design point analysis of the high pressure regenerative turbine engine cycle...
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DESIGN POINT ANALYSIS OF THE HIGH PRESSURE REGENERATIVE TURBINE ENGINE CYCLE FOR HIGH-SPEED MARINE APPLICATIONS
By
GEORGE ANAGNOSTIS
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2007
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Copyright 2007
By
George Anagnostis
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This thesis is dedicated to my parents, Victor and Linda Anagnostis. Without their emotional and financial encouragement this thesis would not exist.
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ACKNOWLEDGMENTS
I thank the members of my graduate committee members: Dr. William E. Lear, Jr.,
Dr. S. A. Sherif, and Dr. Herbert Ingley for their support on this thesis. Dr. Lear was
especially helpful, providing me with critical advice throughout this project. Next, I
would like to thank the Aeropropulsion Systems Analysis Office at the National
Aeronautics and Space Administration Glenn Research Center for their assistance on
Numerical Propulsion System Simulation program. Two members of that group provided
continued technical assistance—Scott Jones and Thomas Lavelle. Lastly, I thank two
special individuals that have provided me with insight and wisdom concerning matters of
engineering and life in general, John Crittenden and William Ellis.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS ................................................................................................. iv
LIST OF TABLES............................................................................................................ vii
LIST OF FIGURES ......................................................................................................... viii
NOMENCLATURE ............................................................................................................x
CHAPTER
1 INTRODUCTION ........................................................................................................1
2 LITERATURE REVIEW .............................................................................................4
Brief History of Turbine Engine Development ............................................................4 Gas Turbine Engine Examples in Marine Applications ...............................................5 Advantages of Gas Turbine Engines in Marine Applications ......................................6 Recuperation and Inter-cooling ....................................................................................7 Semi-Closed Cycles......................................................................................................9 Computer Code Simulators.........................................................................................10 Previous Gas Turbine Research at the University of Florida .....................................12
3 NUMERICAL PROPULSION SYSTEM SIMULATION ARCHITECTURE.........16
Model..........................................................................................................................16 Elements .....................................................................................................................17 FlowStation.................................................................................................................18 FlowStartEnd ..............................................................................................................18 Thermodynamic Properties Package ..........................................................................20 Solver..........................................................................................................................21
4 CYCLE CONFIGURATIONS AND BASE POINT ASSUMPTIONS.....................25
Major Model Features.................................................................................................25 Flow Path Descriptions & Schematics .......................................................................26
Simple Cycle Gas Turbine Engine Model...........................................................26 High Pressure Regenerative Turbine Engine Efficiency Model .........................26
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High Pressure Regenerative Turbine Engine with Vapor Absorption Refrigeration System Efficiency Model ..........................................................27
Simple Cycle Gas Turbine Engine Design Assumptions and HPRTE Cycles Base Point Assumptions .................................................................................................28
5 THERMODYNAMIC MODELING AND ANALYSIS............................................33
Thermodynamic Elements ..........................................................................................33 Heat Exchangers..................................................................................................33 Mixers..................................................................................................................34 Splitter .................................................................................................................35 Water Extractor ...................................................................................................36 Compressors ........................................................................................................37 Turbines...............................................................................................................39 Burner ..................................................................................................................40
Sensitivity Analysis ....................................................................................................41
6 RESULTS AND DISCUSSION.................................................................................43
Cycle Code Comparison .............................................................................................43 Sensitivity Analysis ....................................................................................................44
Simple Cycle Gas Turbine Engine Model...........................................................44 Simple Cycle Gas Turbine Engine Model Sensitivity Analysis..........................48 High Pressure Regenerative Turbine Engine Efficiency Model .........................50 High Pressure Regenerative Turbine Engine Efficiency Model Sensitivity
Analysis............................................................................................................53 Cycle Comparison Analysis .......................................................................................61
Extreme Operating Conditions ............................................................................65 High Pressure Compressor Inlet Temperature Comparison for H-V Efficiency
Model ...............................................................................................................67 Final Design Point Parameter Comparison .........................................................68
7 CONCLUSIONS AND RECOMMENDATIONS.....................................................83
Conclusions.................................................................................................................83 Recommendations.......................................................................................................86
LIST OF REFERENCES...................................................................................................88
BIOGRAPHICAL SKETCH .............................................................................................91
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LIST OF TABLES
Table page 4-1 Comparison of major configuration features ...........................................................29
4-2 Simple Cycle Gas Turbine engine design point parameters.....................................32
4-3 Base case model assumptions for HPRTE cycles [3], [26], [27] .............................32
6-1 Cycle codes comparison: NPSS verses spreadsheet code for HPRTE Efficiency model data run. All temperatures are in °R. ............................................................70
6-2 Summary of the HPRTE Efficiency sensitivity analysis .........................................77
6-3 Comparison of the thermal efficiency maximums and their corresponding overall pressure ratios (OPRs)..................................................................................78
6-4 Comparison of the specific power maximum values and their corresponding OPRs.........................................................................................................................78
6-5 Comparison of exhaust temperature maximum values for the three engine configurations...........................................................................................................79
6-6 Engine cycles comparison for four extreme operating conditions ...........................81
6-7 High pressure compressor (HPC) inlet temperature comparison for the H-V Efficiency engine model...........................................................................................81
6-8 Final performance design point comparison for the engine configurations.............82
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LIST OF FIGURES
Figure page 3-1 Example NPSS engine model [19]...........................................................................23
3-2 State 7 of HPRTE engine cycle................................................................................24
4-1 Simple Cycle Gas Turbine (SCGT) engine model configuration ............................29
4-2 High Pressure Regenerative Turbine Engine model, both efficiency and power configurations represented .......................................................................................30
4-3 High Pressure Regenerative Turbine Engine-Vapor Absorption Refrigeration System, both efficiency and power model configurations represented....................31
4-4 Vapor Absorption Refrigeration Cycle with HPRTE flow connections ..................32
6-1 Thermal efficiency comparison is plotted with respect to OPR. NPSS results (with turbine inlet temperature (TIT) set to 2500°R) are compared to the derived and the ideal Brayton cycle expressions. .................................................................70
6-2 Thermal efficiency vs. OPR with sensitivity to TIT ................................................71
6-3 Specific power vs. OPR with TIT sensitivity...........................................................71
6-4 Thermal efficiency vs. ambient temperature with OPR sensitivity..........................72
6-5 Demonstrates agreement between NPSS and developed theory that describes the low pressure spool ....................................................................................................72
6-6 High pressure spool pressure ratio (HPPR) vs. ambient temperature with low pressure spool pressure ratio (LPPR) sensitivity......................................................73
6-7 Thermal efficiency vs. HPPR showing sensitivity to TIT .......................................73
6-8 Thermal efficiency vs. HPC inlet temperature for recirculation ratio sensitivity ....74
6-9 Thermal efficiency vs. turbine exit temperature (TET) with cooler pressure drop sensitivity .................................................................................................................74
6-10 Specific power vs. TET for HPC efficiency sensitivity ...........................................75
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6-11 Specific power vs. HPPR for HPT efficiency sensitivity.........................................75
6-12 Exhaust temperature vs. OPR for TIT sensitivity ....................................................76
6-13 Thermal efficiency vs. HPPR for turbocharger efficiency sensitivity .....................76
6-14 Thermal efficiency vs. LPPR for TIT sensitivity .....................................................77
6-15 Engine cycles comparison of thermal efficiency vs. OPR .......................................78
6-16 Engine cycles comparison of specific power vs. OPR.............................................79
6-17 Engine cycles comparison of exhaust temperature vs. OPR....................................80
6-18 Engine cycles comparison of thermal efficiency vs. ambient temperature..............80
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NOMENCLATURE
DepV Dependent variable in a Jacobian matrix
IndV Independent variable in a Jacobian matrix
ε Heat exchanger effectiveness
inPP _0Δ Pressure drop as a percentage of the inlet stream pressure
Q& Heat flow rate (Btu/sec)
nm& Mass flow rate at station “n” (lbm/sec)
npC _ Specific heat at constant pressure at flow station “n” (Btu/lbm-°R)
inT _0 Stagnation temperature at the inlet to a physical cycle component (°R)
outT _0 Stagnation temperature at the exit to a physical cycle component (°R)
inP _0 Stagnation pressure at the inlet to a physical cycle component (psi)
outP _0 Stagnation pressure at the exit to a physical cycle component (psi)
inh _0 Mass specific stagnation enthalpy at the inlet to a physical cycle
component (Btu/sec-lbm)
outh _0 Mass specific stagnation enthalpy at the inlet to a physical cycle
component (Btu/sec-lbm)
nFAR Fuel-to-air ratio at state point “n”
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ntotm _& For splitters and separators, total mass flow rate at state point “n”
(lbm/sec)
BPR Flow bypass ratio for splitter elements
liquidOHm _2& Mass flow rate of liquid water being extracted in separator (lbm/sec)
liquidOHh _2 Mass specific enthalpy of liquid water being extracted (Btu/sec-lbm)
CompPR Pressure ratio any compressor
adComp _η Adiabatic efficiency of any compressor
ns _0 Mass specific stagnation entropy at flow station “n” (Btu/lbm-°R)
R Ideal gas constant (Btu/lbm-°R)
idh Mass specific enthalpy change for an isentropic process (Btu/sec-lbm)
inCompR _ Ideal gas constant at a compressor inlet state point (Btu/lbm-°R)
bη Burner efficiency
RQ Lower heating value of the fuel (Btu/lbm)
WAR Water to air ratio, mass basis
TIT Turbine inlet temperature
OPR Overall pressure ratio of a system
γ Ratio of specific heats, v
p
CC
SpPw Specific Power (HP-sec/lbm)
ambT Ambient Temperature (°R), also ambientT
LPPR Low pressure compressor pressure ratio
HPRR High pressure compressor pressure ratio
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adLPC _η Low pressure compressor adiabatic efficiency
adLPT _η Low pressure turbine adiabatic efficiency
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Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science
DESIGN POINT ANALYSIS OF THE HIGH PRESSURE REGENERATIVE TURBINE ENGINE CYCLE FOR HIGH-SPEED MARINE APPLICATIONS
By
George Anagnostis
May 2007
Chair: William E. Lear, Jr. Major Department: Mechanical and Aerospace Engineering
A thermodynamic sensitivity and performance analysis was performed on the High
Pressure Regenerative Turbine Engine (HPRTE) and its combined cycle variation, the
HPRTE with a vapor absorption refrigeration system (VARS). The performance analysis
consisted of a comparison of three engine configurations, the two HPRTE variants and a
simple cycle gas turbine engine (SCGT), modeled after the production marine gas turbine
engine, ETF-40B. The engine cycles were optimized using a parametric analysis; a
sensitivities study was completed to establish which design parameters influence
individual engine model performance. The NASA gas turbine cycle code Numerical
Propulsion System Simulation (NPSS) was the software platform used to complete this
analysis.
The comparison was performed at sea level with an ambient temperature of 544°R.
The results for the SCGT predict a design-point optimized thermal efficiency of 33.4%
and an overall pressure ratio (OPR) of 10.4 with a specific power of 180 HP-sec/lbm.
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The HPRTE engine, called HPRTE Efficiency for this thesis, had an expected design
thermal efficiency of 37.2% (OPR of 32.2) with a specific power rating of 593 HP-
sec/lbm—229% larger than the SCGT specific power. The combined-cycle HPRTE-
VARS, called H-V Efficiency in the analysis, had a predicted design thermal efficiency
of 45.0% (OPR of 32) with a specific power of 629 HP-sec/lbm. The H-V Efficiency
thermal efficiency was 34.7% higher than that of the SCGT designed for maximum
specific power. Exhaust gas temperatures varied significantly between the SCGT and the
HPRTE variants. The model engine exhaust for the SCGT was 1580°R while the exhaust
temperatures of the HPRTE Efficiency and H-V Efficiency were 801°R and 837°R,
respectively. On average, the HPRTE calculated exhaust temperature was 761°R less
than that of the SCGT. High pressure compressor (HPC) inlet temperature sensitivity
was considered for the H-V Efficiency. Two operating cases were considered—the HPC
inlet held constant at 499°R and 509°R. The 499°R case operated with a thermal
efficiency higher by 1.56% and a specific power higher by 1.62%.
The results of the analysis imply that HPRTE duct sizes will be smaller due to the
engine having significantly higher specific power. Since specific fuel consumption is
inversely proportional to thermal efficiency, the H-V Efficiency engine cycle will require
a smaller fuel tank to allow for additional cargo (or if the tank size is unchanged, the ship
range is increased). Future project considerations include an off-design performance
analysis using NPSS or another software package, additional NPSS model benchmarking
with a reputable cycle simulation code, and an analysis of the effects of moist ambient air
on evaporator water flow extraction rates.
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CHAPTER 1 INTRODUCTION
Before the marine gas turbine, naval ships clipped through the water propelled by
sooty coal-fired steam turbines or diesel engines. The 1940s advent of the gas turbine jet
engine introduced a similar technology shift in the marine propulsion industry a decade
later. And now for the last 60 years marine gas turbine engine propulsion advancements
have derived mainly from aeronautical research and development programs. However,
there have been some instances where the marine propulsion industry has led the way in
development—most notably by the introduction of the Westinghouse-Rolls-Royce 21st
century (WR21) ICR program in the early 1990s. Inter-cooled compressors and exhaust
heat recuperation set the WR21 gas turbine engine apart. Ironically, the same ingenuity
that steered the Navy to develop the WR21 program was nowhere to be found during the
decision-making process time for the propulsion system for the 21st century speed ship-
to-shore transport.
The ETF-40B, a workhorse and variant of the original TF-40 that powered the
Navy landing craft air-cushion (LCAC) vessel for the last two decades will provide the
propulsion and lift thrust for the new J-MAC ship-to-shore transport. Despite interest in
new engine technologies, such as the High Power Regenerative Turbine Engine
(HPRTE), funding constraints prevented the Navy from further investigating novel
systems. This thesis will make the case for the HPRTE as an alternative engine concept
to the ETF-40B for the J-MAC program.
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The motivation to compare the HPRTE to the ETF-40B is a result of previous
experimental and computational modeling efforts completed at the University of Florida
(UF) Energy and Gas Dynamics Laboratory to develop alternate engine technologies.
There other design considerations besides cost that drive engine development; the
HPRTE will outperform the ETF-40B, having a higher specific power ratio, improved
off-design performance, and a considerably lower infrared heat signature.
The HPRTE is a semi-closed, compressor inter-cooled, recuperative system. A
demonstration engine has been build and performance tested at UF, and the proof of
concept has been met. The laboratory demonstrator uses engine exhaust heat to power a
vapor absorption refrigeration system (VARS). This is representative of the combined
cycle system, one of the two HPRTE configurations, that is considered in this modeling
and analysis project. The base HPRTE is the other. The combined cycle variant is
expected to outperform the base HPRTE because the VARS unit provides additional
cooling to the high pressure compressor inlet of the engine.
The analysis in this thesis includes a parametric optimization and sensitivity studies
that determine design-critical parameters. There are three engine models total that are
considered—the two HPRTE variants (HPRTE Efficiency and H-V Efficiency) and a
simple cycle gas turbine engine (SCGT). The SCGT is modeled to represent the ETF-
40B engine configuration. Only two of the three engines examined are considered in the
sensitivity analysis; they are the SCGT and HPRTE Efficiency engine models. Sensitive
parameters for the HPRTE Efficiency are expected to be the similar for the H-V
Efficiency cycle, and therefore the exercise was deemed redundant.
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The second part of the project is the cycle comparison analysis which will examine
the performance parameters such as thermal efficiency, specific power, exhaust gas
temperature, and high pressure compressor inlet temperature. Mission specifications and
material and component limitations provide the scope for many of engine variables that
are to be optimized. Being for a military application, the engine is expected to have
robust performance capabilities; therefore, run cases were analyzed representing a wide
range of ambient operating conditions for all cycle configurations.
The model processes were based on thermodynamics relationships. The complete
set of equations used to close the cycle model is discussed later. The flows were all
considered steady-state and incompressible, and the turbomachinery components and
ducting were all represented as adiabatic processes.
These considerations are built in to the cycle code called Numerical Propulsion
System Simulation (NPSS). This is a DOS driven, object-oriented program that has
design, off-design, and transient run operation capabilities. Technical support for this
program was provided by the ASAO group at the NASA Glenn Research Facility.
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CHAPTER 2 LITERATURE REVIEW
Brief History of Turbine Engine Development
Between 150-50 B.C., a Greek named Hero, living in Alexandria, Egypt, boiled
water in a sealed container that had two spouts extending from the top and slightly curved
[1]. As the water boiled, steam billowed from the spouts, rotating the entire container.
At the time it was considered a toy, but today history remembers Hero as the inventor of
the steam turbine.
Despite this early application, the first documented use of the turbine engine for
propulsion purpose was not until 1791; John Barber, a British inventor designed a simple
steam engine with a chain-driven compressor to power an automobile [1]. Then in 1872,
nearly 100 years after Barber engine, steam-powered automobile was designed, Franz
Stolze designed the first axial gas turbine engine [2]. The practicality of the engine was
suspect and it never ran unassisted.
Interest in gas turbine engines continued to increase, and developmental
breakthroughs were made in the 1930s. Great Britain and Germany were the spearhead
of these efforts as tension between the European heavyweights mounted. Faster, more
agile aircraft were being conceived, and the air forces of both nations noticed the
advantages of the jet engine over conventional piston engines. Frank Whittle of Great
Britain worked out a concept for a turbojet engine and won a patent for it in 1930 [3].
Five years later in Germany Hans van Ohaim, working independently of Whittle,
patented his own gas turbine engine system [3]. Ohaim and his colleagues witnessed the
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first flight of their turbojet engine on August 27, 1939, powering the He.S3B aircraft [3].
The Whittle concept was shelved until mid 1935 when finally with the help of two ex-
Royal Air Force pilots the engine was built and tested by Power Jets Ltd [3]. After
working through design setbacks, including fuel control issues, the first British—
designed turbojet-powered aircraft flew in May 1941 [3]. Even though the Germans
could claim the first turbojet powered flight, the British built the first production turbojet
engine, the Roll-Royce de Haviland [3]. Turbojet development sky-rocketed in the 1940s
and 1950s; a Whittle design provided the blueprints for the first American made turbojet
engine, the General Electric I-A [7].
Gas Turbine Engine Examples in Marine Applications
The British were using simple gas turbine engines to power gun boats as early as
1947 [4]. The HMS Grey Goose was the first marine vessel to be powered by a
turboshaft engine with an inter-cooled compressor and exhaust heat recuperation (ICR)
[5]. In 1956, the U.S. Navy contracted with Westinghouse to develop a gas turbine
engine for submersible operation [6]. They designed a two shaft semi-closed ICR engine;
a novel concept that but was limited by fuel-type availability. The use of heavy sulfur
fuels triggered sulfuric acid build-up in the intercoolers which degraded the metal
components in the heat exchanger. A direct effect heat exchanger was tried with sea
water, but this only succeeded in introducing salt into the engine which deposited on the
turbomachinery parts [6]. At the same time the Westinghouse engine was under
development, General Electric was looking to convert their profitable J79 engine into a
marine gas turbine. In 1959 they introduced the LM1500. It was a simple cycle gas
turbine that produced 12,500 SHP [7]. The General Electric LM2500, introduced in
1968, ushered in the second generation marine of marine turboshaft engines. Like the
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LM1500, the LM2500 was a derivate of a proven aero engine that powered over 300 U.S.
Naval ships [8, 7]. Moreover, thermal efficiency was improved on the LM2500 to 37
percent [8].
Advantages of Gas Turbine Engines in Marine Applications
Gas turbine engines have overtaken diesels as the power plant of choice for ferries,
cruise liners and fast-attack military ships. This trend exists because gas turbines offer
higher power output-to-weight ratios, significantly higher compactness, higher
availability, and they produce fewer emissions than marine diesels [9, 4]. The power-to-
weight advantage is best realized with an example comparing a diesel engine to a gas
turbine engine of similar power rating. The 7FDM16 marine diesel offered from General
Electric produces 4100 BHP and weighs 48,800 lbs [10]. In comparison the Lycoming
TF-40 turboshaft marine engine, produces 4,000 BHP and weighs only 1,325 lbs [11].
The significant weight disparity favoring the TF-40 is a prime reason gas turbines are
being chosen to power marine vessels requiring agility and speed. Similarly, the
compactness that gas turbine engines offer greatly improves vessel versatility and crew
and cargo capacity optimization. As an example, the 7FDM16 diesel has a volume of
920 cubic feet, whereas the TF-40 has a volume of less than 43 cubic feet [10, 11].
Subsequently, the compact, light-weight gas turbines are easier to transport and switch-
out of ships. With skilled professionals available from the aviation industry trained on
gas turbines engines, there is an abundance of mechanics and support crew able to
maintain and operate these systems [4]. Moreover, the emission reductions achieved by
gas turbine engines over comparable diesels make them more attractive to commercial
and military forces needing to placate environmental agencies such as the EPA and other
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international bodies. A simple open-cycle gas turbine engine produces 1/3 to ¼ the
emissions of a diesel engine of comparable technology [9].
Recuperation and Inter-cooling
Simple, open-cycle turbo-shaft engines exhaust hot gas products to the atmosphere
wasting high—quality heat energy; an increasingly common use of this available heat
energy in gas turbine engines is to pre-heat the compressed gas flow before the
combustion stage. This process is called exhaust heat recuperation. As a result of raising
the combustor inlet temperature, less fuel is required to achieve the desired turbine inlet
temperature and desired power output. This directly impacts the thermal efficiency and
specific power of the engine, raising thermal efficiency but dropping specific power in
most cases. Any instance in which fuel use can be decreased has a direct positive impact
on the cycle thermal efficiency. It is important to note that gas turbine engine
recuperators generally work better in engines with only moderate pressure ratios [12].
Qualitatively, one can see that as the engine pressure ratio rises, the compressor exit
temperature and turbine exit temperature approach each other. In practice this would
drop the capacity of the recuperator to pre-heat the compressed air before combustion,
thus rendering it ineffective.
A second improvement on the simple gas turbine engine is the addition of an inter-
cooler. Inter-coolers are placed between the low pressure and high pressure compressors
to reduce the air temperature exiting the last stage of the compressor. Assuming the
process is adiabatic and the air is a calorically perfect gas, the power required to drive the
compressor is written as TcmW pcomp Δ= && . This assumes a control volume analysis
around the entire compressor for all stages [3]. The inter-cooler delivers a lower
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temperature fluid to the high pressure compressor stage. If the same pressure ratio is
applied to the high pressure stage, the exhausting fluid temperature would be lower than
if no inter-cooling had been performed. The outcome is that TΔ for the entire
compressor has been decreased, and subsequently, the total power requirement for the
compressor has also been decreased. The net effect on the cycle thermal efficiency is the
same as raising the adiabatic efficiency of the entire compressor. The outcome is a net
available power increase of 25 to 30% [5]. Coolants exist for both sea and air
applications. Jet aircraft have -50°C ambient air available and naval ships have the
abundant salt water reserves of the oceans.
Additionally, combining both compressor inter-cooling and exhaust gas
recuperation provides a further improvement to cycle thermal efficiency. Engines that
employ this technology are referred to as inter-cooling recuperation (ICR) engines. With
the inter-cooler cooling the compressor discharge, the temperature difference between it
and the turbine discharge increases—the outcome is an improved recuperator
performance [12]. In 1953 Rolls Royce introduced the RM60 ICR engine which powered
the gunboat HMS Grey Goose [5]. Though innovative and more efficient than the steam
engine it replaced, the RM60 was too complex to operate using existing controls
technology. A further example reviewed for this project compares two gas turbine
engines, a simple open-cycle and an ICR, for a marine destroyer application. The study
noted that fuel use is reduced by 30% with the ICR engine [5, 13].
In 1990, General Electric began retrofitting their mid-size turboshaft engine, the
LM2500, in hopes of improving its thermal efficiency by 30% [13]. This project was
sidelined in 1991 when a team led by Northrop Grumman won a $400 million, 9-year
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development contract to develop and build a replacement for the LM2500 marine gas
turbine [14]. Program leaders Northrop Grumman and Rolls-Royce chose an ICR engine
design, called the WR-21, for the navies of the United States, Canada, Great Britain, and
France [14]. John Chiprich, who managed the ICR development program, noted that the
new engine will reduce the fuel consumption for the entire marine turbine powered fleet
of the United States by 27 to 30% [14].
One negative aspect to the ICR concept is that it has a lower power limit for it to be
considered effective. Blade tip leakage for gas turbine engines that have a nominal
power rating below 1.5MW overrides any efficiency gained from the implementation of
ICR technology [15].
Semi-Closed Cycles
A semi-closed gas turbine cycle is one in which hot exhaust products are
recirculated, combined with fresh air, and then burned again in the combustion chamber.
Example configurations can include inter-cooling and recuperation, and some are
turbocharged to boost core engine pressures. Despite the added complication of engine
components and weight addition; many semi-closed cycle configurations have significant
performance related benefits. For instance, semi-closed cycles that are turbocharged,
have higher specific power, reduced recuperator size (if a recuperator is present) which
improves heat transfer coefficients, and higher part-load performance characteristics [13].
All semi-closed cycles benefit from reduced emissions since reduced oxygen
concentrations reduce flame temperatures [13].
Some of the earliest semi-closed gas turbine engine configurations were proposed
by the Sulzer Brothers in the late 1940s [16]. Their 20 MW gas turbine system for the
Weinfelden Station was a complex system that achieved a cycle thermal efficiency of
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32% for full load capacity and 28 % for half load capacity [16]. The earliest example of
a semi-closed gas turbine system for naval propulsion was the Wolverine engine
developed by Westinghouse [6]. The submarine engine program which began in 1956
called for a two-shaft, semi-closed, ICR turboshaft engine [6]. It was never a production
engine because of sulfuric acid buildup that degraded the metallic intercooler
components. This was attributed to the high concentration of sulfur in early diesel fuels.
More recent research projects on semi-closed gas turbine cycles conducted by the
University of Florida, Energy and Gas Dynamics Laboratory will be highlighted in the
final section of this chapter.
Computer Code Simulators
Because of the complexity of the cycles that need to be simulated and the iterative
nature of semi-closed cycle modeling, it is convenient to employ the use of a
computational code to perform the numerous calculations. There were several
computational thermodynamic cycle programs that were potential platforms for this
project. Below is a brief overview of the programs surveyed.
Gas turbine Simulation Program (GSP) is a product of the National Aerospace
Laboratory—The Netherlands (NLR) [17]. The GSP website boasts of a user friendly
platform with drag-and-drop components ready for building engines models. The code
can be used for steady-state as well as transient simulation. Material specifications and
life-cycle information can be incorporated for failure and deterioration analysis.
Unknown, however, is whether or not GSP can model semi-closed engine cycles. A
second code called GASCAN was reviewed by Joseph Landon. This code models fluid
movement as well as thermodynamic state variables for engine simulations. Semi-closed
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operation is not explicitly discussed but simple and complex cycles are apparently easily
modeled.
A third modeling program reviewed was Navy/NASA Engine Program (NEPP); it
was developed to perform gas turbine cycle performance analysis for jet aircraft engines.
NEPP is an older component-based engine modeling program that has design and off-
design modeling capabilities with performance map integration. User instantiated
variables can be controlled to hold specific parameters constant while the program
converges to its solution. This program was eliminated because it can not model
recirculated flows [13]. NEPP was only the first of three NASA programs evaluated for
this modeling project. The second NASA code was ROCket Engine Transient
Simulation (ROCETS) developed at Marshall Space Flight Center. This program
provides a suite of engine component modules to assist users in building their models; it
also allows users to create their own modules to model more exotic engine cycles [18].
Like NEPP, ROCETS gives the developer the ability to vary certain parameters until
other constraints are satisfied and a converged solution is determined [18]. Users have
the option of operating in design or off-design mode as the program has the capability of
reading performance maps for compressors and turbines. ROCETS was used in
modeling efforts at the University of Florida in the 1990s. The program is capable of
modeling recirculation in gas turbines and water particulate extraction. Being somewhat
antiquated, the program was dismissed as a possible platform for the project considering
the unlikely availability of user support.
A commercial software package option was the versatile ASPEN PLUS. The
ASPEN PLUS engineering suite is a robust package of software programs that can handle
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all of the modeling requirements for this project. Once again, here is a program that
provides users with the option of running their cycle in design, off-design, or transient
modes. Their website displays screen shots of a pleasant graphic user interface with
drag-n-drop engine components [19].
The third software program from NASA, Numerical Propulsion System Simulation
(NPSS) is a product of the Aeropropulsion Systems Analysis Office (ASAO) at the Glenn
Research Center. NPSS is set up to operate similar to the earlier programs NEPP and
ROCETS. Accordingly, NPSS offers users the convenience of object-oriented engine
components for building cycle models [20]. Off-design and transient modeling are
options in addition to running in the design point mode [20]. The model developer has
control of convergence through constraint handling. Since this program became the
platform of choice for this project, its capabilities will be discussed in further detail in
Chapter 2.
Previous Gas Turbine Research at the University of Florida
In 1995 Todd Nemec performed a thermodynamic design point analysis on a semi-
closed ICR gas turbine engine with a Rankine bottoming cycle [21]. Nemec developed
his model using the ROCETS program discussed earlier—his analysis concluded that the
combined cycle with superheated steam in the bottoming cycle resulted in an overall
efficiency of 54.5% [21]. The next body of work on semi-closed cycles was performed
by Joseph Landon. Landon performed design and off-design point analysis of two
separate regenerative feedback turbine engines (RFTE) [13]. The turbocharger
configuration resembled the topping cycle that Nemec modeled. The other configuration
sent the combustion products through a power turbine before the recuperation heat
exchanger. The analysis predicted that the power turbine configuration produced the
-
13
highest thermal efficiency, 48.2%, compared to 46% for the turbocharger case [13]. Off-
design analysis revealed that the turbocharger model was the most efficient between 20%
and 80% power capacity [13].
Russell MacFarlane used the ROCETS program to model water extraction and
injection on the RFTE engine [12]. MacFarlane found that water removal caused a
decrease in specific fuel consumption and a slight increase of specific power [12]. He
surmised that water removal was particularly influenced by “recirculation ratio, cooler
effectiveness, and first stage pressure ratio” [12]. George Danias extended the study of
the RFTE cycle and investigated design and off-design performance of three separate
configurations for a helicopter engine application [18]. His conclusions stated that the
three RFTE configurations were 30 to 35% more efficient than the T700-701C, baseline
engine [18].
Currently, a research project is underway to design and develop a combined cycle,
power-refrigeration cycle called the HPRTE-VARS. The High Power Regenerative
Turbine Engine (HPRTE) uses exhaust gas heat to power the vapor absorption
refrigeration system (VARS). A design point performance study was carried out by
Joseph Boza analyzing two HPRTE-VARS engine sizes, a small 100 kW engine and a
larger 40 MW engine. Boza calculated the performance parameters based on a constant
high pressure compressor (HPC) inlet temperature of 5 ° C. Excess refrigeration
capacity (that capacity not used to cool the HPC inlet stream) was considered in the
combined cycle efficiency value. The larger engine analysis predicted a combined cycle
efficiency of 63% while the small engine efficiency was determined to be 43% [22]. He
determined that increasing ambient temperature limits the excess refrigeration capacity,
-
14
and at an ambient temperature of 45 ° C the combined-cycle system has no excess
refrigeration. For his analysis, Boza used a spreadsheet cycle code to predict the
performance of the HPRTE; this was in conjunction with a VARS model that he created.
In Chapter 6 the spreadsheet model has been used to benchmark the NPSS program used
in this project. The spreadsheet HPRTE model is not configured to consider the low
pressure spool of the engine as a turbocharger—in the comparison in Chapter 6, the
spreadsheet cycle model will be constrained manually for the turbocharger configuration.
Life cycle cost analyses of the HPRTE-VARS was performed and compared to a
microturbine engine by Viahbav Malhatra. Using a standard life cycle cost analysis
procedure, Malhatra determined that the HPRTE-VARS system exhibited a life cycle cost
savings of 7% over the competing microturbine system [23]. One primary reason for the
cost savings was associated with the HPRTE being turbocharged—this enabled smaller
and less expensive engine components to be considered. The other reason for the cost
savings was directly related to fuel consumption. HPRTE fuel costs were partially
compensated by the proceeds from available refrigeration capacity of the VARS unit
[23]. To obtain his results Malhatra used a Fortran model of the HPRTE-VARS created
by Jameel Khan. Khan performed his dissertation study on the design and optimization
of the HPRTE-VARS combined cycle developing a high fidelity, thermodynamic model
for both the engine and the refrigeration systems. He used the optimization package
LSGRG2 to determine the best design-point engine parameters considering such outputs
as power, refrigeration, and water. His results for the combined cycle with the
OHNH 23 / refrigeration system predicted a cycle thermal efficiency of 40.5% with a
ratio of water production to fuel (propane) consumption of 1.5 [24]. Including the excess
-
15
refrigeration produced by the cycle, a combined cycle thermal efficiency was evaluated
as 44%.
-
16
CHAPTER 3 NUMERICAL PROPULSION SYSTEM SIMULATION ARCHITECTURE
Numerical Propulsion System Simulation (NPSS) was developed by
Aeropropulsion Systems Analysis Office (ASAO) at the National Aeronautics and Space
Administration (NASA) Glenn Research Center, Cleveland, OH in conjunction with the
Department of Defense and leaders in the aeropropulsion industry. The purpose of the
code was to speed the development process of new gas turbine engine concepts for
military and civilian applications. It is a component-based engine cycle simulation
program that can model design and off-design point operation in steady-state or transient
mode [20]. The code can be used as a stand-alone analysis program or it can be coupled
in conjunction with other codes to produce higher fidelity models.
Model
Engine models are created using any standard text editor such as Microsoft
Wordpad. The model file contains the instructions and commands required by NPSS to
build an engine model. The engine model file combines the engine components
(elements) in a systematic manner that is consistent with the engine cycle the user is
modeling. Here, elements are connected to create the flow stations of the engine; these
flow stations are created by linking the flow ports between elements. In the model the
thermodynamic package, solver solution method, and model constraints should also be
specified if different than the defaults. These subjects will be discussed in further detail
later in the Chapter 3.
-
17
Figure 3-1 is a schematic representation of an example engine modeled using
NPSS. The elements are plainly listed; there is an inlet, compressor, burner, turbine,
shaft, duct, and exhaust. The working fluid properties are passed through flow ports from
one element to the next. Shaft ports connect the compressor and turbine with the shaft
element in order to perform the power balance for the engine. The interaction of a
subelement, CompressorMap with its parent element, Compressor, is shown with its
socket link. This particular model has an assembly for the major engine components.
The assembly compartmentalizes any processes or calculations performed by these
components from the rest of the model.
Elements
Elements are the corner stones of the engine model. Although NPSS comes with a
full suite of engine component modules, users are encouraged to create their own
elements to model their unique circumstances using the C++ type syntax of NPSS. As
mentioned above, elements are responsible for performing the individual thermodynamic
processes that simulate the physical engine components. The modules use standard
thermodynamic relationships to simulate these processes. The level of modeling
sophistication is entirely user driven as loss coefficients and scalars may be applied to
variables. Mach number effects are calculable. For higher fidelity models heat and
frictional energy dissipation may be considered. For the purpose of this analysis the
cycle models were kept as simple as possible to shorten computing run-times.
Nevertheless, even simple models require a certain level of complexity—for those
cases there are supplemental routines added to elements called subelements and
functions. Subelements are subroutines that can be called by elements to perform
calculations or performance table look-ups. For instance, the turbine element for a model
-
18
that is operating in off-design mode would use a subelement to determine the efficiency
value from data tables. Functions are a type of subroutine that is user instantiated in a
particular element that requests particular calculations be performed. Function
calculations take precedence over the solver driven calculations. They may be performed
before, after, or during solver run-time depending on the desire of the user.
FlowStation
For an element to perform its calculations, properties and state information must be
known as initial conditions. These initial conditions are set by the user or the computer
and passed to the element through a flow port. When flow ports are used to link two
elements, this bridge is called a FlowStation. There is a main FlowStation subroutine and
then there are the specific FlowStation subroutines unique to each thermodynamic model.
The main FlowStation subroutine is responsible for linking the model to the appropriate
subroutines that handle the subroutine look-ups. When NPSS uses the Chemical
Equilibrium with Applications (CEA) thermodynamic software, the main FlowStation
subroutine links the model file/files with the CEA program allowing the passage of
species and state information between the two programs.
FlowStartEnd
There are elements in NPSS specifically designed to either begin or end a fluid
flow path. Semi-closed gas turbine engine modeling in NPSS makes use of these flow
start/end elements to obtain converged solutions. The solution solver in NPSS requires a
single initial pass through the model elements to create the flow path and flow stations—
and essentially build the engine model. For open cycle gas turbine engines this task
requires no extra consideration by the modeler. The solution solver can logically step
through the engine from the inlet element to the exhaust element for the preprocess pass.
-
19
However, all of the HPRTE configurations have mixing junctions upstream of the core
engine components adding a further level of complexity that the solution solver must
negotiate.
The solution requires added components, FlowStart and FlowEnd elements, and
additional constraints added to the solution solver. For convenience and brevity the
ASAO developed the element FowStartEnd to replace the FlowStart/FlowEnd
elements—this element also contains the additional constraints required, eliminating the
necessity to initialize these in the main model file.
To be complete it is best to describe the coding required to gain convergence of a
regenerative gas turbine model using FlowStart, FlowEnd, and FlowStartEnd elements.
When the solver is stepping through the HPRTE it expects to have a hot-side flow station
already instantiated when it reaches the recuperator inlet after the high-pressure
compressor exit. Therefore, a FlowStart element is created and added to the solver
sequence (responsible for the order of element preprocess loading) before the high-
pressure recuperator flow station is created. Initial conditions are given to the stream
including temperature, pressure, mass flow rate, fuel-to-air ratio, water-air-ratio, and fuel
type. This flow station is 7a.
Now the solver can continue to load the model to the point of the high-pressure
turbine exit flow station. This is the point where the ‘bridge’ is made with the FlowStart
element instantiated earlier. Here, a FlowEnd element is created and the state of the flow
exiting the high-pressure turbine is stored in this element. The flow station here is 7b.
Since the flow conditions cannot be directly passed from the FlowEnd element to the
FlowStart element, the solver is given the task of iterating on all the flow station 7
-
20
parameters until the conditions match in both elements. To make this happen the user
sets up five variables, which NPSS considers ‘independents’, to iterate on until their five
counterpart constraints, which NPSS deems the ‘dependents’, are satisfied. These five
independent variables are listed as: stagnation temperature and pressure, mass flow rate,
fuel-air-ratio, and water-air-ratio.
The constraints are generally written as equations that must be satisfied for solver
convergence to be recognized. One example of a dependent constraint from the
FlowStartEnd element is given below in NPSS syntax.
Dependent dep_P{
eq_lhs = "Fl_I.Pt";
eq_rhs = "Fl_O.Pt";
autoSetup = TRUE;
}
The constraint variable is ‘dep_P’. The left hand side of the equation is set equal to
the stagnation pressure of the flow entering FlowStartEnd, and the right hand side is set
equal to the exiting stagnation pressure. This constraint is added to the solver along with
four others corresponding to the variables listed above. Figure 3-2 shows the schematic
representation of the procedure that was just described.
Thermodynamic Properties Package
Chemical Equilibrium with Applications (CEA), obtains chemical equilibrium
compositions for pre-defined thermodynamic states. Two thermodynamic state
properties must be known for the rest to be calculated or obtained from table subroutines.
This requires two input files:
-
21
1. Thermo.inp—Contains thermodynamic property data in least squares coefficients. These data can be used to calculate reference-state molar heat capacity, enthalpy, and entropy at a given temperature.
2. Trans.inp—Contains the transport property coefficients for the species CEA uses the Gibbs free-energy minimization method to calculate chemical
equilibrium at each state point. Chemical reaction equations are unnecessary when using
the free-energy minimization method and chemical species can be treated individually.
For a detailed description of the theory and methods used in CEA please see reference
[25].
CEAFlowstations are responsible for passing constituent and state point
temperature and pressure from NPSS to CEA.
Solver
The NPSS solver is responsible for bringing the model to a converged solution. In
order to accomplish this task the user must choose which engine parameters to constrain.
Constrained parameters are called model “dependent variables”. To satisfy the dependent
variables a set of “independent variables” must be defined and iterated. This iterative
approach to find a solution begins with an initial state guess, and that is subsequently
refined until a satisfactory solution is found.
The solver solution method is a quasi-Newton method. For a simple description
assume there is only one constraint on the model, and as a result only one variable to
iterate to meet it. The initial value of the independent variable is user specified, and with
that the initial value of the variable desired to be constrained can be found. Then the
independent variable is perturbed a certain amount chosen by the solver and a new value
for the dependent variable is found. The solver now must decide if this new value of the
variable to be constrained is a satisfactory one. A partial derivative error term is
calculated,
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22
( )( )II
II
tValueIndependentValueIndependenalueDependentValueDependentVErrorTerm
−−
= ++
1
1
, (3.1)
where I denotes the iteration number. If it is outside the acceptable tolerance region, the
process is begun again. With a system of constraints a Jacobian matrix would be created
to hold all the error terms. The new perturbation terms would be calculated from the
previous Jacobian matrix:
[ ]
( )( )
( )( )
( )( ) ⎥⎥
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−•••
−••
−
=
+
+
+
+
+
+
11
11
1
111
11
11
11
11
1
IndVIndVDepVDepV
IndVIndVDepVDepV
IndVIndVDepVDepV
J
I
Im
Im
nI
n
II
I
II
I (3.2)
Here there are “n” number of independents and “m” number of dependents.
The Jacobian can be related to the independent variables with the expression
[ ] [ ] ( )[ ]III xFxJ −=Δ⋅ , (3.3)
where [ ]IxΔ is the matrix composed of the independent perturbation values. The ( )[ ]IxF
matrix holds the values of the dependent constraints at the thI ' iteration. The new
independent values may now be calculated with the following:
[ ] [ ] [ ] ( )[ ]IIII xFJxx ⋅−= −+ 11 . (3.4)
With [ ]1+Ix now determined, [ ]1+Δ Ix and ( )[ ]1+IxF can be found and a new Jacobian matrix created. The process continues until the Jacobian error values are within the
acceptable tolerance limits of the solver.
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23
Figure 3-1 Example NPSS engine model [19]
-
24
HPT Recuperator
NPSS Code/Element Representation of Above Engine State
HPT FlowStart
Recuperator
RecuperatorFlowEnd
HPT FlowStartEn
Simplified Code Representation
7a 7b
7a 7b
7temp
Figure 3-2 State 7 of HPRTE engine cycle
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25
CHAPTER 4 CYCLE CONFIGURATIONS AND BASE POINT ASSUMPTIONS
Before discussing the thermodynamics relationships used in the analysis, it is
necessary to give an overview of the cycles from a systems standpoint. This analysis
compares the design point performance of three engine configurations. The first engine
is a simple cycle gas turbine engine (SCGT). It has been modeled to predict the
performance of the production engine, ETF-40B, which powers the military LCAC for
the United States Navy. The SCGT will be compared to two variations of the HPRTE
engine, the base HPRTE and a variant that uses refrigeration capacity to cool the high
pressure compressor inlet stream.
Major Model Features
When comparing engine systems, it is convenient to understand the major features
of each model. Listed in Table 4.1 is a breakdown of the features that distinguish the
engine configurations from one another. The HPRTE cycles are two spool engines with
exhaust gas product heat recuperation. Both are semi-closed and have compressor inter-
cooling. The H-V Efficiency has additional cooling capacity provided by a vapor
absorption refrigeration system (VARS). The additional cooling enables exhausted water
vapor to be condensed and collected for use elsewhere or for injection after the high
pressure compressor.
-
26
Flow Path Descriptions & Schematics
Simple Cycle Gas Turbine Engine Model
As mentioned earlier, the SCGT is a simple, open cycle gas turbine engine. For
this analysis the model with have a total of five flow stations (Figure 4-1). State 1 is the
inlet stream. From State 1 to 2 the flow undergoes an adiabatic compression process in
compressor, C1. From State 2 to 3 there is a constant area, premixed burner, B. The
process from State 3 to 4 is an adiabatic expansion process through the turbine, T1.
Mechanical work generated by the turbine drives the compressor and supplies power for
the ship propellers or lift fans. State 5 is the fuel flow station. JP-4 was the fuel of
choice for this analysis because it is widely used in industry and has a high availability.
High Pressure Regenerative Turbine Engine Efficiency Model
Figure 4-2 is a schematic representation for the Efficiency and Power modes of the
HPRTE cycle. The Power mode concept incorporates a flow splitter to bypass some
exhaust from the high pressure turbine and send it directly to the low pressure turbine.
Initially, the Power mode had been considered for this project to give additional boost
capabilities to the low pressure spool. However, while completing the analysis it was
determined that the Efficiency mode predicts sufficient boost for the system and any
additional boost pressure would result in a turbocharger design outside of modern
technology limits.
There are 14 states for the basic HPRTE (the Power mode has 16). Air enters at
State 1 and undergoes an adiabatic compression process in the low pressure compressor,
LPC, before reaching State 2. Next, the fresh air from State 2 is combined with the
recirculated exhaust gas products from State 10 in an isobaric, adiabatic mixing process.
The resultant State is 2.9. Now the combined flow passes through a sea water cooled
-
27
heat exchanger called the main gas cooler (MGC). The effectiveness, pressure drop, and
process fluid temperature are all given. The resulting State is 3.0. After the gas has been
cooled it goes through another adiabatic compression process in the high pressure
compressor, HPC. The resultant State 4 has the maximum system pressure. Following
the HPC there is a heat recuperation process (RHX) in which high-temperature exhaust
gas product stream preheats the State 4 flow resulting is State 5. From state 5 to 6 the gas
is mixed with fuel and ignited in the combustion chamber, B. A small pressure drop is
applied before State 6 to simulate friction losses in the combustor. The high pressure
turbine inlet temperature, or TIT, was chosen to be 2500°R—an acceptable value for a
medium size engine.
The expansion across the high pressure turbine, HPT, produces the power to drive
the HPC and the net BHP is available power for the vessel. State 7 is State 7.11 in the
Efficiency mode, and that flow passes through the RHX, rejecting heat to State 4. The
only flow splitter for the Efficiency cycle comes at State 9. Here, a user defined
recirculation ratio determines the mass flow rates at State 7.15 and 10. State 10
recombines with fresh air flow from the LPC exit. State 7.2 is also State 7.3 in Efficiency
mode. The final expansion process across the low pressure turbine, or LPT, exhausts to
the environment at State 8.
High Pressure Regenerative Turbine Engine with Vapor Absorption Refrigeration System Efficiency Model
Figure 4-3 is a schematic representation of the H-V Efficiency. The HPRTE-
VARS modes differs from the HPRTE modes only by the addition of two heat
exchangers in the flow path after the recirculated gas products combine with the fresh
inlet air at State 2.9. The generator (GEN) and the evaporator (EVP) are two of the heat
-
28
exchangers that make up part of the VARS. A schematic of the VARS is also included as
Figure 4-4 for clarification. It was not modeled since the scope of this analysis only
included modeling the gas path side of the combined cycle system. The point of water
collection is shown on the figure, as well. The computational model of this cycle
required the addition of a separator element to perform the water extraction. The
separator is discussed in Chapter 5, Thermodynamic Modeling and Analysis.
Notice that the HPRTE cycles require an iterative solution method to obtain model
convergence because of the semi-closed operation. For the first iteration of the engine
cycle an initial guess for the temperature at State10 is given.
Simple Cycle Gas Turbine Engine Design Assumptions and HPRTE Cycles Base Point Assumptions
The SCGT is a medium size, open-cycle gas turbine engine modeled after the ETF-
40B. The ETF-40B has a seven stage axial compressor followed by a single stage
centrifugal compressor yielding an overall pressure ratio of 10.4 [Robert Cole]. The
nominal output shaft horsepower is 4000 SHP. Turbine inlet temperature was assumed to
be 2500°R. Turbomachinery efficiency information was provided by Dan Brown of
Brown Turbine Technologies. All other engine design parameters were chosen based on
conservative current technology limits. See Table 4-2 for complete details.
The base point HPRTE component parameters are listed in Table 4-3. The same
methodology used to determine the design parameters for SCGT was considered when
deciding base-line design values for the HPRTE engine cycle configurations—size and
technology limitations were applied.
There were material and computational limitations that existed and needed to be
accounted for to preserve the fidelity of the engine model. They are as follows: TIT
-
29
maximum was 2500°R, hot side recuperator inlet temperature maximum was 2059°R,
turbocharger pressure ratio maximum was 7.5, and HPC inlet temperature minimum was
491°R (NPSS limitations).
Table 4-1 Comparison of major configuration features
SCGTHPRTE Efficiency * * * *H-V Efficiency * * * * * *
Model FeaturesIntercooled
CompressorsVARS cooling
Water ExtractionModel Semi-Closd
Turbocharger Pressurized Recuperatored
1 2 3 4B
C1 T1
5Fuel
Air
Figure 4-1 Simple Cycle Gas Turbine (SCGT) engine model configuration
-
30
Figure 4-2 High Pressure Regenerative Turbine Engine model, both efficiency and power configurations represented
77.
12
7.2
7.3
86
54
32.
92
1
109
7.11
LPC
RH
X
HPC
MG
CH
PTB
LPT
Fuel
Air
Sea
Wat
er
-
31
Figure 4-3 High Pressure Regenerative Turbine Engine-Vapor Absorption Refrigeration System, both efficiency and power model configurations represented
77.
12
7.2
7.3
86
54
32
1
109
7.11
2.91
2.92
2.9
LPC
MG
CH
PC
RH
X
BH
PTLP
TG
ENEV
P
Fuel
Air
Wat
e
Sea
Wat
erH
P R
efrig
eran
tLP
Ref
riger
ant
-
32
GEN
EVP
CND
CND
2.9 2.91
2.923
PumpExpander
Figure 4-4 Vapor Absorption Refrigeration Cycle with HPRTE flow connections
Table 4-2 Simple Cycle Gas Turbine engine design point parameters Parameter ValueC1 Adiabatic Efficiency 0.858Burner Efficiency 0.99Burner Pressure Drop 0.03Turbine Inlet Temperature 2500°RT1 Adiabatic Efficiency 0.873
Table 4-3 Base case model assumptions for HPRTE cycles [3], [26], [27] Parameter Value
Ambient Temperature 544.67°RSea Water Temperature 544.67°R
Ambient Pressure 14.7 PSILPC Adiabatic Efficiency 0.83
GEN Effectiveness 0.85GEN Pressure Drop 0.03MGC Effectiveness 0.85MGC Pressure Drop 0.03EVP Effectiveness 0.85EVP Pressure Drop 0.03
HPC Adiabatic Efficiency 0.858RHXEffectiveness 0.85
RHX Pressure Drop State 4-5 0.04RHX Pressure Drop State 7.11-9 0.04
B Efficiency 0.99B Pressure Drop 0.03
HPT Inlet Temperature 2500°RHPT Adiabatic Efficiency 0.873
Recirculation Ratio 3LPT Adiabatic Efficiency 0.87
Fuel Hydrogen to Carbon Ratio 1.93:1
-
33
CHAPTER 5 THERMODYNAMIC MODELING AND ANALYSIS
Chapters 3 and 4 addressed the computational structure of NPSS and the cycle
configurations of the models including the design point assumptions. While top level
NPSS calculations are performed by the solution solver, the intermediate operations
performed during every iterative pass to calculate the thermodynamic states are discussed
next. Chapter 5 develops the theory for these auxiliary thermodynamic relations that
drive the model elements (subroutines). These relations are developed using fundamental
thermodynamic concepts.
Thermodynamic Elements
Heat Exchangers
Heat exchangers are an important component in HPRTE cycles. The base HPRTE
Efficiency model mode has two heat exchangers, MGC and RHX; and the combined
cycle, H-V Efficiency, has four heat exchanger elements including three for compressor
inter-cooling. Those for the inter-cooling have defined process inlet flow states. Mass is
conserved by setting the exit mass flow rate equal to the entrance mass flow rate.
User defined inputs include effectiveness, ε , and 1_0 inPPΔ . Let effectiveness be
defined as
( ) ( )( ) ( )
( ) ( )( ) ( )2_01_011
1_01_011
__0__0min_min
__0__0_
max ininpin
outinpin
incoldinhotp
outhotinhothotphot
TTCmTTCm
TTCmTTCm
QQ
−⋅
−⋅=
−⋅
−⋅==
&
&
&
&
&
&ε (5.1)
hotpC _ is the hot side specific heat at constant pressure, and min_pC is the specific heat of
the minimum capacity flow stream.
-
34
Therefore, ( )( )2_01_0
1_01_0
inin
outin
TTTT
−
−=ε . (5.2)
The only unknown in Equation 5.2 is 1_0 outT .
The capacity of the process fluid is set such that it is always the maximum capacity
stream. This ensures that it is not used in the calculation above.
The exit pressure is determined using the following equation:
( )1_01_01_0 1 ininout PPPP Δ−⋅= . (5.3)
Know known are the parameters 1_0 outT , 1_0 outP , and 1outm& . The exit state is set.
Mixers
The mixer is modeled as an adiabatic, constant static pressure process. Because
there is no consideration given for Mach number effects, the stagnation pressures of the
two flows entering the mixer must be identical. This requires a model constraint be set
up by the user for each HPRTE model and satisfied by the solution solver. All HPRTE
models have recirculation mixers which are tasked with combing the recirculated exhaust
gas products with fresh air discharged from the low pressure compressor.
A mass balance requires:
21 ininout mmm &&& += (5.4)
Assuming adiabatic mixing, the energy balance is as follows:
out
ininininout m
hmhmh
&
&& 2_021_01_0
+= . (5.5)
Constant pressure mixing implies:
outinin PPP _02_01_0 == . (5.6)
-
35
Other parameters such as the outFAR and the mass fractions are mass averaged. For
example:
out
ininininout m
FARmFARmFAR
&
&& 2211 += . (5.7)
With outh _0 , outP _0 , outm& , and the exit state mass fractions all known, all other
thermodynamic properties can be found.
Splitter
In Chapter 4 the cycle schematics for the HPRTE cycle models showed flow
splitting occurring at State 9. To accomplish this feature with a computer model a splitter
component must be defined to separates flow into two streams before exhausting to the
environment. The recirculation splitter is tasked with the job of splitting the flow stream
on a mass basis after the high temperature recuperation process (State 9). A portion of
the flow is reconstituted with fresh air before heading back through the core engine
components while the rest is directed to the low pressure turbine (LPT) to power the
turbocharger. A bypass ratio, BPR, is user defined to represent the mass basis split of the
flow streams. The recirculation splitter inlet state is defined by the following know
parameters: inT _0 , inP _0 , intotm _& , inFAR , inh _0 , and mass fractions for all species.
In general BPR is defined as
1_
2_
outtot
outtot
mm
BPR&
&= . (5.8)
For this application the bypass ratio is defined as
exhaustedtot
recirctotcirc m
mBPR
_
_Re &
&= . (5.9)
-
36
recirctotm _& is the mass flow rate recirculated and mixed with fresh air. exhaustedtotm _& is
the mass flow rate that passes directly to the low pressure turbine and be exhausted from
the system at State 8.
The user also reserves the option of applying flow pressure drops to either or both
of the split streams, but for this analysis the splitter is modeled as an isobaric process.
Similarly, the process is adiabatic, as there is no heat transfer. The mass fractions are
unchanged; therefore, the exit state of each flow is defined.
inoutout PPP _02_01_0 == (5.10)
inoutout TTT _02_01_0 == (5.11)
Water Extractor
The water extraction component is only present in the H-V Efficiency
configuration. Because water vapor is present in the recirculated mixed gases and the
cooling capacity of the three heat exchangers is significant to cause condensation to occur
in the flow stream, it is desirable to separate the liquid water from the gas flow before the
inlet to the high pressure compressor. The separation of liquid water from the flow
stream is modeled as an isentropic process. The inlet state is completely defined;
therefore, liquidOHm _2& and liquidOHh _2 are readily available from CEA. The exit state is
defined by first setting the inlet and exit temperatures and pressures equal.
inout PP _0_0 = (5.12)
inout TT _0_0 = (5.13)
Then the exit mass flow rate and enthalpy are set.
liquidOHintotouttot mmm _2__ &&& −= (5.14)
-
37
liquidOHinout hhh _2_0_0 −= (5.15)
The exit state of the water extractor is now defined.
Compressors
Compressors inlet states are defined with the following parameters passed to the
element: inT _0 , inP _0 , intotm _& , inFAR , inh _0 , and mass fractions for all species. The
performance of the compressor is determined by the following parameters: pressure ratio
( CompPR ) and adiabatic efficiency ( adComp _η ).
Exit pressure is determined first with the equation
inCompout PPRP _0_0 ⋅= . (5.16)
The other thermodynamic parameter, the adiabatic efficiency, is used to calculate
the exit state point parameters in the NPSS Compressor module. Define the adiabatic
compressor efficiency as
inout
inidealoutadComp hh
hhworkcompressoradiabatic
workcompressorideal
_0_0
_0__0_ __
__−
−==η . (5.17)
Determining the ideal exit state enthalpy is straight forward knowing outP _0 and
idealouts __0 if idealoutin ss __0_0 = . Since entropy and enthalpy are only functions of
temperature; the exit state ideal temperature is quickly found along with enthalpy. Now,
rearrange and directly solve Equation 5.17 for outh _0 . With the exit pressure and
enthalpy know known, all exit state thermodynamic parameters are readily calculated by
CEA.
The power required by the compressor is also calculated.
outoutininComp hmhmW _0_0_0_0 ⋅−⋅= &&& (5.18)
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38
The power is converted from Btu/sec to HP:
HP
lbfftBTU
lbfftWComp
1sec
5501
778
⋅
⋅⋅& . (5.19)
Polytropic efficiency, polyComp _η , is an output parameter calculated from the
entrance and exit entropies and pressures. The derivation is as follows:
The definition of the polytropic efficiency is
dhdhi
polyComp =_η . (5.20)
To arrive at this equation, first consider a reversible form of the energy equation.
Since PdvvdPdudh ++= , (5.21)
vdPdhPdvvdPPdvdhPdvduTds −=+−−=+= )( (5.22)
Therefore, P
dPRTdhdP
Tv
Tdhds −=−= . (5.23)
Solving Equation 5.23 for Tdh yields
PdPRds
Tdh
+= . (5.24)
For an isentropic process 0=ds . Therefore,
PdPR
Tdhi = . (5.25)
Combining Equations 5.24 and 5.25 results in the following:
PdPRds
PdPR
Tdh
Tdh
dhdh ii
polyComp
+===_η . (5.26)
Integrating Equation 5.26 from the inlet state to the exit state yields:
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39
( )( )CompinCompinout
CompinComppolyComp PRRss
PRRlog
log
__0_0
__ ⋅+−
⋅=η . (5.27)
Turbines
Turbines provide the power to drive the compressors as well as the net power for
the ship propellers and lift fans (if LCAC is the mission). The NPSS model Turbine
element requires a defined entrance state to include such parameters as inT _0 , inP _0 ,
intotm _& , inFAR , inh _0 , and mass fractions for all species present. As was the case with the
compressors, the performance of the turbine components is determined by the defined
parameters: pressure ratio ( TurbPR ) and adiabatic efficiency ( adTurb _η ). NPSS defines
TurbPR differently than most turbomachinery reference texts. Here it is defined as:
out
inTurb P
PPR
_0
_0= . (5.28)
The exit state can be determined by first applying the turbine pressure ratio.
Turb
inout PR
PP _0_0 = . Turbinout PRPP _0_0 = (5.29)
As was the case for the compressor, outh _0 is the other thermodynamic parameter
necessary to in order to define the exit state. The turbine adiabatic efficiency is defined
as:
idealoutin
outinadTurb hh
hhworkturbineideal
workturbineadiabatic
__0_0
_0_0_ __
__−
−==η . (5.30)
The power generated by the turbine is also calculated.
outoutininTurb hmhmW _0_0_0_0 ⋅−⋅= &&& (5.31)
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40
This power is converted to horsepower as it is in the compressor. The polytropic
efficiency is an output parameter calculated using the same approach described in the
compressor section. The final equation is given below.
( )( )TurbinTurb
TurbinTurbinoutpolyTurb PRR
PRRss/1log
/1log
_
__0_0_ ⋅
⋅+−=η (5.32)
Burner
The Burner element is a constant volume burner. The entrance state is completely
defined; those parameters include: inT _0 , inP _0 , intotm _& , inFAR , inh _0 , and mass fractions
for all species. Also specified are the bη and burner inPP _0Δ . The exit stagnation
pressure, outP _0 , is found with the equation:
( )ininout PPPP _0_0_0 1 Δ−⋅= . (5.33)
outT _0 must be specified by the user in order to determine the incoming fuel flow
rate, fuelm& . In order to determine the exit state, the burner subroutine makes an initial
guess for the fuel flow rate, 1fuelm& , using a straightforward energy balance.
(5.34)
The model assumes a lower heating value, RQ , of 18400 Btu / lbm. It also assumes
a constant specific heat, pC , of 0.285 Btu / lbm-R. The inlet conditions and the first fuel
flow rate iteration, 1fuelm& , are then passed to CEA from the NPSS subroutine calcBurn.
CEA calculates the burner exit state point including: equilibrium composition and the
new burner exit temperature iteration, 1_0 outT . The burner exit conditions (1_0 outT , outP _0 ,
⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−=
out
inoutinairfuel T
TTmm
_0
_0_0_
1
285.0/18400&
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41
outFAR , outWAR , outh _0 , and mass fractions for all species) are then passed back to
calcBurn where the burner efficiency is applied to determine the actual burner exit
temperature, actoutT_1_0 .
( ) ininoutbactout TTTT _0_01_0_1_0 +−=η (5.35)
Then, actoutT_1_0 is used to determine the next fuel flow rate iteration,
2fuelm& , with the
energy balance described above (Equation 5.34). An error check is performed on the fuel
flow rate values every iteration to determine when the loop can be exited.
ToleranceErrormmm fuelfuelerrorfuel _12
_ ≤−= &&& (5.36)
Once fuelm& is determined, the exit state point is completely defined.
Sensitivity Analysis
No formal optimization program was used for this project; instead, each engine
cycle model was roughly optimized manually starting from base case assumptions listed
in Chapter 4. The sensitivity analyses were performed on the SCGT and HPRTE
Efficiency models to determine the influences of particular design parameters. The H-V
Efficiency model was not included in these studies because the results would mirror those
for the HPRTE Efficiency model analysis. Two primary dependent parameters
investigated in the sensitivity analysis include thermal efficiency and specific power.
The thermal efficiency is defined as:
Rfuelth Qm
W⋅
=&
&η , (5.37)
where RQ is the lower heating value of the fuel and W& is the net power.
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42
The specific power is defined as: inairm
WSP_&
&= . (5.38)
Influence coefficients are use to quantify the sensitivity of resultant parameters as
they relate to perturbed input parameters. The dimensional influence coefficient is
defined as
( )( )ParameterInput
Resultant∂
∂ . (5.39)
To relate the magnitudes of influence coefficients to one another, they must be non-
dimensionalized is required. This is accomplished by dividing the perturbed value by its
base case quantity:
( )
( )Value BaseParameter Input
ParameterInput Value BaseResultant
Resultant
∂
∂. (5.40)
Such an example of a non-dimensional influence coefficient is given below. Here,
the HPC inlet temperature is perturbed from its base value and the resultant change to thη
is expressed in the following form. A value of 1 suggests that a 1% perturbation in HPC
inlet temperature results in a 1% change in thη . In this way the sensitivity of input
parameters is determined.
( )
base
baseth
th
TinHPCTinHPC
_)_(
_
∂
∂η
η
(5.41)
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43
CHAPTER 6 RESULTS AND DISCUSSION
The results and discussion of the analysis performed using the cycle code NPSS are
presented in Chapter 6. The first section in this chapter, Cycle Code Comparison,
compares results from the spreadsheet code (used by Boza [22]) and the NPSS program
for one operating point of the HPRTE Efficiency model. Next, sensitivity studies were
performed on the SCGT and HPRTE Efficiency cycles and influence coefficients were
calculated. Engine model results are given and compared to derived thermodynamic
expressions. Finally, plots and tables are presented that compare the performance
parameters of the three engine configurations.
Cycle Code Comparison
Before initiating the sensitivities studies, it is important to benchmark the NPSS
program and compare results of one model configuration to those results obtained from
running a proven cycle analysis program. One operating point for the HPRTE Efficiency
model was chosen for the comparison, and the results from the two cycle codes are
presented in Table 6-1. The third column in the table lists the absolute differences of the
two data sets parameters in percentages. Agreement of the data between the two codes is
high; values for thη , OPR, HPT exit temperature (TET), inHPCT _ , and exhaustT are all
within acceptable limits. The SpPw calculated by the spreadsheet model was 12.5%
higher than that calculated in NPSS. There are three possible reasons for the disparity in
the output values. First, it is impossible to implicitly balance the low pressure spool
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44
specific work; therefore the turbine specific work is never properly matched to the
specific power of the compressor. This could very easily result in a different airm& . Two,
different fuels are used in the codes. The hydrogen-to-carbon ratio is 1.93 in NPSS and
2.03 in the spreadsheet code. Because the fuels are different, the curve-fit coefficients
used to calculate the enthalpies for the spreadsheet code could be different than the ones
used by NPSS.
Sensitivity Analysis
Simple Cycle Gas Turbine Engine Model
Of particular interest for this project is the sensitivity of the open-cycle engine
thermal efficiency and specific power to variations in turbine inlet temperature and
ambient temperature. Figures 6-2 through 6-4 show the results of the analysis. Unless
otherwise specified the following parameters remained constant throughout the analysis:
ambient temperature is 544°R, TIT is 2500°R, and nominal power output is 4000 BHP.
Figure 6-2 displays the thermal efficiency as a function of the overall cycle pressure ratio
(OPR). The TIT variations have a strong influence on the outcome of the thermal
efficiency value. Raising TIT has a positive effect on thη which also implies that the
total heat added to the system has been reduced since the power output remains steady.
Let thη be defined by the following relationship:
Rfuelth Qm
W⋅
=&
&η . (6.1)
Since, RQ , the fuel lower heating value, is constant; fuelm& has to decrease in order
to reduce the total heat added to the system in order to raise the thη . For all run cases in
the SCGT analysis, variations in thη are the direct result of variations in fuelm& .
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45
To better un