CHARACTERISTICS OF ALTERNATIVE FUELS AND ALTERNATIVE COOLING OF
THERMAL POWER PLANTS
By
Christopher David Bolin

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Mechanical Engineering - Doctor of Philosophy
2014

ABSTRACT
CHARACTERISTICS OF ALTERNATIVE FUELS AND ALTERNATIVE
COOLING OF THERMAL POWER PLANTS
By
Christopher David Bolin
In regions of the world where the infrastructure for electrical power generation and distribution is unreliable or outdated moving to a distributed power generation is a viable strategy
for the future. Gas turbine engines at all scales can be used to meet local power demands
efficiently. Remote sites will require small engines relying on a variety of fuel sources including alternative fuels (i.e., fuels derived from non-fossil sources) as well as cleaner, from an
emissions standpoint, methods of using fossil sources. Near larger industrial and domestic
loads larger co-generation plants will be necessary. These co-generation plants will require
cooling for a steam condenser to maximize the efficiency of the vapor cycle. In arid locations
surface and sub-surface water sources may be insufficient to meet cooling demands for both
environmental and regulatory reasons. At such locations an alternative cooling strategy will
be required. This work is divided into two parts that investigate fundamental questions
regarding alternative fuel issues for small scale gas turbine engines and cooling issues for
larger co-generation plants.
In the first part of this work the application of biogas to small scale generation systems is
explored. Biogas is a term used for the collection of gases produced by the anaerobic digestion
of organic waste materials such as garbage and animal manure. The resulting gas consists of
CH4 diluted with varying amounts of CO2 , H2 O, N2 , and other trace species. The content
of biogas is feedstock dependent and thus variable. This poses a challenge to combustor
designers. Many modern gas turbine combustors use a fuel-lean, premixed strategy to meet

strict emissions standards. Operating under such conditions, often near the lean-extinction
limit, can be difficult with fuel variability. Empirical relations, determined with simplified
experimental devices, can be used by the designer to provide a first-order approximation
of the operating envelope of a new system. Such relations are available for a range of
traditional fuels but are lacking for newer alternative fuels. Stability limits for a range
of biogas fuel contents are investigated here using stirred-reactor theory. Correlations to
predict lean-extinction limits based on content are developed. Finally, a facility for expanding
this research with a laboratory well-stirred reactor (WSR) for the investigation of biogas
extinction limits and combustion emissions will be described.
The second part of this work explores the use of vapor-compression refrigeration systems
for steam condenser cooling. Larger loads invite the use of combined cycle power systems.
These systems use large industrial or aero-derivative gas turbine topping cycles with conventional steam power bottoming cycles to increase fuel efficiency. An alternative cooling
system using vapor compression refrigeration is an alternative method of cooling that can
reduce or eliminate the need for cooling water. A novel facility for small scale experiments
to explore the operating envelope of the proposed system is described here. The results
of preliminary investigations into the use of R-410a as a steam condenser coolant are also
presented.

To my mother Carole and father Steven for the patience and encouragement

iv

ACKNOWLEDGMENTS

In the completion of this work I have been assisted, supported and encouraged by many
individuals. I would like to thank Dr. Wei Liao, Dr. Norbert Mueller, Dr. Tonghun Lee
and Dr. Patrick Kwon for their guidance and support as committee members. All of the
small details involved with conducting research work as well as classwork would not have
been possible without the assistance of Aida Montalvo, Mary Pease, Lindsey Niesen and
Suzanne Kroll of the Department of Mechanical Engineering office. Many ideas on the
design, construction and maintenance of various lab equipment were greatly assisted by Roy
Bailiff of the department machine shop.
I would also like to thank those of my colleagues who acted as both collaborators and
distractions. In the early portion of this work I collaborated with Dr. Joseph Zelina of the
Air Force Research Laboratory, Dr. Scott Stouffer of the University of Dayton, Dr. Samuel
Manzello of the National Institute of Standards and Technology and Dr. Saeed Jahangirian
and Mr. Daejung Kim of MSU, their assistance in getting my feet under me is greatly
appreciated. A special thanks to Dr. Marco Vagani who acted as a research collaborator
and a helpful distraction as appropriate. Thank you to Ryan, Amol, Venkat and Avinash for
being willing to play some golf or generally get out of the building whenever it was necessary
and several times when it wasn’t.
My family played a large roll in maintaining my balance during this work. Thank you for
your patience, encouragement and understanding throughout this extended process. Mom,
whenever I needed a break you were always there with a lovingly prepared meal and someone
to talk to. Dad, if I needed to do something to take my mind of research, you could always
find some task, usually involving physical labor, to keep me busy. Matt, Sarah and Kelsey,
v

you were always there to talk to about anything other than research or do anything other
than work. For these little distractions, I am extremely grateful.
Finally, I wish to acknowledge and thank my advisor Dr. Abraham Engeda. A quick
hallway meeting in the fall of 2008 started this endeavor. Along the way, you have provided
copious amounts guidance, support, advice, encouragement and patience. I sincerely thank
you for all that you have done for me to reach this point.

vi

TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES

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xi

KEY TO SYMBOLS AND ABBREVIATIONS . . . . . . . . . . . . . . . . . xiv
Chapter 1 Introduction and Objectives . .
1.1 Introduction . . . . . . . . . . . . . . . . .
1.1.1 Gas Turbine Combustors . . . . . .
1.1.2 Challenges of Alternative Fuels . .
1.2 Laboratory Modeling of a GT Combustor .
1.3 Cooling of co-generation steam loops . . .
1.4 Research Objectives . . . . . . . . . . . . .

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Chapter 2 Alternative Fuels in Gas Turbine Combustion
2.1 Emissions . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Oxides of Nitrogen . . . . . . . . . . . . . . . . .
2.1.2 CO and UHC . . . . . . . . . . . . . . . . . . . .
2.1.3 Methods of Emissions Control . . . . . . . . . . .
2.1.3.1 Diluent Injection . . . . . . . . . . . . .
2.1.3.2 Catalytic Combustion . . . . . . . . . .
2.1.3.3 Fuel-Air Mixture Adjustment . . . . . .
2.1.3.4 Post Combustion Treatment . . . . . . .
2.1.3.5 CO and UHC . . . . . . . . . . . . . . .
2.2 Lean Premixed Combustion . . . . . . . . . . . . . . . .
2.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Static Instability . . . . . . . . . . . . . . . . . .
2.3.2 Dynamic Instability . . . . . . . . . . . . . . . . .
2.4 Fuel Flexibility & Alternative Fuels . . . . . . . . . . . .
2.4.1 Fuel Conditioning . . . . . . . . . . . . . . . . . .
2.4.2 Fuel Characterization . . . . . . . . . . . . . . . .
2.4.3 Biogas . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3.1 Biogas Production . . . . . . . . . . . .
2.4.3.2 Biogas Combustion . . . . . . . . . . . .
2.5 The Well-Stirred Reactor . . . . . . . . . . . . . . . . . .
2.5.1 WSR Theory . . . . . . . . . . . . . . . . . . . .
2.5.2 WSR Stability Theory . . . . . . . . . . . . . . .
2.5.3 Laminar Premixed Flame Speeds . . . . . . . . .
2.5.3.1 Governing Equations . . . . . . . . . . .
2.5.3.2 Estimating Laminar Flame Speeds . . .
2.5.4 Laboratory WSR Designs . . . . . . . . . . . . .

vii

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50
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67

Chapter 3 Predicting Laminar Flame Speeds of Biogas-Air Flames
3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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75

Chemical Kinetics
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2.6

2.5.4.1 Spherical WSR . . . . . . . . . . .
2.5.4.2 Hemispherical WSR . . . . . . . .
2.5.4.3 Conical WSR . . . . . . . . . . . .
2.5.4.4 Torroidal WSR . . . . . . . . . . .
2.5.5 Numerical Modeling . . . . . . . . . . . . .
2.5.5.1 Chemical Kinetics Simulations with
2.5.5.2 Reaction Mechanisms . . . . . . .
Summary & Conclusion . . . . . . . . . . . . . . .

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CHEMKIN
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Chapter 4 Static Instability Simulations using Detailed
4.1 Purpose of Experiments . . . . . . . . . . . . . . . . .
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Results & Discussion . . . . . . . . . . . . . . . . . . .
4.3.1 Simulated Lean Extinction . . . . . . . . . . . .
4.3.2 A Correlation to Predict Lean Extinction . . . .
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .

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. 91
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. 96
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. 101

Chapter 6 Combined Cycle Steam Power Generation and Cooling
6.1 Combined Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Topping Cycle . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Bottoming Cycle . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Use of Combined Cycle Power Plants in Distributed Generation . .
6.2.1 Cooling Cycles . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Alternative Cooling Approaches . . . . . . . . . . . . . . . .
6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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102
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134

Chapter 7 Refrigerant Cooled Steam Condenser
7.1 Cooling Fluids and Coolant Cycles . . . . . . .
7.2 A Refrigerant Cooled Steam Condenser Test Rig
7.3 Preliminary Experimental Results . . . . . . . .
7.4 Conclusions . . . . . . . . . . . . . . . . . . . .

viii

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Chapter 5 A Test Facility for WSR Experiments
5.1 WSR Design . . . . . . . . . . . . . . . . . . . .
5.2 Housing and Exhaust . . . . . . . . . . . . . . .
5.3 Facility . . . . . . . . . . . . . . . . . . . . . . .
5.4 Emissions Analyzers . . . . . . . . . . . . . . .
5.5 Sample Probe . . . . . . . . . . . . . . . . . . .
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . .

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Chapter 8 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . 135
8.1 Alternative Fuels for Small Gas Turbines . . . . . . . . . . . . . . . . . . . . 136
8.2 Alternative Cooling Strategies for Future Large Power Plants . . . . . . . . . 137
APPENDIX

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BIBLIOGRAPHY

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ix

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. . . . . . . . . . . . . . . . . 143

LIST OF TABLES

Table 3.1

Conditions used in laminar flame speed calculations . . . . . . . . .

70

Table 3.2

Fuel Compositions used in laminar flame speed calculations

. . . .

70

Table 3.3

Constants used in the proposed model to predict the laminar flame
speed of biogas-air mixtures . . . . . . . . . . . . . . . . . . . . . .

72

Table 4.1

Fuel Compositions used in kinetics simulations . . . . . . . . . . . .

78

Table 4.2

Conditions used in kinetics simulations . . . . . . . . . . . . . . . .

78

Table 4.3

Conditions used in kinetics simulations . . . . . . . . . . . . . . . .

87

Table 7.1

Operating conditions of the three-loop VCRS cooled steam condenser
test rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Table 7.2

Estimated experimental measurement error for experiments with the
three-loop VCRS cooled steam condenser . . . . . . . . . . . . . . . 122

Table 7.3

Percentage variations of condensation rate, heat rejection, COP, ratio of refrigerant to condensate mass flow rates and Uo compared to
calculated values at a coolant temperature of 31.9◦ C and pcp = 0kPa. 133

x

LIST OF FIGURES

Figure 1.1

Sketch of a gas turbine combustor, blue lines indicate cool air, orange
lines indicate recirculation/flame stabalization zones and red lines
indicate product gases. For interpretation of the references to color
in this and all other figures, the reader is referred to the electronic
version of this dissertation. . . . . . . . . . . . . . . . . . . . . . . .

5

Sketch of the relation between fuel-air mixture, temperature (red
line), and emissions of various pollutant species (blue lines). . . . . .

17

Figure 2.2

A general combustion stability loop, adapted from [1]. . . . . . . .

26

Figure 2.3

General WSR schematic with control volume. . . . . . . . . . . . . .

39

Figure 2.4

A sketch of the spherical WSR of Longwell [2], blue arrows indicate
incoming fuel-air mixture and red arrows indicate exhaust ports. . .

51

A sketch of the hemispherical WSR of Wright [3], blue arrows indicate
incoming fuel-air mixture and red arrows indicate exhaust ports. . .

54

A sketch of the truncated cone WSR of Thorton et al. [4], blue arrows indicate incoming fuel-air mixture, orange arrows indicate backmixing zones, and red arrows indicate exhaust ports. . . . . . . . . .

56

A plot of the laminar flame speed as predicted by the model vs. the
laminar flame speed predicted by the detailed kinetics simulations for
φ < 0.6. The green dashed lines indicate deviation of 20% from the
kinetics simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

A plot of the laminar flame speed as predicted by the fit vs. the
laminar flame speed predicted by the detailed kinetics simulations
for φ > 0.6. The green dashed lines indicate deviation of 20% from
the kinetics simulation. . . . . . . . . . . . . . . . . . . . . . . . . .

74

φLE versus LP as computed by three mechanisms (stars GRI-Mech 3.0,
diamonds GRI-Mech 1.2 reduced, squares San Diego) at three different Tin (blue 300K, red 600K, black 900K) and three different
operating pressures for Mix 3: (a) 1atm, (b) 2atm, and (c) 4atm. . .

82

Figure 2.1

Figure 2.5

Figure 2.6

Figure 3.1

Figure 3.2

Figure 4.1

xi

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

φLE versus LP as computed by three mechanisms (stars GRI-Mech 3.0,
diamonds GRI-Mech 1.2 reduced, squares San Diego) at three different Tmathrmin (blue 300K, red 600K, black 900K) and three different
operating pressures for Mix 3: (a) 1atm, (b) 2atm, and (c) 4atm. . .

83

φLE versus LP as computed by the GRI-Mech 3.0 mechanism, at three
different Tin in (blue 300K, red 600K, black 900K) comparing three
mixes to Mix 6 at three operating pressures: (a) 1atm, (b) 2atm, and
(c) 4atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Mole fraction of three radical species and Tr versus LP as computed
by GRI-Mech 3.0 at Pr = 1atm, φ = 0.65, Tin = 300K for three
different mixes: (a) Mix 3, (b) Mix 4, (c) Mix 5, and (d) 50% CH4 ,
16.6% CO2 , 33.4% N2 . . . . . . . . . . . . . . . . . . . . . . . . . .

85

φLE versus LP as computed by three mechanisms (stars GRI-Mech 3.0,
diamonds GRI-Mech 1.2 reduced, squares San Diego) at three different Tin (blue 300K, red 600K, black 900K) and three different
operating pressures for Mix 3: (a) 1atm, (b) 2atm, and (c) 4atm. . .

89

Figure 5.1

A cut view schematic of the assembled WSR with components identified. 92

Figure 5.2

An image of the ceramic halves of the toroidal WSR. . . . . . . . . .

92

Figure 5.3

An image of the fuel-air manifold and jet ring showing the injection
nozzles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

Figure 5.4

A schematic of the fuel/air manifold and jet ring.

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94

Figure 5.5

A schematic the mixing of product and reactant gases. . . . . . . . .

95

Figure 5.6

Schematic of the emissions sampling probe. . . . . . . . . . . . . . . 100

Figure 6.1

A T-s diagram of the simple, open Brayton cycle. . . . . . . . . . . 104

Figure 6.2

A T-s diagram of the Rankine cycle with superheat. . . . . . . . . . 106

xii

Figure 7.1

Experimental layout: Steam loop: 1-Water source, 2- filter and ball
valve, 3-Float control valve, 4-Boiler, 5-Drain valve, 6-Pressure relief valve, 7-Steam outlet valve, 8-Condenser, 9-Air vent valve, 10Thermostatic check valve, 11-Graduated tank; Water loop: 12-Pressure
reducing valve, 13-Thermal expansion tank, 14-high pressure switch,
15-pressure relief valve, 16-Intermediate heat exchanger, 17-low temperature switch, 18-Circulator pump, 19-Rotameter; VCRS loop: 20pressure relief valve, 21-low pressure switch, 22-pressure regulator,
23-accumulator, 24-filter driers, 25-Vibration absorber, 26-AC unit,
27-TXV, 28-Glass Screen, 29-high pressure switch. . . . . . . . . . . 117

Figure 7.2

Photo of the assembled reduced scale refrigerant cooled steam condenser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Figure 7.3

Condensation rate and R-410a mass flow rates at pcw =6.8kPa and
pcp =0kPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Figure 7.4

Heat rejection and COP at pcw =6.8kPa and pcp =0kPa. . . . . . . . 124

Figure 7.5

Overall heat transfer coefficient at pcw = 6.8 kPa and pcp = 0 kPa. . 125

Figure 7.6

Condensation rate and R-410a mass flow rates at pcw = 6.8 kPa and
pcp = −16.943 kPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Figure 7.7

Heat rejection and COP at pcw = 6.8 kPa and pcp = −16.943 kPa. . 127

Figure 7.8

Overall heat transfer coefficient at pcw = 6.8 kPa and pcp = −16.943kpap.128

Figure 7.9

Condensation rate and R-410a mass flow rates at pcw = 6.8 kPa and
pcp = −30.5 kPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Figure 7.10

Heat rejection and COP at pcw = 6.8 kPa and pcp = −30.5 kPa. . . 130

Figure 7.11

Overall heat transfer coefficient at pcw = 6.8 kPa and pcp = −30.5 kPa.131

Figure A.1

Piping schematic of the air feed system to the WSR. . . . . . . . . . 140

Figure A.2

Piping schematic of the fuel feed system to the WSR. . . . . . . . . 141

Figure A.3

Piping schematic of the nitrogen feed system to the WSR. . . . . . . 142

xiii

KEY TO SYMBOLS AND ABBREVIATIONS
¯
Nu

Average Nusselt Number

cP

Isobaric Specific Heat Capacity

m
˙

Mass Flow Rate

T

Period of Oscillation

SL

Laminar Flame Speed

˜
Re

Two-phase Reynolds number

A

Arrhenius Coefficient

D

Diameter

Da

Damk¨ohler Number

E

Activation Energy

h

Specific Enthalpy

k

Reaction Constant of Proportionality

L

Length

MW Molecular Weight
P

Pressure

Q

Heat Release

qc

Specific Heat of Reaction

Ru

Universal Gas Constant

s

Specific Entropy

S.G. Specific Gravity
T

Temperature

t

Time

u

Velocity

Uo

Overall Heat Transfer Coefficient

V

Volume
xiv

W

Work

xf

CH4 Mole Fraction of Biogas

Y

Species Mass Fraction

α

Third Body Efficiency

β

Fraction of Fuel Consumed

χ

Mole Fraction

δ

Flame Thickness

γ

Ratio of Specific Heats

ν

Stoichiometric Coefficient

ω

Rate of Change in Concentration

φ

Equivalency Ratio

φLE

Equivalence ratio at fuel-lean extinction

ρ

Mass Density

τ

Residence Time

τig

Autoignition time

η

Efficiency

F/A Fuel-to-Air Ratio
LHV Lower Heating Value
NOx Total oxides of nitrogen NO + NO2
CHP Combined Heat and Power
COP Coefficient of Performance
EGR Exhaust Gas Recirculation
GRI

Gas Research Institute

GT

Gas Turbine

HRSG Heat Recovery Steam Generator
IHX

Intermediate Heat Exchanger

LMTD Log-Mean Temperature Difference
xv

LP

Chemical Loading Parameter

LP

Fuel-Lean, Premixed

LPP Fuel-Lean Premixed, Prevaporized
MN

Methane Number

MON Motor Octane Number
PaSR Partially-Stirred Reactor
PFR Plug Flow Reactor
PSR Perfectly-Stirred Reactor
RCL Rich-Catalytic-Lean
RQL Rich-Quench-Lean
SCR Selective Catalytic Reduction
SNCR Selective Non-Catalytic Reduction
UHC Unburned Hydrocarbons
VCRS Vapor Compression Refrigeration System
WI

Wobbe Index

WSR Well-Stirred Reactor

xvi

Chapter 1
Introduction and Objectives

1.1

Introduction

The related national goals of energy independence, reducing the emission of various pollutant
species and updating the electrical grid present an intriguing set of engineering challenges. As
methods to achieve the first two of these goals, the development of alternative fuels (i.e., fuels
derived from non-fossil sources) as well as cleaner, from an emissions standpoint, methods of
using domestic fossil sources have generated great interest. Some of these alternative fuels can
be produced at a useful scale near their point of use. A more distributed power generation
system would be well suited to utilize such local local sources and is also a strategy to
achieve the third goal of updating the electrical infrastructure. Such a system would require
a large number power generating facilities of different sizes based on the available local fuel
source. Alternative fuel sites traditionally support small generators (≤ 10 MWe ) driven
by clean, fuel-flexible heat-engines. Natural gas production sites may support generating
systems up to hundreds of MWe . These conventionally fired power generation facilities
would be used in conjunction with other alternative energy sources (e.g., solar, wind and
tidal) to produce electricity for local use. By generating electrical power near its use point,
the losses inherent in long distance transmission of both fuel and electricity can be reduced
or eliminated. Combining distributed generation and alternative fuels presents path towards
a more efficient, cleaner system of power generation.
1

Two alternative fuels in particular are promising candidates for adoption: biogas and
syngas. These fuels are both gaseous at standard atmospheric conditions, which eliminates
the parasitic loss required to vaporize the fuel before combustion, and can be produced from
feedstock readily available in the U.S. Generally, syngas refers to H2 and CO based fuels.
One of the more abundant sources for syngas in the U.S. is coal, though it can also be
produced from biomass and natural gas. Biogas is a term used for the collection of gases
produced by the anaerobic digestion of organic waste materials. This is a process which
takes place naturally in sanitary landfills, manure storage and other sealed organic waste
containers. The result is a mixture of primarily CH4 and CO2 . In the case of large landfills,
the biogas can be pumped from the subsurface in a similar manner to natural gas. Biogas
derived from animal waste or human sewage requires collection of the waste and is normally
produced in specialized digesters located near the collection point.
Both of the primary products of the anaerobic digestion of organic waste, CO2 and
CH4 , are known greenhouse gases. In terms of warming, CH4 is a 21 times more effective
greenhouse gas than CO2 [5]. To prevent buildup of CH4 and ecological damage, gas must
removed in locations like sanitary landfills where it may naturally collect. This effluent may
be required by law to undergo treatment to reduce its impact on the local environment.
One method of treating biogas is to burn it using flares. The combustion of the CH4 in
biogas, which ideally results only in the emission of CO2 and H2 O, acts as a net reduction
in CO2 equivalent greenhouse gas emissions and eliminates a potential fire hazard. There
are, however, no other benefits from the flaring. Using the biogas to generate electricity or
hot water takes the greenhouse gas reduction of flaring and adds useful by-product.
One of the more efficient options for driving electrical generators is the gas-turbine (GT)
engine [6]. GT engines may be roughly subdivided into two groups: micro-turbines and
2

industrial turbines. Micro-turbines produce less than 500 kWe and were developed over the
last 25 years from turbocharger technology or scaling of industrial turbine designs [7]. The
small scale of the GTs often used in alternative fuels applications makes achieving high a
thermal efficiency, a general attribute of GTs, a challenge. As a result, many micro-turbines
run a recuperated cycle. Industrial turbines may be further subdivided into two categories:
pure industrial and aero-derivative. Pure industrial models were purpose designed from the
outset as ground based power generators. Aero-derivative, as the name implies, are based on
engines intended to power aircraft. Modifications are often made to aero-derivative engines
to reduce cost and make them better suited to ground based power production.
The two scales of turbines rely on similar basic architecture to produce power. A common
arrangement is that of a compressor driven by a turbine on a single shaft. In the case of
a micro-turbine, these are typically a single-stage centrifugal compressor and a single stage
radial turbine. This grouping of radial flow turbomachinery may be used through the smaller
scales of industrial turbines (ca. 2MW). Larger industrial and aero-derivative engines rely
primarily on multi-stage axial compressors and turbines. Aero-derivatives also maintain their
multi-spool arrangements for driving different stages of compression at different speeds. In
the flow path between the rotating devices sits the combustor. It takes the compressor
discharge, adds fuel, and reacts the mixture to generate high temperature gas. A portion
of the energy in the gas extracted by the turbine is used to drive the compressor. Any
energy in excess of that required to drive the compressor can be used to drive an electrical
generator, drive other rotating machinery, or produce thrust. Of these components only the
combustor is particularly affected by the additional challenges posed by alternative fuels and
fuel flexibility.
Regardless of scale, fuel efficiency can be improved by using the remaining energy in the
3

turbine exhaust for heating a second fluid yielding a combined heat and power (CHP) system
or a co-generation plant. The small scale and recuperated cycle of micro-turbines generally
limits them to the production of hot water. The water may be used for a variety of purposes
including domestic hot water, energy for absorption chillers, building or process heating,
and boiler feed water pre-heating. Industrial turbines, due to the high mass flow rates and
lack of recuperation, can co-generate high quality steam. This steam is then often used in a
secondary Rankine cycle loop to generate additional electrical power thereby increasing the
fuel efficiency of the system. To maximize the efficiency of the secondary Rankine cycle, a
steam condenser is typically employed to reduce the minimum cycle temperature. As they
do in more typical Rankine cycle systems, these condensers use or consume large quantities
of water. If these larger industrial turbines are to be used in a more distributed fashion,
alternative cooling methods for the steam condensers are required for regions where the
water supply is limited and ambient conditions make evaporative cooling unappealing.

1.1.1

Gas Turbine Combustors

In both aircraft and ground-based GT engines the purpose of the combustor is to convert the
chemical energy, stored in the fuel and air, into high-quality thermal energy. The combustor’s
two main components are the casing and the liner, see Figure 1.1. The casing provides
pressure containment for the system, and the liner is designed to hold the hot combustion
gasses. Fresh air flows into the casing and takes one of three paths into the liner. The
first path, labeled primary air in Figure 1.1, carries the air into a mixing zone where fuel is
added. This mixture then flows into the high temperature region where it acts as the primary
combustion charge. A second path provides cooling air to the liner to prevent mechanical
failure due to excessive temperatures. The final path dumps any remaining air into the liner
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Figure 1.1: Sketch of a gas turbine combustor, blue lines indicate cool air, orange lines
indicate recirculation/flame stabalization zones and red lines indicate product gases. For
interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation.

near the exit through the dilution holes to achieve the desired temperature profile. It follows
that the high temperature region within the liner is commonly divided into three zones:
the primary zone, intermediate zone and dilution zone. Each have different functions and
present their own design challenges [8].
The primary zone is the portion of the combustor that provides space for ignition and
completion of a majority of the combustion processes. It is important for the geometry of
this region to generate sufficient turbulence for the mixing of the reactants, provide a location
for anchoring the flame, and sufficient temperature for the combustion process to occur. In
this zone there may be regions where temperatures are high enough to dissociate CO2 into
CO, which is both a fuel and a pollutant, and O2 . Alternatively, regions may exist where
temperatures are low enough to retard the completion of the conversion of CO to CO2 . To
5

recoup the losses caused by dissociation or complete the burnout of CO an intermediate
combustion zone is used.
The length of the intermediate zone is necessary to perform two tasks. First, in groundbased and aircraft GTs at low altitude it serves as a zone for the reduction of CO in the
product gases from the primary zone. In the case of dissociation due to high temperatures in
the primary zone, this is done by the addition of small amounts of air through the liner wall
which drops the temperature of the mixture. The additional O2 also helps to complete the
combustion of any pockets of unburned fuel. The second role of the intermediate zone takes
place at high altitudes or other operating conditions that slow the reactions in the primary
zone. Here it provides additional space for the primary combustion process to occur. This
compensates for the lower reaction rates at high altitude due to the lower concentration of
O2 or at lower altitudes due to low combustion temperatures. At the end of the intermediate
zone temperatures are still to extreme for injection into the turbine.
In the dilution zone more cool air is added to the combustion products to reduce their
temperature to one suitable for the turbine inlet. The cooling air is injected through the
wall of the liner in such a way to generate the desired temperature profile. This increases
the life of the turbine blades and sealing materials by reducing the temperature where the
mechanical stresses are highest. Because the limiting factor on GT performance is normally
the thermal capabilities of the turbine, a major effort is devoted to producing the desired
temperature profile.

1.1.2

Challenges of Alternative Fuels

Alternative fuels require a combustor of special design. These fuels tend to be of lower
calorific content relative to common fossil fuels like natural gas. Thus, a greater fuel flow is
6

required to attain the same heat release. To compensate, the fuel handling and combustion
systems may need to be larger than systems intended for natural gas. The composition of
many alternative fuels tends to be site specific and can vary from day-to-day or even hour-tohour which requires a degree of fuel flexibility. To be able to respond to the changes in fuel,
specialized control systems and, in some cases, variable geometry are necessary to adjust fuel
flow to meet power demand. Finally, the ongoing desire to further reduce pollutant emissions,
particularly oxides of nitrogen (NOx ) and unburned hydrocarbons, adds yet another layer
of difficulty by requiring careful control of the combustion environment to avoid conditions
where these species are produced.
There are a number of techniques for overcoming the challenges posed by alternative fuels.
One method is ‘upgrading’ which is a process that increases the calorific content by removing
diluent. For fuels whose primary combustible component is CH4 , upgrading essentially
scrubs the alternative fuels into natural gas before it enters the combustor. Additional
capital equipment in the form of filters, separators, and absorption columns are required to
clean the gas. The energy required to run the upgrading equipment is a parasitic loss to
any stand-alone system. Upgrading may alleviate two difficulties associated with alternative
fuels, energy content and variability, but it does little to address pollutant emissions other
than to reduce the H2 S content of the fuel.
The modern practice of fuel-lean premixed, prevaporized (LPP) combustion is a method
for reducing NOx emissions by decreasing combustion temperature. LPP has the added
benefit of reducing fuel consumption which is the only method of reducing CO2 emissions.
Operating in the fuel-lean regime is not without complications which are discussed in Sections 2.2 and 2.3 some of which are exacerbated by the content variation of alternative fuels.
Clearly, the most desirable solution would be a flexible combustor that operate at fuel-lean
7

conditions on relatively low heating value fuels.
To aid the design such a combustor, a systematic analysis of the combustion properties
of alternative fuels of varying constituency is required. It is important to know how much, if
any, processing of the raw alternative fuels beyond that required to remove matter hazardous
to other elements of the GT is necessary for successful, stable combustor operation. Further,
it is necessary to have a baseline understanding of the content and properties of the gas
which will be fed into the turbine and eventually into the atmosphere as exhaust to design
for modern and future emissions requirements. For these reasons, a laboratory model of a
GT combustor in which combustion stability and emissions investigations can be carried out
in a controlled manner is of great use [9]. From experiments performed using such a model
the necessary background knowledge on the combustion characteristics of various grades of
alternative fuels for the design of future combustors can be attained.

1.2

Laboratory Modeling of a GT Combustor

Many of the major steps of the combustion process in a GT take place in the primary zone
of the combustor. Therefore, if an investigation into the use of alternative fuels in a GT is
to be undertaken, an accurate model of this zone required. While it is possible to use the
combustor out of a production GT, the flow patterns tend to be geometry specific. Thus,
results may not be applicable to all systems. For this reason using a simplified model of the
primary zone is a preferred way to investigate the combustion properties new fuels [9].
Two primary methods of modeling are available: numerical and physical experiments.
Each has its benefits and drawbacks. Numerical experiments are convenient, from a safety
standpoint, in that they do not require physical combustion to take place. They also allow

8

for very precise variation of the boundary conditions. However, without experiments to
calibrate them, the model’s predictions cannot be guaranteed to be valid. Experimental
data, when gathered carefully, accurately characterizes what actually happens in a system,
but practical considerations affect the resolution and precision of the information. Following
either route requires a model whose complexity should be a compromise between its ease
of application and accuracy of representation. To which extreme the model approaches is
based on the nature of data desired.
One relatively simple model, useful in both numerical and physical experiments, of the
primary zone of a GT combustor is the well-stirred reactor (WSR). The WSR is a laboratory version of the theoretical perfectly-stirred reactor (PSR). Like the primary zone,
the combustion inside a WSR is characterized by intense turbulent mixing of burned and
unburned gases. Additionally, operating conditions within the WSR can be controlled reasonably and safely in a laboratory setting allowing for the investigation of basic combustion
science problems. Thus, the WSR provides a benchmark useful for combustor modeling and
design [2, 8, 10].

1.3

Cooling of co-generation steam loops

Steam-cycle power generating facilities are the largest consumers of water in the United
States [11, 12]. The primary consumer of water in the Rankine cycle is the steam condenser.
Though they consume less water than traditionally fired Rankine cycles, combined-cycle
GT applications may still require large quantities of water depending on condenser design.
Three different condenser designs are commonly used. The once-through design relies on
a continuous stream of water to cool the steam exiting the turbine. Condensers of this

9

type are large users of water but not large consumers. Due to the large quantity of water
required, power plants using once-through condensers must be located near rivers, lakes or
ocean coasts. If a large source of water is not available, closed-cycle condensers may be
employed. Instead of using high flow rates like once-through designs, closed-cycle systems
employ evaporative cooling. The primary coolant is recycled through the condenser in a
closed loop. This reduces the usage of water, but greatly increases the consumption of
water due to the evaporation of a portion of the cooling water. Finally, there is the dry
cooling option which relies on air movement to condense the steam. No additional water
is required, so plant location is less dependent on the availability of local water sources.
However, minimum temperatures are dictated by the ambient wet bulb temperature leading
to seasonal swings in plant efficiency.
The design of a condenser is limited by both the load of the cycle and statutory limits
on thermal pollution. For once-through condensers the limit is the temperature rise of the
cooling water supply. Limits may be placed on both the temperature rise and the maximum
temperature of the body of water into which cooling water is discharged [13]. For closedloop cooling systems the issues arise from the thermal plume of saturated air created by the
cooling towers. The plumes, if located near roadways or airports, can cause visibility issues
or lead to surface icing in sub-freezing atmospheric conditions. Both open and closed-loop
cooling systems operate in a range of temperatures that promote the growth of the legionella
bacteria which can be carried by plumes from cooling towers [12].
Combined-cycle plants generally consume less water that steam cycle plants. To further
reduce usage most new combined-cycle power plants opt for a closed-loop cooling systems.
Closed-loop systems offer better temperature stability that dry systems [14]. Water usage
may be eliminated for the full range of steam power plant sizes is to use closed-loop refrig10

eration systems to remove heat in the condenser. In this case the condenser of the Rankine
cycle acts as the evaporator in the refrigeration cycle.
The use of refrigerants offers three basic advantages over water. The most obvious is the
elimination of water from the cooling circuit. Second, refrigerants have higher heat transfer
rates than water or air increasing the efficiency of the condenser. Lastly, using a refrigerant
cycle will stabilize the efficiency of the Rankine cycle by providing a nearly constant minimum
cycle temperature regardless of season. The primary disadvantage of such a system is the
parasitic load it imposes on the power cycle.

1.4

Research Objectives

The objectives of the present research are as follows:
• Study the effect of CO2 dilution on laminar flame speeds of CH4 -air combustion in a
WSR with detailed chemical kinetics
• Study the effect of CO2 dilution on the fuel-lean extinction limits of CH4 -air combustion in a WSR with detailed chemical kinetics
• Design of a laboratory scale WSR for alternative fuels combustion research at MSU
• Investigate the cycle impact of refrigerant cooling on combined-cycle steam plants
• Design a laboratory scale model of a steam power plant condenser with refrigerant
cooling for more detailed investigations

11

Chapter 2
Alternative Fuels in Gas Turbine
Combustion
There are many aspects of combustion in stationary GTs that are challenging to the design
engineer. These include, but are not limited to: fuel flexibility, combustion stability and
emissions. In this chapter a review of the archival literature is presented to provide necessary
background information on these issues. Some focus will be on the development and use of
WSR models to study and combustion phenomena.

2.1

Emissions

Since the passage of the Clean Air Act in 1955 and its updates in 1963, 1970, 1977, and
1990, designers have been challenged to create ever cleaner combustion systems. Methods of
controlling the emission of pollutant species like unburned hydrocarbons (UHC), CO, and
NOx are competitive. The conditions that lead to a reduction of UHC and CO cause the
rate of NOx production to increase and vice versa. This section will examine the processes
that lead to the production of pollutant species as well as some modern methods that are
used to reduce emissions of these controlled pollutants.

12

2.1.1

Oxides of Nitrogen

The pollutant species nitric oxide (NO) is a minor product formed primarily by the oxidation
of nitrogen, present in either the oxidizer or fuel, in high temperature regions (above 1800K).
It is a key component of photochemical smog and, when further oxidized to NO2 , acid
rain. In the upper atmosphere NO is converted to NO2 in reactions that consume ozone
which can lead to increased ultraviolet radiation reaching Earth’s surface. For these reasons,
NOx (NOx = NO + NO2 ) is one of the more tightly controlled pollutant species around the
world [15]. In this section the three primary mechanisms for the production of NOx in a GT
engine are introduced.
The thermal, or Zeldovich, mechanism is the major source of NO in high temperature
(> 1800 K) regions of the combustor. This is a mechanism for the oxidation of atmospheric
N2 in the following chain reactions [16]

O + N2 ⇄ NO + N

(2.1)

N + O2 ⇄ NO + O

(2.2)

N + OH ⇄ NO + H

(2.3)

The mechanism is controlled by Eq. (2.1) which requires high temperatures to provide the
energy necessary to split N2 . Generally the peak production of NO is found slightly fuel-lean
of stoichiometric, see Section 2.2 for definitions. Under these conditions there are both an
excess of oxygen and sufficiently high temperatures to drive the mechanism. Compared to
fuel oxidation, NO formation is slow and generally occurs downstream of the flame [8].
Many techniques for reducing NOx emissions, as will be discussed later, rely on keeping
13

temperatures low enough to reduce the effectiveness of the thermal pathway. In these situations other mechanisms become responsible of for NO production. The N2 O mechanism
has been shown to be important in the production of NO, especially in fuel-lean conditions.
This mechanism consists of three steps

O + N2 + M ⇄ N2 O + M

(2.4)

H + N2 O ⇄ NO + NH

(2.5)

O + N2 O ⇄ 2NO

(2.6)

The importance of this pathway increases with pressure in fuel-lean combustion and dominates in low emissions combustors [17, 18]
The third mechanism for forming NOx acts in regions of a combustor where insufficient
time has passed for the thermal pathway to have completed. NOx generated in such regions
is termed ‘prompt’. In experiments, Fenimore [19] discovered that near the flame front, NO
production is linked to the combustion chemistry of the hydrocarbon fuel. In these zones the
hydrocarbon radicals attack the molecular nitrogen in the following series of rapid reactions

CH + N2 ⇄ HCN + N

(2.7)

CH2 + N2 ⇄ HCN + NH

(2.8)

CH2 + N2 ⇄ H2 CN + N

(2.9)

C + N2 ⇄ CN + N

(2.10)

14

From here the exact path to NO production varies depending on the fuel/air ratio [20].
Generally, the next step is the formation of amines and cyano compounds. These are then
oxidized to produce NO. This process is coupled with the thermal mechanism and can become
complex.
Nitric oxide emissions are closely tied to a few combustion parameters. Combustion
temperature is considered to be the most important of these [21, 22, 23]. Temperatures
most obvious impact is on production via the thermal pathway which, as discussed above,
becomes important only at sufficiently high temperatures. A second parameter of some
importance is residence time in the hot zone. The thermal mechanism is slow relative to other
reactions. Thus, sufficient residence time at high temperatures are required for significant
production. There is also a slight negative dependence on pressure [17, 22]. These factors
primarily influence the production of NOx through the thermal pathway. Most of the control
strategies discussed in Section 2.1.3 are designed to avoid this pathway.

2.1.2

CO and UHC

The production of CO is closely related to the reactant mix as well as the temperature of
the primary zone. A fuel-rich, see Section 2.2 for definition, primary zone will have CO as a
major product species due to a lack of O2 to complete the oxidation to CO2 . If the primary
zones is designed to operate at stoichiometric or slightly fuel-lean, then the presence of CO
in the product gases is due to dissociation of CO2 at high temperature. Accordingly, the
gradual addition of cooling air should, in principle, reduce CO emissions.
In contrast to predictions made with equilibrium theory, CO production is highest when
combustion temperatures are low (< 1100K). This has three likely causes [8]:

15

• Residence time or fuel-to-air ratios too small to produce adequate burning rates.
• Poor mixing of fuel and air leading to locally rich zones as well as zones too fuel-lean
to support combustion.
• Reaction quenching along cool liner walls.
Oxidation of CO is often the determining factor in the design of practical combustors
with respect to average temperature and residence time [8]. Dry oxidation of the CO present
after the primary zone is difficult to sustain due to the high activation energy of the reaction
between CO and O2 . In practical systems where a certain amount of water from the combustion of a hydrocarbon fuel is present, oxidation takes place in one of two wet reactions
dependent on temperature. At high temperatures the equilibrium reaction

CO + OH ⇄ CO2 + H

(2.11)

is the primary means of reducing CO. At lower temperatures the water-gas shift reaction

CO + H2 O ⇄ CO2 + H2

(2.12)

becomes the important reaction [24].
Unburned hydrocarbons, like CO, are the result of rich combustion and low temperatures.
The majority of UHC emitted are the products of incomplete combustion and may take
different forms. They may take the form of the fuel species or, if the fuel was a blend or
consisted of higher hydrocarbons, they can be smaller hydrocarbon species that result from
the break down of the original fuel. Liquid fuel droplets may also pass through the combustor
when inadequately atomized [8]. In fuel-lean mixtures, UHC often occurs due to poor flame
16

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Figure 2.1: Sketch of the relation between fuel-air mixture, temperature (red line), and
emissions of various pollutant species (blue lines).

propagation through the mixture [24].

2.1.3

Methods of Emissions Control

There is a narrow range of temperatures where UHC, CO, and NOx can be reduced simultaneously, see Figure 2.1. Older combustion systems, sometimes called ‘traditional’, employed
diffusion flames. In these combustors fuel and air are introduced into the primary zone
where both reactant mixing and combustion take place. Thus, the combustion is diffusion
controlled and tends to take place at near stoichiometric conditions (φ = 1 in Figure 2.1)
leading combustion temperatures that fall outside the ideal zone for pollutant emission reduction [25]. A number of methods have been developed over the last 40 years to either
promote combustion in the ideal temperature range for pollutant emissions reduction or
abate emissions from more traditional designs. Much of this effort has been focused on

17

limiting NOx emissions. The reduction of CO and UHC is sometimes compromised by this
technological focus [26].
The primary goal of combustor design strategies to reduce NOx emissions to limit the
rate of production from the thermal mechanism [8]. This is accomplished mainly by reducing
maximum combustor temperatures. Reduction of average maximum temperature is not
sufficient to meet NOx emissions goals. As such, effective mixing is also required to attempt
to eliminate local hot spots. Mixing in the flame front has been shown to increase NOx
emissions, so mixing must take place before combustion to create a homogeneous incoming
charge [18]. Finally, residence time in the primary zone is minimized to further reduce the
production of NOx [17]. Several methods have been developed to accomplish these tasks
with varying degrees of popularity.

2.1.3.1

Diluent Injection

Early methods of reducing NOx production in the combustor included the injection of various
diluents. The additional mass acts to reduce the combustion temperature, thereby avoiding
the thermal mechanism, and increase power output at the same turbine inlet temperature
by increasing mass flow through the turbine [27]. Using diluents also allows the combustor
to operate near stoichiometric conditions for added stability.
One of the first diluents tested was H2 O. Liquid H2 O injection reduces combustor temperatures by using combustion energy for vaporization. If available, steam may also be
injected to act as a thermal sink. Several methods of water/steam injection have been
used [25, 27, 28]. Special nozzles that inject the fuel and either water or steam co-locally are
commonly used. Liquid water may also be injected upstream of the combustor and allowed
to vaporize in the air stream before fuel mixing. In terms of NOx emissions reduction, liquid
18

water is more effective than steam [29, 30]. If either liquid water or steam are to be injected
into the combustor, they must be of high purity to avoid fouling or damage to downstream
components. Damage to these systems may lead to increased CO and UHC emissions.
Recirculating gas from the exhaust stream back into the combustor (EGR) as a diluent
is another way reducing primary zone temperatures [31]. The exhaust gas has two effects.
First, it reduces the concentration of O2 in the reactants which slows the kinetics and reduces
maximum flame temperatures. Second, the presence of CO2 and water vapor in the exhaust
increases the heat capacity of the reactants [24, 25]. The implementation of EGR may require
the use of an intercooler to reduce the temperature of the exhaust before injection into the
combustor [8, 32]. OxyFuel combustion, fuel and oxygen rather than air, combined with
EGR also has potential as a CO2 capture technique [32].
Diluent injection alone may not always be sufficient to achieve the levels of NOx required
by current and future standards [23]. This has led to the development of methods requiring
more complex changes to combustor geometry or operation in different combustion regimes.
These techniques have the advantage of not requiring additional plumbing to facilitate the
injection of species other than fuel and oxidizer into the GT.

2.1.3.2

Catalytic Combustion

Enhancing combustion reactions using catalysts is another method of reducing NOx . In systems employing catalytic combustion, fuel and air are premixed, below flammability limits,
prior to entering the combustor. Within the combustor is a catalyst matrix carried by a
support structure to initiate the combustion reaction. The limited energy content of the
mixture prevents combustion temperatures from approaching those required for activation
of the thermal NOx pathway. Ideally, because the mixture is below the flammability limit,
19

flashback is not a possibility. However, autoignition in the mixing apparatus is possible
near the fuel injectors where locally flammable mixtures may be present [26]. It is vitally
important that the fuel and air be well mixed before reaching the catalyst as the efficiency of
the reactions is dependent on stoichiometry. The reactions are also temperature dependent
and, at part load, may require a pre-burner to reach the required temperature range. Temperatures that are too high lead to scintering of the catalyst and its support structure and
vaporization of the catalyst. In large industrial GTs increasing combustor exit temperatures
for greater thermal efficiency has led to the development of staged catalytic combustion. To
avoid overheating the catalyst and its support structure, only a portion of the fuel is reacted.
The rest is added downstream in a secondary burner which is stabilized by the hot gas from
the catalytically supported section of the combustor [33, 34, 35].

2.1.3.3

Fuel-Air Mixture Adjustment

Adjusting the combustion mixture to be fuel-rich is another method of reducing combustion
temperatures. Systems of this type also premix the fuel and air to ensure that the combustion takes place at the desired ratio. Unlike catalytic combustors, the fuel-rich primary zone
is capable of maintaining a stable flame. The excess of fuel and dearth of O2 in the primary
zone reduces combustion temperatures but leads to excessive quantities of CO and UHC.
Careful addition of air in the intermediate zone and dilution zone may be used to complete
the combustion process [8]. Another technique to burn out the CO and UHC is the richquench-lean (RQL) combustor. Through the addition of air and the geometry of the liner, the
reactions of the rich primary zone are quickly quenched to pass through the stoichiometric
point as rapidly as possible. The now fuel-lean mixture maintains sufficient temperature to
complete the burnout of CO and UHC in a second combustion zone [36, 37, 38]. RQL com20

bustors have been shown to be promising in instances where fuel bound N2 is a concern [38].
Rich-catalytic-lean (RCL) combustors use a catalyst rather than just liner geometry flame
stabilization in the fuel-lean zone. Using a fuel rich mixture allows a wider range of catalysts
to be employed and helps catalyst life [39].
Fuel-lean premixed (LP) combustion follows an approach that is a middle ground between
the catalytic and rich primary zone methods. Fuel is premixed with an excess of air, but the
mixture is maintained above the lower flammability limit. The excess air acts as a diluent
and reduces the combustion temperature to mitigate NOx production from the thermal
pathway. LP combustion is a popular method of reducing NOx emissions in ground based
GT engines [26]. The ideal scenario is to maintain combustion near the fuel-lean flammability
limit throughout its range of operation. Practically, this is not possible without some form
of fuel or air staging. Fuel staging is the easiest to implement. As load demand changes
some of the fuel nozzles are alternately fed or cut-off from the fuel supply to maintain the
desired combustor temperature and fuel-air mix. Staging is generally either radial or axial.
In either method a pilot flame using a locally richer mixture may be used to stabilize the
combustion [25]. Air staging is mechanically more complex as it requires the diversion of
the high-temperature compressor discharge. When combined with fuel staging, air staging is
preferable because it increases the operating range [40, 41]. Due to its popularity, Section 2.2
is dedicated to this fundamentals of this technique.

2.1.3.4

Post Combustion Treatment

Post combustion treatment options generally involve reduction of NOx to N2 and H2 O using
injected chemicals and catalysts. In selective non-catalytic reduction (SNCR) nitrogen containing compounds (e.g., ammonia, urea, and cyanuric acid) are injected into the exhaust
21

stream. In a narrow temperature range (1200 - 1370 K) these chemicals reduce NOx . Addition of these chemicals outside of this temperature range leads to either little or no decrease
in NOx (low temperatures) or increased levels of NOx (high temperature) [42, 43]. The addition of catalysts to the process, now called selective catalytic reduction (SCR), allows for
the reactions to take place at lower temperatures. The catalysts are commonly base metal
oxides, precious metals in a ceramic matrix or zeolites. The reduction agent is injected into
the effluent stream before the mixture passes across the catalytic bed. Catalysts reduce the
necessary reaction temperatures to 400 - 700 K [43, 44]. In both SNCR and SCR the reductant must be added in the proper proportion and be well mixed in the flue gas to prevent
ammonia, a controlled pollutant as well, from passing through the system [45]. A reduction
of NOx content of up to 95% is possible with these techniques. The added complexity of
SCR and SNCR systems limits their practicality in some applications [46].
Other methods of NOx abatement include: non-thermal plasma, absorption, electron
beam flue gas treatment, and bioprocesses (e.g., using nitrogen fixing bacteria in compost or
soil). These techniques are either still in the development phase or in limited implementation [44]. It is apparent that if a post combustion solution is to be implemented, additional
capital equipment in the form of storage tanks, reductant injectors and control systems, and
catalytic or growth beds are required.

2.1.3.5

CO and UHC

The rates of UHC and CO emissions are decreased by similar methods. The most effective
solutions involve higher combustion temperatures and longer residence times at elevated
temperature. This is contradictory to most methods used to reduce NOx which rely on
lowering combustion temperatures. Better mixing of reactants, also useful for reducing
22

NOx , helps to avoid pockets with a local excess of fuel, in systems designed to operate with
excess air, where UHC and CO can be produced. Fuel or air staging like that used in LP
combustion can also be used to increase combustion efficiency and thereby reduce emissions
of UHC and CO over an engines operating range. Finally, careful addition of cooling air
avoids reaction quenching near the walls of the combustor [8, 24].

2.2

Lean Premixed Combustion

The increased interest in fuel-lean combustion systems in the stationary GT market has been
driven by need for more fuel efficient, cleaner power generation. Volatility in the fuel market,
both currently and projected in the future, is pushing consumers to demand increased fuel
efficiency. Meanwhile, regulatory pressure to decrease emissions of pollutant species requires
original equipment manufacturers to design cleaner systems. Some clean-up is possible with
post combustion treatment systems (e.g., SCR as discussed earlier), but decreasing pollutant production is preferable based on capital and operational considerations [47]. Lean
combustion is beneficial in that it produces lower combustion temperatures, reduced NOx
production, and fuel consumption rates. LP combustion has become one of the most popular
methods of balancing pollutant emissions with efficiency.
Combustion can be categorized by its global chemistry as fuel-lean, stoichiometric or
fuel-rich. The boundaries between zones are defined using the equivalency ratio, φ, which
can be defined as
φ=

F/A
(F/A)s

(2.13)

where F/A is the molar fuel to air ratio and the subscript s indicates stoichiometric conditions (i.e., only CO2 , H2 O, N2 in the products). When φ is unity, the combustion is
23

stoichiometric. Fuel-lean combustion takes place at φ < 1 and fuel-rich when φ > 1. The
excess of oxidizer or fuel in off-stoichiometric combustion cools the reaction and introduces
additional major species into the product mix.
In general, fuel-lean combustion has multiple benefits. The lower combustion temperatures of fuel-lean mixtures inhibits the thermal NOx pathway decreasing the emission of the
controlled species. Decreased fuel consumption has obvious economic advantages. Lower
carbon levels in the reactants means that possible emissions of CO2 and CO are reduced.
Lastly, the thermodynamic properties of the reactants in a fuel-lean system lead to increased
thermal efficiency [48]. Lean combustion systems are more complex than traditional combustors, and their implementation introduces an interesting set of engineering challenges.
Inside a GT combustor, fuel-lean combustion refers specifically to a fuel-lean primaryzone. This often requires special geometry to ensure combustion occurs under the desired
conditions. For cooling purposes, regardless of the primary-zone φ, the overall fuel-to-air
ratio is always fuel-lean in a GT combustor. A larger percentage of the total air is required
to flow through the primary zone in LP systems than in diffusion controlled combustors.
This limits the available air for liner cooling and dilution which affect liner life and the
temperature profile entering the turbine, respectively [47].
Combustion in the fuel-lean regime can be accomplished only through premixing of the
fuel and oxidizer. If not premixed, the fuel and oxidizer will tend to combust under stoichiometric or near-stoichiometric conditions after diffusion mixing in the combustor. The degree
of premixing is important to emissions. Incomplete mixing will lead to pockets of relatively
rich mixtures. These pockets will yield hot spots which can increase NOx emissions [49].
Conversely, relatively fuel-lean pockets can increase UHC emissions due to incomplete combustion.
24

In practice the mixing section of a LP combustor uses geometry to enhance mixing
without greatly increasing residence time in the mixer. The addition of swirl inducing
vanes and step geometry changes are common methods for increasing mixing rates. Rapid
mixing ensures that ignition takes place in sections designed for high-temperatures and at
the intended φ.
Of major importance to the design of the premixing section of LP systems is the autoignition process. In premixed systems the rate at which the combustion reactions take place is
exponentially dependent on temperature. For autoignition this is captured in ignition delay
time, τig , which is a measure of the time required for combustion reactions to accelerate.
When combined with the bulk through flow velocity, τig can be used to size the premixer.
Ignition delay may be calculated from a correlation taking the form [50]

τig = A exp

E
Ru T

[O2 ]a [f ]b

(2.14)

where A, a, and b are constants, E is the activation energy of the global reaction, Ru is the
universal gas constant and [O2 ] and [f ] are the molar concentrations of oxygen and fuel in
the reactant mix, respectively. The constants of Eq. (2.14) are determined experimentally
using a variety of methods, see [50].
Once lit, a combustor’s continuously stable operation is critical to the function of a GT.
Determining the static instability limit of a specific combustor or range of similar combustors
is often the result of extensive testing [51]. In traditional combustors, blowout determined
the turndown for the system. The limits are even more critical for the various dry low-NOx
approaches. To effectively reduce temperatures, LP combustors need operate near the fuellean extinction limit. The importance of stability issues in LP combustors combined with

25

)ODVKEDFN

)XHO $LU 5DWLR

6WDWLF 6WDELOLW\
/LPLW

6WDEOH
%XUQLQJ

$LU )ORZ 5DWH
Figure 2.2: A general combustion stability loop, adapted from [1].

their popularity has led to an intense research focus

2.3

Stability

Under ideal circumstances the combustor would operate at a φ that generates the minimum
combination of UHC, CO and NOx . However, practical considerations may force φ to be
richer or leaner than this ideal case. In either direction there are static stability limits.
Even when operating between these limits there may be combinations of φ and air flow-rate
where the acoustic and heat release characteristics of the combustor couple causing dynamic
instabilities. Either avoidance or control of these instabilities is of great importance to the
reliable operation of LP combustors.
The stability of a GT combustor depends on its operating condition as characterized by
φ, m
˙ and fuel constituency. Within the primary-zone the flame anchors in areas where the
local flame speed and matches the gas speed [52]. The effects of changing φ (flame speed)
and air flow rate (gas speed) on the stability of a combustor are plotted against each other
26

in a stability loop. A general stability loop for a GT combustor, fuel type, and operating
pressure, adapted from [1], is shown in Figure 2.2. The static stability limit, extinction or
blowout, is divided into two parts about the maximum air flow rate which occurs at φ ≈ 1.
Above this point the combustion is extinguished by an excess of fuel, rich-extinction, and
below it by an excess of air, lean-extinction. At low air flow rates there is a risk of the flame
propagating upstream (i.e., flame speed is greater than bulk flow speed) out of sections
of the combustion system designed to withstand high temperatures, a condition known as
flashback. Stable burning within the combustion chamber occurs when the conditions lie
within the space bounded by the stability loop and the flashback limit.
The major drawback to LP combustion is its susceptibility to a variety of instabilities.
Depending on the proximity of the fuel-lean extinction limit to the operating point of the
combustor, slight variations in the fuel or air flow rates can lead to the flame being blown
out of the combustor. Flashback may occur due to changes in fuel content that increase
the flame speed. Temperatures in the mixing section must be carefully controlled to avoid
autoignition in components not designed to survive combustion temperatures. Variations
in fuel composition or air flow rate may cause the combustor to enter a dynamically unstable operation point. Due to the benefits of LP combustors, control and identification of
phenomena that affect their stability has been an area of intense research.

2.3.1

Static Instability

Static instabilities are important to all GT combustion systems. They represent the hard
operating bounds of the combustor. In traditional diffusion based systems, these bounds
limited turndown which is of prime importance to both aircraft and ground application [8].
Static limits have an increased level of importance in LP combustors relative to traditional
27

systems. The weak extinction limit not only affects turndown but also limits the lowest
possible NOx emissions. Identifying and, if possible, extending the stability limits is an
important part of the development of a combustor design.
Stability limits are governed by combustor geometry as well as combustion parameters.
For a combustor under development, the static stability limits are identified experimentally.
Stable combustion is established and fuel flow is decreased until the flame is blown-out of the
combustor. This establishes the value of φ at fuel-lean extinction. Increasing fuel flow until
blow out identifies φ at rich-extinction. The procedure is repeated for several air flow-rates.
When plotted they establish the stability loop for the combustor. In aircraft applications
stability loops are determined for a variety of pressures (real or simulated by water injection
or nitrogen dilution [10]) to simulate altitude [8].

2.3.2

Dynamic Instability

When operating near the stability limits the combustor may exhibit dynamic instabilities
which are a coupling of the acoustics of the combustor and variations in heat release from the
combustion process [53]. Depending on their strength, dynamic instabilities may cause excess
noise, prematurely extinguish combustion, or mechanical failure of the combustor. While
static instabilities have been a concern since the advent of the GT [8], the issue of dynamic
instabilities has become more prevalent as GT combustors have pushed LP technology.
The onset of such dynamic instabilities is governed by the modified Rayleigh criterion [54]
T
V

T

P ′ (x, t) Q′ (x, t) dtdV ≥

0

V

0

Li (x, t) dtdV

where P ′ is the combustor pressure oscillation, Q′ is the oscillation in heat release,
28

(2.15)

Li

represents the net acoustic losses in the combustor, x is the position vector within the
combustor, t is time, and T is the period of oscillation.

The left-hand-side of Eq. (2.15)

represents the addition of acoustic energy to the system. The right-hand-side represents
the removal of acoustic energy. When the combustor is unstable, the energy production
outweighs the removal of energy.
Forcing a combustor into unstable operation may be accomplished by increasing the
magnitude Q′ , decreasing the phase difference between P ′ and Q′ , or a combination of the
two. Much of the instability is controlled by the geometry of the combustor, fuel and air
injection strategies, and flame patterns [55]. Models have been developed to predict the
conditions for a given combustor and fuel will lead to dynamic instabilities [53, 56, 57].
Dynamic instabilities are beyond the scope of this work and the interested reader is directed
to Lieuwen’s book on combustion instabilities [58].
When an LP combustor is exposed to a fuel supply whose content varies, its regions
of stable operation shift with the changing fuel. The effect of various minor hydrocarbon
species as well as diluents can be counterintuitive. In natural gas, changes in the C2 H6
and C3 H8 content affects the flamespeed and thereby the risk of flashback. In biogas CO2
does not behave as an inert diluent and fluctuations in its mole fraction lead to a variety of
stability issues. The desire for future GT systems to be as fuel-flexible as possible has led to
interest in methods to expand the stability envelopes of LP combustors.

2.4

Fuel Flexibility & Alternative Fuels

Since the fuel crises of the latter part of the 1970’s and early 1980’s, it has been recognized
that fuel sources of non-fossil origin would eventually be necessary to meet the world’s energy

29

needs. Early work on the effect of alternative fuels and the merits of the fuel flexibility of GTs
with traditional combustors took place at this time [59]. It was also in this time frame that
the demand for tighter emissions controls led to the development of LP combustion systems.
Subsequent drops in fossil fuel prices relative to income in the US limited alternative fuels to
a niche market through the end of the century. Fluctuation in fossil fuel costs, geo-political
instability in resource-rich regions, the desire to develop technology able to use otherwise
flared gas and public concern over the climatological effects of greenhouse gas emissions
during the first decade of the 21st century have greatly increased interest in alternatives to
traditional fuels.
Generally, individual LP combustors are designed to operate on a limited variety of fuels
for stability and plumbing reasons. Beyond the intended range, changes must be made
to the fuel handling and control systems and, possibly, to the combustor itself. This is a
trade-off between fuel flexibility and emissions. In aviation, the quality standards of the
various fuel types are tightly controlled for obvious safety reasons. However, the stationary
GTs used to generate electrical power are forced to operate on fuels whose content is not as
strictly controlled. Natural gas, a primary fuel source for many stationary GTs, is generally
controlled to energy content, but it’s constituents can vary widely depending on source [60].
Alternative fuels such as biogas and syngas have contents that vary based on the feedstock
to their respective production processes [61, 62, 63, 64, 65]. Thus, there has been a focus on
the effects of fuel variation on the operation of GT engines using LP combustion in power
generation applications [26].

30

2.4.1

Fuel Conditioning

Due to corrosion and fouling issues that may arise, manufacturers often require that some
minor species be removed before any gaseous fuel is used in their prime movers. Included
in this group of species are those that form controlled pollutants when oxidized, those that
can clog passages and species that may condense in the fuel system. This process is known
as fuel conditioning. These fuel cleaning steps are required regardless of fuel source in order
to meet emissions and operability constraints.
Oxidized sulfur compounds, SO2 and SO3 collectively known as SOx , are controlled
pollutants. In addition to being toxic, SO3 reacts with H2 O to form H2 SO4 . If this occurs
in the hot section of the GT, especially in the presence of alkali metals, corrosion becomes
a serious issue [66]. Virtually all sulfur in the fuel is converted into SOx in the combustion
chamber; thus, the only available method of reducing SOx production is to eliminate sulfur
compounds in the fuel [8, 24].
If sufficiently high combustion temperatures are reached, siloxanes present in the fuel
oxidize into SiO2 . In downstream components the SiO2 collects as a powder on turbine
blades and can fill the narrow passages in heat-exchangers and catalytic reducers [67]. Like
H2 S and SOx , the only method of reducing these effects is the removal of siloxanes from the
fuel stream.
Liquids and gases that are near their dew point present a number of challenges. Fuel is
typically passed through a liquid knock-out step to remove volatile organics and/or water.
Aromatics and other higher hydrocarbons are precursors to soot and slow to react [68]. these
volatile organics, if they pass through or are formed in the combustor, contribute to UHC
emissions and are also found in photochemical smog [24]. They are removed to avoid this as

31

well as their condensation in the fuel handling system.

2.4.2

Fuel Characterization

As a first step to ensure that a change in fuel does not greatly alter the effectiveness of the
combustion system, it must be able to deliver sufficient energy content to the system. To
identify fuels which can deliver similar total heat release using fixed fuel system geometry
and combustor pressure drop the Wobbe Index is often used

WI =

LHV
(S.G.)0.5

(2.16)

where LHV is the fuel’s lower heating value and S.G. is the fuel’s specific gravity relative to
air at a standard condition (293K, 101.32kPa). Fuels with identical WI can be expected to
generate the same heat output in a combustor using the same pressure drop and fuel control
valve settings. Typically, a window of ±5% WI from design point is allowed in a GT without
modification to the control system or combustor [59]. Outside this range control valves, fuel
compressors, fuel nozzle pressure drops, and combustor liner modifications are necessary
to meet the various performance and environmental restrictions placed on a unit [47]. A
modified Wobbe index is also used

W IT =

LHV
(S.G.)0.5

Tstd 0.5
T

(2.17)

where Tstd is a standard temperature (293K) and T is the fuel temperature in K, is often
used to correct for the effect of variation in fuel temperature due to the fuel preparation or
production processes.

32

Other methods of characterizing CH4 based fuels exist. To characterize the knock resistance of fuels for use in piston engines, the motor octane number (MON) is often used

MON = −406.14 + 508.04

H
C

− 173.55

H 3
H 2
+ 20.17
C
C

(2.18)

where H
C is the hydrogen to carbon ratio for the fuel, excluding the carbon in the diluents.
An empirical relation has been developed to relate the MON of a gaseous fuel to that of
CH4 . The so-called ‘methane number’ (MN) [69]

MN = 1.624MON − 119.1

(2.19)

is an index that characterizes the effect of various minor hydrocarbon species found in natural gas on combustion phenomena related to knock (i.e., autoignition). This correlation is
limited to fuels with H/C ≥ 2.5 and diluent mole fractions less than 5%. Experiments using
a commercial micro-GT and natural gas fuel with various diluents, both higher hydrocarbons and inerts, have shown relatively poor correlation between both the WI and MN and
emissions when inert diluents are added [70].
As discussed in Section 2.3, LP combustion is susceptible to a variety of instabilities
many of which are directly affected by fuel type. While useful, the WI and MN are not
fully capable of characterizing the effect of fuel content change on the operation of a GT
combustor. Fuels may have similar WI and yet have differing flame speeds, combustion
chemistry, and flame temperatures. These properties directly affect the static and dynamic
stability of the combustor as well as the emission of controlled pollutants [1, 60, 70].

33

2.4.3

Biogas

Using waste derived fuels to offset energy costs is not a new concept. Treatment plants
for human sewage used CH4 produced by anaerobic digestion to generate electrical and
mechanical power for the plant in the middle part of the 20th century [71]. This fell out of
favor as electrical power from centralized generating stations became more affordable. In the
late 1970’s the concept of offsetting fossil fuel use through the production of fuels from solid
wastes was once again considered. Much of this work focused on the direct combustion of
municipal wastes in steam boilers, but it was recognized that the quantity of potential fuel
available from human/animal sewage and sanitary land fills was promising [72].

2.4.3.1

Biogas Production

Biogas, depending on source, may have a range of constituents and is generally characterized
as a low to medium-energy content fuel [59]. The feedstock is waste organic material from a
number of sources. Biogas for industrial usage is collected from two general sources: sanitary
landfills and animal/human sewage. In both cases, microbes break down the organic material
in a chemically complex process to generate a combination of CH4 , CO2 , H2 , N2 , and H2 S.
The anaerobic digestion process which results in biogas stores more of the chemical energy
present in the organic waste in a useful form, CH4 , than aerobic processes which convert
much of the energy to sludge [71]. The content of the product gas is tied to the organic
feedstock and other process variables. The trace species in both digester and landfill gas
vary but can include volatile organics, H2 S, siloxanes, and aromatics [61].
Digestion takes place in two steps. First, the large organic molecules are broken down
by enzymes, the exact process is dependent on the organic molecule, producing smaller
molecules that are useful for microorganisms. Anaerobic bacteria metabolize the smaller
34

molecules to low molecular weight acids. In the second step methanogenic bacteria degrade
the acids into CH4 , CO2 , and H2 . Digestion can take place over a range of temperatures
(4 − 60◦ C) if the temperature is held constant. Variations in temperature, however, can
upset the process causing the content and quantity of gas to change or shutdown the process
entirely. Other factors that influence gas production are pH and moisture content [71].
Landfill biogas contains CH4 , CO2 , N2 , and O2 in varying amounts depending on garbage
content and environment. The ratio of CH4 to CO2 typically ranges from 60%/35% to
35%/55% [73]. Because the gas is drawn from the landfill using a vacuum system and the
landfill is not a fully sealed enclosure, atmospheric air may be drawn in to the landfill as
the fuel demand changes. This has two effects. First, O2 is introduced into the fuel stream.
In most cases O2 only appears in trace amounts and has little influence on combustion.
The second effect is to change the chemistry of the digestion process by adding oxygen and
promoting aerobic digestion which leads to higher CO2 content gas [61]. Rain, or lack thereof,
also affects the output of the landfill. Higher moisture contents promote gas production and
increase the ratio of CH4 to CO2 [74].
Biogas from anaerobic digestion systems using either human or animal waste tends to
be more consistent in content than gas from landfills. This is due to the more controlled
nature of their operation relative to landfills [61]. Waste is collected by a sewage system
and processed in specially constructed in digesters. Control systems are used to maintain
digester temperature (typically 30 − 40◦ C known as the mesophilic range), moisture content,
feed rate, and pH [71]. Like landfills, digesters are subject to process upset when the narrow
range of conditions in which the bacteria thrive is violated. The ratio of CH4 to CO2 ranges
from 75%/25% to 55%/45% [62, 73, 75].

35

2.4.3.2

Biogas Combustion

The diluents remaining in biogas after fuel conditioning, primarily CO2 , H2 O, and N2 , affect
the combustion in a variety of ways. Fuel N2 affects the adiabatic flame temperature and
specific heat of the reactant mixture much as it does as a component of air [1, 76]. Though
typically assumed to be chemically inert at the conditions in an LP combustion system,
CO2 and H2 O do affect other aspects of the combustion [77]. Both affect the specific heat
and flame temperature in much the same way as N2 , but the effect is more pronounced.
As discussed in Section 2.1.3, this is the reason EGR and water/steam injection are used
to reduce NOx . However, the presence of CO2 and H2 O vapor in both the products and
reactants also increases the radiative heat transfer and thereby the preheating the fuel.
Preheating increases flame speed, the extent of the flammability limits, and the risk of
flashback especially in fuel-lean mixtures [78]. Computational studies in a variety of systems
have shown that, when radiation is ignored, dilution with CO2 rather than N2 slows flame
speeds by retarding the kinetics [79].
A number of studies in laboratory combustors have been undertaken to explore the effect
of dilution on flame stability. Experiments in a representative swirl-stabilized combustor
demonstrated that flow effects (i.e., centrifugal stratification) may limit the effect of CO2
dilution on blowout [76]. Experimental and numerical studies in a simplified LP combustor
show that the effect of CO2 dilution on flame stability and anchoring location is pronounced.
For similar equivalency ratios, biogas (61% CH4 , 34% CO2 , 5% N2 ) and methane flames have
different anchoring patterns. Anchoring patterns, viewed via chemillumensence of CH, that
were associated with instability, as measured by a dynamic pressure transducer, in pure
methane flames were stable when the fuel was biogas [80].

36

Studies of emissions and static instabilities in biogas combustion have primarily been limited to application-specific experiments or simplified aerodynamic systems. Multiple workers
have reported on the effect of running various sizes GT generator systems on a biogas from
different sources on emissions and power output (e.g., [81, 82, 83, 84, 85]). Lafay et al. used
a simplified GT configuration to investigate the stability of biogas flames and found that
laminar flame speed best correlated with flame structure [80]. In a further simplification
of the flow system, Qin et al. studied simulated landfill gas under fuel-lean conditions in a
stagnation flow geometry both experimentally and numerically. They found that the presence of CO2 in the fuel mixture effected the kinetics of the reaction through radiation and
CH2 reactions, that increased fuel CO2 increases NOx emissions by increasing fuel demand
and prompt NOx , and reduces the laminar flame speed [86]. Jahangirian et al. determined
using counterflow diffusion flame experiments with simulated, diluted biogas that fuel CO2
reduces the presence of soot precursors, NOx , and greenhouse gases even when temperatures
are similar to those of a pure CH4 flame. Fackler et al. studied LP combustion of CH4 flames
diluted with CO2 and N2 , to simulate landfill gas, in a jet-stirred reactor to determine the
effect of diluents on NOx production. They found that dilution with N2 increases NOx emissions compared to CO2 dilution at similar temperatures and that NOx emissions increase
with dilution [87].
The effect of dilution of CH4 -air flames with CO2 , N2 , and H2 O has also studied in
machines using EGR. Cold EGR in a perfectly premixed system is similar to raw biogas
combustion. A concern in combustors with cold EGR is a reduction in the extent of the
stability limits [88]. A limiting factor for combustor stability is considered to be an O2
percentage of 16-18% in the reactant mix [89]. Røkke and Hustad tested the addition CO2 ,
N2 and O2 , individually, to either the fuel or air inlet of a research combustor capable
37

of operating in premixed and diffusion modes. They determined that diluents, including
O2 , increase the fuel-lean extinction limit in both premixed and diffusion flames [90]. This
was confirmed by ElKady et al.

in their study of EGR in a research combustor using a

commercial GT fuel nozzle. They found that stability limits could be extended through
the use of a diffusion pilot flame. With pilot flames the limit of EGR was identified as CO
emissions levels [91]. Stability limits may also be extended through the addition of H2 [92].
In their studies of methane-oxycombustion, a condition where the N2 has been removed from
the air and replaced by exhaust gas, Amato et al. showed that in CO2 diluted CH4 /O2 flames
the extent of the extinction limits are contracted by the kinetic effect of CO2 . The effect
may be predicted qualitatively by chemical time scaling near stoichiometric operation [77].

2.5

The Well-Stirred Reactor

It has long been recognized that laboratory models that simulate GT combustion processes
are a preferred method for evaluating the effect of changes in fuel types [9]. Several different experimental apparati have been designed to approach WSR operation with varying
degrees of success. Their results have proven useful in the development of modern computational codes and kinetics models [93]. This section introduces the governing theory behind
WSR operation, the design of laboratory devices, and the use of WSR theory in numerical
simulations of GT combustors.

2.5.1

WSR Theory

The theory governing the operation of the WSR is a combination of fluid mechanics, thermodynamics, heat transfer and chemical kinetics. Briefly, the WSR is a fixed volume with a

38

7U
3U
9
<L

KL LQ
<L LQ

KL RXW
<L RXW

Figure 2.3: General WSR schematic with control volume.

constant influx of fuel and air at a constant temperature, see Figure 2.3. Near instantaneous
mixing of the reactants and products is achieved through the careful design of the reactor.
Inside the volume the mixture of gases is at a steady temperature and pressure. Due to the
intense mixing, the gas mixture exiting is identical in composition to that within the volume.
Finally, the reactor is essentially adiabatic.
A more detailed analysis begins with the conservation of species i for the control volume
shown in Figure 2.3
dmi,cv
=m
˙ ′′′
˙ i,in − m
˙ i,out
i V +m
dt

(2.20)

where the left-hand-side represents the rate at which i accumulates within the control volume
and the terms on the right-hand-side represent the rate-of-production within the volume, influx and out-flux of i, respectively. The production term is a consequence of the chemical
reactions taking place within the WSR. It acts as a sink for reactant species and a source
for product species.
From chemical kinetics the production of species i can be described in terms of reaction

39

rates. A chemical reaction involving N species can be written as
N

νi′ Xi ⇆

νi′′ Xi

(2.21)

i=1

where νi is the stoichiometric coefficient of species Xi and the single and double primes
indicate reactant and product side, respectively, for the forward reaction. Reactions rarely
consist of a single-step, often referred to as ‘global’, rather several intermediate reactions occur involving multiple additional species. These multi-step reactions are called mechanisms.
According to the law of mass action, the rate of change in concentration, ω, of species i in
reaction j is proportional to the product of the concentrations of the reacting species, [Xi ]
which has dimensions of moles per unit volume, raised to νi′ [68]


ωj = νi′′ − νi′ kfj

N

′
[Xi ]νi

i=1

N

− krj
i=1



′′
[Xi ]νi 

(2.22)

where kfj and krj are the reaction specific constants of proportionality for the forward
and reverse reactions, respectively. For irreversible reactions kbj is zero. The concentration
exponents, stoichiomehtric coefficients νi′ or νi′′ in EQ. (2.22), can take a variety of values
and do not have to be a whole number and may not even be indicative of the number of
molecules participating in the reaction [20]. This is more common in global and quasi-global
mechanisms. If a reaction requires a third body, Eq. (2.22) is modified by multiplying the
right-hand-side by
N

αlj [Xl ]

(2.23)

l

where αlj specify the increased efficiency of species l in reaction j. If a species is ineffective
as a third body, the αlg takes a value of zero [94].
40

Arrhenius’ law is generally used to determine the value and temperature dependence of
kj using
c
kj = Aj T j exp

−Eaj
Ru T

(2.24)

β
where Aj is the Arrhenius factor which takes into account molecular collisions, T j is a

temperature correction and Eaj is the activation energy required to start the reaction. The
pressure sensitivity of the reaction may be modeled in a variety of ways. Above or below
certain pressure limits the reaction approach limiting reactions which may be modeled with
Eq. (2.24). Between these limits the reaction behaves like a combination of the limiting
reactions and its rate description is complex [94]. Different practical methods of dealing
with pressure dependent reactions are described in Section 2.5.5. The production term of
Eq. (2.20) can now be written as

m
˙ ′′′
i

M

=

′′ − ν ′ ω MW
νij
j
i
ij

(2.25)

j=1

where and MWi is the molecular weight of species i.
A further set of simplifications can be made to Eq. (2.20) based on the operating state
of the WSR. If the WSR is operated at steady-state, the left hand side is zero. Additionally,
composition is the same in the outflow as it is with in the reactor. By substituting Eq. (2.25)
and ignoring any diffusional transport, Eq. (2.20) can be rewritten for an M-step reaction
mechanism as
M
′′ − ν ′ ω MW V + m
˙ Yi,in − Yi,out = 0
νij
j
i
ij
j=1

41

(2.26)

where Yi is the mass fraction of species i and is related to the molar concentration by

Yi =

[Xi ] MWi
N

(2.27)

Xj MWj

j=1

For a system of N reacting species Eq. (2.26) yields N equations with N + 1 unknowns.
The conservation of energy is used to close the system resulting from Eq. (2.26). In a
control volume under steady-state conditions with steady inflow and outflow and negligible
changes in kinetic and potential energies, the conservation of energy is

Q˙ = m
˙ (hin − hout )

(2.28)

where h is the specific enthalpy of the mixture. If the specific heat of reaction of the
reactants is qc and the mixture can be assumed to be ideal, then Eq. (2.28) becomes

Q˙ = m
˙

qc
(Tr − Tin )
Tf − Tin

(2.29)

where Tf is the adiabatic flame temperature and Tr is the reactor temperature. Now the
determination of the composition of the reactor and it temperature is reduced to solving
N species equations and Eq. (2.29) which can be done using a number of numerical techniques [24].
Another parameter of interest in WSR studies is the residence time, τ which characterizes
the amount of time a particular fluid element remains within the reactor volume. It is
calculated by
τ=

ρV
m
˙

42

(2.30)

where ρ is the mean density within in the reactor volume, V . The mixture mean density
is calculated using the ideal gas equation of state and the mixture’s mean molecular weight
as determined by its composition.
The well-stirred nature of a reactor is estimated by comparing the representative mixing
time scale to the representative chemical time scale of the reactor. This ratio, the Damk¨ohler
number Da, is useful in separating different reaction regimes. In the case of the WSR

Da =

L/u′
δ/S

(2.31)

where L is a characteristic turbulent length scale, u′ is RMS velocity fluctuation which
can be estimated from turbulence theory by assuming that the kinetic energy of the fluid
entering the reactor is dissipated during its residence time, and δ/SL is the laminar flame
thickness divided by the laminar flame speed of the mixture. For Da ≤ 0.1 the system
may be considered to operate in the distributed reaction regime and, therefore, be wellstirred [24, 95].

2.5.2

WSR Stability Theory

Static instabilities in WSR models have been related to a grouping of reactor operating
conditions called a loading parameter. In their investigation of high temperature reaction
rates using a WSR Longwell and Weiss related extinction to [2]

m
˙
= f (φ, T )
V Prn

43

(2.32)

where the left-hand-side is the chemical loading parameter, Pr is the reactor pressure, n is
an effective reaction order (1.8 for iso-octane [2], 1.25 for propane [96]) and the function on
the right side is related to the efficiency of fuel consumption. The content of the reactor is a
mixture of air, fuel, and product gases. For CO2 diluted CH4 -air systems, like biogas, this
function can be determined from the global reaction for fuel-lean mixtures

φ xf CH4 + 1 − xf CO2 + 2xf (O2 + 3.76N2 ) → φ 1 + xf (β − 1) CO2
+2φβxf H2 O + φ (1 − β) xf CH4 + 2 (1 − φβ) xf O2 + 7.52xf N2

(2.33)

where xf is the mole fraction of CH4 in the fuel, β is the fraction of CH4 consumed in
the reaction, and it is assumed that the CO2 present in the biogas does not dissociate. It
is important to recall that CO2 is not inert, see Section 2.4; rather the combustion temperatures are expected to be low enough to avoid the thermal pathway to NOx production
and, therefore, below the temperatures where extensive dissociation is expected. The RHS
of Eq. (2.33) represents the contents of the reactor. Following the procedure of Longwell and
Weiss [2] and Ballal and Lefebvre [97], if it is assumed that the reaction is of order n, then
the rate of consumption of CH4 within the reactor is
φβxf m
˙
= AG Trc exp
MWCH V
4

−Ea,G
Ru Tr

Pr n m
χCH χn−m
4 O2
Ru Tr

(2.34)

where the subscript G indicates the global reaction, Trc is to compensate for the temperature
dependence of AG , and χCH and χO are the mole fractions of CH4 and O2 in the reactor,
4
2

44

respectively. From the RHS of Eq. (2.33) the mole fractions of fuel and oxidizer are
φxf (1 − β)
χCH =
4
φ + 9.52xf

(2.35)

2xf (1 − βφ)
χO =
2
φ + 9.52xf

(2.36)

and

respectively. Substituting Eq. (2.35) and Ex. (2.36) into Eq. (2.34) and rearranging yields
MWCH AG
m
˙
4
=
exp
V Prn
Run Trn−c

−Ea,G
Ru Tr

(1 − β)m (2 (1 − φβ))n−m
βφ1−m x1−n
φ + 9.52xf
f

n

(2.37)

It has been suggested that the value of n is related to φ at fuel-lean extinction [20, 98].
A second expression for the loading parameter comes from the work of Lefebvre and
Halls [99]
m
˙
3
D P2

(2.38)

where D is the diameter of the reactor and is characteristic of its volume. The reaction
order n = 2 is based on an analysis that indicated that the reaction order should be between
1 (fast reactions) and 2 (fast mixing). This version of LP has also been used to correlate
extinction in GT combustors to their operating conditions [8].
Conditions at extinction are useful in the determination of overall reaction order and kinetics limits for different fuels [2]. A variety of tools have been used to determine maximum
combustor air flow rates in both diffusion and premixed flames at representative GT conditions. Spherical reactors intended to be kinetically controlled (i.e., approach well-stirred
conditions) and thus approach the absolute extinction limits were used in the study of a

45

number of fuels [2, 100, 101, 102]. Other workers have used flames stabilized behind bluff
bodies to more closely approximate conditions in a GT combustor [97]. In the early 1990’s
a series of laboratory combustors of increasing complexity were used to determine the effect of changing system back pressure on the stability of annular combustors using diffusion
flames [51, 103]. Much of the work has focused on determining empirical relations useful for
design.

2.5.3

Laminar Premixed Flame Speeds

Though the flow field within a WSR is highly turbulent, its stability, and the characteristics
of turbulent flames in general, are often related to the laminar flame speed of a mixture.
The laminar flame speed captures the effects of unburned gas temperature, stoichiometry,
pressure and fuel type on the structure of a flame [24]. Along with flame thickness, the
laminar flame speed may be used to determine characteristic time scales which, in turn, may
be used to predict instabilities. A brief introduction to the theory and modeling of laminar
flame speeds is included here.

2.5.3.1

Governing Equations

The governing equations of a laminar premixed flame propagating in a combustible mixture
are broadly similar to those of the WSR. The primary differences arise from the presence of
spatial gradients which account for the finite flame zone. Starting with the conservation of
mass
dm
˙ ′′
=0
dx

46

(2.39)

continuing with the conservation of species

m
˙ ′′

dYi d
ρYi ui,dif = ωi MWi
dx dx

(2.40)

where ui,dif is the diffusional velocity of species i which may be due to gradients of concentration, temperature, pressure or body forces, [24], and finally conservation of energy

m
˙ ′′′ c

d
dT
+
P
dx dx

dT
−k
dx

N

+
i=1

dT
ρYi vi,dif cP,i
=−
dx

N

hi ωi MWi

(2.41)

i=1

To solve this system of equations constitutive equations for ui,dif , a kinetic mechanism (see
Section 2.5.5) to determine ωi , and species properties are required [104]. The temperature
boundary conditions on Eq. 2.41
T (−∞) = Tu

(2.42)

where Tu is the temperature of the unburned reactant mixture, and it is assumed the downstream boundary is located in a region where the temperature has become spatially uniform

dT
(∞) = 0
dx

(2.43)

Because ui,dif may be related to a concentration gradient, Eq. 2.40 is second-order in Yi [24].
The mass fraction boundary conditions on Eq. 2.40 are

Yi (−∞) = Yi,u

47

(2.44)

where Yi,u is the unburned mass fraction of species i, and a the downstream boundary is,
again, spatially uniform
dYi
(∞) = 0
dx

(2.45)

For freely propagating flames m
˙ is an eigenvalue of the problem. To solve the system an
additional boundary condition must be specified or a degree of freedom removed. One
approach is to fix the location of the flame within the domain by constraining the temperature
at one point. The location must be carefully chosen to ensure that the gradients disappear
near the boundaries of the domain [104].

2.5.3.2

Estimating Laminar Flame Speeds

The importance of laminar flame speeds to predicting a variety of combustion phenomena
has led to the development of models and correlations for estimating their value. Based on
a simplified version of the governing equations discussed above, Turns [24] suggests that the
flame speed should scale as

SL ∝

Tu + Tb 0.375
−n/2 (n−2)/2
Tu Tb
P
exp
2

−Ea
2 ∗ Ru Tb

(2.46)

where Tb is the temperature of the product gases downstream of the flame and n is, again, the
effective reaction order. It is immediately apparent that SL is a strong function of temperature. If the effective reaction order is ≈ 2, then, based on Eq. (2.46), it might be concluded
that pressure has little effect on SL . This assumption of reaction order is generally used for
most simple bimolecular global reactions as well as for the WSR as discussed in Section 2.5.1.
Correlations based on experimental data have generally agreed with the temperature scaling
suggested by this simplified model, but they disagree with its pressure scaling.
48

This agreement/disagreement is borne out by the work of Andrews and Bradley [105]
who examined the experimental CH4 -air data from a number of sources and developed the
correlation
SL = 10 + 3.71 × 10−4 (Tu )2

(2.47)

where SL is in cm/s. Most experimenters have demonstrated a negative correlation between
SL and pressure. When comparing experiments performed at different pressures, Andrews
and Bradley determined that
SL = 43 (P )−0.5

(2.48)

where SL is in cm/s and P is in atmospheres, best predicts the laminar flame speed of a
mixture.
Later, the laminar flame speed of a variety of fuel-air mixtures were determined in experiments by Metghalchi and Keck. They then attempted a number of correlations before
finding [106]
SL = SL,ref

Tu
Tu,ref

a

P b
(1 − 2.1Ydiluent )
Pref

(2.49)

where
SL,ref = BM + B2 (φ − φM )2

(2.50)

with BM , B2 , and φM as fuel dependent constants, Tu,ref and Pref are reference conditions
(298K and 1atm, respectively), a and b depend φ

a = 2.18 − 0.8 (φ − 1)

(2.51)

b = −0.16 + 0.22 (φ − 1)

(2.52)

49

and Ydiluent is the mass fraction of non-fuel and non-oxidizer species. The decrement of SL
by the presence of diluent species, in this case to compensate for any recirculated exhaust
gas, is of interest in biogas flames due to the presence of CO2 in the fuel stream.
A model of the type described by Eq.s (2.49) - (2.52) has been used by other workers to
investigate a variety of fuel-air mixtures. Kobayashi et al. used such a model to describe
turbulent burning velocities of methane-air flames at elevated temperatures and pressures.
Using a Bunsen-type flame stabilized over different sizes of burners at φ = 0.9, parameters a
and b were found to be 1.9 and −0.5, respectively [107]. Coh´e et al. confirmed the pressure
exponent in studies of CO2 diluted CH4 -air flames. Both the work by Coh´e et al. [108] and
previous work by Kobayashi et al. [109] confirmed that SL decreases as the mole fraction
of CO2 in the reactant mixture increases. Coh´e noted that the effect of CO2 dilution was
less important than that of pressure [108].

2.5.4

Laboratory WSR Designs

Various laboratory apparati have been designed to approximate the well-stirred condition.
These devices have proven quite useful in the study static instabilities, high-temperature
reaction kinetics, soot formation, and pollutant emissions. Four designs are described here.
While others exist, these four are illustrative of the development laboratory WSRs.

2.5.4.1

Spherical WSR

The earliest effort to construct a laboratory WSR was that of Longwell and Weiss [2]. Sometimes called the ‘Longwell Bomb,’ it was designed for high-temperature kinetics and extinction investigations of hydrocarbon-air systems. As such, the reactor was capable of operating
over a wide range of temperatures, both inlet and reactor, and pressures. Residence times
50

Figure 2.4: A sketch of the spherical WSR of Longwell [2], blue arrows indicate incoming
fuel-air mixture and red arrows indicate exhaust ports.

could be varied from 0.1 to 15ms. The design was extremely useful in developing correlations between extinction and loading parameter. These works concluded that the pressure
exponent in the loading parameter, see Eq. (2.32), should be set to 1.8 for a variety of
fuels [2, 100].
Their reactor was a spherical shell, carved in two halves, of refractory brick, see Figure 2.4
for a sketch. The brick was chosen for its ability to withstand high temperatures (≤ 1900K)
and approach adiabatic operation. Reactor volumes ranged from 230 to 1880mL. Premixed,
pre-heated fuel-air mixture was fed into the center of the reactor by a perforated spherical injection manifold. The injector had between 68 and 102 holes, drilled symmetrically,
depending on reactor volume. Reactants exited the injection holes at sonic velocity. The
number injection points and gas velocity was intended to yield vigorous mixing of reactants
and products. Products exited through a series of symmetrically arranged ports in the re51

actor shell. The reactor was contained within a nickel shell again constructed in two halves
and bolted together. The entire assembly was further enclosed in pipe sections to create a
pressure vessel for elevated pressure testing. Both the pipe sections and nickel shell were
manufactured with the necessary fittings and optical accesses for measurement, monitoring,
and control equipment.
The major drawbacks of this design were primarily due to the insulating material and
lack of conclusive evidence of homogeneity in the reactor volume. Though intended to be
nearly adiabatic, there was high heat loss through the brick. Operation at near stoichiometric
conditions and small residence times, i.e., high reactor loading, greatly reduced the life of
the brick. At these conditions only one or two tests were possible. Lighter loading extended
life. Measurements of oxygen consumption and other species made across the volume of
one reactor did show that the device had time-averaged homogeneity. Though there was no
evidence of non-homogeneity, the reactor could not be proven to be homogeneous.
To address some of these concerns, the spherical design was modified to determine the
effect of injector geometry and pressure drop on mixing within the reactor. Initial experiments investigated changes in injector geometry by varying the body shape. The spherical
shape of Longwell and Weiss was compared to cylindrical injectors with holes drilled either
perpendicular to the cylindrical surface or at angled towards the center of the injector (i.e.,
as if the were drilled from the surface of a sphere). In blowout tests of propane-air mixtures, spherical and cylindrical with perpendicular hole injector geometries yielded similar
results. It was also determined that mixing played a significant role in the conditions at
blowout [101]. To determine how the number of holes and pressure drop across the injector
affected the reactor’s performance two additional experiments were undertaken. In the first,
the pressure drop was held constant while the number of holes in a cylindrical injector was
52

varied from 3 to 68. It was via visualization studies with a water model that the extreme
geometries, 3 and 68 holes, were associated with large scale recirculation patterns. These
patterns were compared to those associated with the spherical injector of Longwell and Weiss
and shown to be similar. The effect of variation in pressure drop was determined by maintaining a constant hole pattern and varying the diameter of the holes. Blowout conditions
were not appreciably affected until the pressure drop reached 20% of the reactor pressure. It
was concluded that flow patterns, which are dominated by reactor injector geometry, have
major effects on blowout performance [102]. This was confirmed by a fluid dynamics study
comparing spherical and cylindrical stirred reactors [110]. Hottel et al. showed that the
shape of the jets coming from the centered injector led to the outer portion of the reactor
approaching the well-stirred condition while the regions near the injector did not [111]
Building on these results, a final set of experiments attempted to determine the maximum
loading of propane-air and propane-oxygen systems using a spherical reactor. It was found
that at φ near unity the loading parameter satisfactorily predicted the blowout condition
when the pressure exponent was 2 [112]. This agrees with the work of Lefebvre and Halls [99]
discussed earlier.
Even with the modified injectors, the design still suffered from many of the issues related
to the insulation. High heat loss through the walls and the injector were noted and treated
as an equivalent loss in reactant enthalpy [2, 100, 101, 102, 112]. Though flow visualization
was performed [102], there was still little evidence to prove the well-mixedness of the entire
reactor volume. Work by Hottel et al. also showed that there is an optimal number of
injectors to produce the best mixing in a spherical reactor. The number of holes should be
that for which the jet angle matches the angle between jets on the spherical surface of the
injector ball [113]. If these conditions were met, then the reactor approached well-stirred in
53

Figure 2.5: A sketch of the hemispherical WSR of Wright [3], blue arrows indicate incoming
fuel-air mixture and red arrows indicate exhaust ports.

cold-flow experiments.

2.5.4.2

Hemispherical WSR

The spherical WSR was further modified by Wright to alleviate the inherent effect of the
tubes feeding the injector on symmetry [3]. The reactor volume was modified by filling half
with refractory to create a hemispherical reaction volume, see Figure 2.5. A single tube
fed premixed, pre-vaporized fuel to to the injector through the solid half of the sphere. The
injector body was spherical in shape but half buried in the refractory yielding a hemispherical
injector. Product gases exited though exhaust ports in the shell of the reactor as before.
The change in reactor shape led to strongly back-mixed combustion that more accurately
represented the conditions in a GT combustor than other aerodynamic configurations [114,
115].
54

This reactor was used by several investigators to explore soot inception in back-mixed
combustion and NOx production. Early work by Wright using this reactor found that sooting
in pure higher-hydrocarbon fuels was dependent on the presence of hydrocarbons in the
product gases. It was also found that the sooting behavior is distinctly different for different
fuels in back-mixed combustion [3]. This was confirmed by the work of Blazowski for blends of
higher-hydrocarbon fuels [115, 116]. Later experiments by Wright determined that the effect
of back-mixing was to dilute the combustion gases which is equivalent to lowering combustion
pressure. Lower combustion pressures were associated with lower soot production when other
parameters were held constant [117]. Engleman et al. used measurements from a reactor of
this type to determine the accuracy of kinetics calculations for H2 , CO, and C3 H8 flames.
They found H2 and CO models showed good agreement with WSR measurements whereas
C3 H8 models were not as accurate [118].
The hemispherical reactor overcame some of the deficits found in the spherical design but
was unable to eliminate all of them. The use of a single feed line eliminated the effect of the
fuel feed tubes on the reactor volume. However, the hemispherical shape also eliminated the
overall symmetry present in the spherical reactor. There was still little proof of well-stirred
operation [10].

2.5.4.3

Conical WSR

The spherical WSR has been further simplified to conical or truncated-conical shapes by
various workers (e.g., [4, 119, 120]). Like the spherical and hemispherical designs, these
reactors are constructed of refractory material or other ceramic insulators. In these reactors
a single or small number of jets eject reactants from the tip towards the base of the conical
reactor. There the jets impinge on the wall and are forced out and back towards the jet
55

Figure 2.6: A sketch of the truncated cone WSR of Thorton et al. [4], blue arrows indicate
incoming fuel-air mixture, orange arrows indicate back-mixing zones, and red arrows indicate
exhaust ports.

source. Product gasses finally exit the reactor either around the outer surface of the injector
or through radial ports near the tip of the cone. The net effect is back mixing of combustion
products with the incoming reactants especially in the region near the base of the cone. The
design is simple and easy to modify [121]. It exists in a range of reactor volumes, but based
on the work on mixing in stirred reactors of Evangelista et al. [122] smaller volumes (i.e.,
tens of mL) are preferred.
The design of Thorton et al. [4] which was modified by Corr et al. [123] has been used
extensively and warrants further description, see Figure 2.6 for a sketch. Due to the method
of back mixing (i.e., impingement on the base of the cone) a high degree of erosion, similar to
that found in spherical reactors, was expected if the reactor was to be constructed entirely
of ceramic insulator. For experiments where this is a particular concern, the base may
be replaced by high-temperature alloy to extend life. The walls are still high-temperature

56

refractory material (e.g., Zirconia or Alumina). In it’s initial configuration, well-stirred
operation was approached by using fuel-lean H2 -air combustion products as the primary
inlet gas. The compound of interest was introduced to the product gases of the H2 -air
combustion at levels below the flammability limit before the mixture entered the reactor.
This resulted in the incoming jet having very nearly the same temperature (1000 - 1300K) as
the reactor eliminating the difficulty of mixing fluids of different densities [4]. Later studies
on NOx production used cold gases and hydrocarbon-air mixtures above the flammability
limits to reach temperatures sufficient to produce measurable levels of NOx and expanded
operation to elevated pressures [17, 22, 123]. When measurements are made near the base
of the cone, the results are well predicted by WSR theory [17].
Like the spherical and hemispherical reactors the level of mixing within conical reactors
is dependent on operating condition. When the walls are heated to make the system truly
adiabatic, up to 80% of a conical reactor with a rounded base can be considered wellstirred [120]. Without heated walls reactors of this type exhibited poor mixing particularly
at low loading [121]. The work of Williams et al. confirmed that the region near the base of
the cone behaves as if it were well-stirred for certain conditions. They questioned whether a
conical reactor would meet the well-stirred condition for methane-air combustion at elevated
pressures [124].

2.5.4.4

Torroidal WSR

Another effort to improve mixing within a WSR resulted in the torroidal WSR of Nenniger [125]. In this design, the reactor volume is a torus with premixed reactants injected
on the outer radius and products ejected at the inner radius. Reactants are fed into the
reactor via a series of small jets angled off the radial to produce intense swirling flow. Like
57

the other designs the injection ring is constructed of temperature resistant metals and the
reactor volume is made of ceramic insulator. Due to the angle of the jets, impingement on
the reactor walls is avoided; thus, hot gas erosion is limited and reactor life is extended. A
detailed description of the construction of this reactor can be found in Chapter 5.
The intense mixing found in this reactor is produced by a jet-in-crossflow flow pattern.
Circulation is produced by canting the feed jets 20◦ off radial. This was later shown to
produce sufficient jet penetration and swirling flow to create well-stirred conditions in the
torus [95, 126, 127]. Reactors of this type have been used to investigate polycyclic aromatic
hydrocarbon (PAH) production [125, 128, 129], pollutant emissions [127, 130, 131, 132, 133],
and instabilities [130, 132, 133, 96].

2.5.5

Numerical Modeling

Numerical simulations have become increasingly popular in the early stages of the combustor design process. The simplest method of numerically simulating a GT combustor
consists of using a WSR for the primary zone followed by a PFR for the remainder of the
combustor [134]. As computational power has increased, the complexity of combustor models possible to simulate has followed. Many such models rely on the CHEMKIN chemical
kinetics code and its updates, [135, 136, 137], to solve coupled equations describing the thermodynamics and chemistry of simple reactors. Modern techniques use a series of simple
reactors to model the complex mixing and reacting zones within a combustor [138]. These
techniques have become especially important in the design of LP combustors.
The PSR calculations assume perfect mixing at both the macro and micro-scales which
may not always be true. Macro-scale mixing is controlled by fluid mechanical structures (i.e.,
jet in cross flow) whereas the micro-mixing is controlled by diffusional processes. Because
58

conditions within an experimental device are not perfectly mixed, many devices are simulated
using a series of PSRs to simulate the different phenomena within the reactor [87]. By
varying the flow split and the residence time in each reactor a range of chemistry can be
investigated. The effect of imperfect micro-mixing has also been investigated with partially
stirred reactor (PaSR) models. Micro-mixing is simulated using various techniques including
coalescence/dispersion [139] and interaction by exchange with the mean [93].
Comparisons between the measurements made in various WSR experiments have been
made to a CHEMKIN routine developed to model a PSR [140]. The relatively simple PSR
model has proven useful for modeling the stability of a range of alternative low energy
content fuels [141]. However, direct comparisons between emissions measurements made
experimentally and simulated can be made difficult by probe effects [10, 132]. To compensate,
reactor networks have been used to more accurately capture the complex interaction between
fluid mechanics and chemistry found in these compound systems [138].

2.5.5.1

Chemical Kinetics Simulations with CHEMKIN

The process of simulating the chemical kinetics of combustion requires three pieces of information. First, a reaction mechanism which includes a number of reactions whose kinetics
may be described by Eq.s (2.21)-(2.24) or physically equivalent methods. Second, the thermodynamic properties of all species participating in in the reaction mechanism must be
specified. For reacting gasses, the thermodynamics may be described by curve-fit functions
that describe the dependence of the isobaric specific heat, cP , on temperature. Knowing
the temperature and cP allows the calculation of other important thermodynamic properties
through integrals (e.g., enthalpy and entropy) and other relations (e.g., isochoric specific
heat, cV , and Gibbs free energy). Finally, for systems with spatial or temporal gradients,
59

the transport properties for all species are required.
One software that is popular for performing chemical kinetics calculations is the CHEMKIN
code developed at Sandia National Lab by Kee et al. [135]. CHEMKIN was developed as a
general purpose package determining thermodynamic properties and reaction rates in problems including complex chemistry. For those cases where the reactions of interest take place
in a reactor alongside other physics, an supplementary piece of software is required to define
and solve the additional governing equations.
Within the CHEMKIN software, chemical reactions are treated in the manner of Eq.s (2.21)(2.22). Unless otherwise specified, the molecular concentration exponents for each reaction
are assumed to be their stoichiometric coefficients. For reactions that are reversible, the
constants in Eq. (2.24) are specified by the user for the forward reaction rate constant, kfj .
The reaction rate constant for the reverse reaction, kbj , may be specified similarly. If the
constants for kbj are not specified, which is common in large mechanisms, then it is related
to kfj by the equilibrium constant, Kj ,
kfj
P
=
Kj =
kbj
Ru T

N ν ′′ −ν ′
i=1 ji ji

exp

∆Sjo
Ru

−

∆Hjo
Ru T

(2.53)

where ∆Sjo is the change in standard state entropy defined as

∆Sjo

N

=

′′
νij
− ν ′ ij

i=1

Teq
0

cPi
dT
T

(2.54)

cP i dT

(2.55)

∆Hjo is the change in standard state enthalpy

∆Hjo =

N

′′ − ν ′ ij
νij

i=1

60

Teq
0

and Teq is the equilibrium temperature.
Pressure dependent unimolecular reactions may be treated using any of three different
but related approaches in the CHEMKIN solver. All three are based on the assumption
that the reaction rate constant at an intermediate pressure k is related to the rate constants
above a high pressure limit, k∞ , and below a low pressure limit, k0 , by
k
=
k∞

k0 [M] /k∞
1 + k0 [M] /k∞

F

(2.56)

where [M] is the concentration of the mixture minus the reacting molecule and F is a
function [142]. If F takes the value of unity, then Eq. (2.56) is the Lindemann-Hinshelwood
model. The Troe formulation [142] of F is

logFcent

logF =
1+

2
c+logk0 [M ]/k∞
n+d(c+logk0 [M ]/k∞ )

(2.57)

where
c = −0.4 − 0.67logFcent

(2.58)

d = 0.14

(2.59)

n = 0.75 − 1.27logFcent

(2.60)

Fcent = (1 − a) exp {−T /T ∗∗∗} + a exp {−T /T ∗ } − exp {−T /T ∗∗ }

(2.61)

and a, T ∗ , T ∗∗ , and T ∗∗∗ are reaction specific constants which must be specified. The final
approach to pressure dependent reactions supported by CHEMKIN was developed from the

61

Troe formulation by Stewart et al. which defines F as [143]

F = [aexp {−b/T } + exp {−T /c}]

1+log2 k0 [M ]/k∞

−1

(2.62)

where a, b, and c are constants that must be specified. Additional flexibility is provided by
modifying Eq. (2.62) with

F =

−1
1+log2 k0 [M ]/k∞
e
dT [aexp {−b/T } + exp {−T /c}]

(2.63)

where d and e must be specified. All three of the proceeding approaches may also be used
to define chemically active bimolecular reactions [137].
The definition of the reactions within a mechanism results in a series of ordinary differential equations. Often the equations involve a variety of time scales due to the presence of
radical species (quick reacting) and stable species (slow reacting) rendering them numerically
stiff. A number of methods for solving differential equations of this type exist [94, 144].
The numerical PSR model employed in this work solves Eq.s (2.26)-(2.28). The conservation of energy, Eq. (2.28), is restated in unsteady form as

dTr
=m
˙
(ρV ) c¯p
dt

N

hi,in − hi,out + Q + V
i=1

dPr
dt

(2.64)

where c¯p is the mean isobaric specific heat of the mixture in the reactor, Q represents the
heat transfer to/from the reactor and heat release from any reactions [104]. The series of
stiff differential equations are solved using the DASPK algorithm of Li and Petzold [144].
This scheme uses an implicit backwards differentiation formulation to discretize the system
of ODEs in time and a modified Newton’s method to integrate at each time step. The details
62

of the DASPK technique are described in [144].
Laminar flame speed estimates made in this work are solved using packaged CHEMKIN
routines. A computational domain, whose size is specified by the user, is discritized using a
finite difference scheme where the number of cells is also set by the user. The grid is nonuniform becoming finer in regions of higher gradients. Two dicretization options are available.
The first is a first-order in space windward method. This method is less dependent on the
initial guess but introduces artificial diffusion in the regions of coarser mesh. A second-order
in space central difference method is also available. The central difference method is more
accurate but prone to convergence issues [104]. The second derivatives of the governing
equations are discretized using central difference schemes where the coefficients within the
derivatives are evaluated as averages between grid points points. Diffusional velocities are
evaluated in a similar way [104].

2.5.5.2

Reaction Mechanisms

A number of global, quasi-global, and detailed reaction mechanisms have been suggested in
the literature for CH4 -air combustion. Global and quasi-global mechanisms sacrifice accuracy for reduced computational intensity. As such, they are popular for use in conjunction
with CFD for modeling GT combustors. Detailed mechanisms include too many individual reactions to be solved efficiently along with the equations governing the turbulent flow
in combustors. However, they make more accurate predictions of minor species which are
important to meeting modern emissions standards.
Global mechanisms and quasi-global reactions attempt to predict the rates of production
of the major species (i.e., Fuel, Oxidizer, CO2 , and H2 O) in a single reaction or small
number of reactions. Single-step global mechanisms, like those of Bradley et al. [145] and
63

Westbrook and Dryer [146, 147], usually have a limited range of applicability in terms of
reaction temperature, pressure, and stoichiometry. Often, such mechanisms are focused on
matching experimental measurements of specific combustion properties [146]. In quasi-global
mechanisms, a single-step reaction of the type

Cx Hy + O2 ⇆ CO + H2

(2.65)

is followed by a set of reactions describing the oxidation of CO and H2 to CO2 and H2 O [146].
The constants used to describe the reaction rates (i.e., A, β, Ea and the species concentration
exponents) are chosen to best match aspects of experimental measurements (e.g., laminar
flame speed, ignition delay, species profiles). Mechanisms including just a single additional
reaction, called a 2-step, like that of Westbrook and Dryer [146], or multiple steps involving
other minor species like the 4-step mechanism of Jones and Lindstedt [148] and the 21-step
mechanism of Westbrook and Dryer [146]. These larger mechanisms offer better matching
to experimental data at the cost of additional computational requirements.
Detailed combustion mechanisms attempt to be more complete in their description of the
elementary reactions that take place during the combustion process than is possible in global
and quasi-global mechanisms. They can contain many hundreds or thousands of reactions
depending on the fuel species considered. The size and complexity of detailed mechanisms
has led to a number of methods of construction having been sought. The Gas Research Institute (GRI) has developed, via funding several researchers, a series of detailed mechanisms
that describe natural gas combustion with a focus on the oxidation of CH4 . The most recent
version, GRI-Mech 3.0, consists of 325 elementary reactions considering 53 species [149].
Most reactions have been studied individually to provide accurate reaction rates. Not all of

64

the reactions or species included are relevant to all CH4 combustion problems, but they are
included for completeness and flexibility. The mechanism developed at University of California San Diego (235 reactions including 46 species) was built up from simple mechanisms
adding complexity only as necessary. The resulting mechanism combines the influence of
many elementary reactions into single steps. This limits the applicability of the mechanism
to certain conditions and phenomena, but it also reduces the sources of uncertainty by reducing the number of reaction parameters [150]. The mechanism of Glarborg and Bentzen,
developed based on experiments in environments containing high concentrations of CO2 ,
consists of 424 reactions involving 60 species. It is an example of a mechanism made up of
sub-mechanisms (i.e., detailed mechanisms describing simpler processes like CO or CH3 OH
oxidation). In this case, the sub mechanisms were previously described by the authors. To
fit the problem of interest the combined mechanism was ’tuned’ with special emphasis on
reactions involving CO2 [151].
A compromise between detailed and quasi-global mechanisms are the reduced mechanisms. The goal in developing the smaller mechanisms from larger mechanisms is to reduce
the computational intensity while maintaining the accuracy, to a certain extent. There are a
number of methods for reduction (e.g., approximation of partial equilibrium, lumping, and
response modeling) which result in varying levels of simplification and accuracy [152, 153].
Many reductions aim to create mechanisms that are computationally better suited to specific problems. One such reduced mechanism that is used in CH4 combustion is the reduced
version of GRI-Mech 1.2 which was developed to maintain some of the capabilities, particularly predictions of ignition delay and laminar flame speeds, of the full GRI-Mech 1.2
(117 reactions, 32 species). The result is a mechanism consisting of 84 reactions involving
22 species that is able to replicate the predictions, within 11%, of the full mechanism over
65

a range conditions [154]. Care must be taken when applying these reduced mechanisms to
problems for which they were not designed due to the nature of the reduction process [152].
Simulations using detailed kinetic mechanisms in different computational models have
been used to investigate the effect of various combustion phenomena on chemistry. Sturgess
used a stirred reactor model to approximate fuel-lean extinction in various commercial aeroGT diffusion flame combustors. As the combustors approached fuel-lean extinction, the
flames lifted from the fuel nozzles leading to zones premixing of reactants and products
before combustion. Using CFD and empirical correlations, Sturgess was able to identify
a portion of the primary zone that could be reasonably modeled as a WSR. The WSR
predictions, made using a variety of chemical kinetic mechanisms, agreed satisfactorily with
measurements [155]. In their work suggesting a mechanism for dynamic instabilities in
LP combustors, Lieuwen et al.

developed an unsteady PSR model using a single-step

propane mechanism to investigate the role of chemical kinetics. They determined that the
amplitude of the dynamic instability in reaction-rate, forced by oscillations in φ, increases
by two orders of magnitude as average magnitude of φ decreases to 0.75 from unity [55]. A
similar technique was used by Lilleberg et al. to investigate the effect of different forcing
amplitudes, parameters (reactor loading, φ, and inlet temperature) and kinetic mechanisms
on the reaction rates for various species. They found that increasing the amplitude of the
forcing function led to a linear increase in the amplitude of the oscillation in reaction rate.
This was true for all forcing parameters. The effect of decreasing φ on the reaction rate
was species dependent with CO2 and OH increasing, CO and H2 decreasing, and H2 O not
changing significantly. Additionally, when the fuel and oxidizer concentration exponents in
global reaction mechanism have a non unity value, the mechanism can force the amplitude
of the oscillations in reaction rate to increase with decreasing φ. This is true even under
66

conditions where the amplitude increase is not seen when using detailed mechanisms [156].

2.6

Summary & Conclusion

In this chapter the necessary theory and applicable previous work has been discussed. A
number of conclusions can be formed from this research:
• Governmental and social pressure has forced manufacturers power generation systems
to develop low pollutant emissions options
• Gas turbine manufacturers have found several possible paths to reducing pollutant
emissions among them the fuel-lean premixed combustion approach
• Combustion systems operating in the fuel-lean premixed regime are susceptible to
combustion instabilities which may lead to extinction or mechanical failure
• Fluctuations in the global energy market and social pressures have lead to interest in
alternative fuels such as biogas
• Variability in the species constituency of a fuel like biogas alters the combustion chemistry and stability characteristics of a GT combustor
• WSR models, both experimental and numerical, have been developed to attempt to
characterize combustion processes, stability and pollutant emissions of GT combustors
• There have been only very limited applications of the WSR model to the investigation
of the effect of alternative fuels like biogas on the stability of modern fuel-lean premixed
GT combustors. Those limited studies focused mostly on pollutant emissions.

67

Chapters 3 and 4 of this work are dedicated to the description of a series of investigations
into the effect of CO2 dilution of the fuel stream, like that seen in biogas, on the stability of
CH4 -air combustion systems.

68

Chapter 3
Predicting Laminar Flame Speeds of
Biogas-Air Flames
Previous workers have noted the effect of diluents on laminar flame speeds [106, 108, 109].
In their numerical investigations biogas flames, Jahangirian and Engeda pointed to the lack
of correlations to predict the laminar flame speed in biogas-air mixtures [157]. The work
of Coh´e et al. has partially filled this deficit [108]. This chapter expands on these previous
results and attempts to develop a more comprehensive correlation.

3.1

Methods

Laminar flame speeds were investigated using CHEMKIN’s PREMIX algorithm [158, 104]
solved using CHEMKIN 10101 (Reaction Design, San Diego, Ca) software.

This one-

dimensional algorithm solves the governing equations outlined in Section 2.5.3. For these
simulations the GRI mechanism version 3.0 for natural gas was employed. This mechanism has been used previously to investigate the effect of kinetics on laminar flame speeds
of biogas mixtures [157, 108]. Other workers have indicated that earlier versions the GRI
mechanism, particularly 2.11, are better at predicting laminar flame speeds at pressures
above 5 bar [109, 107]. This work is focused on conditions found in micro-GT combustors
which operate in conditions near or below 5 bar. The 3.0 version of the mechanism is chosen
69

to be consistent with the work of Jahangirian and Engeda [157].
The conditions simulated were chosen to represent those found in micro-GT combustors
with varying levels of recuperation burning biogas. The combustor operating conditions
are tabulated in Table 3.1. Different reactant mixes are chosen to represent the range of
fuels produced by anaerobic digestion of organic materials from low heating contents typical
of sanitary landfill gas to higher quality gas produced by well controlled digesters. Pure
methane is included for a reference. Diluents are modeled as CO2 only. Previous workers
have linked its effect on kinetics to be more influential than that of N2 [79]. The range of
fuels tested are tabulated in Table 3.2. Due to convergence issues that occurred as the level
of dilution increased, the first-order windward scheme was employed to solve the governing
equations.
Table 3.1: Conditions used in laminar flame speed calculations
V (L) Tin (K) Pr (atm)
0.25 300 − 900
1−4

φ
0.5 − 1.0

Table 3.2: Fuel Compositions used in laminar flame speed calculations
Mix No.
1
2
3
4
5
6

Fuel Composition (By Vol.) WI (kJ/kg)
100% CH4 - 0% CO2
70, 621
80% CH4 - 20% CO2
46, 056
70% CH4 - 30% CO2
37, 922
60% CH4 - 40% CO2
30, 790
50% CH4 - 50% CO2
24, 435
40% CH4 - 60% CO2
18, 696

70

The fit method of Metghalchi and Keck [106] was chosen as the basis for the results
presented here. Though based on experiments with higher hydrocarbon and blended fuels,
this method was chosen because it was originally formulated to include diluents (simulated
combustion products 85% N2 and 15% CO2 ). However, the diluent term is modified here to
better reflect the effect of pure CO2 dilution of CH4 -air combustion

SL = SL,ref

Tu

a

Tu,ref

P b
c − d ln χf
Pref

(3.1)

where the exponents a and b, SL,ref and χf are defined as before. The constants in this
equation have been modified to better fit the biogas flames simulated here.

3.2

Results & Discussion

The fit scheme was divided into two sections due to an apparent change in behavior with
increasing φ. This effect has been noted by others in CH4 -air flames [159]. Though both
regions can be predicted well by the type of model described in Eq. (3.1), the constants
take different values. The best point to split the data was around φ = 0.6. In the regions
above and below this φ, the dependence on pressure and diluent were similar. Indeed, the
effect of diluent is nearly identical. The influence of temperature, though of similar form,
was markedly different. Also SL,ref behaved differently above and below this dividing line.
The values of all of the constants and those in Eq. (3.1) are in Table 3.3.
The exponents for the influence of temperature and pressure take similar forms to those
of Metghalchi and Keck [106] (see Eq.s (2.51) and (2.52))

a = a1 + a2 (φ − 1)
71

(3.2)

and
b = b1 + b2 (φ − 1)

(3.3)

where a1 , a2 , b1 , and b2 differ between the two regions.
The influence of temperature in these CO2 diluted mixtures is more dependent on φ
than found by Metghalchi and Keck in mixtures diluted by a combination of CO2 and N2
especially at lower values of φ. Above φ = 0.6 the offset coefficient found here is similar to
that found by Metghalichi and Keck (2 compared to 2.18); whereas below φ = 0.6 the offset
is smaller here (1.51 compared to 2.18). Both above and below φ = 0.6 the slope of the
exponent term is larger in magnitude. The magnitude is approximately twice as large here
above φ = 0.6 (1.5 compared to 0.8) and over five times larger below φ = 0.6 (4.3 compared
to 0.8) [106].
The reference laminar flame speed is predicted in a similar manner to that suggested by
Metghalchi and Keck [106], see Eq. (2.49), where BM , B2 and φM vary between the two
regions. The reference flame speeds (fuel was assumed to be pure CH4 ) were determined
using the same CHEMKIN model as the rest of the data presented here. The φ modifier,
φM , is only different by 2% where as the two other constants are 80% larger for φ ≤ 0.6.
Table 3.3: Constants used in the proposed model to predict the laminar flame speed of
biogas-air mixtures
a1
a2
φ
≥ 0.60 2.00 −1.50
< 0.6 1.51 −4.30

b1
b2
BM
B2
−0.30 0.30 0.38 −0.65
−0.30 0.25 0.21 −0.36

φM
c
d
1.25 1.00 0.45
1.22 1.00 0.45

Plots of the fit model’s predictions versus the flame speeds calculated by the detailed
kinetic model are shown in Figures 3.1 and 3.2. Agreement in both ranges is generally
72

3.5

Correlation SL (m/s)

3
2.5
2
1.5
1
0.5
0
0

1

2
Kinetic SL (m/s)

3

Figure 3.1: A plot of the laminar flame speed as predicted by the model vs. the laminar
flame speed predicted by the detailed kinetics simulations for φ < 0.6. The green dashed
lines indicate deviation of 20% from the kinetics simulation.

good. The RMS error between the correlation and the predicted flame speeds is 19.5%
below φ = 0.6 and 20.6% above φ = 0.6. Figures 3.1 and 3.2 include lines indicating ±20%
deviation from the flame speeds calculated using detailed kinetic, green dashed lines. Most
of the error occurs at low flame speeds where dilution is high. As pressure increases the
scheme becomes more accurate as noted by Metghalchi and Keck [106].

73

3.5

Correlation SL (m/s)

3
2.5
2
1.5
1
0.5
0
0

1

2
Kinetic SL (m/s)

3

Figure 3.2: A plot of the laminar flame speed as predicted by the fit vs. the laminar flame
speed predicted by the detailed kinetics simulations for φ > 0.6. The green dashed lines
indicate deviation of 20% from the kinetics simulation.

74

3.3

Conclusions

In this chapter the laminar flame speeds of CO2 diluted CH4 -air mixtures have been simulated over a range of conditions similar to those found in small GT combustors. The fuel
mixtures approximate the content of biogas from a variety of sources or the effect of EGR
into fully premixed combustion system. Two fit models of the type proposed by Metghalchi
and Keck [106] were established to predict the laminar flame speed of these mixtures. These
fits, split around φ = 0.6, adequately predict value of SL over the range of conditions simulated. Fits of this type can be useful as components of methods for predicting a variety of
combustion phenomena including both static and dynamic instabilities.

75

Chapter 4
Static Instability Simulations using
Detailed Chemical Kinetics

4.1

Purpose of Experiments

Kinetic modeling of fuel-lean static stability limits of the combustion of biogas type fuels
in a model of an ideal primary zone of a GT combustor is presented here. In this study,
CH4 is diluted with CO2 to simulate a range of gases representative of the products of
anaerobic digestion of organic materials from different sources (e.g., landfill and animal
waste digester). Fuels of this type are of interest for use in small gas turbines in distributed
generation applications. Predictions made by two detailed mechanisms (GRI-Mech 3.0 and
San Diego) and one reduced mechanism (GRI-Mech 1.2, reduced) are employed to investigate
the underlying kinetics near fuel-lean extinction. Approximate correlations to predict fuellean extinction are extracted from these results and compared to those of other fuels.
The WSR is an established tool for evaluating combustion kinetics through measurements
made at extinction. From these experiments useful correlations relating fuel-lean blowout to
combustor loading have been established for a variety of fuels [2, 100, 101, 96]. As outlined in
Section 2.5.1 and following the work of Longwell and Weiss [2] and Ballal and Lefebvre [97],
a set of fuel-lean stability curves for simulated biogas with varying CO2 content have been
made. Any variation in φ and reactor chemical loading parameter at blowout with CO2
76

content will be correlated to important physical parameters and boundary conditions of the
reactor.

4.2

Methods

It has been suggested that the value of the reactor order n is related to φ at blowout,
φLE [98, 20]. As an example, from investigations into the stability limits of propane-air
flames Ballal and Lefebvre [97] showed that φLE at blowout is predicted by

φLE =

0.16
m
˙
CV Pr1.25 exp (Tin /150))

(4.1)

where m
˙ is the mass flow rate of air and C is determined empirically.
Following the work of Jahangirian and Engeda [157], three different mechanisms were
compared in this investigation. The first is the GRI-Mech 3.0 detailed mechanism. This
mechanism includes 325 elementary reactions and thermodynamic and transfer properties
of 53 species including NOx formation chemistry [149]. The second detailed mechanism is
the San Diego mechanism [150] (release 2009/11/22) including the NOx mechanism (release
2004/12/9 (2)). This mechanism includes 46 species and 235 reactions. Finally, a reduced
mechanism developed from GRI-Mech 1.2 [154] which does not include nitrogen chemistry
is used for comparison. This mechanism includes 19 reacting species, inerts N2 and Ar, and
84 reactions.
The governing equations for the unsteady PSR model, see Sections 2.5.1 and 2.5.5, are
solved using CHEMKIN 10101 (Reaction Design, San Diego, Ca) software assuming an
adiabatic, fixed volume reactor operating at constant pressure. Five levels of CO2 diluted

77

CH4 and one blend of CH4 , CO2 , H2 O, and N2 were investigated in these simulations. See
Table 4.1 for the different fuel mixes. Air was modeled as a mixture of 21% O2 and 79%
N2 , by volume. In each simulation, the reactions were initiated by assuming an elevated
reactor temperature (1800K) and a LP in the stable region. Conditions within the reactor
were then allowed to stabilize before LP was increased gradually while φ was held constant.
Extinction was determined by a sharp decrease in reactor temperature. The conditions in
the reactor were chosen to simulate those found in micro-GT combustors with varying levels
of recuperation, and the reactor size was chosen to be consistent with previous experimental
studies from other investigators [2], [96], [131], see Table 4.2.
Table 4.1: Fuel Compositions used in kinetics simulations
Mix No.
1
2
3
4
5
6

Fuel Composition (By Vol.)
80% CH4 - 20% CO2
70% CH4 - 30% CO2
60% CH4 - 40% CO2
50% CH4 - 50% CO2
40% CH4 - 60% CO2
50% CH4 - 16.6% CO2 - 16.6% N2
- 16.6% H2 O

WI (kJ/kg)
46, 056
37, 922
30, 790
24, 435
18, 696
27, 927

Table 4.2: Conditions used in kinetics simulations
V (L) Tin (K) Pr (atm)
0.25 300 − 900
1−4

φ
0.5 − 0.8

78

4.3
4.3.1

Results & Discussion
Simulated Lean Extinction

Lean extinction points as calculated by the three different mechanisms for Mix 3 are shown in
Fig. 4.1. An effective reaction order n = 1.75 has been chosen for these plots. The units of LP
(mol/s L atmn ) are chosen to be consistent with previous work from others [2], [96]. All three
mechanisms predict similar extinction points over the range of temperatures, pressures, and
fuel mixes simulated here. The reduced GRI-Mech 1.2 mechanism tends to predict extended
fuel-lean extinction limits. This effect increases with Pr . The prediction of extended stability
is due to the reduced mechanism’s prediction of higher concentrations of minor species,
specifically H radicals which are important in the breakdown of CH4 , as seen in previous
studies [157]. The GRI-Mech 3.0 mechanism is the most conservative predictor of extinction
(i.e., highest φLE for a fixed reactor LP) with the San Diego mechanism generally falling
between the two other mechanisms. Results presented from here on will be based on the
predictions of GRI-Mech 3.0.
The effects of Pr and Tin on simulated fuel-lean extinction for three different fuel mixes,
are shown in Fig. 4.2. As LP increases so does φLE in a manner that indicates a power law
relation similar to Eq. (4.1). The slope of the relation seems to change around a φLE of 0.6.
Increasing Tin causes φLE to decrease for a given reactor loading. This effect is consistent
across the range of fuel mixes tested. The influence of Pr is smaller than that of Tin which
is similar to the work of Ballal and Lefebvre [97]. Across the range of fuel mixes the effect
of increased Pr is to increase φLE .
The effect of fuel CH4 content on φLE is illustrated in Fig. 4.2 and Fig. 4.3. Lowering
the CH4 content of the fuel increases φLE for a fixed LP, compare (a) and (b) of Fig. 4.2.
79

When the diluent is a mixture of species, as in Mix 6, φLE for a fixed LP is lower than that
for a fuel with similar CH4 content mixed only with CO2 , Mix 4, confirming the role of CO2
is not limited to that of an inert diluent near fuel-lean extinction, compare (b) and (c) of
Fig. 4.2. In Fig. 4.3 three fuel mixes (1, 3, and 4) are compared to Mix 6 at three different
levels of Tin and Pr . Mix 1 and Mix 6 have similar ratios of CO2 to CH4 . Mix 4 and Mix 6
have identical CH4 content but different diluents. A comparison of the extinction curves
for this combination of Mixes elucidates the effect of CO2 and other diluents on fuel-lean
extinction. The extinction curve of Mix 1 is shifted towards lower φLE compared to that of
Mix 6 confirming that the effect of the other diluents in Mix 6 is to reduce the fuel-lean extent
stable operating range. If the CO2 was playing no role kinetically it would be expected that
the extinction curves for Mix 4 and Mix 6 would be identical. However, replacing a portion
of the CO2 with other diluents shifts the extinction curve for Mix 6 towards lower φLE . The
fuel mix which matches best with Mix 6 is Mix 3 which has a higher CH4 content. Thus,
the effect of replacing 2/3 of CO2 in the diluent with other species is akin to increasing the
CH4 content of the fuel indicating a kinetically active role for CO2 .
For two fuel mixes with the same φLE but different levels of CH4 , the presence of radical
species necessary for the continuation of combustion is decreased in two ways. First, dilution
of the combustion mixture causes reduced concentrations and lower reaction temperatures;
thus, reducing reaction rates. Second, when CO2 is the diluent, as in fuel Mixes 1-5 of this
work, there is a competition for H radicals between the reaction CO2 + H CO + OH and
chain branching reactions [160]. To show this Fig. 2.1 is plots of reactor temperature and
mole fractions of H, O and OH versus LP at a fixed inlet φ of 0.65 and Tin of 300K for
Mix 3, Mix 4, Mix 6 and a mix where the H2 O in Mix 6 is replaced by N2 . Extinction occurs
near 1500K for all four fuel mixes. As LP increases the fraction of H, O, and OH increase
80

until near extinction for all four fuel mixes, and all three species fractions fall off before
extinction is indicated by the Tr profile. The H2 O in Mix 6 increases the hydrogen content
of the fuel stream to be similar to that of Mix 4. Reactor temperatures are below those
at which a large percentage of the H2 O in the fuel stream would be expected to dissociate
to add additional H radicals to the reaction. However, both Mix 4 and Mix 6 have similar
species profiles, compare Fig. 2.1(a) and Fig. 2.16(c). Eliminating the water from the diluent
mix and replacing it with N2 , shown in Fig. 2.16(d), produces a similar mole fraction of H
in the reactor and extends the LP at extinction relative to Mix 6. The increased H content
of the reactor is more a function of the reduced CO2 content in the fuel rather than of the
additional H provided by the H2 O.

4.3.2

A Correlation to Predict Lean Extinction

When generating the curve fits for qualitatively predicting fuel-lean extinction the focus was
on micro-GT applications. Mixes 15 plus simulations of 100% CH4 are used, because the
fuel is often dried before combustion to avoid condensation in the fuel system. Additionally,
fitting focused on combinations of Tin and Pr that are practical (e.g., at elevated Pr fitting
focused on higher Tin due to heat of compression or recuperation). The method presented
here follows the work of Longwell and Weiss, [2], and Ballal and Lefebvre, [97], by relating
LP and φLE . Other methods such as those that use Damkhler number relations like that of
Amato et al. [77], based on laminar flame speed like that recommended by Lafay et al. [80]
or other methods like those reviewed by Hoffmann et al. [161] are also possible.
Based Fig. 4.2, Fig. 4.3 and Eq. (4.1) two fits were made due to an apparent change in
slope near φLE 0.6. Above this point extinction behavior was generally similar for all fuels
and operating conditions. Below φLE 0.6 the behavior was more strongly dependent on fuel
81

0.9
0.8

GRI−Mech
Reduced
San Diego

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

0

10

Tin 900K
2

10
LP (mol/s L atm1.75)

(a) 1atm
0.9
0.8

GRI−Mech
Reduced
San Diego

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

0

10

Tin 900K
2

10
LP (mol/s L atm1.75)

(b) 2atm
0.9
0.8

GRI−Mech
Reduced
San Diego

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

0

10

Tin 900K
2

10
LP (mol/s L atm1.75)

(c) 4atm
Figure 4.1: φLE versus LP as computed by three mechanisms (stars GRI-Mech 3.0, diamonds
GRI-Mech 1.2 reduced, squares San Diego) at three different Tin (blue 300K, red 600K, black
900K) and three different operating pressures for Mix 3: (a) 1atm, (b) 2atm, and (c) 4atm.
82

0.9
0.8

Tin 600K

Pr 2atm
Pr 4atm

φLE

0.7

Pr 1atm

0.6
0.5
Tin 300K
0.4

0

Tin 900K
2

10
10
LP (mol/s L atm1.75)

(a) Mix 1
0.9
0.8

Tin 600K

Pr 2atm
Pr 4atm

φLE

0.7

Pr 1atm

0.6
0.5
Tin 300K
0.4

Tin 900K

0

2

10
10
LP (mol/s L atm1.75)

(b) Mix 4
0.9
0.8

Tin 600K

Pr 2atm
Pr 4atm

φLE

0.7

Pr 1atm

0.6
0.5
Tin 300K
0.4

Tin 900K

0

2

10
10
LP (mol/s L atm1.75)

(c) Mix 6
Figure 4.2: φLE versus LP as computed by three mechanisms (stars GRI-Mech 3.0, diamonds
GRI-Mech 1.2 reduced, squares San Diego) at three different Tmathrmin (blue 300K, red
600K, black 900K) and three different operating pressures for Mix 3: (a) 1atm, (b) 2atm,
and (c) 4atm.
83

0.9
0.8

Mix 1
Mix 3
Mix 4
Mix 6

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

0

Tin 900K
2

10
10
LP (mol/s L atm1.75)

(a) 1atm
0.9
0.8

Mix 1
Mix 3
Mix 4
Mix 6

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

Tin 900K

0

2

10
10
LP (mol/s L atm1.75)

(b) 2atm
0.9
0.8

Mix 1
Mix 3
Mix 4
Mix 6

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

Tin 900K

0

2

10
10
LP (mol/s L atm1.75)

(c) 4atm
Figure 4.3: φLE versus LP as computed by the GRI-Mech 3.0 mechanism, at three different
Tin in (blue 300K, red 600K, black 900K) comparing three mixes to Mix 6 at three operating
pressures: (a) 1atm, (b) 2atm, and (c) 4atm.
84

−3

x 10

3.66

2500

x 10

2500
H
O 2000
OH

2.2

1500

2.2

1500

1.46

1000

1.46

1000

0.732

500

0.732

500

19.2 37.4
LP (mol/s L atm1.75)

χi
0
0.983

0

19.2 37.4
LP (mol/s L atm1.75)

(a) Mix 3

(b) Mix 4
−3

−3

3.66

0

x 10

3.66

2500

x 10

2500
H
O 2000
OH

2.2

1500

2.2

1500

1.46

1000

1.46

1000

0.732

500

0.732

500

0
0.983

19.2 37.4
LP (mol/s L atm1.75)

χi

Tr (K)

2.93

χi

2.93

H
O 2000
OH

0
0.983

0

(c) Mix 6

19.2 37.4
LP (mol/s/L/atm1.75)

Tr (K)

0
0.983

Tr (K)

2.93

χi

2.93

H
O 2000
OH

Tr (K)

−3

3.66

0

(d) 50% CH4 , 16.6% CO2 , 33.4% N2

Figure 4.4: Mole fraction of three radical species and Tr versus LP as computed by GRIMech 3.0 at Pr = 1atm, φ = 0.65, Tin = 300K for three different mixes: (a) Mix 3, (b) Mix 4,
(c) Mix 5, and (d) 50% CH4 , 16.6% CO2 , 33.4% N2 .

85

content and pressure. This change in behavior is similar to that seen in the laminar flame
speed study presented in Chapter 3 though speed was affected more by temperature below
this limit. For consistency both fits have the same form
N˙
= C1 exp {C2 Tin } φz
V Prn

(4.2)

where the values of C1 , C2 and z are different for the two fits. The dependence of fuel-lean
extinction on fuel content is approximately logarithmic, so C1 is a function of the form

C1 = C3 ln xf + C4

(4.3)

See Table 4.3 for the values of C2 , C3 and C4 . The term that makes up z is more complex
and contains two functions of the form of Eq. (4.1) where both terms include a temperature
correction. A further pressure correction was also necessary to improve fit. For φLE < 0.6,
z is

z (φLE < 0.6) =
−0.38
Pr
((0.0007Tin − 0.542) lnxf + 1) (lnxf + 16) exp {−0.0025Tin }
101325

(4.4)

And for φLE 0.6, z is

z (φLE > 0.6) =

−0.38
Pr
((0.0011Tin − 0.942) lnxf + 1) (lnxf + 6.5) exp {−0.002Tin }
101325

The temperature and pressure dependence of z is not seen in similar expressions describing fuel-lean extinction for pure fuels [97]. These dependencies may be due to the kinetic

86

influence of CO2 and require further investigation.
Table 4.3: Conditions used in kinetics simulations

C1 (C3 )
C1 (C4 )
C2
n

φLE < 0.6
515
1000
−0.0075
1.975

φLE > 0.6
74.25
113
0.0013
1.75

As noted by Zelina and Ballal in their work with propane, the value of n changes with
φLE . These simulations suggest that n varies from 1.75 to 1.975 as φLE decreases whereas
Zelina and Ballal indicate that n varies linearly from 1 to 1.25 with φLE [96]. The value of
n for all values of φLE is consistent with that predicted by Longwell and Weiss (1.8, [2]).
It is important to note that the method presented here to predict fuel-fuel-lean extinction
is limited to CO2 diluted CH4 -air flames. The presence of other diluents will affect the
extinction point as shown earlier. The results of the fit are plotted with the results of some
representative simulations in Fig. 4.5. The value of n in Fig. 4.5 changes at φLE of 0.625 from
1.975 to 1.75 to be consistent with the curve fits. Fuel-lean extinction points for conditions
similar to those found in micro-GT combustors (Pr 2atm-4atm and Tin 600K-900K) shows
good qualitative agreement between predictions and simulations. The most accurate fits
are made for φLE ¿ 0.6 due to the more comparable behavior for these extinction points
across the range of temperatures, pressures and fuel mixes simulated. For cases where φLE
falls below 0.6, the Tin dependence was closer to quadratic than it was to exponential as
suggested by Eq. (4.1). This leads to increasing error at the extreme values of Tin where
the divergence from exponential behavior is greatest. Lower mole fractions of CH4 in the
87

fuel (e.g., Mix 5 in Fig. 4.5(c)) are also less accurate due to deviation from the logarithmic
dependence on CH4 mole fraction at low Tin .

4.4

Conclusions

In this work a series of detailed chemical kinetics simulations using a perfectly-stirred reactor
model to investigate the effect of different of fuel dilution on fuel-lean extinction limits were
performed. The fuel, CH4 , and diluent, CO2 or a mixture of CO2 , H2 O, and N2 , mixtures
were chosen to be representative of the alternative fuel biogas from different sources. Reactor
operating conditions were chosen to simulate conditions within the combustor of a micro
gas-turbine for use in a distributed generation application. It was found that increasing the
diluent content of the fuel increases φLE for a fixed LP (i.e., reduces the fuel-lean extent
of the stability loop) across the range of operating conditions simulated. Increasing inlet
temperature decreases φLE for a fixed LP (i.e., expands the fuel-lean extent of the stability
loop) for all fuel mixtures. By comparing two fuel mixtures with similar CH4 contents but
different diluent constituents, it was determined that pure CO2 dilution reduces the mole
fraction of H radicals present in the reactor. Replacing the CO2 with a mixture of CO2 , H2 O
and N2 increases the mole fraction of H in the reactor which is consistent with previous work
from others [160]. The effect of the increased mole fraction of H as well as other radicals due
to reduced CO2 content is to reduce φLE at a fixed LP.
A set of equations to predict LP at fuel-lean extinction for dry fuel mixes of CH4 diluted
with CO2 were developed. They suggest that reactor loading has a power law relation with
φLE , the influence of fuel CH4 mole fraction is logarithmic, and the dependence on inlet
temperature is exponential. The fit was broken into two ranges around a φLE of 0.6 based

88

0.9
0.8

Mix 1
Mix 3
Mix 5

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

Tin 900K

0

10

2

LP (mol/s/L/atmn)

10

(a) 1atm
0.9
0.8

Mix 1
Mix 3
Mix 5

Tin 600K

φLE

0.7
0.6
0.5
Tin 300K
0.4

Tin 900K

0

10

2

LP (mol/s/L/atmn)

10

(b) 2atm
0.9
0.8

Mix 1
Mix 3
Mix 5

Tin 600K

Tin 300K

Tin 900K

φLE

0.7
0.6
0.5
0.4

0

10

2

LP (mol/s/L/atmn)

10

(c) 4atm
Figure 4.5: φLE versus LP as computed by three mechanisms (stars GRI-Mech 3.0, diamonds
GRI-Mech 1.2 reduced, squares San Diego) at three different Tin (blue 300K, red 600K, black
900K) and three different operating pressures for Mix 3: (a) 1atm, (b) 2atm, and (c) 4atm.
89

on an apparent change in the relation between φLE and LP at this point. Above φLE =0.6, the
fuel-lean extinction points behaved in a similar fashion over the range of reactor conditions
tested than it did below. The influence of inlet temperature and pressure are consistent with
previous experimental work by others, [2], [96], and [131]. The dependence on fuel CH4 mole
fraction as well as the exponent of φLE requires experimental validation. Expansion of the
method to include other diluents is also recommended.

90

Chapter 5
A Test Facility for WSR Experiments
The operation of a WSR requires several layers of precision equipment. A facility capable of
safely and accurately operating a WSR for future alternative fuels research at MSU would
be of great use in this important field. This chapter describes a facility currently under
construction including the reactor design, safety equipment, and the emissions measurement
and sampling systems.

5.1

WSR Design

As discussed in Chapter 2.5, the primary goal of the laboratory-scale, practical WSR is
to achieve a state of near uniformity with in the reactor volume. The aim of this facility
is to simulate the conditions in the primary-zone of a micro-GT combustor. After careful
evaluation of the designs found in the archival literature, it was decided that the toroidal
design is best suited for this application. Its toroidal flow pattern is similar to that caused
by the combination of induced axial swirl and a sudden increase in flow area found in many
modern fuel-lean premixed GT combustors. This reactor has also been shown to approach
a well-stirred state over a substantial portion of its volume [10].
The reactor design chosen for this facility is identical to that designed by Nenniger [125]
and modified by Zelina [10] and later by Stouffer [129]. The basic design features a ceramic
250 cm3 torroidal reactor cast in two halves, shown pictorially in Figure 5.1 and schematically

91

8SSHU +DOI
0DQLIROG

/RZHU +DOI
Figure 5.1: A cut view schematic of the assembled WSR with components identified.

Figure 5.2: An image of the ceramic halves of the toroidal WSR.

92

Figure 5.3: An image of the fuel-air manifold and jet ring showing the injection nozzles.

93

-HW 5LQJ

0DQLIROG
Figure 5.4: A schematic of the fuel/air manifold and jet ring.

in Figure 5.2. The lower half has four access ports along its center-line for an ignition source
and temperature, pressure, and emissions measurement equipment. The upper half has
an exhaust port at it’s center. Sandwiched between the two reactor halves is the fuel-air
manifold and jet ring, see Figure 5.3. Fresh fuel-air mixture is fed to the reactor through the
jet ring. Within the reactor the fresh mixture is rapidly mixed with product gases. The high
temperature product gases provides the necessary energy to initiate the combustion of the
fresh mixture. Product gases are exhausted through eight ports at the center of the torus.
This process is shown schematically in Figure 5.5.
Special materials are required for the manufacture of the reactor halves due to the extreme
conditions at which they are expected to operate. To maintain the conditions stipulated for

94

([KDXVW
3RUW
Figure 5.5: A schematic the mixing of product and reactant gases.

well-stirred operation, the reactor must be nearly adiabatic. It must also be able to survive
some thermal cycling and extended periods of elevated temperature conditions. Finally, the
reactor must withstand the frictional forces associated with the high speed flows necessary
to maintain well-stirred conditions.
Reactors constructed of two materials. The first is an alumina ceramic. This material is
commonly used in high temperature applications. Alumina is somewhat delicate and prone
to cracking and is intended for use in less demanding tests (i.e., those without fast thermal
cycling). For more extreme experiments, a reactor cast of silica-carbide is available. This
material withstands cycling better than the alumina but is also more expensive.
Uniform delivery of the premixed fuel and air is of paramount importance to maintaining
well-stirred conditions. The fuel-air manifold and jet ring, shown schematically in Figure 5.4,

95

are constructed of nickel alloys and provide the high velocity inflow condition necessary to
maintain well-stirred operation. The reactant mixture enters through the two feed tubes and
is exhausted into the WSR by forty-eight jets of 1 mm inner diameter. The jets are angled
20◦ off radial which promotes efficient mixing [95]. High velocity is achieved by maintaining
a sufficient pressure drop across the jets to guarantee a sonic or near sonic exit condition. To
prevent autoignition in the manifold, it is cooled by impinging flows of nitrogen from above
and below.
Assembly of the WSR is a straight forward process. The jet ring is first aligned and
sandwiched between the two reactor halves. To prevent catastrophic failure of the reactor,
both halves are wrapped in thin steel bands. This assembly is held together by two steel
plates tethered by threaded rods. The lower plate has access ports and plumbing connections
which align with those in the lower reactor half. Once the end plates are in place the WSR
is ready to be lowered into its containment vessel.

5.2

Housing and Exhaust

The containment vessel is made of welded steel flanges and pipe designed to hold the WSR
and provide connection points to the required feed and monitoring systems. The vessel is
manufactured from 0.925 cm thick and 30 cm inner diameter steel pipe. Like the reactor,
the vessel consists of two parts. The lower part has connections for the fuel-air feed system,
nitrogen cooling system and access to the ports on the lower steel plate of the WSR assembly.
The upper part has a flange for mating to the exhaust section. At this point the containment
vessel is not designed to be gas tight. initially all experiments envisioned for the facility are
to be conducted at atmospheric pressure. Thus, the vessel does not need to be sealed. This

96

further reduces the risk of catastrophic failure of the vessel. In the future if high pressure
experiments are desired, the vessel may be modified in a manner similar to that used by
Stouffer et al. in their development of a high pressure WSR facility.
The exhaust section varies depending on the experiment to be performed, generally consists of a 15 cm inner diameter steel pipe lined with alumina sleeves. The sleeves reduce
its inner diameter to the desired test section for a plug flow reactor (PFR) or the diameter
of the exhaust port of the WSR (5 cm). Its purpose is to direct the effluent of the WSR
into the facilities ventilation system as well as provide additional residence time to complete
combustion. The exhaust is transformed into a PFR with the addition of a flow straightener
in the exhaust port of the WSR. Specialized sections can be added to provide connections for
air and water (for cooling, combustion completion in high φ experiments) as well as adapters
for measurement probes.

5.3

Facility

All experiments are carried out in the Turbomachinery Research Laboratory in the Engineering Building at Michigan State University. A combination of standard building systems
and custom built equipment supply the facility. Compressed air and cold water are supplied
by building systems. The supplied air is filtered (0.01 µm) and dried to a dew point no
greater than 275K before being fed into the metering and control system. Fuel, diluents and
nitrogen are supplied from bottles through custom manifolds. The fuel, air and, nitrogen
piping systems are shown schematically in the Appendix.
Experimental conditions are set using LabView (National Instruments) control system
(DAQ and VI) which monitors the fuel and air handling systems. Air flow rate is controlled

97

by a Brooks thermal mass flow controller (SLA5853) capable of controlling flow between 100
and 1100 SLPM with an accuracy of 1% of full scale. The fuel is metered through a Dwyer
thermal mass flow controller (GFC-1144) capable of supplying 0 to 500 SLPM at an accuracy
of 1.5% of full scale. A rotometer and needle valve are in-line with the flow controller for
calibration. Diluents are metered by a similar Dwyer thermal mass flow controller to that
used in the fuel system. Flow measurements are corrected for temperature and pressure
variations in real time using T-type thermocouples and pressure transducers in the piping
system.
To operate in well-stirred conditions, the fuel and air are required to completely premixed
and at a controlled temperature before entering the reactor. Prior to mixing with the fuel,
the air is heated to simulate the temperature conditions leaving the compressor of a GT.
This is accomplished by a 3 kW electric heater (WatLow). Air temperature upstream and
downstream of the heater is monitored by thermocouples to detect conditions that may cause
damage to the heating element. A PID temperature controller (Love Controls Series 16c) is
used to hold desired temperature conditions at a thermocouple placed in the stream after
fuel is mixed. Mixing of the fuel and air is ensured by flowing through a static mixer.
The fuel and air systems are capable of feeding the reactor over a wide range of operating
conditions. Residence times can be varied from 2.5 to 23ms and inlet temperatures up to
450K are possible. This allows for a range of reactor loading levels to be investigated while
operating at the relatively safer condition of atmospheric pressure. Equivalency ratios can
be varied from fuel-lean extinction to φ = 2.
Safety systems are multi-layered and located through out the facility. Product gases
are removed by a ventilation system capable of exhausting 42,500 SLPM. A positive flow
switch is used to indicate sufficient exhaust flow to the control system. Emergency shut-off
98

switches as well as hazardous gas monitors are located throughout the facility. Fuel flow is
automatically ceased by activation of any of the switches, an alarm from the gas monitor, a
low flow rate condition in the ventilation system or a loss of power to the facility. Experiments
are monitored from a control room located a safe distance from the reactor assembly.

5.4

Emissions Analyzers

Two VA-3000 series (Horiba) emissions systems containing a total of 5 analyzer modules are
available for use in experiments. The five modules are: VA-3111 CO2 0 − 25%, VA-3111
CO 0-10000ppmV, VA-3111 CH4 0-10000ppmV, VA-3012 NOx 0-2000ppmV, and VA-3012
SO2 0-2000ppmV. Emissions samples are prepared in a pair of Horiba VS-3000 series sample
conditioners (VS-3001 for the VA-3111 and VS-3003 for the VA-3012) each drawing 500 mL
per minute. To prevent condensation, emissions are fed from the sampling probe to the
sample conditioners in a heated sample line maintained above 328 K.
The analyzers measuring CO2 , CO, CH4 , and SO2 rely on the non-dispersive infrared
(NDIR) technique. Gases absorb and emit light in specific spectra depending on their constituents. The NDIR detector uses an infrared light source tuned to the spectra of a specific
species which is directed through the measurement cell to a detector. Modulation via a
chopper wheel is used to offset thermal background signals. When the sample gas flows into
the measurement cell, it absorbs the light proportional to the concentration of the species
of interest altering the intensity of the light reaching the detector. A reference gas, in this
case N2 , flows through a second chamber to provide a baseline signal.
Measurement of NOx concentrations is made using the chemilluminescence principle.
Within the sample conditioning unit (VS-3003) any NO2 is converted to NO and ozone (O3 )

99

5HDFWRU *DV

&RRODQW RXW
&RRODQW LQ
Figure 5.6: Schematic of the emissions sampling probe.

is generated. These two streams are fed to the detector unit in which the following reaction
occurs:
NO + O3 → NO2 ∗ + O2

(5.1)

where the NO2 ∗ molecules are in an excited state. As they return to the ground state they
release energy according to
NO2 ∗ → NO2 + hv

(5.2)

where h is Planck’s constant and v is the frequency of the emitted light. The intensity
of the emitted light, detected and amplified by a photomultiplier, is proportional to the
concentration of NO before the reaction. Because the NO2 in the sample was converted to
NO in the conditioner, the measurement representative of the NOx in the sample.

100

5.5

Sample Probe

To withdraw gas from the WSR an oil-cooled stainless steel sample probe was designed
following the work of Blust et al. [162]. The probe consists of three concentric stainless steel
tubes, see Figure 5.6. The innermost tube conveys the sampled gas through the probe to
the sample line. The two larger tubes are designed to allow a pathway for the cooling oil to
pas. Oil heated to 425 K by a MOKON HTF 350 is used to cool the probe and quench any
reactions.

5.6

Conclusion

This chapter has described a WSR facility designed for installation in the Turbomachinery
Research Laboratory at MSU. The initial construction of the facility has been completed.
Much of the necessary infrastructure including the fuel, reactor and cooling air, and auxiliary
cooling system has been finished. Preliminary work on the control and pollutant emissions
measurement equipment has also been completed. The remainder of the work to be done
has been described here in a manner to allow completion by future workers.

101

Chapter 6
Combined Cycle Steam Power
Generation and Cooling
The benefits offered by using GT engines in power generation at small scales also apply to
medium (¡10MWe) and large scales. These larger turbines, which are now used for both
peaking and base load, have higher air flow rates and exhaust temperatures due to their use
of simple Brayton cycle architectures. This excess energy can be used to generate steam
for a Rankine cycle plant that increases overall system fuel efficiency. In a distributed
generation system, combined-cycle plants can be used to provide clean, fuel flexible base
load near large population or manufacturing centers. In this chapter a background review of
combined-cycles, their uses and the need for advances in cooling technology are discussed.

6.1

Combined Cycles

To further increase the fuel efficiency of GT engines used in electric power generation, they
may be grouped with a water vapor cycle to produce additional power. The aggressive,
high temperature environment that the hot-sections of GT engines are designed to survive
make ideal hot gas generators. However, GTs are limited by the exit pressure which must
remain in a range dictated by the surge limit of the compressor and the pressure drop of the
exhaust system. The high exhaust temperature (≈ 800K) caused by the exhaust gas pressure
102

considerations limits the possible thermal efficiency of the Brayton cycle. The Rankine cycle
is well suited to take advantage of the exhaust temperatures from the GT. Fuel efficiency
is increased by using the exhaust in a heat recovery steam generator. Efficiency gains are
increased by the condenser of the Rankine cycle which lowers the minimum temperature of
the combined cycles. The different temperature regimes lead to the GT being referred to
as the topping cycle and the steam system being referred to the bottoming cycle. The two
cycles may be linked on a single shaft, both cycles power the same electric generator, or
multi-shaft arrangements where each cycle powers its own electric generator.

6.1.1

Topping Cycle

The simple, open Brayton cycle was described generally in Chapter 1 and ideally consists
of isentropic compression, isobaric combustion and isentropic expansion stages, an example
T-s diagram is in Figure 6.1. In Large industrial turbines, compression (station 1t to station
2t) is accomplished by multiple stages of axial or centrifugal compressors and power extraction/expansion (station 3t to station 4t) by multiple stages of axial turbines. Combustion
systems are similar to those described in Chapters 1 and 2. Recuperation is difficult at this
scale due to the size of the heat exchanger required.
The topping cycle’s primary levers to increase the fuel efficiency of the combined cycle are
compressor pressure ratio and turbine inlet temperature. The cycle efficiency of the topping
cycle may be written as
ηt =

˙ 3t−4t − W
˙ 2t−1t
W
Q˙ 3t−2t

(6.1)

assuming a cold air-standard cycle with constant specific heats and negligible fuel flow

103

3t

4t

T

4ts
2ts 2t

1t

s
Figure 6.1: A T-s diagram of the simple, open Brayton cycle.

compared to air flow, Eq. 6.1 may be rewritten as [163]

ηt = 1 −

1
γ−1
P2t
γ
P1t

(6.2)

Increasing pressure ratio will increase topping cycle efficiency when turbine inlet temperature is fixed. Similarly, increasing the turbine inlet temperature increases the fuel efficiency
of the topping cycle for a fixed pressure ratio through increasing the Carnot efficiency. Maximum compressor pressure ratios are limited by footprint and shaft dynamics considerations.
Aero-derivative GT engines traditionally have higher pressure ratios than other types of
industrial turbines owing to their initial design operating environment of the upper troposphere. Turbine inlet temperatures are limited by available hot-section materials for all GT
engines. The development of thermal barrier coatings and film cooling of high pressure turbine stages have progressively increased temperatures. However, life and system complexity
considerations limit turbine inlet temperature to about 1200K. Improved high temperature
104

material properties is an area of intense research.

6.1.2

Bottoming Cycle

The hot gas exiting the topping cycle at 4t is used as the heat source for the bottoming
cycle shown in Figure 6.2. A simple Rankine cycle is shown here as an illustration, but more
complex cycles can be used. Water is pumped up to operating pressure (stations 1b to 2b)
before being fed to the boiler. The boiler (stations 2b to 3b’) in combined cycle plants is
a heat recovery steam generator placed in the exhaust stream of the topping cycle. It may
include an economizer and superheater depending on the final application of the steam. In
electrical power production both are usually used. The expansion of the steam (stations
3b’ to 4b) is accomplished through a steam turbine (for mechanical drive or electricity
generation) or other equipment depending on application (e.g., absorption chiller, district
heating system, etc.). Steam condensation is accomplished between stations 4b and 1b.
Because the bottoming cycle uses the waste heat from the topping cycle, its major influence
on the efficiency of the plant is through the condenser.
Like the topping cycle, efficiency gains to the combined cycle are made through the heat
exchangers. The efficiency of the bottoming cycle may be written as

ηb =

˙ 3b′−4b − W
˙ 2b−1b
W
Q˙ 3b′−2b

(6.3)

Several studies of full scale steam power plants, without topping cycles, have indicated that
the boiler and condenser are the primary sources of energy escape [164, 165, 166]. For a
combined-cycle plant the boiler is using waste heat from the topping cycle. If no additional
heat input is necessary for super-heating, then there are no additional combustion losses in
105

3R´

3R

T
2R
4R

1R

s
Figure 6.2: A T-s diagram of the Rankine cycle with superheat.

the bottoming cycle. Looking more specifically at the turbine

ηb,turb =

h4b − h3b′
h4bs − h3b′

(6.4)

The condenser is a lever to adjust combined cycle plant fuel efficiency by changing the
bottoming cycle temperature at station 4b. Lowering this temperature, thus increasing the
pressure drop across the turbine for the same boiler temperature, increases the work output
of the plant and increases its efficiency for the same heat input [167, 168]. The focus of
the remainder of this work is a method of lowering bottoming cycle condenser pressure and
reducing its seasonal variability.

106

6.2

Use of Combined Cycle Power Plants in Distributed
Generation

Industrial and dense population centers are better suited to large power generating stations.
In a distributed power generation system these areas could be powered by medium to large
scale combined-cycle plants. Unlike the micro-GTs discussed previously, the large industrial
GTs used in the combined-cycle plants will likely be sited near more traditional fuel sources
like natural gas pipe lines. These sources are commonly available near industrial and population centers. The choice of the cooling source for the bottoming-cycle is a primary concern
when siting a large combined-cycle or steam power plant power plant near its load. However,
condenser cooling options may be limited by climate or regulatory factors.

6.2.1

Cooling Cycles

The combined-cycle’s low temperature is usually dictated by one of three cooling cycles
currently in use for steam condensing: single pass, closed loop and dry cooling. Shell and
tube condensers are most common for the wet methods with the coolant flowing through
the tube side and the steam through the shell side. Dry cooling systems use different heat
exchanger geometries. The amount of possible cooling from these methods is dependent to
some extent on the ambient conditions. Hybrid systems, combining closed loop and dry
cooling, attempt to minimize the variability by changing the cooling technique depending
on the season.
Single pass cooling systems use large quantities of water making a single transit through
the condenser before being discharged. The total flow of water is dictated not only by
cycle requirements but also by local regulations which limit temperature rise in the coolant
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source. Maximum temperature rise limitations (e.g., The Clean Water Act of 1972) have
been enacted to reduce or eliminate the effect on aquatic species of thermal plumes resulting
from the discharge of cooling water. In addition, these limit reduce water consumption by
the condensers by limiting evaporation. These limits increase the flow of water required. The
regulations also place restrictions on cooling water inlet construction to ensure sufficiently
low inlet velocities to avoid ingestion of fish, shell fish and aquatic plants. Steam condenser
operating temperatures for single pass systems are limited by the water source’s temperature
which in most cases is seasonably variable [14].
Closed-loop cooling systems use less water than open-loop systems but consume more
through evaporation. The heat absorbed from the steam by the coolant is released through
direct contact with atmospheric air in a cooling tower. Rather than passing through the
condenser a single time, the water continuously circulates between the condenser and the
cooling tower. Make up water is added to the loop to replace that lost through evaporation.
Minimum cycle temperatures in the steam cycle are dictated by the wet bulb temperature
of the air entering the cooling tower.
Water consumption and usage is reduced or eliminated in dry and hybrid cooling systems.
In dry cooling the water in the steam loop is cooled by indirect contact with air in a cooling
tower. Minimum cycle temperature varies with ambient temperature and humidity limiting
the utility of dry cooling systems in hot, arid environments. Hybrid cooling systems use
cooling towers equipped for both dry and closed loop cooling. The system in use depends
changes seasonally with ambient conditions to minimize water consumption.
Population growth and changes in climate have led to concern over the management of
limited water resources. In regions located far from ocean coasts, steam condenser cooling
may compete with agricultural and domestic uses for fresh water. Some municipalities now
108

mandate that a certain percentage of cooling water used in steam condensers be reclaimed
(i.e., treated sewage) to reduce the consumption of potable water [11]. Recent heat waves
in western Europe led to output reductions and shutdown at a number of plants due to
insufficient cooling. Drought conditions have exacerbated the issue by reducing the quantity
of cooling water available [169]. Dry cooling systems, despite the additional capital costs
associated with them, have received more interest to eliminate the need for cooling water to
avoid these power reductions/shutdowns [170].

6.2.2

Alternative Cooling Approaches

A group of alternative cooling techniques using ammonia in addition to water are under
investigation. One proposed alternative uses a phase change ammonia loop to augment a
wet-dry hybrid cooling system. The addition of the ammonia loop reduces the capital costs
of a dry cooling system by 25 to 45% [171]. In a similar system proposed by Goswami et
al. , the working fluid is a binary mixture of ammonia and water which is used to produce
shaft power, through a turbine, and refrigeration (tri-generation). The binary vapor mixture
leaving the turbine is sufficiently cool to chill water through transfer of sensible heat. The
mixture then passes through a water cooled absorber to condense [172]. This system was
proposed to use low temperature heat sources like solar and geothermal.
A second proposed system uses excess power available during off peak load hours to charge
a cooling storage system with a hybrid cooling system. Two turbines are cooled by a dry
cooling system, first turbine, and a closed-loop wet cooling system, second turbine. Power
from the second turbine is used to drive a refrigeration system for the cooling storage or
directly cool the wet condenser. Warm water leaving the wet cooling system passes through
the cold storage system rather than a cooling tower to reject the absorbed heat. Depending
109

on configuration, the output of the plant can be increased by up to 33% at 50◦ C [173].
This design was modified to include two refrigeration systems and three modes of operation.
When grid demand is small enough to drive the first refrigeration system with the excess
available power, the condenser water is cooled directly by refrigeration. If enough excess
power is available to drive both refrigeration systems, the second refrigeration system is
used to charge the cooling storage system. Finally, at peak demand the condenser is cooled
using the cooling storage system. This modification to the cycle further increases the plant’s
power output at peak demand [174].

6.3

Conclusions

In this chapter the design and application of combined cycle power plants has been discussed.
Focus was on the limits placed on the steam condenser of the bottoming cycle by both
environmental and regulatory changes. From this review the following conclusions were
drawn:
• Combined cycle power plants use the best features of the Brayton (topping) and Rankine (bottoming) cycles to increase overall plant efficiency
• The efficiency of the combined cycles is limited by operating temperature of the steam
condenser in the bottoming cycle
• Most current cooling technologies, both wet and dry, cause condenser operating temperature to be seasonally variable
• Governmental and environmental pressures are limiting the water available for wet
condenser cooling
110

• Dry cooling systems add up to 15% to the cost of electricity generation
• Alternative cooling approaches based on refrigeration technology are a promising path
to reducing or eliminating water usage and stabilizing plant efficiency
Chapter 7 discusses the design and preliminary testing of a proof of concept test rig for a
VCRS cooled steam condenser. A condenser of this type would have applications in larger
combined cycle power plants as a part of a more distributed electrical generation system.

111

Chapter 7
Refrigerant Cooled Steam Condenser
Here we investigate using a vapor-compression refrigeration system (VCRS) to cool a steam
condenser. Both well documented in literature and commercially viable, a VCRS offers an
intriguing solution to steam condenser cooling issues. There is no requirement for cooling
water unlike wet cooling systems, though water may be used to cool the condenser of the
VCRS. Additionally, refrigerants offer better heat transfer rates and lower operating temperatures compared to water or air. Unlike dry cooling, VCRS operating temperatures would
not depend on the local dry bulb temperature. In this chapter we discuss different cooling cycles, the development of a novel, reduced-scale experimental model of a VCRS cooled
steam condenser and some preliminary results of experiments conducted with R-410a as a
steam condenser coolant.

7.1

Cooling Fluids and Coolant Cycles

A number of refrigerant cycles may be integrated into the bottoming cycle of a combinedcycle plant for condenser cooling. All will be a parasitic load on the plant. In many cases it
may be preferable to use these mechanical cooling systems to augment traditional condenser
cooling approaches rather than as stand alone systems. Optimization of the cooling cycle is
beyond the scope of this work.
Excess heat from either the topping cycle or bottoming cycle could be used to drive a

112

vapor absorption chiller. The heat source may come from a bleed off either the GT exhaust
gas entering the heat recovery steam generator (HRSG) or the steam generated. Such a
system is similar to the hybrid power-cooling systems described earlier [171, 172]. The work
input required by an absorption chiller system would be less than that required by a similarly
sized VCRS. The trade-off is a lower COP compared to a VCRS and a required secondary
cooling source to maintain a suitable absorber temperature.
A Brayton refrigeration cycle implemented between the steam condenser (cold region)
and the ambient environment (hot region) is a possible solution in warmer climates. Similar
systems, on smaller scales, are used in aircraft cabin cooling applications. Other than for
start up, a Brayton refrigeration system would be minimally parasitic to the combined-cycle
plant unlike an absorption chiller or VCRS. However the cycle does not include a phase
change of the refrigerant; thus, it is less efficient than a VCRS or absorption chiller. To
compensate, larger mass flows of coolant would be required resulting in a larger footprint
and more expensive turbomachinery.
Recent work has investigated, in more detail, the specifics of integrating a VCRS into a
vapor power generation loop. An analytic study has compared water to R-134a for condenser
cooling. The authors found that R-134a outperforms water [175]. In a continuation of the
study, R-134a was compared to several other commercial refrigerants. Of the refrigerants
studied, R-410a performed the best due to its higher operating pressure and heat transfer
properties [176]. As noted in Chapter 6 the work of Hegazy has identified potential methods
of integrating a VCRS cooled steam condenser into a standard steam power plant [173, 174].

113

7.2

A Refrigerant Cooled Steam Condenser Test Rig

To perform proof-of-concept testing for a VCRS cooled steam condenser, a novel reducedscale model of the system has been constructed. The facility is located in the Turbomachinery
Research Laboratory at Michigan State University. All utilities are provided by building connections. The initial design consisted of a commercially available steam generator, domestic
air conditioner condenser unit and a commercial ASME 150lb rated shell and tube steam
condenser. A three-loop system, including a chilled water loop, was ultimately necessary for
safety and economic reasons, see Figure 7.1 for a schematic and Figure 7.2 for photos. The
additional chilled water loop is an intermediate step that is convenient for experiments. A
commercial system would eliminate this loop.
The first loop in the system was the open steam loop. Steam was supplied by a 9kW
commercial steam generator (CMB-9A, Chromalox, Pittsburgh, PA). The heat rate was
fixed and steam was supplied in a saturated condition. Consequently, steam mass flow rate
is dictated by the temperature set point and inlet water temperature. The water level in the
boiler was maintained at a safe level by a boiler-feed-water valve. Practically, the maximum
saturation temperature was limited by water feed pressure. The system was capable of
producing steam at a pressure of up to 68.9 kPa less than feed pressure (377.1 kPa in this
facility). For safety reasons pressure was ultimately limited by a 790.8 kPa pressure relief
valve. The steam ran in an open loop from the building water supply through the steam
generator and the shell side of the steam condenser (SX2000U, Standard-Xchange, Buffalo,
NY) to a building drain. A thermostatic condensate valve and water column were used
to maintain pressure inside the steam condenser. The capabilities of the condensate valve
limit the minimum steam condenser pressure to −30.500 kPa. Condensate flow rates were

114

measured by using a graduated tank installed between the exit of the condenser and the
drain and hand operated timer.
Due to a lack of commercially available shell an tube heat exchangers rated for the
high pressures necessary for R-410a use in a vapor-vapor exchanger, an intermediate, closed
chilled-water loop was added. This loop used a commercially available R-410a-water shell
and tube heat exchanger, intermediate heat exchanger (IHX), (SST-200A, Standard Refrigeration, Wood Dale, IL) as a link to the VCRS loop and the ASME rated shell and tube
steam condenser as a link to the open steam loop. The water flows through the tube side of
the steam condenser and the tube side of the water chiller. Water is circulated through the
system by a variable speed pump. Safety in this loop is provided by a high pressure switch,
a low temperature switch, to prevent freezing, and a pressure relief valve. System performance measurements are made in this loop due to the relative safety of pressurized water
compared to refrigerant or steam. Water flow rate is measured by a rotameter (FLD107,
Omega Engineering, Inc., Stamford, CT), temperature is measured by T-type thermocouples
and pressure is measured by bourdon gauges. Operating conditions in this loop are listed in
Table 7.1.
The VCRS loop was based on a commercially available domestic air conditioner condenser charged with R-410a. The condenser unit (Dayton 3.0 Ton 14.5 SEER, Grainger,
Chicago, IL) and the steam generator were matched in power consumption. Chilled water
temperature was adjusted by the refrigerant charge and pressure. A pressure relief valve and
high pressure switch were used to maintain safe operation of the system. Short cycling of
the AC compressor is prevented by a pressure regulator that smoothly loads the system. A
pair of filter/driers in the liquid and vapor lines kept debris out of the thermal-expansion
valve and refrigerant compressor, respectively. An accumulator tank and a section of heated
115

tubing ensured that only refrigerant vapor is fed to the compressor. Heat from the refrigerant condenser is rejected to the room where building systems are used to remove it from the
area.

116

Figure 7.1: Experimental layout: Steam loop: 1-Water source, 2- filter and ball valve, 3-Float control valve, 4-Boiler, 5-Drain
valve, 6-Pressure relief valve, 7-Steam outlet valve, 8-Condenser, 9-Air vent valve, 10-Thermostatic check valve, 11-Graduated
tank; Water loop: 12-Pressure reducing valve, 13-Thermal expansion tank, 14-high pressure switch, 15-pressure relief valve,
16-Intermediate heat exchanger, 17-low temperature switch, 18-Circulator pump, 19-Rotameter; VCRS loop: 20-pressure relief
valve, 21-low pressure switch, 22-pressure regulator, 23-accumulator, 24-filter driers, 25-Vibration absorber, 26-AC unit, 27TXV, 28-Glass Screen, 29-high pressure switch.
117

Figure 7.2: Photo of the assembled reduced scale refrigerant cooled steam condenser.

To ensure safe operation of the entire test system, experiments were carried out in a
manner that kept the VCRS loop within design constraints. The steam loop and chilled
water loops were started first to provide a heat load to the VCRS loop. Once an adequate
load was established, the VCRS was brought on line and allowed to stabilize. Settings in the
steam and chilled water loops were adjusted to meet intended operating conditions once the
VCRS was stable. Heat losses in the steam system required the saturation temperature set
point to be about 1◦ C above that required by the desired condenser pressure. Refrigerant
pressures were closely monitored at all times. Test conditions were chosen to best match the
power output from the steam condenser to that absorbed by the VCRS loop. This minimized
safety risks.
System performance measurements are made once a safe, stable operating point has been
established. Equilibrium was determined to be when system temperatures varied by less than
the accuracy of the measurements, see Table 7.2, for six minutes. At each operating point
fluid temperatures and pressures in all three loops and input voltage and current to the
VCRS condenser unit were measured. The VCRS power measurement includes both the
118

compressor and condenser cooling fan loads. The duration of each measurement was 3 to 5
minutes. Variations in water loop pressure had a negligible effect on system operation and
is ignored here. The heat rejected by the steam condenser was calculated by

Q˙ = m
˙ cw cPcw Tcw,out − Tcw,in

(7.1)

where the condenser is assumed to be adiabatic due to the insulation. In all equations in
this chapter subscript cw refers to the cooling water and subscript R is refrigerant. Similarly
the flow rate of refrigerant is calculated based on the heat balance between the VCRS and
chilled water loops across the IHX

˙ cw cPcw Tcw,out − Tcw,in
m
˙ R cPR,vap TR,out − cPR,liq TR,in = m

(7.2)

VCRS COP is calculated using

COP =

m
˙ cw Tcw,out − Tcw,in
(V I)AC

(7.3)

Finally, the overall heat transfer coefficient Uo is calculated from

Uo =

m
˙ cw cP Tcw,out − Tcw,in
Ao LMTD

(7.4)

where Ao is the outer surface area of the condenser tubes and LMTD is calculated with

LMTD =

Tcw,out − Tcw,in
T −T
ln T sat−T cw,in
cw,out
sat

119

(7.5)

These relations, COP and Uo , will be used to evaluate the condenser test rig.
The data collected from the new test rig can also be used to investigate different proposed empirical correlations for the Nusselt number of film condensation for a R-410a cooled
condenser. Models of this type were first developed by Nusselt. He assumed that the wall of
the tubes were at constant temperature, the condensate film was laminar, the thickness of
the film was small compared to the tube diameter, heat transfer in the film was limited to
conduction only, the temperature distribution inside the film is linear and that all properties
are constant. This resulted in the well known relation [177]

¯ = 0.728
Nu

where F =

ρ2cond ghfg D 3
¯
µcondkcond ∆T

0.25

˜2
= 0.728 F Re

0.25

(7.6)

gDo hfg µcond
˜ = ρcond uDo is the two-phase Reynolds number, ∆T
¯ is
, Re
kcond ∆T u∞
µcond

calculated by
∆T = Tsat − Tw
Tw =

(7.7)

Tcw,in + Tcw,out
2

(7.8)

2
1
and all condensate properties are calculated at T ∗ = Tw + Tsat . Shekriladze and Gomer3
3
lauri [178] took vapor shear into account by assuming the cylinder wall was isothermal, the
condensate film is laminar and boundary layer separation can be neglected. Their derivation
resulted in
¯ Re
˜ −0.5 = 0.64 1 + (1 + 1.69F )0.5
Nu

0.5

(7.9)

Butterworth adapted for pure vapors Eq 7.9 by taking into account low vapor velocities [179]

¯ Re
˜ −0.5 = 0.416 1 + (1 + 9.47F )0.5
Nu
120

0.5

(7.10)

Rose further modified Eq 7.9 to

¯ Re
˜ −0.5 =
Nu

0.9 + 0.728F 0.5
1 + 3.44F 0.5 + F

0.25

(7.11)

Fujii et al. performed a series of experiments on low pressure steam condensation through
tube banks of different arrangements. This experimental data was correlated by [180]

¯ Re
˜ −0.5 = 0.96F 0.2
Nu

Lakshmi et al.

(7.12)

developed a mathematical model for the condensation of turbulent films

flowing both parallel and normal to horizontal condenser tubes. It was assumed constant
heat flux at the tube wall. They concluded that condenser pressure and steam approach
velocity have a significant effect on the heat transfer coefficient. The following correlation
was proposed [181]
¯ t Re
˜ −0.5 = 0.8732
Nu

ϕ0.3124
(F S)0.03376 q 0.1306

(7.13)

1/3

¯ l Re
˜ −0.5 = 0.4103 (F S)
Nu
q 1/3
¯ 3 = Nu
¯ 3 + Nu
¯3
Nu
t
l

(7.14)
(7.15)

These empirical formulations will be compared to the present experimental data to determine
the best fit for the VCRS cooled steam condenser.
Table 7.1: Operating conditions of the three-loop VCRS cooled steam condenser test rig
m
˙H O
Condenser H2 O Tin
2
56 to 131 g/s
9 to 32◦ C

Condenser P
−30.5 to 0 kPa

121

Table 7.2: Estimated experimental measurement error for experiments with the three-loop
VCRS cooled steam condenser
Device
Rotameter
Thermocouple
Condensate Collector
Calculated Parameter
–
–
–
–
–
–
–
–
–

7.3

Measurement
Error
Water Volume Flow Rate
±3% of full scale
Fluid Temperature
±0.3◦ C
Condensate Volume Flow Rate
±3.3%
Coolant Water Mass Flow Rate
±3.01%
Heat Rejection
±3.9%
LMTD
±2.59%
COP
±4.42%
Uo
±4.15%
Refrigerant Mass Flow Rate
±4.32%
˜
Re
±5.1%
F
±4.30%
˜
Nu
±0.34%
¯ Re
˜
Nu
±3.06%

Preliminary Experimental Results

Figure 7.3 shows the effect of inlet coolant water temperature on the condensate and refrigerant mass flow rates. Decreasing the coolant water temperature increases the rate of
steam condensation due to the increased temperature difference between steam and coolant,
similar trends were observed by [182]. For the same inlet coolant temperature, when water
flow rate increases the condensation and refrigerant mass flow rates also increase. Figure 7.3
can be used for selection of the required R-410a mass flow to condense 1 kg of steam at a
design condition.
The effect of changes in R-410a mass flow rate on heat rejected to the ambient and COP of
the VCRS is shown in Figure 7.4. Decreasing inlet coolant temperature, which increased the
rate of condensation and refrigerant mass flow rate, increased the heat rejection. Similarly,
increasing cooling water flow rate also increased heat rejection. Trends of this type have been

122

Figure 7.3: Condensation rate and R-410a mass flow rates at pcw =6.8kPa and pcp =0kPa.

identified by other investigators [168], [182], [183]. The variation of COP with inlet coolant
temperature is also shown in Figure 7.4. The COP of the VCRS increased with chilled water
flow rate and decreased inlet coolant water temperature. Increasing COP by decreasing
chilled water temperature increases the overall steam power plant efficiency by decreasing
the power demand of the VCRS and reducing the temperature of the steam condenser.
The effect of inlet coolant temperature and water mass flow rate on Uo is depicted in
Figure 7.5. Decreasing inlet coolant temperature enhances Uo below 22◦ C. Above this
temperature little change with inlet water temperature is noted. The trend with water mass
flow rate is different than that seen in Figure 7.3 and Figure 7.4. This may be attributed to
the reduction of outlet coolant temperature with increasing its mass flow rate. The result is
a rate of increase of coolant heat rejection by less than the rate of increasing LMTD when

123

Figure 7.4: Heat rejection and COP at pcw =6.8kPa and pcp =0kPa.

124

Figure 7.5: Overall heat transfer coefficient at pcw = 6.8 kPa and pcp = 0 kPa.

125

Figure 7.6: Condensation rate and R-410a mass flow rates at pcw = 6.8 kPa and pcp =
−16.943 kPa.

the coolant temperature increases and coolant mass flow rate decreases.
Trends of condensation rate, refrigerant mass flow rate, heat rejection, COP and Uo are
shown in Figures 7.6, 7.7 and 7.8, at Pcp = −16.943 kPa, and Figures 7.9, 7.10 and 7.11, at
Pcp = −30.500 kPa. When comparing Figures 7.3, 7.6 and 7.9, it is evident that increased
levels of vacuum result in higher rates of condensation and refrigerant mass flow. The rate
of increase in the condensation rate is higher than the rate of increase in the refrigerant
flow rate as condenser pressure decreases. That means that operating the steam condenser
under vacuum will be more efficient for the VCRS when used in condenser cooling applications. This lower operating pressure enhances steam condenser performance and the overall
steam cycle efficiency and decreases the condenser total temperature difference as reported
elsewhere [167], [168].
126

Figure 7.7: Heat rejection and COP at pcw = 6.8 kPa and pcp = −16.943 kPa.

127

Figure 7.8: Overall heat transfer coefficient at pcw = 6.8 kPa and pcp = −16.943kpap.

128

Figure 7.9: Condensation rate and R-410a mass flow rates at pcw = 6.8 kPa and pcp =
−30.5 kPa.

129

Figure 7.10: Heat rejection and COP at pcw = 6.8 kPa and pcp = −30.5 kPa.

130

Figure 7.11: Overall heat transfer coefficient at pcw = 6.8 kPa and pcp = −30.5 kPa.

131

Comparing the corresponding Figures 7.4, 7.7 and 7.10 reveals that COP and heat rejection increase when both steam condenser pressure and inlet coolant water temperature
decrease. Best performance occurs at Pcp = −30.500 kPa and m
˙ cw = 0.131kg/s as will be
discussed later, see Table 7.3. Reducing the condenser pressure enhances Uo especially at
m
˙ cw = 0.056kg/s as evidenced on comparison of Figures 7.5, 7.8 and 7.11. A similar effect
was documented by [184] that local heat transfer coefficient decreases with higher steam
pressures. This may be attributed to the dependence of Uo on LMTD which depends on
outlet coolant temperatures as discussed earlier.
The percentage variations of m
˙ cond , Q, COP, m
˙ R−cw , and Uo from a reference condition
are tabulated in Table 7.3. The reference values are calculated at a coolant temperature of
31.9◦ C and condenser pressure of 0.000 kPa. At m
˙ cw = 0.056kg/s by decreasing the coolant
temperature from 31.9◦ C to 9.6◦ C results in enhancements of the condensation rate, heat
rejection, COP, mass ratio and Uo of 14.94%, 36.66%, 36.61%, 44.05% and 14.92%, respectively. If in addition to reducing the coolant temperature from 31.9◦ C to 9.6◦ C, the condenser
pressure is also reduced from pcp = 0 to −16.943 kPa, the levels of improvement changed
to be 20.96%, 34.28%, 34.24%, 32.68% and 21.77%, respectively. Further, decrease of condenser pressure yields more improvement in performance as shown at pcp = −30.500 kPa in
Table 7.3.
Similar trends are seen using the same calculation procedures at m
˙ cw = 0.11 and
0.131kg/s. It may be inferred from Table 7.3 that working under more vacuum in the steam
condenser increases the possible quantity of condensate. Moreover, it widens the pressure
difference across the turbine which increases the work output. Both the decrease of m
˙ R−cw
and increase of COP lead to a reduction in power consumption by the AC unit which increases system efficiency. The enhancement percentage ratio for Uo at m
˙ cw = 0.056kg/s. As
132

Uo increases from 14.92% to 31% at m
˙ cw = 0.056kg/s while it increases from 9.1% to 24.4%
at m
˙ cw = 0.131kg/s. The smaller levels of enhancement in Uo with increasing coolant mass
flow rate at the same condenser pressure may be related to the outlet coolant temperature
effect as discussed earlier.
Table 7.3: Percentage variations of condensation rate, heat rejection, COP, ratio of refrigerant to condensate mass flow rates and Uo compared to calculated values at a coolant
temperature of 31.9◦ C and pcp = 0kPa.
❵❵❵
❵❵❵
m
˙ cw (kg/s)
❵❵❵
❵❵❵
pcp (kPa)
❵❵❵

0

−16.943

−30.500

m
˙ cond %
Q%
COP %
m
˙ R−cw %
Uo %
m
˙ cond %
Q%
COP %
m
˙ R−cw %
Uo %
m
˙ cond %
Q%
COP %
m
˙ R−cw %
Uo %

0.056

0.110

0.131

14.94
36.66
36.61
44.05
14.92
20.90
34.28
34.24
32.68
21.77
20.42
34.84
34.79
41.51
31.00

14.82
32.84
32.80
49.52
12.24
17.84
31.16
31.17
44.17
18.57
19.37
32.67
32.65
45.80
27.47

12.32
28.81
28.81
38.34
9.10
15.46
27.83
27.84
33.60
15.80
16.44
29.46
29.47
33.54
24.40

The results of the present study fall within the scatter of the data collected by Fujii [180]
for horizontal tube condensers. This is expected based on the geometry of the condenser
used in the test system. The correlations proposed by Nusselt Eq (7.6), Shekriladze and
Gomelauri Eq (7.9), Butterworth Eq (7.10), Rose Eq (7.11), Fujii et al.
Lakshmi et al.

Eq (7.12) and

Eq (7.15) have all been compared to the present data. The Butterworth

correlation [179] and the related Lakshmi correlation [181] best predict the results reported

133

here. To improve the accuracy of the prediction, the leading coefficient of Eq 7.10 is modified

¯ Re
˜ −0.5 = 0.4415 1 + (1 + 9.47F )0.5
Nu

0.5

(7.16)

This modification agrees with the present data with a mean error of 4.43%.

7.4

Conclusions

Alternatives for water based steam power plant cooling are becoming necessary due to environmental and regulatory pressures. The use of refrigeration cycles to provide enhanced
cooling for steam plants has been investigated here. An experimental model of a steam
power plant has been designed to investigate the potential for a vapor compression refrigeration cycle to cool a steam condenser. The system consists of three interconnected loops:
an open-loop steam condenser, an intermediate closed-loop chilled water circuit and a closed
loop vapor compression refrigeration system. The links be tween the loops are two heatexchangers. Experimental performance measurements indicate that the refrigeration cooled
condenser is capable of delivering sufficient cooling to, at least, offset water consumption.
Further the power consumption of the refrigeration system is reduced as the coolant temperature is reduced and condensate flow rates increase. This increases the efficiency of the
Rankine power cycle and the COP of the refrigeration system.

134

Chapter 8
Conclusions and Future Work
This work has investigated two potential hurdles to a modern distributed electrical generation
grid. The first is the adaption of small gas turbine engines to alternative fuels. A particular
focus was on fuels from anaerobic digestion of organic materials as a source of renewable
energy. There are a few commercially available engines that operate on fuels of this type, but
a foundation of the operating limits of these fuels is lacking in the archival literature. To this
end, a series of investigations into the effect of dilution on flame speeds and extinction limits
have been reported. In an effort to expand on this research a test facility has been described
and is under construction. The second avenue of investigation involves larger power plants
intended for large population centers and industrial facilities. Due to the increased power
demands and potential uses for steam, combined-cycle plants are of interest at these sites.
The population growth in arid climates in the U.S. and global warming concerns has brought
cooling of steam condensers to interest. A method of reducing the reliance of steam power
cycles on natural water sources for cooling of steam condensers by using vapor compression
refrigeration has been proposed. To investigate the effectiveness of such a system, a novel
test rig has been designed. Initial results from this model have shown the promise of this
method. This chapter is divided into two sections to describe the future of the research
presented here.

135

8.1

Alternative Fuels for Small Gas Turbines

Two drivers have emerged to increase interest in micro-GT engines for small scale power
production. The first is a push for industrial facilities to control their electrical energy
supply. In some parts of the world this is due to inadequate or unreliable electrical grids. In
the U.S. the desire for control is due to both volatility in energy prices and state incentive
programs that rebate much of the initial capital investment (e.g., California’s Self-Generation
Incentive Program). The second driver is increasing regulatory pressure to limit the emissions
of pollutants and reduce flaring of waste gases. Many states are investigating legislation to
limit flaring to locations where there are no other economically viable alternatives. At remote
oil and gas production sites the most logical use for the waste gas is electrical generation
to power the site. Both drivers lead back to small fuel flexible GT engines as potential
solutions.
Though recent discoveries of large, domestic natural gas reserves and advances in fossil
fuel production methods have lessened the immediate need for alternative fuels, many drill
sites are in remote locations where grid power is not initially available. Using Diesel fueled
generators can be cost prohibitive due to the expense of shipping fuel. The available fuel
stream from the producing wells is not always of pipeline quality. Heating contents can
vary widely from site to site. Thus, fuel flexibility is a major concern for power generation
equipment which may be moved between sites.
In this work we have investigated some of the limiting phenomena associated with diluted
fuels. Previous work by Jahangirian and Engeda [157] pointed to a need for a study of laminar
flame speeds of CO2 diluted CH4 fuels. This work has partially filled that void by proposing
a correlation to predict the flame speed of a fuel based on content. Using an established

136

numerical model, the lean extinction limits in an ideal lean-premixed gas turbine have been
explored. Based on this data a model for predicting limits based on operating conditions
and fuel content was proposed. These two correlations may be used by future combustor
designers to better predict the effect of fuel changes on combustor stability.
To expand on the alternative fuels research presented here, an experimental facility has
been proposed and construction initiated. The well-stirred reactor is based on a design that
has been used before with success to simulate conditions in a gas turbine combustor. The
facility was designed with the goal of validating some of the lean-extinction work presented
here. There is the opportunity to expand the facility for high pressure experiments to validate
the pressure dependence suggested here. The well-stirred reactor facility is the most direct
extension of this work.

8.2

Alternative Cooling Strategies for Future Large
Power Plants

The other end of the size scale was covered by the second part of this work. Large combinedcycle plants are well suited for clean generation of electricity for large industrial facilities or
population centers. Though they would run primarily on standard fuels like pipeline quality
natural gas, the cooling of the steam condensers in the bottoming cycle is an area of concern.
Large scale use and consumption of natural water supplies by steam power plants is facing
increasing regulatory and environmental pressure. Alternative methods of condenser cooling
will be necessary in the near future.
In this work we discuss the potential for applying vapor compression refrigeration systems
to steam condenser cooling. Recent work by other investigators has pointed to potential
137

methods of integrating a refrigeration system in to a water vapor power cycle [173, 174]. To
further advance this approach an experimental facility has been designed and constructed.
This facility uses commercial ‘off the shelf’ components to model a reduced scale steam
condenser cooled by a refrigeration system charged with R-410a. Initial results from the novel
test setup described here indicate that the system becomes more efficient as the operating
pressure in the steam condenser decreases. This is true for both the vapor power cycle and
the refrigeration system.
The next step in this investigation would be to modify the test rig to eliminate the
intermediate water loop. This moves the system closer to the intended application. The
correlation to predict the Nusselt number in the condenser recommended here can be used
to design the new system. This new system should be used to explore lower operating
pressures in the steam condenser. Further testing in varying ambient conditions should also
be undertaken to understand the effect of climate on the efficiency of the proposed system.
These investigations will be necessary before a large scale refrigerant cooled steam condenser
can be made commercially viable.

138

APPENDIX

139

APPENDIX: PIPING DIAGRAMS

0)&
7R :65
7R 6HFRQGDU\
$LU 0DQLIROG
3UHVVXUH 5HJXODWRU
3UHVVXUH *DXJH
7KHUPRFRXSOH
&RQWURO 9DOYH
&KHFN 9DOYH
%DOO 9DOYH

3DUWLFXODWH )LOWHU
0HPEUDQH 'U\HU
$LU +HDWHU

Figure A.1: Piping schematic of the air feed system to the WSR.

140

0)&

3

)XHO
0DQLIROG

7R :65
0)&

'LOXHQW
0DQLIROG

Figure A.2: Piping schematic of the fuel feed system to the WSR.

141

1LWURJHQ
0DQLIROG

5HDFWRU &RROLQJ
3QHXPDWLF 9DOYHV
)XHO 3XUJH

Figure A.3: Piping schematic of the nitrogen feed system to the WSR.

142

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