on Available Output- 85 % Effectiveness. 5

1.5 Traditional Evaporative Cooler Section.………………….…………...... 6

1.6 Typical Fogging System Diagram ……………………………………… 7

1.7 Mechanical Chilling Schematic for Turbine Inlet Air Cooling ………….. 8

1.8 Wet Compression ( High Fogging) System Layout……….……………… 10

1.9 Ambient Temperature Effect on The Power Gains for Combustion

Turbines………………………………………………………………… 11

1.10 Limits of Operation with Wet Compression……………………..………. 13

2.1 Limits for Splashing and Deposition of Droplets (Mundo et al., 1995)…. 27

2.2 Schematics of: (A) The Major Physical Phenomena Governing Film Flow

(B) The Various Impingement Regimes Identified in the Spray-Film

Interaction Model. (Stanton and Rutland, 1998)…….…….……….. 28

2.3 Velocity Vector and Locus of Water Droplet Inside the Compressor

(Utamura et al., 1999)……………………………………….……………. 30

2.4 Droplet Trajectories in a Spray …………………….………………..…… 31

2.5 Distribution of Droplet Parcels in a Spray Field.……………..………….. 32

2.6 Unsteady Blade Row Interaction Mechanisms……………………..…….. 37

3.1 Types of The External Forces Exerted on The Droplet……..………..…… 51

3.2 Universal Laws of The Wall (Fluent, 2006)……………………….…….. 58

3.3 Near-Wall Treatments in FLUENT………………………………...…….. 58

3.4 Outcomes of Collision…………………………………………………….. 65

x

3.5 "Wall-Jet'' Boundary Condition for the Discrete Phase………………….. 68

3.6 Flow Chart of the Solution Procedure………………………………...….. 70

3.7 Coupled Discrete Phase Calculations……………………………………... 71

3.8 NACA Eight-Stage Axial Flow Compressor…………..………………… 72

3.9 Schematic of The Compressor…………………………………………… 72

3.10 The Computational Domain ………………………..……………………. 75

3.11 First Rotor Surface Mesh…………………………………………………. 76

3.12 First Rotor Mesh. (Zoomed)………………………………………………. 76

3.13 Grid of The First Three Stages of the Compressor (Repeated)...………… 77

3.14 Pressure Coefficient at Second Stator Mid-Span for Three Mesh

Densities…………………………………………………………………... 78

3.15 Averaged Static Pressure Variation at Domain Mid-Span for Three

Meshes.......................................................................................................... 78

3.16 Convergence History of Area-Weighted Average of Total Temperature at

Domain Exit………………….…………………………………........… 82

3.17 Convergence History of Area-Weighted Average of Total Pressure at

Domain Exit…………………………………….………………………… 82

4.1 Dry Compressor Characteristics at Design Speed (Relative to the dry

Operating Point.)....................................................................................... 84

4.2 Meridional Variation of Static Pressure (PS) and Total Pressure (PO) at

Mid-Span………....…………….................................................................. 87

4.3 Meridional Variation of Static Temperature (Ts) and Total Temperature

(TO) at Mid-Span……………...........................................................……... 87

4.4 Meridional Variation of Absolute Velocity Magnitude at Mid-Span……. 88

4.5 Meridional Variation of Absolute Mach Number at Mid-Span. ………… 88

4.6 Spawise Variation of Total Pressure at Exit of Each Blade Row Referred

to That at the Compressor Inlet………………………….……………….. 89

4.7 Spanwise Variation of Total Temperature at Exit of Each Blade Row

Referred to That at the Compressor Inlet ……………….……………….. 89

xi

4.8 Spanwise Variation of Static Temperature at Exit of Each Blade Row....... 90

4.9 Spanwise Varaiation of Static Pressure at Exit of Each Blade Row…....… 90

4.10 Contours of Static Pressure at the Whole Compressor (3D View)………. 91

4.11 Contours of Static Pressure at a Radial Section (R=6 in) for Three

Passages (Repeated)………………….………….........................……… 91

4.12 Contours of Static Pressure at Different Axial Locations along the

compressor ………………………….....................……….…………….. 92

4.13 Droplet Tracks Through The Domain Colored with Droplet Diameter

(Base Case: 5µm Initial Diameter, 1% Injection Ratio)……..………….. 95

4.14 Mean Droplet Diameter at Exit of Stages (at Sampling Planes)………….. 95

4.15 Droplet Diameter Distribution at Exit of Each Stage ..........……………… 96

4.16 Mean Droplet Temperature at Exit of Each Stage.……….………………. 97

4.17 Meridional Variation of (Evaporated) Mean Methanol Mass Fraction on a

Mid-Span Surface….....………………………………………………… 97

4.18 Spanwise Variation of (Evaporated) Mean Methanol Mass Fraction at

Exit of Each Stage........................................................................................ 98

4.19 Contours of Methanol Mass Fraction at Exit of Each Stage.........………... 98

4.20 Meridional Variation of Mean Static Temperature on a Mid-Span Surface 100

4.21 Spanwise Variation of Mean Static Temperature at Exit of Each Stage..... 100

4.22 Meridional Variation of Mean Static Pressure on a Mid-Span Surface..... 101

4.23 Spanwise Variation of Mean Static Pressure at Exit of Each Stage……… 101

4.24 Meridional Variation of Mean Velocity Magnitude on a Mid-Span

Surface........................................................................................................ 102

4.25 Spanwise Variation of Absolute Velocity Angle at Inlet of Each

Stator….......................................................................................………… 102

4.26 Compressor Operating Point Variation in Wet Compression……………. 104

4.27 Mean Droplet Diameter for Different Injection Ratios…………….……. 106

4.28 Mean Droplet Temperature for Different Injection Ratios……..……….. 106

4.29 Droplet Diameter Distribution at Exit of Each Stage for Different

Injection Ratios …………………………………………………………… 107

xii

4.30 Meridional Variation of (Evaporated) Mean Methanol Mass Fraction on a

Mid-Span Surface for Various Injection Ratios….....…………………….. 108

4.31 Spanwise Variation of (Evaporated) Mean Methanol Mass Fraction at

Exit of Third Stage for Various Injection Ratios………...………………. 108

4.32 Meridional Variation of Mean Static Temperature on a Mid-Span Surface

for Various Injection Ratios……...…….……………………………...... 110

4.33 Spanwise Variation of Mean Static Temperature at Exit of Third Stage

for Various Injection Ratios…………………………………………….. 110

4.34 Meridional Variation of Mean Static Pressure on a Mid-Span Surface for

Various Injection Ratios………………………………………………… 111

4.35 Spanwise Variation of Mean Static Pressure at Exit of Third Stage for

Various Injection Ratios…………………..……………………………… 111


Surface for Various Injection Ratios..…………………………………….. 112

4.37 Spanwise Variation of Velocity Angle at Inlet of Third Stator for Various

Injection Ratios………...…………….............…………………………… 112

4.38 Effect of Varying Injection Ratio on Performance of the Compressor…… 114

4.39 Effect of Varying Injection Ratio on the Operating Point............................ 114

4.40 Mean Droplet Diameter Variation for Three Initial Diameters…………… 115

4.41 Mean Droplet Temperature for Different Diameters……………………… 115

4.42 Meridional Variation of Mean Methanol Mass Fraction on a Mid-Span

Surface for Various Diameters…….……………………………………… 116

4.43 Spanwise Variation of Mean Methanol Mass Fraction at Exit of Third

Stage for Various Diameters……………………………………………… 116


for Various Diameters..………………..………………………………….. 118

4.45 Spanwise Variation of Mean Static Temperature at Exit of Third Stage

for Various Diameters…………………………………………………….. 118

4.46 Meridional Variation of Mean Static Pressure on a Mid-Span Surface for

Various Diameters………………………………………………………… 119

xiii

4.47 Spanwise Variation of Mean Static Pressure at Exit of Third Stage for



Surface for Various Diameters..………………………………………….. 120

4.49 Spanwise Variation of Mean Velocity Angle at Inlet of Third Stator for


4.50 Spanwise Variation of Mean Velocity Angle at Inlet of First Stator for


4.51 Effect of Varying Injected Droplet Size on Performance of the

Compressor………………………………………………………………... 122

4.52 Effect of Varying Injected Droplet Size on the Operating Point................. 122

4.53 Droplet Tracks Through the Domain Colored with Droplet Diameter

without Collision (5µm Initial Diameter, 1% Injection Ratio, No

Collision) …………………...…………………………………………….. 124

4.54 Mean Droplet Diameter at Exit of Stages with and without Collision...…. 124

4.55 Droplet Diameter Distribution at Exit of Each Stage with and without

collision in the Base Case (5 µm, 1 %)…...........................….…………… 125


with and without Collision………………………………………………... 126

4.57 Compressor-Discharge Temperature for Different Water and Alcohol

Injection Rates (Baron et al., 1948)........................................................

127

4.58 Compressor-Discharge Radial Temperature Variation for Different Water

injection rates (Baron et al., 1948) ………………………………………..

128

xiv

Nomenclature

Symbol Definition

A Area [m2].

Cd Aerodynamic drag coefficient.

mC Moment Coefficient

C Vapor concentration [kg/m3], Specific heat [J/kg.K].

D, d Diameter [m], Mass diffusion coefficient [m2/s].

E Total energy [J/kg]

e Unit vector.

F Force [N].

h Specific enthalpy [J/kg], Convective heat transfer coefficient [W/m2.K]

fgh Latent heat [J/kg]

K Thermal conductivity, [W/m.K].

k Turbulence Kinetic Energy [m2/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].

xv

Sh Sherwood number.

Sc Schmidt number.

T Temperature, [K]., Torque [N.m]

t Time [s].

u Velocity parallel to the wall [m/s].

u , v , w Fluid fluctuating Velocities [m/s]

u Dimensionless velocity.

V Velocity, [m/sec].

We Weber number.

y The normal distance to the wall [m], Non-dimensional droplet distortion.

y Dimensionless wall distance.

jY Mass fraction of the 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.

xvi

I Inlet, term number, tensor index (1, 2, 3).

inlet Inlet of Compressor

j Term number, tensor index (1, 2, 3).

k Tensor index (1, 2, 3).

l Vector tensor.

Max Maximum

o Total conditions, reference, operating point.

P droplet, at constant pressure.

R Radial, relative, rotor, rotation.

Ref Reference.

S Surface.

T Turbulent

w Wall.

WB Wet bulb

x Component in x-direction.

Y Component in y-direction.

Z Component in z-direction.

carrier phase

Abbreviations:

AMF Air Mass Flow

B.L. Boundary Layer Mesh

DSM Domain Scaling Method

OEM Original Equipment Manufacturer

O.P. Operating Point

S.P. Specific Power

1

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND

A major disadvantage of the gas turbine based power plants is their sensitivity

to the ambient conditions. The ambient pressure can vary significantly with

elevation, but it does not usually exhibits large variation at a certain location.

Regarding humidity, the inlet mass flow rate decreases as the humidity increases.

This is because the density of water vapor is less than that of the air. Consequently,

as humidity increases the gas turbine output power decreases. However the effect

of the variation in ambient humidity is small on the gas turbine performance. Out

of all factors, the ambient temperature is the one that influences the gas turbine

engine performance significantly. Temperature exhibits significant variation over

the year. The increase of the ambient temperature decreases the air density (i.e.

mass flow rate) and consequently increases the compressor specific work. This

leads to a decrease in the engine net output power.

Changes in the ambient conditions influence the compressor operating point.

Referring to Fig. (1.1), when the compressor inlet temperature increases the

compressor operating corrected speed as well as the ratio ( 13 TT ) decreases. This

causes the operating point to move left and down, as shown in the figure, resulting

in a decrease in both pressure ratio and corrected mass flow rate. Also Fig. (1.2)

indicates that, for constant maximum temperature, the turbine exhaust temperature

and consequently the heat rate increases (thermal efficiency decreases) as the

ambient temperature increases. In addition to these, the compressor discharge

temperature increases, and the compressor discharge pressure decreases.

Consequently, the net area representing the net specific work is further decreased.

Chapter (1) Introduction

2

On average, drop by 0.5 to 0.9 % in the output power happens for every 1 Co

increase in the ambient temperature. In heavy duty gas turbines, power output loss

of approximately 20% can be experienced when ambient temperature reaches 35°C

(Bhargava and Meher-Homji, 2002). This is coupled with a heat rate increase of

about 5 %.

The compressor is the most engine component sensitive to the changes in the

ambient temperature. It consumes about 50 % to 60 % of the turbine output power

(Zheng et al., 2002). Therefore, efforts should be directed toward decreasing the

compressor consumed power. This will lead to an increase in the net output power

of gas turbine. Cooling of the inlet air to the gas turbine compressor is one of the

techniques to reduce the compression work and thereby increases the net output

power. The net output power can further increase by letting water droplets to get

into the compressor. Due to the large latent heat of water, when it evaporates

within the blade path, a thermodynamic intercooling effect is achieved. The

resulting adiabatic process causes the air temperature to drop. Since it takes less

energy to compress relatively cooler air, reduction in compressor work will be

S

Constant Firing Temperature

Lower

Pressure

Hot day

T

Fig. 1.2 T-S Diagram on a hot

day

P2

P1

Fig. (1.2) T-S Diagram on a Hot 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


3

Hot

achieved and hence an increase in net output power of the gas turbine will be

accomplished. This process is known as "wet compression".

Several air cooling techniques that are commercially available for gas turbine

power augmentation are illustrated in Table (1.1). These techniques can be divided

into the following four major categories:

• Evaporative Cooling Methods: These include wetted media and fogging

techniques.

• Inlet Air Chilling (Using Chillers): These include the use of either mechanical or

absorption chillers to cool the inlet air. These could be combined with thermal

storage to manage energy consumed by the chillers with the variation in the inlet air

temperature.

• LNG or LPG vapourisation: This technique is based on utilizing the cooling

effect resulting from the vaporization of either LNG (Liquefied Natural Gas) or

LPG (Liquefied Petroleum Gas).

• Hybrid systems: A hybrid system could be a combination of any two of the

aforementioned techniques, with consideration to the limitations of each technique.

Table (1.1) Inlet Air Cooling Techniques

Wetted Media

Fogging

Wet compression/Overspray

SwirlFlash® Technology

Evaporative Methods

Mechanical

Chillers

Absorption

Chillers

Direct Chillers

Thermal Energy Storage

Inlet Air Chilling LNG or LPG Vaporization Hybrid Systems

Inlet Air Cooling Techniques


4

It is important to mention that wet compression can be achieved by using any

of the aforementioned techniques. For example, in case of using evaporative

cooling technique, wet compression can be achieved if there is an overspray beyond

that necessary for inlet air cooling. On the other hand, in case of chiller cooling wet

compression can be achieved if cooling went below the wet bulb temperature of the

incoming air.

1.2 EVAPORATIVE COOLING METHODS

1.2.1 Evaporative Cooling Theory

Evaporative cooling process works on the principle of reducing the

temperature of an air stream through evaporation of injected water spray. The

energy for evaporation is drawn from the air stream. The result is cooler and more

humid air as shown schematically on the Psychrometric chart, Fig. (1.3). The

minimum temperature that can be achieved is limited by the wet-bulb temperature.

Practically, this level of cooling is difficult to achieve. The actual temperature is

usually higher than the wet-bulb temperature depending on both the equipment

design and atmospheric conditions. The equipment performance is expressed in

terms of effectiveness which is defined as follows:

WBDB

DBDB

TT

TT

21

21

(1.1)

Where

DBT1 = Entering air dry bulb temperature.

DBT2 = Leaving air dry bulb temperature.

WBT2 = Leaving air wet bulb temperature.

Typical evaporative cooler effectiveness is in the range from 85 % to 90 %

(Jones and Jacobes, 2002) depending on the contact area between the air and water

as well as the water droplet size. The exact increase in power available from a


5

particular gas turbine, as a result of air cooling, depends on the machine

specifications and site altitude, as well as on the ambient temperature and humidity,

as illustrated in Fig. (1.4).

1.2.2 Wetted-Honeycomb Evaporative Cooler

It was the first technique to be used for turbine inlet air cooling. In this

technique, the inlet air is exposed to a film of water in a wetted media. A honey-

comb-like medium is one of the most commonly used, as shown in Fig. (1.5).

Water splashes down on a distribution pad and then it seeps into the media. At the

same time air is passing through the media. The extent of cooling is limited by the

wet bulb temperature and it is therefore dependent on the weather with the greatest

cooling benefit is realized when employed in warm, dry climates. The effectiveness

of a traditional wetted-honeycomb cooler is somewhat low and is typically 85%

(Craig and Daniel, 2003). It is one of the lowest capital and operating cost and

requires low water quality. On the other hand, it causes a high inlet pressure drop

that degrades the engine output and efficiency and consumes large amounts of

water.

Fig. (1.3) Psychrometric Chart Fig. (1.4) Effect of Evaporative Cooler

on Available Output - 85% Effectiveness

(Jones and Jacobes, 2002)


6

1.2.3 Inlet Fogging

Fogging is a method of air cooling where demineralized water is converted

into a fog by means of high-pressure pumps and special atomizing nozzles

operating at )21070( gbar . This fog then provides cooling when it evaporates in

the air at the inlet duct of the gas turbine. This technique allows 100 %

effectiveness to be obtained at the gas turbine inlet and thereby gives the lowest

possible temperature. Droplet size is a critical factor for the efficiency of the inlet

air fogging process. Smaller droplets, in the range of 5 to 10 microns , have the

advantages of remaining airborne, higher evaporation rate and less likely to cause

erosion. A typical inlet fogging system is shown in Fig. (1.6). It consists of a high-

pressure pump skid, a nozzle array located in the intake duct after the filters, and a

PLC based control system integrated with a weather station. The advantages of the

fogging system include:

Inlet pressure drop is lower than that of evaporative media.

Potential for higher effectiveness than evaporative media (~ 95 %).

On the other hand, this technique suffers from shortcomings. These include:

Requires demineralized water and stainless steels for all wetted parts.

Higher parasitic load than evaporative media for high-pressure systems

DISTRIBUTION

Fig. (1.5) Traditional Evaporative Cooler Section

(Craig and Daniel, 2003)


7

1.3 INLET AIR CHILLING

The two basic categories of inlet chilling systems are direct chillers and

thermal energy storage. Thermal energy storage systems take the advantage of off-

peak power periods to store thermal energy in the form of ice (or chilled water) to

perform inlet chilling during periods of peak power demand. Direct chilling

systems use mechanical or absorption chilling. In these systems, inlet air is drawn

across cooling coils, in which either chilled water or refrigerant is circulated.

Accordingly, air is cooled to the desired temperature. Mechanical chillers, as

shown in Fig. (1.7), could be driven by either electric motors or steam turbines.

Absorption chiller requires thermal energy (steam or hot water) as a primary source

of energy. On the other hand it requires much less electric energy than the

mechanical chillers.

As with evaporative cooling, the actual temperature reduction from a cooling

coil is a function of equipment design and ambient conditions. Unlike evaporative

coolers cooling coils are able to lower the inlet dry-bulb temperature below the

DEMIN

WATER SUPPLY

Fig. (1.6) Typical Fogging System Diagram

(Craig and Daniel, 2003)

)


8

ambient wet-bulb temperature. The main disadvantage of inlet chilling systems is

that it consumes higher power than that needed in case of evaporative techniques.

1.4 LIQIFIED GAS VAPORIZERS

When liquefied natural gases (LNG) or liquefied petroleum gases (LPG) are

used as fuels, they need to be vaporized before entering to the gas turbine

combustor. Gas turbine inlet air can be used for providing the necessary heat for

vaporization. A reduction of 5.6°C in inlet air temperature is typical for this system

(Jones and Jacobes, 2002). Because the fuel needs to be vaporized anyway, using

this technique is considered as energy recovery into useable power.

1.5 HYBRID SYSTEMS

Hybrid systems incorporate some combination of previous technologies.

The hybrid system is optimized for a specific plant based on the power demand,

electricity prices and availability of thermal energy.

Fig. (1.7) Mechanical Chilling Schematic for Turbine

Inlet Air Cooling (Craig and Daniel, 2003)

)

Centrifugal Chilling Unit


9

1.6 WET COMPRESSION /OVERSPRAY COOLING

Early experiments on the continuous injection for large volumes of water (or

any other coolant) into a compressor inlet, which is now referred to as wet

compression, began in the early 1940's. Wet compression is a process in which

small water droplets are, intentionally, injected into the compressor inlet air in a

proportion higher than that required to fully saturate the air. The large amount of

latent heat of water when it evaporates within the blade path has a thermodynamic

intercooling effect. The resulting adiabatic process causes the air temperature to

drop. Since it takes less energy to compress relatively cooler air, there is savings in

compressor work. As mentioned before, the compressor consumes about ½ to ⅔ of

the turbine power so any saving in the compressor work will be directly reflected on

the total gas turbine output power.

Some notes must be marked when speaking about wet compression

1. Wet compression is not haphazardly spraying water into the compressor

inlet; care must be taken as there is an expensive and high precision turbine

downstream. The system must be properly integrated with the turbine and

turbine controls.

2. The technology of wet compression is often confused with that of fogging;

however in reality they are significantly different. A fogging system inject a

small amount of water to cool the air (just close to saturation), whereas a wet

compression system may inject four times the quantity injected in case of

fogging into the compressor inlet. The “excess” moisture is absorbed by the

air in subsequent compressor stages. This means that wet compression takes

the evaporative cooling effect into the compressor.

3. Wet compression system could be complementary to other turbine inlet air

cooling techniques like evaporative cooling, fogging, or chilling.


11

1.6.1 System Description

The wet compression system, shown in Fig. (1.8), consists of the following

major components:

1. A nozzle rack: a grid of nozzle arrays installed in the air intake and located

relatively close to the compressor inlet (to avoid droplet agglomeration).

2. A pump skid: to deliver the high pressure demineralized water to the nozzles.

3. Stainless steel tubing: to deliver water from the pumps to the nozzle arrays.

4. Local control unit: governs the pump skid and exchanges signals with the

engine core controller.

1.6.2 Advantages of Wet Compression over Other Power Augmentation

Technologies

Power gains from all inlet cooling technologies are limited by ambient

conditions. Evaporative cooling (media-based and fogging) systems must have a

temperature difference between the dry-bulb and wet-bulb temperatures in order for

power gains to be achieved. With Wet Compression, gains are not limited due to

increased ambient conditions. Figure (1.9) shows typical percent power gains for

Fig. (1.8) Wet Compression (High fogging) System Layout

(Cataldi et al., 2005)


11

combustion turbines, with traditional evaporative cooling, and with wet

compression. It can be seen that wet compression gives a constant increase in

power regardless of the ambient conditions. Note that wet compression is typically

not utilized in temperatures below 7 Co .

1.6.3 Challenges to Wet Compression Technology

Wet compression is a very promising technology for power augmentation but

it has some issues which have to be considered to ensure engine protection, safety

of operation and maximum benefit. These issues of particular importance are

described together with their solutions:

a) Foreign Object Damage [FOD] Considerations

With the presence of a large number of nozzles in the air stream, FOD has

high tendency to occur. The danger comes from loosening of the nozzles or

damage of the grid structure due to flow induced vibration. Regarding the

Fig. (1.9) Ambient Temperature Effect on the power Gains for Combustion

Turbines (Shepherd and Faster, 2003)

Delta T (F) Between Dry-Bulb & Wet-Bulb

Pow

er G

ains


12

loosening of the nozzles, lock wiring of the nozzles provides a line of defense.

Flow induced vibrations and poor pressure distribution may cause failure on the

structure but with conservative design, this risk can be eliminated.

b) Ice formation in the first compressor blade row.

Because of the flow acceleration within the inlet guide vanes of the

compressor, water may condense from the air stream and ice can be formed. Air

inlet cooling exacerbates this problem as it reduces the temperature at the

compressor inlet and increases the water content of the flow. Therefore, wet

compression operation is limited to a certain minimum ambient wet-bulb tem-

perature at which the system must be turned-off. Several original equipment

manufacturers (OEMs) publish a combination of relative humidity and temperatures

at which anti-icing measures are turned on. Figure (1.10) shows the corresponding

limiting curve in terms of ambient temperature and relative humidity for the GT24/

GT26 engines.

c) Induced distortion of the temperature profile at the compressor inlet.

Temperature distortion is a phenomenon where the compressor inlet

temperature differs significantly from one side to the other. As a result, the “cold”

section of the compressor runs at high aerodynamic speed and produces a high

pressure ratio as expected for a low inlet temperature. The “warm” section of the

compressor runs at a reduced aerodynamic speed but has to achieve the increased

pressure ratio prescribed by the low temperature section. Thus, the surge margin in

the “warm” section is reduced (Chaker et al., 2002, part A). Accordingly, inlet

temperature distortion ( ITD ) can be caused by the following reasons:

Malfunctions of inlet cooling systems, such as blocked nozzles.

Poor aerodynamic design of the fogging system or the air intake.

Operating wet compression system as a standalone system at low water

mass flow for extended periods of time.

Velocity profile at inlet section.


13

The following equation provides a criterion for ITD at an aero-derivative

machine. Different machines would have different criteria.

03.0

,

60min,60max,max

faceavg

avgavg

avg T

TT

T

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)


14

d) Axial compressor fouling

When good quality demineralized water is used and inlet ducts and silencers

are clean, no problems of deposits have been noted. In fact, operator experience

indicates that there is a washing effect from the fog itself. It is possible that using

fog on a nearly continuous basis for power augmentation, results in a continuous

washing effect which may result in savings of on-line wash costs.

e) Compressor blade erosion due to impingement of water droplets

Erosion resulting from water droplets impacting compressor blades has been a

concern with any system that introduces water droplets at the inlet to compressor.

One of the major advantages of wet compression systems over inlet fogging

systems is the placement of the nozzles near the compressor inlet. The potential for

droplet agglomeration and coalescence on objects within the duct are minimized.

Since the application of this technology is recent, tremendous progress has been

made in understanding the concerns with this system and steps to be taken to assure

satisfactory system performance. The GT-24 wet compression system (Sanjeev

Jolly, 2003) has been operational for more than one year for about 16 hours a day.

A borescope inspection performed during a recent outage did not show excessive

erosion compared with that normally found during scheduled maintenance.

f) Compressor casing distortion due to non-uniform water distribution

The casing temperature distribution did not appear to be impacted by wet

compression and there is no limiting factor for this. But in some cases, rubbing of

compressor blades occurred with the casing in case of higher coolant mass flow

rates.

g) Electro-static charge build-up on the compressor rotor

A grounding brush is usually installed to eliminate the possibility of electro-

static charge build-up on the rotor. This is a very important procedure if the coolant

used in wet compression is combustible like Methyl Alcohol.


15

1.7 OBJECTIVES AND METHODOLOGY OF THE PRESENT WORK.

The present work aims at numerically investigate the effect of wet

compression on the performance of a multistage axial flow compressor. This work

also explores the advantages of using Methanol as an evaporative media in wet

compression. This is attributed to its advantages as biofuel, non corrosive, volatile

and low density liquid. These characteristics offer the advantages of the dual use of

Methanol as an evaporating media for wet compression and as a primary fuel for the

gas turbine. Methanol which injected for wet compression is very lean to be used

for combustion in the gas turbine. It could be supplemented by any gaseous or

liquid fuel in the combustor of the gas turbine. Considering the advantages of

methanol as bio- and renewable fuel, additional environmental gain will be

achieved when Methanol is used.

Also Methanol is non corrosive compared with the use of water in wet

compression. Furthermore, its density is less than that of water, which ensures less

erosion due to less collision impact when the droplets impinge the compressor

blades. Add to these the high volatility of Methanol offers the chance of using it at

relatively low pressure ratio compressors.

This thesis consists of five chapters including this introductory chapter. The

next chapter presents a survey and analysis for the previous work related to the

subject. A discussion of the previous work at the end of that chapter will route and

clarify the scope of the present work. Chapter (3) presents the different aspects of

the mathematical and numerical model considered. The case studied will be

described at the end of that chapter. The obtained results will be presented and

discussed in Chapter (4). A summary of this work, the main findings, and

suggestions for the future work will be presented in Chapter (5). Necessary details

about modeling turbomachines in FLUENT are included in the appendix.

16

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

Water injection into gas turbine compressor inlets has been studied and

applied since the forties. Early studies were done by Wilcox (1950) and Hensley

(1952). Wet compression was described in detail in several text books on gas

turbines written in the 50s. Water injection was used in the older jet engines to

boost take-off thrust when aircraft were operating on hot days or from high altitude

airports. The power gain came mainly from the cooling of the intake air (i.e., lower

inlet temperature) and from the intercooling effect in the compressor. Recently,

with the advancement in high-pressure water fogging technology, wet compression

has gained popularity in the industrial gas turbine and is being applied in the power

and cogeneration industries.

Wet compression is a complex process deals with many phenomena. It

includes gas compression, droplet evaporation and droplet interactions. The

occurrence of these phenomena in a multistage axial compressor increases the

complexity of the problem. In wet compression, interaction between the droplets

and the air flow inside the compressor is taking place. This could lead into changes

in the air flow pattern inside the compressor which in turn will affect the

compressor performance. Not only this, but also droplet-droplet interaction affects

the droplet behavior inside the compressor. This is attributed to either droplet

agglomeration or droplet shuttering due to droplet collision. This will have an

impact on the compressor performance as a result of the change in the droplet

trajectory and evaporation rate. Accordingly, wet compression can be characterized

as a two phase flow problem. In the following sections, a review of the previous

Chapter (2) Literature Review

17

work about wet compression and its related topics as well as the axial compressor

simulation will be presented.

2.2 WET COMPRESSION

Baron et al. (1948), have conducted an experimental investigation of thrust

augmentation of an axial-flow turbojet engine by means of water-alcohol injection

at the compressor inlet at sea-level conditions. The exhaust nozzle was adjusted to

fix the exhaust temperature during the investigation. The engine performance was

determined at constant rotor speed and exhaust-gas temperature for various

mixtures and flow rates. The thrust augmentation by injection of water and alcohol

at the compressor inlet was limited by centrifugal separation of the injected liquid

and air in the compressor. Although the maximum thrust augmentation was

obtained at the highest water flow (6.7 % of air flow), this injection rate was

considered injurious to the engine. It caused localized hot spots in the turbine and

large radial temperature distortion. This causes rubbing of the compressor blades

on the casing. An injected water flow of 5.4 % leads to thrust augmentation of 4.15

% at a rotor speed of 7635 rpm , an exhaust gas temperature of 925 K , and an inlet

air temperature of 304 K . The injection of alcohol, at constant water injection rate,

resulted in a marked decrease in fuel flow, in addition to thrust augmentation.

Large decrease in compressor discharge temperature was observed for all water and

alcohol flows. The air mass flow and the compressor discharge pressure increased

slightly. Based on these results, they concluded that water-alcohol injection at the

compressor inlet can be used to the best advantage only when the engine inlet air

temperature is high enough and the initial relative humidity is low enough to

provide considerable evaporation of the injected liquid before compression.

Wilcox and Trout (1950) conducted a thermodynamic model to calculate the

thrust augmentation of a turbojet engine resulting from the injection of water at the

compressor inlet. This model was carried out for various amounts of water injected.

The effects of variation of flight Mach number, altitude, ambient-air temperature,


18

ambient relative humidity, compressor pressure ratio, and inlet-diffuser efficiency

are taken into account. For a typical turbojet engine, the maximum theoretical ratio

of augmented to normal thrust was 1.29. The ratio of augmented liquid

consumption to normal fuel flow for these conditions, assuming complete

evaporation, was 5.01. Both the augmented thrust ratio and the augmented liquid

ratio increased rapidly as the flight Mach number was increased and decreased as

the altitude was increased. Although the thrust augmentation possible from

saturating the compressor-inlet air is very low at flight speeds, appreciable gains in

thrust are possible at high flight Mach number. At standard sea-level atmospheric

temperature, the relative humidity of the atmosphere had a small effect on the

augmented thrust ratio for all flight speeds investigated. At sea-level and zero flight

Mach number conditions, the augmented thrust ratio increased as the atmospheric

temperature increased. Water injection therefore tends to overcome the loss in take-

off thrust normally occurring at high ambient temperatures. For very high

atmospheric relative humidities, the ambient temperature had only a small effect on

the augmented thrust ratio.

Hensley (1952) has evaluated the theoretical performance of a gas turbine with

inlet water injection of an axial-flow compressor operating at compressor pressure

ratios of 4, 8, and 16. He assumed continuous saturation throughout the

compression process. The assumption of choked turbine nozzles and a compression

efficiency at any point in the compressor depend on the evaporative cooling prior to

that point were used. Based on these assumptions, the changes in mass flow,

compressor pressure ratio, compressor work, and overall compressor efficiency

with water injection were determined. The analysis indicates that the compressor

work per unit mass of turbine gas flow is lower with inlet water injection than

without. This is valid even at low altitudes, high Mach numbers as well as high

compressor pressure ratios. Accordingly, engine output per unit mass of turbine gas

flow is greater with injection than without. Hensley’s calculations show that the

inlet temperature for some of flight conditions considered is below the freezing

point, which necessitates the addition of a nonfreezing liquid to the injected water.


19

Hill (1963) presented an analysis of the thermodynamic effects of inlet coolant

injection on axial compressor performance, in comparison with tests on turboshaft

engines. His results showed that the evaporation of the coolant inside the

compressor implies a continuous cooling of the air. This leads to a reduction in the

compression work for a given pressure ratio, and a change in the stage work

distribution. These effects lead to large augmentation of the shaft power of the

turbine engine, especially when the compressor inlet temperature is high. He also

reported an increase in compressor airflow at a given speed and pressure ratio. This

is coupled with unload of the first few stages and load the last stages more heavily.

The maximum desirable ratio of coolant to air flow may be limited by combustion

efficiency, stall, or blade rub. The results showed good agreement with

experimental results.

Ludorf et al. (1995) has extended an existing one dimensional stagewise

compressor stability analysis program to incorporate a model of humidity and

droplet evaporation. The modified program shows the extent of stage re-matching

when ingesting modest amounts of water. The water distribution through the flow

is assumed to be homogenous. The stage interactions of an aircraft engine

compressor are investigated for different environmental operating conditions. The

effects of humidity on stage loading are small while the evaporation of water causes

significant shift of the operating point. No experimental validation was performed

in this work.

Utamura et al. (1998) proposed and examined the possibilities of a new

technology, Moisture Air Turbine (MAT) cycle, of increasing the output of a gas

turbine by introducing a fine water spray into the incoming air to the compressor.

They considered the isentropic work for moist air with phase change. The

theoretical work decline was 6.8% with regard to 1% water spray by mass. They

also verified their results with an experiment using 15 MW axial flow compressor.

According to their measurement, 4% reduction in compressor work is achieved at 1

% water injection by mass. Following this, Utamura et al. (1999) had developed a


21

special spray nozzle to generate water droplets with a sauter mean diameter of 10

μm. Their calculation showed that droplets with that diameter is not seen to collide

with rotor blades and provides maximum evaporation efficiency. Experiments, on a

115 MW simple cycle commercial gas turbine, showed that injection of spray water

of 1 % to air mass flow rate would increase output power by about 10 % and

thermal efficiency by 3 % compared with that in hot summer days. The magnitude

of power increase becomes higher as ambient temperature is higher and humidity is

lower. Given the temperature profile through the compressor stages, they performed

quasi-steady heat and mass transfer calculations in terms of single water droplet.

The life time of the droplet was found to increase as the diameter increases.

The most complicated model was developed by Loebig et al. (1998). They

constructed a three dimensional aero thermal analysis model to aid in the design of

optimum water/methanol injection system, for maximum evaporation of the

multicomponet-droplets, with minimal impingement on the casing. Their model

was built on the basis of the stream line curvature method to study the 3D

compressor flow field. The model also includes computations for 3D droplet

trajectories, evaporation characteristics, and droplet impingement locations on both

the hub and casing surfaces of the compressor. The motion of the droplet is

described by the 3D Lagrangian equations. The model does not take into account

the droplet interaction with the blade. They found that the three-dimensional flow

field strongly influences droplets evaporation characteristics. The evaporation of

the droplet is mainly due to convection and it is a strong function of the droplet

Reynolds number. Computations showed that droplets with initial diameters greater

than 50 microns will impinge on the casing. Maximum air temperature reduction

and complete evaporation will be achieved for small droplets (less than 20

microns). These small size droplets are also found to well track the flow and don’t

impinge on the casing.

Horlock (2001) developed a one-dimensional model to illustrate the effect of

water injection on compressor off-design performance. His model was based on the


21

assumption of known amount of evaporation within the compressor. He used the

perturbation method, assuming small perturbations of design performance. His

analysis showed that, wet compression pushes the operating points of the

evaporating stages away from design and up their temperature rise characteristics.

Wet compression also leads the later evaporating stages in the compressor to

approach their stalling points.

Chaker et. al. (2002-a, b, c) presented the results of extensive experimental

and theoretical studies of nearly 500 inlet fogging systems on gas turbines. Their

studies covered the underlying theory of droplet thermodynamics and heat transfer

and provided practical points relating to the implementation of inlet fogging to gas

turbine engines. They provided experimental data on different nozzles and

recommended a standardized nozzle testing method for gas turbine inlet air fogging.

Bhargava and Meher-Homji (2002) presented a comprehensive parametric

study on the effect of the inlet fogging (both evaporative and overspray) on various

gas turbines. A commercial program was used to evaluate the thermodynamic

performance at different operating conditions (such as changes in ambient

temperature, ambient relative humidity, as well as inlet evaporative and overspray

fogging). The results showed that the aero derivative gas turbines, in comparison to

the heavy-duty industrial machines, have higher performance improvement due to

inlet fogging effects. More recently, Bhargava et al. (2006) expanded their analysis

to combined cycle power plants (CCPs). Their results showed that high pressure

fogging is effective also in case of CCPs.

White and Meacock (2004) examined the impact of evaporative process on

compressor operation, focusing on cases with substantial overspray. They used a

simple numerical method for the computation of wet compression processes, based

on a combination of droplet evaporation and mean-line calculations. They applied

the method to“generic” compressor geometry in order to investigate the behavior

that results from evaporative cooling. Their work was restricted to small droplets of


22

5µm diameters, which follow the gas-phase velocity with negligible slip. For this

condition, higher evaporation rate with minimum erosion probability was achieved.

This was for water injection rate varies from 1 to 10 % of the air mass flow. Mean-

line compressor calculations showed that water injection shifts the characteristics to

higher mass flow and pressure ratio. Individual compressor stages will operate off-

design, with front stages moving toward choke and rear stages toward stall. This

has the effect of lowering the aerodynamic efficiency and narrowing the efficiency

peak. Based on these results, they suggested that some redesign of the compressor

would be necessary to achieve the full benefits that are possible with water-

injection cycles.

More recently, Meacock and White (2006) have developed their computer

program and extended their mean-line calculations to study the effects of water

injection in two shafts industrial gas turbines. Preliminary results showed similar

trends to that predicted for single-shaft machines. The LP compressor in particular

operates at severely off-design conditions. The predicted overall performance of a

three-shafts machine shows a substantial power boost and a marginal increase in

thermal efficiency.

Kang et al. (2005) has provided thermodynamic and aerodynamic analysis on

wet compression in a centrifugal compressor of a micro turbine. They coupled the

meanline performance analysis of the centrifugal compressor with the

thermodynamic equation of wet compression to get the meanline performance of

wet compression. They aimed at investigating the impeller exit flow angle

deviation due to wet compression and its effect on the matching of impeller and

vaned diffuser. The most influencing parameter in his study was the evaporation

rate of water droplets. They found that, the exit flow angle decreases as evaporation

rate increases. They also related the change in exit flow angle 2 to water/air mass

flow rate, X, through the following correlation:

4

2 43473000 (2.1)


23

El-Salmawy and Gobran (2005) developed a detailed model to study the

impact of controlling inlet conditions on gas turbines performance. The inlet

conditions are controlled either by evaporative cooling, as well as mechanical or

absorption chillers. The effect of wet compression has been modeled in addition to

the variation of the specific heat and gas composition over the cycle. A simplified

two zones combustor model has been considered too. Making benefit of the

developed model, they conducted a case study to evaluate the impact of controlling

inlet conditions to "Cairo South II" combined cycle power plant. Their results

showed that the improvement in the output power and heat rate are primarily

attributed to wet compression, pressure ratio recovery and increase in air mass flow.

The case study of Cairo South II plant showed that substantial energy, economical

and environmental advantages can be achieved when inlet conditions to the plant

are controlled. Also evaporative cooling is more attractive than chiller cooling.

Roumeliotis and Mathioudakis (2006) examined the effect of water injection at

the compressor inlet or between stages, on its operation. They used wet

compression model together with an engine performance model. It consists of a

one-dimensional stage stacking model, coupled with a droplet evaporation model.

The effect of water injection on overall performance and individual stage operation

was examined. The possibility to evaluate the effect on various parameters such as

power, thermal efficiency, surge margin, as well as the progression of droplets

through the stages was demonstrated. The results showed that, the surge margin

reduces even with low injection quantities. Water injection causes significant stage

rematching, leading the compressor toward stall. Also performance enhancement is

greater as the injection point moves towards the compressor inlet.

Bhargava et al. (2007-І, ІІ, and ІІІ ) presented a comprehensive review on the

current understanding of the analytical and experimental aspects of inlet and

overspray fogging (wet compression) technology as applied to gas turbines.

Practical aspects including climatic and psychrometric aspects of high-pressure inlet

evaporative fogging is also provided. Discussion of analytical and experimental


24

results relating to droplet dynamics, factors affecting droplet size, characteristics of

commonly used fogging nozzle, and experimental findings are presented. They

reported that most machines operate with an overspray level not exceeding 2 % of

the air mass flow, where the limiting amount of injected water is machine specific.

2.3 DROPLET EVAPORATION

Droplet evaporation (Aweny, 2003) involves simultaneous heat and mass

transfer processes. The heat required for evaporation is transferred to the droplet

surface by conduction and convection from the surrounding gas. The vapor is

transferred by convection and diffusion into the gas stream. The overall rate of

evaporation depends on the pressure, temperature, transport properties of the gas,

the velocity of the droplets relative to that of the surrounding gas, and the loading

ratio. For single droplet, evaporation can be theoretically illustrated by considering

the case of a droplet that is suddenly immersed in a gas at higher temperature.

Initially, almost all of the heat supplied to the droplet serves to raise its temperature.

This period is known as the heat up period. Eventually, this stage ends when the

droplet stabilizes at its wet bulb temperature.

Based on experimental measurements, after an initial transition period (heat up

period), steady state evaporation is soon established. All the heat transferred to the

droplet is used to provide the latent heat of vaporization of the droplet. The droplet

diameter, during the steady-state period, decreases with time according to the

following relationship:

tDDo 22 (2.2)

This is called the " 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.


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)


26

Where t is the life time of the droplet in seconds, aed is the aerodynamic

diameter of the initial droplet in centimeters, and RH is the air relative humidity.

Miller et al. (1998) evaluated a variety of liquid droplet evaporation models.

They considered both classical equilibrium and non-equilibrium formulations. All

the models perform nearly identically for low evaporation rates at gas temperatures

significantly lower than the boiling temperature. For gas temperatures at and above

the boiling point, large deviations were found between the various models. The

simulated results also revealed that non-equilibrium effects become significant

when the initial droplet diameter is lower than 50 µm.

2.4 DROPLET INTERACTION

It includes droplet-wall interaction. The outcome of droplet interactions plays

an important role in droplet dynamics. The major dimensionless groups governing

droplet impact include (Mundo et al., 1995):

Reynolds number

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 .


27

Mundo et al. (1995) have performed experimental studies of liquid spray

droplets impinging on a flat surface. They aimed to formulate an empirical model

describing the deposition and the splashing processes. Monodisperse droplets,

produced by a vibrating orifice generator were directed towards a rotating disk and

the impingement was visualized using an illumination synchronized with the droplet

frequency. A rubber lib was used on the rotating disk to remove any film from

previous depositions. The test matrix involved different initial droplet diameters,

velocities, impingement angles, viscosities, and surface tensions. The liquids used

to establish the different viscosities and surface tensions were ethanol, water and a

mixture of water-sucrose-ethanol. One major result from the visualization is a

correlation of the deposition-splashing boundary, in terms of Reynolds number (Re)

and Ohnesorge number (Oh), in the form 25.1Re.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)


28

Stanton and Rutland (1998) have developed and validated a multi-

dimensional, fuel film model to help account for the fuel distribution during

combustion in internal combustion engines. Spray-wall interaction and spray-film

interaction are also incorporated into the model. The fuel film model simulates thin

fuel film flow on solid surfaces. This is achieved by solving the continuity,

momentum, and energy equations for the two-dimensional film that flows over a

three-dimensional surface. The major physical processes considered in the model

are shown in Fig (2.2, a). In order to adequately represent the drop interaction

process, impingement regimes and post impingement behavior have been modeled.

The regimes modeled for spray-film interaction are; stick, rebound, spread, and

splash as shown in Fig.(2.2, b). The fuel film model is validated through

comparison with experimental data. The model provided a predictive means of

determining spray-wall interactions with the eventual formation of liquid films that

can be used for multi-dimensional simulations.

Weiss (2005) studied the impingement of coarse sprays on vertical walls with

and without an additionally supplied wall film. The main outcome of wall

interaction for the coarse spray is splashing. It is found to be suppressed with

increasing the wall film thickness. The splashed droplets form a secondary spray

Fig. (2.2) Schematics of : (a) The Major Physical Phenomena Governing Film

Flow (b) The Various Impingement Regimes Identified in the Spray-Film

Interaction Model. (Stanton and Rutland, 1998)

(a) (b)


29

hit the primary spray in a cross stream configuration after ejection from the wall.

This inter-droplet collision plays an important role in the impingement dynamics

and on the quantity of liquid deposited on the wall. The collision outcome was

simulated tacking into account droplet coalescence and secondary breakup due to

stretching separation.

2.5 EROSION

Erosion of compressor blades due to liquid droplets impingement is the main

problem of wet compression technique. Erosion probability increases from large

droplets which possess higher momentum and separate from air stream to impinge

blades. Accordingly, droplet size is the main factor affecting the droplet path and

hence erosion. Another factor affecting the droplet path within the compressor is

the injected liquid density. Dense liquid droplets have higher momentum and tend

to separate and impinge on blades causing erosion.

Many preliminary studies about erosion have been conducted. Performance

monitoring of wet compression systems for long term operation has also been

investigated. All assured that wet compression is a safe technique in view of blade

erosion provided using small droplet diameters and relatively low density liquids.

Utamura et al. (1999) conducted a numerical analysis to determine the

condition at which the water droplet avoid collision with rotor blades in view of

blade erosion. Two dimensional potential flow field along gas path was solved

using computational fluid dynamics (CFD) model. Given the velocity of water

droplet at the exit of inlet guide vane, the locus of the water droplet in the flow field

and the velocity vector at each point on the locus were calculated. Calculations are

performed by solving Newton's equation of motion for a representative water

droplet of a given diameter. Figure (2.3) shows the calculation results. Due to the

dominancy of inertia effect, the droplet of the diameter 100 µm has the velocity

vector not much away from its initial velocity vector. On the contrary, the velocity

vector of the droplet with the diameter of 20 µm or below almost coincides with


31

that of air. The lower graph displays the locus of the water droplet within the flow

path. It is apparent that 10 µm water droplet is not seen to collide against rotor

blade.

Fig. (2.3) Velocity Vector and Locus of Water Droplet Inside

the Compressor (Utamura et al., 1999)

Sanjeev Jolly (2003) presented the performance effects of applying wet

compression to an advanced frame combustion turbine, the Alstom GT-24, for

many years. His work also addresses the relative changes in compressor and

turbine operating conditions and how these affect component life. The GT-24 wet

compression system has been operational for more than one year for about 16 hours

a day. A borescope inspection performed during a recent outage did not show

erosion to be manageable within normally scheduled maintenance.

Bhargava et al. (2007-Part ІІІ) focused their study on operational experience

and reviewed the work pursued by gas turbine OEMs in the field of wet

compression. They reported that previous CFD studies showed that relatively small

water droplets (less than 15-20 microns) will tend to follow the air stream and hence

cause no erosion. They also reported that the operational experience showed that

wet compression systems have not resulted in excessive erosion problems.


31

2.6 TWO PHASE PREDICTION APPROACHES

There are two main approaches (Crowe et al., 1998) used to predict the two-

phase flow, namely the Lagrangian and the Eulerian approaches.

2.6.1 Lagrangian Approach

The Lagrangian approach can deal with the dilute and dense two- phase flow.

The dilute flow is the case when the droplets motion is controlled by the droplet

fluid interaction, body forces, and particle-wall collision. The dense flow is the

case when the droplet-droplet interaction controls the dynamics of the droplets but it

is also influenced by the hydrodynamic and body forces as well as droplet-wall

interaction. There are two main methods to implement the Lagrangian approach;

the trajectory method, and the discrete element method. In the trajectory

method, the carrier phase is almost steady. The flow field is subdivided into a set of

computational cells as shown in Fig. (2.4). The inlet stream of the dispersed phase

is discretized into a series of representing starting trajectories.

More details can be known by descretizing the starting conditions according to

a size distribution as well. But more detail requires more trajectories and this will

increase the needed computational time. After the termination of all trajectories

calculations, the properties of the dispersed phase in each computational cell can be

determined. Each property can be determined by carrying out a summation over all

the trajectories, which traverse the computational cell.

Fig. (2.4) Droplet Trajectories in a Spray (Crowe et al., 1998)


32

Fig. (2.5) Distribution of Droplet Parcels in a Spray Field

(Crowe et. al, 1998)

Regarding the discrete element method, it is recommended when the flow is

unsteady and/or dense (droplet-droplet collision is important). In this method

calculation for each individual droplet is performed. Accordingly, the properties

such as motion, position, and temperature of individual droplets or representative

droplets are tracked with time. The tracking of all droplets, which can be presented

in the domain, may not be computationally feasible. Therefore a smaller number of

computational droplets are chosen to represent the actual droplets, where each of

them represents a number of physical droplets. It has been found that the required

number of representative droplets to accurately simulate the dispersed phase is not

excessive. The computational droplet is regarded as a parcel of physical droplets,

which have the same properties as the represented computational droplet, as shown

in Fig. (2.5). The equation of droplet motion takes into account the droplet-droplet

interaction. The droplet displacement can be calculated by integrating the equation

of motion with respect to time. In the same time the droplet temperature, diameter

and other properties can be calculated. During each time step, there may be droplet-

droplet collisions that alter the trajectories and change the distribution of the parcels

in each computational cell. This is treated using a suitable collision model.

2.6.2 Eulerian Approach.

The Eulerian approach (Lee et al., 2002) considers the dispersed phase to be a

continuous fluid interpenetrating and interacting with the fluid phase. This

approach is commonly used for dense particulate flows since it is convenient to

model the inter-particle stresses using spatial gradients of the volume fraction. This


33

requires solving extra continuity and momentum equations for the dispersed phase

with separate boundary conditions. The resulting governing equations of the

dispersed phase are quite similar to Navier-Stokes equations for the carrier phase.

The interaction between the two phases takes place through mass, momentum, and

heat exchange mechanisms.

2.7 NUMERICAL SIMULATION OF AXIAL COMPRESSORS

There have been many approaches to predict the overall performance

multistage axial flow compressors with a good degree of confidence. All of which

can be categorized into the following three approaches: one-dimensional mean-line

models, two-dimensional through flow models and three-dimensional

computational fluid dynamics (CFD) models, as shown in Table (2.1). It is possible

to mix some elements of the above models, creating quasi-one-dimensional, two-

dimensional and three-dimensional models. The term ‘quasi’ is used to indicate

that some three-dimensional effects are included within the correlation set utilized.

Perhaps, the simplest model of compressor simulation is the zero-dimensional

model or simply the thermodynamic model. This model is not included in the

above classification because it is important only from the thermodynamic point of

view and don’t produce any aerodynamic information about the compressor. In this

model, the compressor is simulated as a closed box where its performance is

governed by isentropic relations. In the following, a brief review is presented for

the most common models used to simulate compressors.

Table (2.1) Axial Compressor Simulation Models.

Numerical Simulation

of Axial Compressors

One-dimensional

Mean line)) Models

Two-dimensional

(Through flow) Models

Three-dimensional

CFD Models


34

2.7.1 Quasi-One-Dimensional Models

It is often termed mean-line methods, where a radial mean height is usually

selected for the position of the single calculation streamline. There are different

methods to quantify the aerodynamic conditions across a blade row. In order to

account for the three-dimensional flow effects within each stage, a highly empirical

approach is necessary. For this reason, the success of the prediction is heavily

dependent upon the quality of the correlations used within the model. Although this

type of flow analysis represents a gross simplification of a complex three-

dimensional system, which can now be modeled more accurately by many of

today’s computational fluid dynamics (CFD) packages, it does offer the advantages

of simple input requirements and fast convergence times.

Expansion of the model to simulate multistage machines is possible. This can

be done by stacking the pressure and temperature ratios of each blade row to give

an overall performance prediction. This stage-stacking procedure starts at the inlet

and works through each blade row, using the exit conditions from the previous row

as inlet conditions for the next row.

Considering this model Horlock (2001) and White and Meacock (2004) have

used a droplet evaporation model to illustrate the effect of water injection on

compressor off-design performance. White et al. (2002), have also used this

prediction model and employed it within an optimization program. The developed

program was used in restagering the variable stator vanes in a multistage

compressor to obtain the optimum compressor performance during off-design

operation. Its good results, encourages the use of such model as a cost effective

tool for quick and reasonably accurate solutions.

Other one-dimensional models (Lindau and O’Brien, 1993; Adam and

Leonard, 2005) used different methods to quantify the aerodynamic conditions

across a blade row. The model is based on mass, momentum, and energy balances

applied to a one-dimensional discretization of the compressor. The computational


35

domain is the compressor flow path, using a row-by-row, quasi-one-dimensional

representation of the machine at mid-span. The basic Euler equations have been

extended by including source terms expressing the blade-flow interactions. The

source terms are determined using the velocity triangles for each blade row, at mid-

span. The losses and deviations undergone by the fluid in each blade row are

supplied by correlations. Due to generality of source terms approach, this model

could be extended to combustion chambers and turbines, to simulate the operation

of a whole gas turbine engine. Water ingestion, blade fouling or cooling devices

may also be introduced.

2.7. 2 Two-Dimensional Models

The two-dimensional models are usually termed as the through flow or

streamline curvature models. In these models, the flow is considered in the

meridional plane, assuming the flow in the circumferential direction is steady. This

type of model is most often used to design the blade geometry given the desired

pressure and temperature rise. A secondary role is for performance prediction when

the blade geometry and some information about the blade performance are given. A

number of radial stations from hub to tip are selected for analysis at each blade row

through the compressor.

Loebig et al. (1998) constructed a three dimensional aero thermal analysis

code to aid in the design of optimum water/methanol injection system. Their code

was built on the basis of the stream line curvature method. It was aimed to study

the 3D compressor flow field and combines it with the computations of 3D droplet

trajectories, evaporation characteristics, and droplet impingement locations on both

the hub and casing.

Petrovic et al. (2000) have performed flow calculation and performance

prediction of a multistage axial flow turbine. They considered compressible steady

state inviscid through-flow code. The aim was to optimize the hub and casing

geometry and inlet and exit flow parameters for each blade row.


36

2.7.3 Three-Dimensional Models

Solution of the compressible Navier–Stokes equations in Reynolds averaged

form, is the most rigorous method used to predict the three-dimensional flow field

within a compressor. Obviously, this type of modeling is the best approach to

predict all aspects of the flow. Yet it does come with the penalty of very high

computational requirements. For this reason, a full three-dimensional analysis is

usually applied only in the final stages of the design process. Therefore, the quasi-

one-dimensional and two-dimensional methods remain important tools. Where they

can supply the more rigorous three-dimensional model with early estimates for the

flow parameters and suitable boundary conditions.

With the great advance in the modern computer capabilities and numerical

schemes for computational fluid dynamics (CFD), 3-D models became an

achievable task. Many researchers used 3-D models in their analysis to obtain

detailed solutions for all flow aspects as will be discussed in the next section. The

present study will rely on this model.

2.8 BLADE ROW INTERACTION

Most turbomachines include many stages to do more work than could be

accomplished with a single blade row. Moreover, the flow is often characterized by

unsteady, viscous and may be transonic. Unsteady interaction effects play a

significant rule in the performance of such multistage turbomachines, especially

when the adjacent blade rows are placed closely for compact design.

Experimental data from jet-engine tests have indicated that unsteady blade row

interaction effects can have a significant impact on the performance of compressors.

Modern compressors can experience three types of unsteady flow mechanism

associated with the interaction between adjacent blade rows, as shown

schematically for a turbine cascade in Fig. (2.6). The first interaction mechanism is

referred to as potential-flow interaction. It results from the variations in the


37

velocity potential or pressure fields (or propagating pressure waves) associated with

the blades in adjacent rows. This type of interaction is of important concern when

the axial spacing between adjacent blade rows is small or the flow Mach number is

high. The second interaction mechanism is wake interaction. It is the effect on the

downstream blade row due to the vortical waves shed by one or more upstream

rows. The third interaction mechanism is called shock wave interaction. It is

caused by the shock system in a given blade row extending into the passage of an

adjacent blade row.

Fig. (2.6) Unsteady Blade Row Interaction Mechanisms

(Turbine Cascade)

The different blade row interaction mechanisms require different levels of

viscous flow modeling complexity to capture the physics associated with a given

flow field. There are several methods (Dorney, 1997; Chima, 1998) for predicting

the flow field, losses, and performance quantities associated with axial compressor

stages. These methods include: (1) the steady single blade row (SSBR) method, (2)

the steady coupled blade row (SCBR) method, (3) the loosely coupled blade row

(LCBR) method, and (4) the fully coupled blade row (FCBR) method. These

methods are ordered in the direction of increasing modeling complexity and are

shown in Table (2.2). These methods are discussed in the following sections.


38

Table (2.2) Levels of Blade Row Interaction Modeling Complexity

2.8.1 Steady Single Blade Row (SSBR) Method

It is the least sophisticated modeling method for multiple blade row

geometries. In SSBR simulations, each blade row is solved in isolation, i.e. in

absence of any interaction effects. Successive blade rows are analyzed from inlet to

exit, using average flow properties from the exit of one blade row as inlet boundary

condition for the next. This method is simple and has been used by many

researchers to model multistage turbomachines (Chima, 1987; Davis et al., 1988).

Yet it introduces many modeling challenges. First, since blade rows are often

closely spaced, it is unclear how far to extend the computational grid for each blade

row, and whether it is reasonable to overlap grids. Second, many numerical

boundary conditions are not well-behaved when applied too close to a blade. Third,

average flow properties are not well-defined. Since flow properties are related

nonlinearly, it is impossible to define an average state that maintains all the original

properties of the three-dimensional flow. Fourth, for subsonic flow, the inlet

velocity profile and mass flow develop as part of the solution. Although it may be

possible to match the overall mass flow by iterating on the imposed back pressure,

it is generally not possible to match the spanwise distributions of properties between

the blade rows. Finally, the method ignores physical processes such as wake

mixing, acoustic interaction, and other unsteady effects that may be important in

real turbomachinery.

Interaction

Modeling

Level

Steady Single

Blade Row

(SSBR)

Steady Coupled

Blade Row

(SCBR)

Loosely Coupled

Blade Row

(LCBR)

Fully Coupled

Blade Row

(FCBR)


39

2.8.2 Steady Coupled Blade Row (SCBR) Method

SCBR method is the second level in modeling complexity of the blade row

interaction. In SCBR simulations, all blade rows are solved simultaneously. They

are exchanging spanwise distributions of averaged flow quantities at a common grid

interface plane between the blade rows. So that the name “Averaging-Plane” is

generally used to express this method, referring to the averaging process occurs at

the interface plane. There are many methods for obtaining average flow variables at

the averaging-plane. The most famous method is known as “mixed-out” averages

from which the name “mixing-plane” model is derived. Averaging-Plane methods

(SCBR) have been used by many researchers (e.g. Chima, 1998; Prasad, 2005). In

spite of the possibility of some missing physics in this analysis, the output of this

method has shown excellent agreement with experiments.

Chima (1998) has used a modified averaging-plane approach to analyze the

flow in a two-stage turbine. He used the characteristic boundary conditions to

exchange information between the blade rows. Comparison with experiments

showed that the use of characteristic boundary conditions ensures that information

propagates correctly between the blade rows. It also allows close spacing between

the blade rows without forcing the flow to be axisymmetric, as in conventional

numerical boundary conditions. This property overcomes a main limitation of the

averaging-plane codes.

2.8.3 Unsteady Loosely Coupled Blade Row (LCBR) Method

It is also known as “Average-Passage” method. It is a rigorous means of

modeling unsteady blade row interaction using a steady analysis. In this method,

unsteady boundary conditions are specified at the inlet and exit of each blade row to

account for the interaction mechanisms. The inter-blade-row boundary conditions

are periodically updated to couple the unsteady flow effects from the upstream and

downstream blade rows. The LCBR method has been shown to be computationally


41

efficient (Dorney et at., 1995), while retaining a significant amount of the unsteady

flow physics. Because of its complexity it has not been widely used.

2.8.4 Unsteady Fully Coupled Blade Row (FCBR) Method

In the unsteady fully coupled blade row (FCBR) technique the flow fields of

multiple blade rows are solved simultaneously. The relative position of one or

more of the of the blade rows is varied to simulate the blade motion. FCBR

solution techniques presumably avoid all modeling issues and can accurately predict

the unsteady flow phenomena in compressor stages (within the limits of turbulence

and transition modeling). FCBR solution is usually used to validate other steady

solutions. But this method is very expensive computationally, and finally still

requires averaging at the end to produce useful results.

To consider fully unsteady rotor/stator interactions with reduced costs, the

computational domain can be limited to a minimum number of blade passages per

row. For unequal pitch configurations, where the number of blades in one row is

not a multiple of the other, small numbers of blade passage cannot generally be

selected. In this case, different methods can be used to retrieve the space and time

flow periodicity on a minimum number of blade passages. They are gathered into

three categories: (1) methods that use relations to derive time-lagged boundary

conditions in the gap region (Hah, 1997), (2) methods that account for the space-

time periodicity by a transformation of coordinates, and (3) methods that remove

the time periodicity constraint by scaling one blade row geometry in order to

retrieve equal pitch distances on both sides of each rotor/stator interface. This is

called here as Domain Scaling Method (DSM) (Hildebrandt et al., 2005; Dorney

and Sharma, 1997).

The first two methods are complex to generalize to multistage rotor/stator

configurations. To remove these constraints, the computational domain may be

scaled to yield identical pitch distances on both sides of each rotor/stator interface.

This pitch wise scaling requires another scaling in the axial dimensions to maintain


41

a constant solidity and therefore a compensation of the blade loading (space/chord

ratio). The space and time flow periodicity are then uncoupled and the unsteady

flow field may be resolved on a reduced number of blade passages per row. This

can be done without having to consider any time periodicity in the boundary

treatment.

Dorney and Sharma (1997) presented and compared between the previous

methods namely FCBR, SCBR, SSBR, and LCBR. The analysis has been evaluated

in terms of accuracy and efficiency. The modeled case was a transonic compressor

stage containing 76 IGVs (Inlet Guide Vanes) and 40 rotor blades. In numerical

simulations, the compressor is modeled using 2 IGVs and 1 rotor blade. Thus, the

number of IGVs in the first row was increased to 80 and the size of the airfoils was

reduced by a factor of 76/80 to maintain the same blockage (space/chord ratio).

FCBR simulation have been time-averaged and chosen to serve as the base line

results. The SCBR and the LCBR techniques provided a reasonable representation

of the FCBR results. The SSBR method significantly under predicted the IGV loss

and over predicted the stage efficiency in case of passage shocks.

Aube and Hirsch (2001) investigated the effect of unsteady loss sources

generated in rotor/stator interactions on the performance a 1-1/2 axial turbine stage.

Two levels of approximation were used, quasi-steady and full unsteady. The quasi-

steady approximation is performed using the "mixing-plane model" while the

unsteady one is performed using the "sliding grid" model. The results of the two

models compare well with the experimental results and allow capturing of the main

flow structure of the turbine passage. Only the fully unsteady (fully coupled)

calculation resolves the complex loss mechanisms encountered mainly in the rotor

and downstream stator components. These unsteady interactions are observed

through time variations of the entropy, absolute flow angle and static pressure.

The main difference between a full-unsteady simulation and the mixing-plane

solution is the lack of all unsteady effects in the later. This returns to the absence of


42

the so called “Deterministic Stress Terms”, DST, as a result of averaging process in

the case of the mixing plane. For this reason and to improve the efficiency of the

mixing-plane model in predicting unsteady effects, Stridh and Eriksson (2005)

incorporated these DST to the conventional mixing-plane model. The objective was

to enable it to approximately model the unsteady effects of neighboring blade rows.

They used the linearized harmonic approach, applied to rotor/stator interaction by

Chen (2000), to predict the DST. They applied their linearized technique to a 3D,

1-1/2 stage transonic fan and compared the results with the full unsteady and

conventional mixing-plane results. This method makes it possible to evaluate

unsteady effects, such as time dependent blade loads due to wake interaction. It is

also indicated that when the steady flow is continuously updated by the DST, the

surge line can be approached in the compressor map, i.e. it is possible to obtain a

numerical estimation closer to the surge line in comparison to the conventional

steady computation.

Adami et al. (2001) developed a full 3-D unstructured solver and applied it to

the simulation of the 3-D VKI annular turbine stage. The peculiar aspect of their

work, compared to the previous work, was given by the completely hyprid-

unstructured nature of the approach. This feature allows an easy and flexible mesh

generation and refinement, especially for more complex geometries. The higher

CPU and memory demand, often encountered with this type of grids, had been

overcome by the use of the parallel computations. The results compare favorably

with a set of time average calculations and the available experimental data. As a

result their unsteady Euler approach allows a realistic description of the flow pattern

especially when phenomena, such as shock interaction, blade loads and flow

distribution, are not physically accounted for by steady state computations.

Hildebrandt et al. (2005) have conducted a steady and unsteady flow

simulation of a 1.5-stage low speed research compressor. They used a one-equation

turbulence model, Spalart Allmaras, with a semi-empirical transition. The steady

analysis were performed with the mixing plane model using the real geometry,


43

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.


44

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.


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.

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

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)


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)


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)


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


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)


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)


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.


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


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)


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


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 ).


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.


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 .


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


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.


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)


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)


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 .


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


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)


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


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.


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


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


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


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


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


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


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


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)


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


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


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.


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.


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


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

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.

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)


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 .


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.


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


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


88

50

100

150

200

0 0.2 0.4 0.6 0.8 1


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


Ab

so

lute

Ma

ch

Nu

mb

er

Fig.(4.5) Meridional Variation of Absolute Mach Number

at Mid-Span.


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 .


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


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


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


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


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.


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)


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


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


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


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



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.


111

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

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



111

90

100

110

120

130

140

150

0 0.2 0.4 0.6 0.8 1


Me

an

Sta

tic

Pre

ss

ure

(K

Pa

)

Dry

Wet

Fig.(4.22) Meridional Variation of Mean Static Pressure


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



112

60

80

100

120

140

160

180

0 0.2 0.4 0.6 0.8 1


Mea

n V

elo

cit

y M

ag

nit

ud

e (

m/s

) Dry

Wet

Fig.(4.24) Meridional Variation of Mean Velocity Magnitude


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


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 %.


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


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


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

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


118

0

0.0025

0.005

0.0075

0.01

0.0125

0.015

0 0.2 0.4 0.6 0.8 1


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


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.


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).


111

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

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


111

90

100

110

120

130

140

150

0 0.2 0.4 0.6 0.8 1


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


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


112

60

80

100

120

140

160

180

0 0.2 0.4 0.6 0.8 1


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


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.


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).


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


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


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


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


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.


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.


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


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


119

90

100

110

120

130

140

150

0 0.2 0.4 0.6 0.8 1


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


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


121

60

80

100

120

140

160

180

0 0.2 0.4 0.6 0.8 1


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


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


121

0

0.25

0.5

0.75

1

29 30 31 32 33 34 35 36


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


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


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).


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


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


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


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.


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)


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

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.

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


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.


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.

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

Appendices Appendix (A)

2A

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


3A

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)


4A

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

).


5A

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


6A

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


7A

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


8A

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.


9A

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)


11A

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.


11A

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

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

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

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

١ -

(مشرفا ) د أحمد فايز عبدالعظيم.أ

سم هندسة القوى الميكانيكية جام ة الز ازيق –كلية الهندسة

٢-

د دمحم محروس شملول.أ

سم هندسة القوى الميكانيكية جام ة الز ازيق –كلية الهندسة

٣-

الزقازيق جامعة٨٠٠٢

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

m.sc.thesis-reda ragab-2008

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