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

Copyright 2007

By

George Anagnostis

This thesis is dedicated to my parents, Victor and Linda Anagnostis. Without their emotional and financial encouragement this thesis would not exist.

iv

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.

v

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

vi

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

vii

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

viii

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

ix

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

x

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”

xi

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

xii

adLPC _η Low pressure compressor adiabatic efficiency

adLPT _η Low pressure turbine adiabatic efficiency

xiii

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.

xiv

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.

1

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.

2

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.

3

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.

4

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

5

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

6

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

7

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

8

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

9

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

10

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

11

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

12

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,

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.

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

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)

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:

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)

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&

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.

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)

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

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& .

45

To better un