DEVELOPMENT OF A CYCLE DESIGN SOFTWARE

FOR TURBOSHAFT ENGINES

A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY

BY

MERT ERK

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR
THE DEGREE OF MASTER OF SCIENCE
IN
MECHANICAL ENGINEERING

SEPTEMBER 2015
 Approval of the thesis:

DEVELOPMENT OF A CYCLE DESIGN SOFTWARE FOR TURBOSHAFT

ENGINES

submitted by MERT ERK in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering Department, Middle East
Technical University by,

Prof. Dr. Gülbin Dural Ünver

Dean, Graduate School of Natural and Applied Sciences __________________

Prof. Dr. R. Tuna Balkan

Head of Department, Mechanical Engineering __________________

Prof. Dr. M. Haluk Aksel

Supervisor, Mechanical Engineering Dept., METU __________________

Examining Committee Members:

Prof. Dr. Kahraman Albayrak

Mechanical Engineering Dept., METU __________________

Prof. Dr. M. Haluk Aksel

Mechanical Engineering Dept., METU __________________

Assoc. Prof. Dr. M. Metin Yavuz

Mechanical Engineering Dept., METU __________________

Asst. Prof. Dr. Cüneyt Sert

Mechanical Engineering Dept., METU __________________

Asst. Prof. Dr. Ö. Uğraş Baran

Mechanical Engineering Dept., TED University __________________

Date: 30.09.2015
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also declare
that, as required by these rules and conduct, I have fully cited and referenced
all material and results that are not original to this work.

Name, Last Name: Mert Erk

Signature :

iv
 ABSTRACT

DEVELOPMENT OF A CYCLE DESIGN SOFTWARE FOR TURBOSHAFT

ENGINES

Erk, Mert

M.S., Department of Mechanical Engineering

Supervisor: Prof. Dr. M. Haluk Aksel

September 2015, 98 pages

In this thesis, a computer software for the cycle design of a turboshaft engine is
developed. Firstly, a numerical air model was implemented and the model of the
turboshaft to be used in the simulation was selected. The first requirement for the
software is the capability of performing design point calculations and parametric
studies. This feature, which is the initial part of an aircraft engine design, was
integrated into the software. At this point, to have a better estimation of the
component performances, basic efficiency estimation modules of compressor,
combustor and turbines were developed and embedded into the code. After setting
the design point of the engine, the software can give insight to the designer about
operating at different points from the design point in the operating envelope of the
aircraft. In order to accomplish the off-design performance estimations, the map
scaling technique was used with the reference maps and matching of the components
of the designed turboshaft was programmed with the Newton-Raphson iteration
technique. In addition to the off-design performance estimations, the dynamic
behavior (transient) estimation module of the software was developed. After all, a
GUI (Graphical User Interface) was constructed for the use of each parts of the
software in a “user-friendly” environment. The results of the code were compared

v
with the engine performance data and the commercially available program
“GasTurb11” in order to confirm the reliability of the software to perform
preliminary engine design studies.

Keywords: Gas Turbine Model, Thermodynamic Matching Model, Turboshaft

Simulation, Inlet Distortion Model, Turboshaft Preliminary Design

vi
 ÖZ

TURBOŞAFT MOTORLARI İÇİN ÇEVRİM TASARIM YAZILIMI

GELİŞTİRİLMESİ

Erk, Mert

Yüksek Lisans, Makine Mühendisliği Bölümü

Tez Yöneticisi: Prof. Dr. M. Haluk Aksel

Eylül 2015, 98 sayfa

Bu tezde turboşaft motoru çevrim tasarımı için bilgisayar yazılımı geliştirilmiştir.

Öncelikle, hava modeli oluşturularak simülasyonlarda kullanılacak turboşaft modeli
belirlenmiştir. Daha sonra, yazılımın gereksinimi olan ve hava aracı için ilk ve kritik
aşama olan tasarım noktası hesaplamaları ve parametrik çalışma kabiliyetleri
programa entegre edilmiştir. Bu noktada, komponent performanslarının olası
değerlerine daha iyi yakınsama yapılabilmesi amacıyla, kompresör, yanma odası ve
türbinler için temel verimlilik tahmin modülleri geliştirilmiş ve kodun içine
eklenmiştir. Tasarım noktası seçildikten sonra yazılımın kullanıcısına, tasarlanan
motorun, hava aracının tasarım noktası dışında kalan işletim zarfında nasıl çalışacağı
hakkında fikir vermesi gerekmektedir. Bu nedenle, komponent referans haritaları
üzerinde harita ölçeklendirme tekniği ile ölçeklendirme özelliği yazılımın içerisine
eklenmiştir. Tasarlanan turboşaft motorunun komponentlerin eşleşmesi ise Newton-
Raphson iterasyon tekniği ile programlanmıştır. Buna ek olarak, motorun dinamik
davranışını tahmin eden ivmelenme modülü geliştirilmiştir. Son olarak, yazılımın
her bir modülünden daha “kullanıcı-dostu” bir ortamda faydalanılabilmesi için bir

vii
kullanıcı arayüzü oluşturulmuştur. Yazılımın ön tasarım aracı olarak kullanılabilmesi
için gerekli olan güvenilirliği doğrulamak için yazılımın sonuçları da literatürde
mevcut motor performans verileri ile ve ticari bir yazılım olan “GasTurb11” ile
karşılaştırılmıştır.

Anahtar kelimeler: Gaz Türbin Modeli, Termodinamik Eşleşme Modeli, Turboşaft

Simülasyonu, Giriş Akım Bozukluğu, Turboşaft Ön Tasarım, Turboşaft Çevrim
Yazılımı

viii
Anneme ve babama …

ix
 ACKNOWLEDGEMENT

First of all, I would like to thank to my family for fully supporting me throughout my
educational progress. In addition, special thanks go to my best friend Orhan Ziya for
his endless support and encouragement in the difficult times during advancing the
educational steps.

I would like to thank my supervisor Prof.Dr. M. Haluk Aksel for his support and
guidance throughout this thesis.

I would also like to thank Taylan Ercan and Gökhan Aran for their contribution to
have attracted my attention at this part of science and support for understanding key
concepts of this thesis topic and guiding me in preliminary design studies and needs
of preliminary design tool with their experience in gas turbine industry.

Lastly, thanks also go to my colleagues Emrah Güllü, Mustafa Bilgiç, Ozan Çelik
and Burak Gülsaçan for their support, encouragement during this work and aid in the
proofreading of this thesis.

x
 TABLE OF CONTENTS

ABSTRACT ................................................................................................................. v

ÖZ .............................................................................................................................. vii

ACKNOWLEDGEMENT ........................................................................................... x

TABLE OF CONTENTS ............................................................................................ xi

LIST OF TABLES .................................................................................................... xiv

LIST OF FIGURES ................................................................................................... xv

LIST OF ABBREVIATIONS ................................................................................. xviii

LIST OF SYMBOLS ................................................................................................ xix

CHAPTERS

1 INTRODUCTION ............................................................................................ 1

1.1 Gas Turbines and Brayton Cycle ............................................................... 1

1.2 Component Details .................................................................................. 10

1.3 Design Methodologies ............................................................................. 17

1.4 Modelling of Gas Turbines ...................................................................... 18

1.5 Literature Survey ..................................................................................... 20

1.6 Objectives ................................................................................................ 24

1.7 Thesis Outline .......................................................................................... 25

2 ON-DESIGN PERFORMANCE ESTIMATION ........................................... 27

2.1 Turboshaft Model and Air Stations ......................................................... 27

2.2 Air Model ................................................................................................. 29

2.3 On-Design Calculations ........................................................................... 32

2.4 Parametric Design .................................................................................... 37

xi
 3 COMPONENT DESIGN PERFORMANCE ESTIMATIONS ...................... 41

3.1 Compressor Design Mode........................................................................ 41

3.2 Compressor Efficiency Calculation Mode ............................................... 44

3.3 Turbine Efficiency Calculation Mode ..................................................... 48

3.4 Combustor Design Mode ......................................................................... 57

4 OFF-DESIGN PERFORMANCE ESTIMATION.......................................... 59

4.1 Map Scaling ............................................................................................. 59

4.2 Beta-Line Technique ................................................................................ 61

4.3 Component Matching in Off-Design Calculations .................................. 62

4.4 Changing Parameters at Off-Design ........................................................ 64

4.5 Operating Lines ........................................................................................ 65

4.6 Handling Bleed Effects ............................................................................ 67

5 SIMULATION OF INLET DISTORTION EFFECTS ................................... 69

5.1 Methodology ............................................................................................ 69

5.2 Sample Results and Comparison with GasTurb11 .................................. 72

6 TRANSIENT PERFORMANCE ESTIMATION ........................................... 75

6.1 Heat Soakage Model ................................................................................ 79

7 COMPARISON OF THE DEVELOPED SOFTWARE RESULTS WITH

THE LITERATURE ............................................................................................... 81

7.1 Steady – State Performance Comparison ................................................. 81

7.2 Transient Performance Comparison ........................................................ 82

8 CONCLUSIONS AND FUTURE WORK ..................................................... 85

8.1 Conclusion ............................................................................................... 85

8.2 Future Work ............................................................................................. 86

REFERENCES ........................................................................................................... 89

APPENDICES
xii
A. NEWTON-RAPHSON ITERATION METHOD ................................................. 93

B. SCREENSHOTS OF THE DEVELOPED SOFTWARE ..................................... 95

xiii
 LIST OF TABLES

TABLES

Table 2.1 - Air Stations used in the developed software ............................................ 28

Table 2.2 – Dry air property constants ....................................................................... 31

Table 2.3 - Kerosene property constants .................................................................... 31

Table 3.1 - Air Stations used in centrifugal compressor efficiency estimation ......... 47

Table 3.2 - Air Stations used in turbine efficiency estimation ................................... 49

Table 4.1- Comparison of results of the developed software and GasTurb for given
sample inputs .............................................................................................................. 67

Table 4.2 - Operating line power output comparison of the developed Software and
GasTurb11 .................................................................................................................. 67

Table 5.1 - Inlet distortion effect on performance ..................................................... 73

Table 7.1 - Comparison of certification data of LHTEC CTS800-4N with model in

the developed software ............................................................................................... 82

xiv
 LIST OF FIGURES

FIGURES

Figure 1.1 - Simple turboshaft engine [1] .................................................................... 1

Figure 1.2 - Air standard Brayton cycle [3] ................................................................. 2

Figure 1.3 - Efficiency versus pressure ratio [2] .......................................................... 4

Figure 1.4 - T-s diagram for compressor [2] ................................................................ 5

Figure 1.5 - Comparison of stage by stage and total temperature rises [2].................. 7

Figure 1.6 - Forces acting on blades [4]..................................................................... 11

Figure 1.7 - Airfoil angle of attack relative to approaching air [4] ............................ 11

Figure 1.8 - Axial compressor velocity triangles [5] ................................................. 12

Figure 1.9 - Compressor performance map [4] .......................................................... 13

Figure 1.10 - Annular combustor types (forward and reverse flow annular
combustors) [5] .......................................................................................................... 14

Figure 1.11 - Combustor parts and sample equivalence ratios [5]............................. 15

Figure 1.12 - Turbine velocity triangles [5] ............................................................... 16

Figure 1.13 – Design sequence of preliminary design [6] ......................................... 18

Figure 1.14 - Performance simulation models' accuracy versus complexity graph ... 21

Figure 1.15 - Development phase commitments [23] ................................................ 24

Figure 2.1 - Model of turboshaft engine with power turbine ..................................... 28

Figure 2.2 - Sample input of design point calculations .............................................. 33

Figure 2.3 - Sample output of design point calculations with the inputs in Figure 2.2
.................................................................................................................................... 36

Figure 2.4 - Output of "GasTurb" software with the inputs in Figure 2.2 ................. 37

xv
Figure 2.5 - Sample input parameters of parametric design calculation .................... 38

Figure 2.6 - Output of parametric design module with given input in Figure 2.5 ..... 38

Figure 2.7 – Results of parametric study example in the same graph ........................ 39

Figure 3.1 – Main outputs of the developed component performance estimation

modules ...................................................................................................................... 41

Figure 3.2 - Velocity triangle nomenclature of compressor [3] ................................. 42

Figure 4.1 - Performance characteristics of axial and centrifugal compressors [32] . 60

Figure 4.2 - Compressor map and beta lines .............................................................. 62

Figure 4.3 - Off-design matching algorithm .............................................................. 64

Figure 4.4 – Sample output of operating line in compressor map in the developed
code ............................................................................................................................ 65

Figure 4.5 – Sample output of operating line in HP turbine map in the developed
code ............................................................................................................................ 66

Figure 4.6 – Sample outputs of operating line in power turbine map in the developed
code ............................................................................................................................ 66

Figure 4.7 - Handling bleed effect on operating line ................................................. 68

Figure 5.1- Inlet distortion output of the developed software .................................... 72

Figure 5.2 - GasTurb11 output with inlet distortion .................................................. 73

Figure 6.1 - Transient matching algorithm................................................................. 76

Figure 6.2 - Sample output of transient performance on component maps ............... 77

Figure 6.3 - Sample output of transient performance - output figures of Tt4 and Ncorr
.................................................................................................................................... 78

Figure 6.4 - Comparison of Tt4 and GG spool speed of GasTurb11 and the developed
software ...................................................................................................................... 78

Figure 7.1 - HP turbine inlet temperature versus time elapsed .................................. 83

Figure 7.2 - Power turbine inlet temperature versus time elapsed ............................. 83

Figure A.1 – Newton-Raphson method...................................................................... 93

xvi
Figure B.1 - TEImep home page ................................................................................ 95

Figure B.2 - TEImep turbine module ......................................................................... 96

Figure B.3 - TEImep parametric study ...................................................................... 96

Figure B.4 - TEImep operating line sample result ..................................................... 97

Figure B.5 - TEImep transient sample screenshot ..................................................... 97

Figure B.6 - Transient sample map result .................................................................. 98

xvii
 LIST OF ABBREVIATIONS

CFD Computational Fluid Dynamics

VIGV Variable Inlet Guide Vane

NGV Nozzle Guide Vane

ISA International Standard Atmosphere

MDO Multidisciplinary Design Optimization

HPT High Pressure Turbine

PT Power Turbine

GUI Graphical User Interface

SFC Specific Fuel Consumption

AIP Aerodynamic Interface Plane

FAA Federal Aviation Administration

TEImep Developed Program – TEI Modelling and Estimation of Gas Turbine

Performance

OEI One Engine Inoperative Power Rating

COEI Continuous One Engine Inoperative Power Rating

xviii
 LIST OF SYMBOLS

Speed of Sound (m/s)

Distorted Section Angle (

Absolute Flow Angle (

Customer Bleed Air Percentage (%)

Specific Heat Ratio

High Pressure Turbine Nozzle Guide Vane Cooling Air Percentage

(%)

High Pressure Turbine Rotor Cooling Air Percentage (%)

Efficiency (%)

Cooling Effectiveness

Isentropic efficiency with zero tip clearance

Dynamic Viscosity (Pa.s)

Head Coefficient

Pressure Ratio of Gas Turbine Component i

Density (

Fuel Pump Time Constant (s)

Enthalpy Ratio of Gas Turbine Component i

Temperature Dependent Portion of Entropy (kJ/kgK)

Stage Flow Coefficient

Burner Loading (

Area (

Specific Heat Capacity (kJ/kgK)

xix
 Compressor Efficiency Decrease Rate with Relative Clearance

Pressure Distortion Coefficient

Temperature Distortion Coefficient

Polytropic Efficiency (%)

Exhaust Pressure Ratio

Fuel to Air Ratio

Specific Enthalpy (kJ/kg)

Heat Transfer Coefficient

Hub to Tip Radius Ratio

Heat Transfer Constant

Heat Soakage Time Constant (s)

Enthalpy of the gas entering the component i

Enthalpy of the gas leaving the component i

Polar Moment of Inertia of High Pressure Spool (

Work Input Coefficient

Combustion Intensity

Cooling Constant

Loss Correction Factor

L Combustor Loading (

Length of the Combustion Chamber (m)

Lower Heating Value of Fuel (kJ/kg)

̇ Mass Flow Rate (kg/s)

Mach Number

Stage Number

Rotational Speed (rpm)

xx
 Pressure (Pa)

Pressure Ratio

Stage Pressure Ratio

Reduced Pressure

Power Off-take (kW)

Total pressure of the gas entering the component i

Total pressure of the gas leaving the component i

̇ Heat Transfer Rate (kW)

Compressor Volumetric Flow Rate ( )

Gas Constant (kJ/kgK)

Degree of Reaction

Reynolds Number

Relative Tip Clearance

Speed-work Parameter

T Temperature (K)

Temperature (K) divided by 1000

Elapsed Time (s)

Residence time (s)

Impeller Speed (m/s)

Unbalanced Power on Shaft (kW)

Absolute Flow Velocity (m/s)

Volume of the Combustor ( )

Relative Flow Velocity (m/s)

̇ Power (kW)

Mass Flow Rate (lbm/s

xxi
 Fuel Flow Rate (kg/s)

Subscripts

Axial Component

Whirl Component

Burner

Customer Bleed Flow

High Pressure Turbine Nozzle Guide Vane Cooling Air

High Pressure Turbine Rotor Cooling Air

Compressor

Corrected to Standard Day Conditions

Cooling

Diffuser

Design value of the engine to be designed

Design point

Exhaust

High Speed Spool

Hub

Any component of turboshaft engine

Design value of the reference maps

Value of the interested point for scaling

Mechanical

Mean-Line

Maximum

Mixer 1 (High Pressure Turbine Nozzle Guide Vane Cooling)

Mixer 2 (High Pressure Turbine Rotor Cooling)

xxii
 Nozzle

Power off take Spool

Ram

Relative

Rotor

Stage

Stator

Standard Day Conditions

Total Property, Tip

High Pressure Turbine

Power Turbine

Turbine

Vaned diffuser

Vaneless diffuser

Superscripts

Ideal Process

xxiii
xxiv
 CHAPTER 1

1 INTRODUCTION

1.1 Gas Turbines and Brayton Cycle

Gas turbine engines are the engines that are widely employed in aircrafts and
industrial plants. It has three main parts which are the compressor, combustion
chamber and turbine. The most simplified versions of gas turbines are turbojet and
turboshafts. The schematic of a turboshaft is given in Figure 1.1.

Figure 1.1 - Simple turboshaft engine [1]

Basic operation begins by increasing the air pressure using a compressor towards the
combustion chamber. Fuel is then injected into the high pressure air in the
combustion chamber where the combustion process occurs. After combustion,
acquired high energy flow is converted into mechanical energy by expanding the
flow to a lower pressure in a turbine. This drained energy is used to operate the

1
compressor. There is a remaining energy that is obtained when the fuel is more than
required to rotate only the compressor. Since the main purpose of an engine is to
produce more power than the amount required just to rotate the compressor, this is a
must [2]. This remaining energy of the flow is used to produce thrust by increasing
the air velocity in the nozzle. Industrial or helicopter applications differ at this point
since there is no need for thrust. In these cases, an additional turbine extracts the
remaining energy of the flow and its shaft is connected to the location where the
mechanical power is required.

Gas turbine operations can be best modeled by a Brayton cycle. The simplest
Brayton cycle approach uses the assumption of an air-standard model and gives an
idea about the fundamental operation of this cycle.

1.1.1 Ideal Cycle

Figure 1.2 - Air standard Brayton cycle [3]

The schematic representation of an air standard cycle of turbojet engine and the
corresponding p-v and T-s diagrams are given in Figure 1.2. Assuming that there is
no bleed, compressor and turbine powers can be found as [3]

2
 ̇ ̇ (1.1)

̇ ̇ ̇ (1.2)

where ̇ is the compressor power, ̇ is the turbine power, ̇ is the mass

flow rate of operating gas, ̇ is the fuel flow rate and is the total enthalpy of the
operating gas. In addition, numbered subscripts denote the corresponding air stations
as seen in Figure 1.2.

Net total power output for this type of gas turbine is

̇ ̇ ̇ (1.3)

where ̇ is the net total power output.

Combustion is modeled in this simple cycle with heat addition and the amount of the
heat addition is given by

̇ ̇ ( ̇ ̇ ) ̇ (1.4)

where ̇ is the heat addition rate at combustor whereas is the lower heating
value of the fuel.

The resulting efficiency of the cycle can be defined as

̇ ̇ (1.5)

Furthermore, if the specific heats are assumed to be constant throughout the cycle
(gas is calorifically and thermally perfect), if the air flow rate is assumed to be much
more than the fuel flow rate and finally if the compressor and turbine efficiencies are
assumed to be 100%, the cycle efficiency can be written as [3]

(1.6)

where is the pressure ratio of the compressor and is the specific heat ratio
of the operating gas.

3
This formula can be represented in an efficiency versus pressure ratio graph as
shown in Figure 1.3.

Figure 1.3 - Efficiency versus pressure ratio [2]

Another important parameter for a turboshaft engine is the specific fuel consumption.
It is defined by the ratio of the fuel consumption of the engine over the delivered
shaft power. Specific fuel consumption, , can be expressed in formulation as

̇
̇ (1.7)

where is the fuel consumption of the turboshaft engine.

Moving on to actual cycles rather than ideal cycles requires the discussion and
explanations about efficiency definitions for the fundamental components of gas
turbines and pressure losses. This enables the understanding of the actual cycle
behavior.

1.1.2 Actual Cycle

In the actual cycles, there are sources of losses that degrade the performance of the
gas turbine engine. The irreversible process in compressors and turbines, the pressure
losses in the burner and the ducts are the examples of these losses. In order to
understand the basics of these losses, it is required to investigate the gas turbine
components in detail.

4
1.1.2.1 Efficiencies of Compressors and Turbines

The ratio of the actual to the ideal work transfers is the efficiency definition for any
machine. The ideal process in turbomachines is isentropic since turbomachines
essentially operate in an adiabatic way [2].

Taking the stagnation properties into account, the isentropic efficiency for a
compressor is defined as

(1.8)

where is the enthalpy change for ideal compression whereas is the change in
enthalpy in actual compression.

For a perfect gas,

(1.9)

where is the specific heat capacity and is the temperature and subscript t
denotes the total (stagnation) property of the working gas.

Because of the assumption of constant , the Equation (1.8) can be rearranged by

using air station numbers, which are defined in Figure 1.2, as

(1.10)

where denotes outlet temperature under ideal compression in compressor and

is the isentropic compressor efficiency. The actual and ideal processes for
compressor can be shown in T-s graph in Figure 1.4.

Figure 1.4 - T-s diagram for compressor [2]

5
Besides, the isentropic turbine efficiency is defined as

(1.11)

where is the isentropic turbine efficiency.

It is the reciprocal of given by Equation (1.8) since turbines operate to absorb

energy from the operating gas. Rewriting the above equation with the assumption of
constant and using the same station numbers given in Figure 1.2, one can obtain

(1.12)

where denotes the outlet stagnation temperature under ideal expansion in turbine.

It should also be noted that, for an isentropic process [2]

( ) (1.13)

where P is the pressure of operating gas. Using Equation (1.13), the exit temperature
of a compressor can be obtained in terms of the inlet total temperature, isentropic
efficiency and pressure ratio as

( ) (1.14)

Similarly, for turbines, the exit temperature can be found by using

( ) (1.15)

Another widely used efficiency definition is the polytropic efficiency. In cycle

parametric studies with varying pressure ratios, a question arises about whether
fixing the values of the compressor and turbine isentropic efficiencies is a logical
way or not. Since it is found that the isentropic efficiency of the compressor tends to
decrease with increasing pressure ratio whereas the turbine isentropic efficiency
tends to increase with it [2]. Therefore, the main reason for defining polytropic
efficiency is to remove this controversy.

6
Assuming that the compressor has a certain number of stages and isentropic
efficiency of each stage is constant, the increase in the overall total temperature rise
can be given by

∑ (1.16)

where subscript denotes stage whereas denotes that the process is an ideal one.
Using the definition of the isentropic efficiency for a compressor given in Equation
(1.8) with the assumption of constant , the overall total temperature rise is

(1.17)

Combining Equations (1.16) and (1.17) yields

∑
(1.18)

Figure 1.5 - Comparison of stage by stage and total temperature rises [2]

It can be seen from Figure 1.5 that ∑ is larger than . This implies that is
larger than and the difference between them increases as the pressure ratio
increases. The physical interpretation can be given as follows: friction in one stage
requires more work in the next stage which can be termed by ‘preheat’ effect [2].
This approach can be used in turbines and it results in > .

The isentropic efficiency of each stage during the compression process is assumed to
be constant and it is defined as the polytropic efficiency. In formulation,

7
 =constant (1.19)

where is the polytropic efficiency of the compressor.

For an isentropic process,

(1.20)

So that

(1.21)

Combining Equations (1.20) and (1.21)

(1.22)

Integrating this equation between the inlet and the exit of the compressor results in

( )
(1.23)

This equation can be used for finding the polytropic efficiency by using the measured
values of the total pressure and temperature at the inlet and the exit of the
compressor. The polytropic efficiency can be related to the isentropic efficiency
using Equations (1.10) and (1.23) as

( )
(1.24)
( )

A similar procedure can be applied for the expansion process in turbines and the
resulting equation relating the isentropic efficiency of the turbine to the turbine
polytropic efficiency can be obtained as

8
 ( )
(1.25)
( )

where is the polytropic efficiency of the turbine.

1.1.2.2 Pressure Losses

Pressure losses in ducts and inlet sections of engines should be introduced for actual
cycles. These losses are mainly due to friction and curvatures along the path of
operating gases which significantly affect the engine performance. In addition,
burner pressure losses should be accommodated in the actual cycle modelling due to
the aerodynamic resistance of flame stabilizing- mixing devices and momentum
changes produced by exothermic reaction [2].

1.1.2.3 Mechanical Losses

Friction and windage in bearings are the main source of mechanical losses in a gas
turbine. A mechanical efficiency of 98 to 99 percent can be used for the estimation of
the performance of actual cycles.

1.1.2.4 Variation of Specific Heat

For real gases in normal operation conditions, the specific heat value can be
approximated to be dependent only on temperature. The assumption of constant
specific heat results in some error in cycle calculations which degrades the
performance estimation. In order to overcome this issue, a gas model, which will be
explained in next chapter, is introduced into the developed code and the air
properties are updated with respect to the temperature of working gas at each station.

1.1.2.5 Bleeds

In gas turbines, an increase in the exit temperature of the combustion chamber results
in higher thermal efficiency and lower specific fuel consumption. However,
limitations in materials because of metallurgical reasons direct the engine
manufacturers to cool the materials. Besides, state of the art coatings or metallurgical
improvements in materials are used in turbine blades. The turbine cooling air bleed is
extracted from the compressor discharge air due to its high pressure which enables a
9
cooling operation without external power requirements. Mixing of the cooling air
with the main stream air is modeled with no pressure loss in the developed software
and the temperature calculations will be given in detail in the next chapter.

Another bleed usage is termed as customer bleed extraction and it may be used for
aircraft cabin pressurization. Usually discharge air at the exit of the compressor is
used as modeled in the developed software.

In addition, handling bleed may also be needed in the gas turbine applications.
Handling bleeds can be extracted from the interstage or the discharge air passing
through the compressor depending on needs. Briefly, it is used to ease the concerns
on the phenomenon of surge in compressors.

1.2 Component Details

In order to have a broader understanding of how the engine behaves in different

conditions, a deeper investigation of the gas turbine components is needed. With this
aim, details of the main components will be introduced in this section.

1.2.1 Compressors

The high pressure air in gas turbines are provided by the compressor and its
performance is generally presented by plotting the pressure ratio against the
corrected airflow. These plots are used in the cycle off-design calculations and will
be mentioned in detail later. Mainly, two types of compressors are used which are
centrifugal and axial compressors. The axial compressor is used at medium and high
power applications whereas the centrifugal compressors are used in low powered gas
turbines. The compressor operation in both types is limited due to the phenomena of
‘stall’ (or surge) and ‘choking’ (or Stone Wall) at certain conditions of airflow,
pressure ratio and rotational speed [4].

Airflow over airfoil exerts forces on blades and they can be separated into
components as in Figure 1.6.

10
 Figure 1.6 - Forces acting on blades [4]

Looking from the aerodynamic perspective, two important parameters strongly affect
the successful operation of a compressor which are the angle of attack of the airfoil
and the speed of the airfoil relative to the approaching air.

Figure 1.7 - Airfoil angle of attack relative to approaching air [4]

It can be seen in Figure 1.7b that, for large positive angle of attacks may result in the
flow not following the convex surface of the airfoil. In another case (Figure 1.7c),
large negative values of the angle of attack may result in separation from concave

11
surface of the airfoil. The drag increases for both of these cases. Furthermore,
excessive speeds may result in shock waves and increase in drag force on blade as
well [4].

Figure 1.8 - Axial compressor velocity triangles [5]

In Figure 1.8, it is possible to see how the velocity components are defined. The
power required to operate the compressor can be estimated via these triangles with
the help of Euler turbine equation, which will be illustrated in the component
efficiency estimation section.

The point of stall is defined as the incidence at which the airfoil loss coefficient
doubles its minimum value. In multistage compressors, stalled operation is
acceptable up to a certain degree. To illustrate, front stages of the compressor may
stall at low speeds whereas steady state operation is possible at rear stages.
Moreover, if stall increases its intensity, compression operation may result in surge
phenomenon, which is the point that blades cannot support the adverse pressure
gradient and instantaneous breakdowns in the flow. A sudden action such as opening
the bleed valves or reducing the fuel flow should be applied to prevent the
breakdown of the engine and/or flameouts [5].

As the flow is increased in the compressor at constant speed, no dynamic impact

such as stall occurs but the operation is very inefficient at these points. In addition,
the operation at these points will result in high temperatures in the turbine.

With these limitations, the compressor performance can be presented by plotting the
pressure ratio against corrected airflow for a number of corrected speed lines and
efficiency islands as shown in Figure 1.9.

12
 Figure 1.9 - Compressor performance map [4]

The main reason lying under the usage of the pressure ratio versus corrected airflow
plots is explained in reference [2] in detail. To briefly explain, the main parameters
that affect the operation of the compressor are diameter, speed, airflow, total pressure
and temperature at the inlet and the exit of the compressor. After applying
Buckingham-Pi theorem, the resulting non-dimensional parameters are the total
pressure ratio, total temperature ratio, corrected airflow and corrected speed. Total
temperature ratio can be related to total pressure ratio by the isentropic efficiency
definition. Therefore, the resulting four parameters are completed by using the
isentropic efficiency rather than using the temperature ratio. The total pressure ratio
and the corrected airflow are selected as the vertical and horizontal axis respectively
whereas the numbers of corrected speeds are plotted on the compressor performance
map. Isentropic efficiency contours are also placed on the plot to finalize the
presentation of the compressor performance. Furthermore, it should be noted that the
turbine maps are generated in the same way that the compressor maps are generated.

1.2.2 Combustion Chamber

Combustion chamber (or burner) is the component in which the chemical energy of
the fuel is converted into thermal energy in gas turbines. With the increasing usage of
Computational Fluid Dynamics (CFD) in the design of the combustion chamber, the
complex flow in these components can be optimised to obtain the maximum
efficiency. Different of types of combustors exist and the most widely used ones in

13
aircraft applications are the forward and the reverse flow annular combustors. The
can-annular type combustor can be seen schematically in Figure 1.10.

Figure 1.10 - Annular combustor types (forward and reverse flow annular combustors) [5]

Before examining how the combustion occurs in gas turbines, it is helpful to

investigate the main sections of the combustion chamber. Mainly, the combustion
chamber is divided into three parts which are primary, secondary and tertiary zones.
These zones are shown in Figure 1.11.

14
 Figure 1.11 - Combustor parts and sample equivalence ratios [5]

Operation of the combustor needs airflow with a low velocity so that the burning
operation continues steadily and sufficient time exists for the combustion process.
Since the core (primary zone) temperatures are extremely hot to be directed to the
turbine, nearly half of the main flow of air is used only for cooling this hot core. In
the secondary zone there is some combustion process as well but with the help of the
fresh air, equivalence ratio decreases rapidly. In the tertiary zone, there is no
combustion and the only process is cooling of the air for turbine operation.

There are combustor parameters that affect the cycle performance strongly, namely
the combustion efficiency and the combustion pressure loss. Combustion efficiency
is the ratio of the fuel burnt to the total fuel input [5]. The latter one is generally
presented in percentage loss and is a result of mixing of flows and friction. For small
gas turbines like turboshafts, the combustion efficiency of 99.5 - 99.9% and the
pressure loss of 3-4% can be taken as standard values.

On the other hand, there are also parameters that are important in the basic sizing of
the combustion chamber. These are the combustor loading, the combustion intensity,
the residence time, the local Mach numbers, equivalence ratios and outlet
temperature distributions. The loading gives the idea about the difference between
the expected work and the work capability of the designed chamber whereas the

15
intensity shows the rate of heat release per unit volume of the combustor. Finally, the
residence time is the time required for air to pass through the combustion chamber.

1.2.3 Turbines

Turbines are one of the turbomachines that extract power from working fluid by
expanding it from higher to lower pressures. Similar to the compressors, two types of
turbines are common, namely axial and radial turbines. However, radial turbines are
rather inefficient with respect to the axial ones. In addition, since the pressure ratio of
the inlet and the exit is favorable and not adverse as in the compressor, it is possible
to reach much higher pressure ratios in one stage. Due to these reasons, the axial
ones are widely used.

Generally, turbines are designed for choked operation in design condition for ease of
control of the gas turbine operation. The affecting parameters are the same as the
compressors and the parameters of the performance map of the turbines are the same
as the compressor namely pressure ratio, isentropic efficiency, corrected flow and
corrected speed. However, because of the choked operation in the turbine, the
corrected mass flow in the turbine maps are very close to each other throughout the
most of the operating envelope. To detect where the turbine operates from the turbine
map easier, the horizontal axis is selected as the corrected speed multiplied by the
corrected mass flow rather than the corrected mass flow. Furthermore, the velocity
triangles can be drawn in a manner similar to the compressors as shown in Figure
1.12.

Figure 1.12 - Turbine velocity triangles [5]

16
1.3 Design Methodologies

The aircraft engine design process starts with the constraint analysis in which the
forces on the aircraft such as weight, lift, drag and thrust are examined. The next step
is to determine and define the mission profile of the aircraft. Then, it is time to start
the design of the specific engine that the aircraft can accomplish the missions that are
defined in mission profiles and the engine is capable of overcoming the forces that
are examined in the constraint analysis. The objective of this step is to estimate the
performance parameters in terms of design limitations, flight conditions and design
choices. This is achieved by assuming 1-D flow of a perfect gas with non-ideal
efficiencies of engine components. To find an optimum engine for a particular
application, the operating point is selected within this step of design process by
comparing several numbers of operating points. After this point, the off-design
analysis of an engine should be made in order to estimate the engine performance in
the flight envelope [6]. From now on, sizing of the determined engine should be
made with the aim of estimating the installed performance of the engine. Lastly, the
components of the engine such as inlet, exhaust, compressor, turbine and burner must
be designed in order to provide the desired power from the engine. This part is
known as the engine component design. The design sequence of preliminary design
of an engine is shown in Figure 1.13.

17
 Figure 1.13 – Design sequence of preliminary design [6]

The tool to be developed aims to be capable of performing cycle analysis, parametric

analysis for cycle selection and engine steady/unsteady behavior estimations.

1.4 Modelling of Gas Turbines

There are four main matching models according to reference [5] and a brief
introduction will be given in this section about these models.

1.4.1 Thermodynamic matching transient performance model

Steady-state matching equations (work and flow compatibility equations) for

matching the components are used in this model. The difference that turns the
model into transient is the application of an unbalanced power onto the shafts.
Fuel flow value, which is provided by the user or the control system of the
engine, will be compared with the fuel value coming out from the model with

18
 the specified corrected speed. After matching these two values, next time step
calculation is done until the unbalanced power reaches zero. Heat soakage,
volume and/or combustor dynamics, which will be mentioned later in this
thesis, may be included in order to improve the quality of the simulation. This
type of model is the most accurate representation of the transient simulations
of engine performance according to reference [5] and the used in:
 Engine control design philosophy
 Control schedule design such as fuel flow, variable inlet guide vanes
(VIGVs) etc. in order to maintain safe operation of engine
 Engine transient performance examination during design phase
 Engine performance prediction in some points of operating envelope
that it is not practical to test the engine
 Examination of maneuvers that may be expensive or not practical to
test

Due to the need of iterations inside the model, rarely the model of this type
can achieve real time simulation of the engine performance. Hence, in order
to combine with hardware control system of engines, real time models are
developed.

1.4.2 Real time aerothermal transient performance model

For matching, a steady state point is run and then the model switches into the
transient mode where the model continuously run at points at the intervals of
time corresponding to the digital controller update frame. The volumes
between the turbomachinery parts of the engine are important in this model
and the values at time t is found by previously found dP/dt’s at time t-1
calculated by volume dynamics. To explain, the time rate of change of
pressure at some sections of the engine are related to the temperature with
some constants that are defined specifically for the interested engine. Speeds
are also updated with the unbalanced power on the shafts by considering the
spool inertias. Component maps are used in order to calculate temperatures.
After completing the calculations, the code passes to the next time step and

19
 so, one step of the transient performance is completed. Compared with the
thermodynamic matching model, it has significant improvement in execution
time; however, the accuracy is lower than that model since no iteration is
done during the simulation. This model is often used for the engine control
system hardware and flight simulators. To have detailed information about
this method, reference [5] can be used as a guide.

1.4.3 Real time transfer function transient performance model

The key performance parameters are related to the fuel flow in this type of
model and the time constants to be used must be derived from the outputs of
the transient matching model or the engine test data. This model is mostly
used in flight simulators due to its simplicity and fast solution capability.
Generally, the accuracy is lower than the real time aerothermal transient
performance model. In addition, auxiliary system parameters such as oil or
starter system can be modelled with this approach in an engine performance
simulation.

1.4.4 Real time lumped parameter transient performance model

From test data or aerothermal models of the engine, the matrix of the steady
state and the transient performance parameters are generated in this type of
model and partial derivatives are obtained with respect to all other
parameters. These obtained matrices are used for the simulation of the
transients of the engine. This type of model is more favorable to be used in
flight simulators but less commonly encountered than the previous model.

1.5 Literature Survey

With the aim of modelling the gas turbine engines, there are a number of studies in
the literature. As mentioned in the previous part, the highest accuracy can be reached
with the thermodynamic matching transient performance model and the main interest
of this thesis is this type of modelling. In reference [7], there is an overview of the
performance simulation methods with respect to their complexity and accuracy
which can be seen in Figure 1.14.

20
 Figure 1.14 - Performance simulation models' accuracy versus complexity graph

Figure 14 illustrates the choice of using component matching model in this thesis and
the available sources in the literature about this method will be mentioned at first. In
the same reference, gas turbine model is developed with the component map
matching and the model is validated by comparison of the results with available
literature data. In addition, the interaction between the gas turbine operation and the
electrical-thermal systems is investigated with the developed model.

Mostly referenced studies in the thermodynamic matching type of model are

executed by, Kurzke, Saravanamuttoo, Walsh and Fletcher. The fundamental
equations and approaches are explained at References [5], [8], [9] and [2]. The main
idea underlying these references is the same and they concluded that the use of this
method is the most practical and accurate way for estimating the gas turbine
performance. Furthermore, Kurzke developed a commercial product named as
GasTurb which is available for both educational and commercial use. In reference
[8], the introduction of this program is mentioned and typical helicopter cycle
optimization is stated as the illustration of the usage of GasTurb. It is stated that the
code covers all significant aspects of cycle design point selection, off-design and
transient operation estimations with reasonably short simulation times.

There are a number of studies which compares the results of GasTurb with
experimental data or models of their own such as in references [10], [11], and [12].
In the first one, Kong et al. (2001) developed a performance simulation program for
KT-1 turboprop engine. Scaled maps of a similar engine are used in the off-design

21
and transient simulations and the results are validated by comparing the results with
GasTurb and the performance data provided by the engine manufacturer. In the next
study, Wemming (2010) conducted a master thesis about the prediction of aircraft
performance by using the rubber engine performance model. GasTurb is used for the
simulation models and the conclusion is that GasTurb can be used to make accurate
engine performance model and can be incorporated to multidisciplinary design
optimization (MDO) environment. Lastly, Martinjako (2014) mentioned in his thesis
that GasTurb is validated for predicting the performance of LM2500 and Garrett
GTCP85-98D.

For the usage in previously mentioned aims such as engine transient performance
examination during the design phase, the accuracy is the most important feature of
the software instead of the speed of the model. In the case of real time simulation
models which is needed by the engine control system, one of the most interested and
referenced studies is Ballin’s work [13] . This reference paper can be used for the
purpose of developing a real-time controller for gas turbine engines. In this study,
real-time simulation of T700-GE-700 turboshaft engine is developed with a model of
control system based on UH-60A Black Hawk Helicopter. Validation of this study is
demonstrated by the comparison of the results with analysis-oriented simulations
developed by the manufacturer. In addition to this work, Koçer (2000) developed a
real-time model for a small turbojet and investigated the hot-gas ingestion scenario
using aerothermal model of T800-LHT-800 turboshaft model [14]. In Novikov’s
master’s thesis (2012) [15], after the development of real-time T700 model, inlet
distortion and engine deterioration simulations were demonstrated.

In reference [16], Alexio et al. (2005) described the modelling of a turbofan engine
using an object-oriented simulation tool named as EcosimPro. The results are then
compared with those models that are accepted by industry and the possible adaptivity
feature of the model is demonstrated.

In reference [17], Lazzaretto et al (2001) created gas turbine design and off-design
models. In this study, off-design maps were generated with map scaling technique
and analytical model was implemented via a commercial equation solver. In addition,
the Neural Network Model is presented as an alternative way to analytical modelling.

22
In reference [18], Shahroudi (1994) participated in a study that aims to obtain a tool
in preliminary design phase of a gas turbine based aircraft engine. The software was
named as Computer Aided General Engine Design (CAGED) and multivariate
Newton-Raphson method is used in obtaining high speed in iterations. Engine
models were generated for any engine configuration and variables can be changed in
the software with developed graphical user interface (GUI).

In reference [19], Panov (2009) stated that a new Simulink library called
GasTurboLib is developed. Using the prepared blocks, the user can create any type
of the engine configuration and carry out steady state and transient performance
analyses in Simulink. In addition, a control method is developed for full simulation
of the engine. To illustrate, engine can be started, operated and shut down in
simulations via a governor model. In this referenced paper, demonstration of
modeled single and twin shaft engine is available with developed Simulink
GasTurboLib library blocks and validated by comparison with the available engine
test data.

In reference [20], Garrard (1995) presented his study which is a time dependent
simulation of gas turbine engine, named as ATEC (Aerodynamic Turbine Engine
Code). The engine operation is simulated by solving conservation equations
expressed as one dimensional time dependent Euler equations with additional
turbomachinery source terms. Furthermore, the transients can be simulated by
combining both implicit and explicit equation solvers inside the program that have
the capability of simulating the possible stall in the compressor.

In reference [21], Visser (2014) synthesized the gas turbine performance modelling
and simulation available in literature and explained the development of commercial
software GSP from beginning to the current version of GSP. Starting from gas
turbine performance models, the author introduced the modellings used in GSP and
illustrated the applications of the program. In addition, the author stated that this
study can be used for an insight for further developments in gas turbine performance
modelling.

In reference [22], Janikovič (2010) mentioned that estimation of the life of the engine
parts (required due to calculation of operating costs) has become an essential part in

23
the airline industry due to the growth in competitiveness. The author conducted this
study with the aim of developing the needed tool. He added that high fidelity engine
models are needed to accurately predict the variations of thermodynamic parameters
of engine. Two transient methods, namely rapid transient performance method and
thermodynamic matching method are tested in this study. As a conclusion, due to the
greater stability and robustness of the thermodynamic matching method, this method
is adopted and used in the performance analysis of a gas turbine engine which is
needed for estimation of the operating costs.

1.6 Objectives

It should be noted that very important decisions are made during the preliminary
design phase of a gas turbine engine. Based on the available technology level, the
flow annulus and the bearing arrangement are selected. Hence, most of the necessary
resources are committed on completion of the preliminary design phase [23] and the
commitments in development phase can be seen in Figure 1.15.

Figure 1.15 - Development phase commitments [23]

The pre-development stage determines the success of the project, since there is no
way to return back and change the initial parameters after a certain time. As quick as
possible, a good estimation of what the engine will look like and how heavy it will be
should be determined.

Making a competitive engine requires high thermal efficiency which results in low
specific fuel consumption. The basis of this criterion is strongly dependent on

24
thermodynamic cycle selection [23]. Therefore, cycle studies have a crucial
importance on engine design.

In order to perform cycle studies, a cycle performance estimation program should be

used. In this thesis, a computer software is developed in order to achieve a good
estimation of turboshaft engine performance in different operating points.

1.7 Thesis Outline

In Chapter 2, the design point analysis mode of the developed software is explained
in detail. The turboshaft model used and the numbering of air stations are stated. The
developed air model that is used in all of the modules of the software is mentioned in
detail. Then, on-design calculations are explained with the definitions before going
into details of the parametric design.

In Chapter 3, component performance estimation modules in the software are

investigated and detailed calculations are presented. Compressor, turbine and
combustor parameters can be calculated via references given in this chapter and these
modules lead the designer to set realistic expectations from the main components of
the turboshaft and model the cycle by keeping these expectations in mind.

In Chapter 4, off design performance estimation of the modeled turboshaft is

discussed. Map scaling and beta line techniques are explained in detail to
approximate the off-design behavior of the turbomachinery parts of the engine. After
setting the performance maps for the compressors and turbines, the components of
the turboshaft engine are matched. The matching procedure is explained in this
chapter with using the Newton-Raphson iteration method. Sample results of off-
design estimations are then compared with GasTurb11.

In Chapter 5, simulation of inlet distortion effects is discussed and modelling of this

phenomenon is explained. Modelling results are then validated with the results of
GasTurb11.

In Chapter 6, transient performance estimation methodology is mentioned. After

explaining the model used with built-in algorithm, comparison of the results of the
software with GasTurb11 is presented.

25
In Chapter 7, comparison of literature results with the models that are constructed in
the developed software is presented. Dividing into two parts, off-design and
transient, some of the key parameters are compared with the available data in the
literature and the differences between these parameters are stated in a tabulated form.

In Chapter 8, the summary of what has been done in this thesis, their causes and the
possible improvements about this study are discussed.

26
 CHAPTER 2

2 ON-DESIGN PERFORMANCE ESTIMATION

For the design point calculations, the fundamental equations of references [5], [8],
[9] and [2] are widely used throughout this chapter. This chapter begins with a
turboshaft model and the air station numbering used throughout the chapter and the
thesis are indicated in Figure 2.1.

2.1 Turboshaft Model and Air Stations

The model used as a turboshaft engine is a twin-spool configuration with a free

power turbine and can be seen in Figure 2.1. The operation begins by sucking
ambient air from station 0 to station 1. Through the inlet portion, there are some
losses such as friction losses so that the properties of air may change (station 1 to
station 2). Then the compressor increases the air pressure towards the combustion
chamber (station 2 to station 3). Some bleed air is taken out at the burner exit for
turbine cooling and customer usage. Fuel is then injected into the high pressure air in
the combustion chamber where the combustion process occurs (station 3.1 to station
4). After combustion, some cooling is required to cool down the nozzle vanes with
coolant mixer 1 (station 4 to station 4.1). Then, the high energy flow is converted
into mechanical energy by expanding the flow to a lower pressure in a turbine
(station 4.1 to station 4.4). This drained energy is used to operate the compressor.
Turbine rotor also requires cooling and it is modeled with a coolant mixer 2 (station
4.4 to station 4.5). There is a remaining energy that is obtained when the fuel is more
than required to rotate only the compressor. Since the main purpose of an engine is to
produce more power than the amount required just to rotate the compressor, this is a
must [2]. This remaining energy of the flow is extracted with an additional turbine

27
(station 4.5 to station 5) and its shaft is connected to the location where the
mechanical power is required. At last, the operating gas is thrown out at the station 8.

Figure 2.1 - Model of turboshaft engine with power turbine

Stations and locations can be shown in Table 2.1.

Table 2.1 - Air Stations used in the developed software

Station Location

0 Freestream

1 Inlet or diffuser entry

2 Inlet or Diffuser exit - Compressor inlet

3 Compressor exit

3.1 Burner entry

4 Burner exit - Nozzle vanes entry - Coolant mixer entry

Nozzle vanes exit - Coolant mixer 1 exit - High pressure turbine

4.1
entry

4.4 High Pressure Turbine exit - Coolant Mixer 2 entry

4.5 Coolant mixer 2 exit - Power Turbine inlet

5 Power Turbine Exit

8 Nozzle exit

28
2.2 Air Model

The air model is embedded into software by using formulations of reference [5]. By
definition,

(2.1)

By using temperature (K) and fuel to air ratio, the calculation of the required
parameters of the working fluid can be calculated via formulas (2.1) to (2.10).

The specific enthalpy (kJ/kg), , of the operating gas is calculated by

( ( ) ( ) ( )

( ) ( ) ( ) ( )

( )

( )( ( ) ( ) (2.2)

( ) ( ) ( ) ( )

( ) ))

The temperature dependent portion of entropy (kJ/kgK) , is calculated by

∫ (2.3)

Assuming that reference temperature is equal to 0K, the formula for calculation of
the temperature dependent portion of entropy is reduced to

29
 ( ( ) ( ) ( )

( ) ( ) ( ) ( )

( )( ( ) ( ) (2.4)

( ) ( ) ( ) ( )

( ) ))

The specific heat capacity (kJ/kgK), , of the operating gas is calculated by

( ) (2.5)

The gas constant (kJ/kgK), , of the operating gas is calculated by

(2.6)

where f is the fuel to air ratio.

The specific heat ratio (kJ/kgK), , of the operating gas is calculated by

(2.7)

The reduced pressure, , of the operating gas is calculated by [6]

30
 (2.8)

where kJ/kgK (2.9)

Lastly, the speed of sound (m/s), , of the operating gas is calculated by

√ (2.10)

There are some cases that input T is not available for these formulas. In this case,
Newton-Raphson iteration is performed with an initial guess of the temperature to
find the temperature that matches with the input of enthalpy or reduced pressure.
Newton-Raphson iteration technique will be explained in Appendix A.

In Ref [5], the defined constants for the calculation of the air model are shown in
Table 2.2.

Table 2.2 – Dry air property constants

0.992313 7.097112

0.236688 -3.234725

-1.852148 0.794571

6.083152 -0.081873

-8.893933 0.422178

0.001053

In this thesis, kerosene is used as the fuel and the constants related to this fuel are
shown in Table 2.3.

Table 2.3 - Kerosene property constants

-0.718874 3.081778

8.747481 -0.361112

-15.863157 -0.003919

17.254096 0.0555930

31
 -10.233795 -0.0016079

2.3 On-Design Calculations

After creating the sub-functions for calculating the air properties, design point
calculations can be made.

Input parameters of the design point mode are as follows:

 Altitude
 Deviation from International Standard Atmosphere (ISA) temperature
 Inlet Mach number,
 Power off-take,
 Customer bleed air percentage,
 High pressure turbine (HPT) nozzle guide vane (NGV) cooling air
percentage,
 HPT rotor cooling air percentage,
 Intake pressure ratio,
 Free stream recovery pressure ratio,
 Compressor polytropic efficiency,
 Compressor pressure ratio,
 Burner efficiency,
 Burner pressure percentage loss,
 Lower heating value of fuel,
 HPT inlet total temperature,
 HPT polytropic efficiency,
 Power turbine (PT) polytropic efficiency,
 Exit duct pressure ratio,
 Exhaust pressure ratio,
 Mechanical efficiencies of each shafts in turboshaft model namely offtake,
high pressure (HP) and power turbine spools,
 HP spool speed,
 Power turbine spool speed.

32
The graphical user interface (GUI) of design point calculation inputs can be seen in
Figure 2.2.

Figure 2.2 - Sample input of design point calculations

The link between the temperature and the pressure at the inlet with the altitude is
achieved by the formulas of ISA [24] given by

(2.11)

⁄
(2.12)
)

The ratio of the total stagnation pressures and the total temperatures between the inlet
and the exit of the engine component i are defined as [6]

(2.13)

(2.14)

One additional definition is needed for the design point calculations specifically for
the turboshaft engine, namely the exhaust pressure ratio

33
 (2.15)

It represents the ratio of the total pressure at exhaust to ambient pressure and it is
selected by the designer. Mostly, the value of this parameter is in between 1.02 and
1.04. Therefore, it is an input for the developed software since it changes from
engine to engine.

Besides, mass flows throughout the engine are

̇ ̇ ̇ (2.16)

̇ ̇ (2.17)

̇ ̇ (2.18)

̇ ̇ (2.19)

̇ ̇ (2.20)

where is the customer bleed air percentage, is the high pressure turbine (HPT)
nozzle guide vane (NGV) cooling air percentage and is the HPT rotor cooling air
percentage.

The fuel-to-air ratio and the bleed percentages are defined as

̇
(2.21)
̇

̇
(2.22)
̇

̇
(2.23)
̇

̇
(2.24)
̇

The corrected mass flow at any station is calculated by

34
 √
̇ ̇ (2.25)

where ̇ is the mass flow rate corrected to standard day conditions, is the
standard temperature 298.15K and is the standard pressure 101.325 kPa of a
standard day conditions.

The stagnation pressure ratios of the compressor, high pressure and low pressure
turbines are dependent on the polytropic efficiencies as

(2.26)

(2.27)

(2.28)

respectively. Furthermore, as explained in the introduction part, the isentropic

efficiency of the compressor and the turbine components are linked with their
polytropic efficiencies and the total pressure ratios by using the following formula
[2]

(2.29)

For burner modelling, the following burner energy balance equation is used,

( ) ( ) (2.30)

where ref subscript denotes fuel reference temperature which is assumed to be

298.15 K. There would be one additional term if the fuel reference temperature is
different than the reference temperature.

There are some important points during the construction of the software that should
be kept in mind in order to estimate the design point of a turboshaft engine correctly.

35
 i. HPT pressure ratio can be found by ensuring energy balance between
HPT and compressor as

(2.31)

where POT is the power off-take from high pressure spool, is the power
off-take shaft mechanical efficiency and is the mechanical efficiency of
the spool of the gas generator section of the turboshaft engine.

This formula sets which is needed for the HPT pressure ratio calculation.
After finding this value, and can be obtained. Then, the total
pressure at the inlet of the power turbine is calculated by

(2.32)

ii. PT Pressure ratio can be found as

(2.33)

After gathering the formulas and definitions mentioned before together, the design
mode of the developed software is generated.

A sample output of design point mode is shown in Figure 2.3.

Figure 2.3 - Sample output of design point calculations with the inputs in Figure 2.2

With the same inputs, the commercially available product “GasTurb” results are
shown in Figure 2.4. In this figure, WRstd is the corrected mass flow rate, PWSD is
the shaft power, WF is the fuel flow rate, W is the actual mass flow rate, A8 is the
exit area and Therm Eff is the thermodynamic efficiency of the designed turboshaft.

36
 Figure 2.4 - Output of "GasTurb" software with the inputs in Figure 2.2

When the results are compared, the largest difference is approximately 0.1%, which
is a negligible value.

2.4 Parametric Design

In order to select a design point, comparison of different operating points is

necessary. As mentioned before, the design point of the engine has to be selected
carefully in order not to waste the engine capability by not operating it at its optimum
point. Design phase of the components starts immediately after the selection of the
design point. As soon as it is selected, large changes in the design point will
definitely result in delay in the due date of the engine program and additional costs
due to this delay may put the program at a risk of losing lots of money. Therefore,
lots of points should be examined in order to fit the design point in the most
beneficial way for the user in the operating envelope of the air vehicle. The
restrictions are the contractual values which must be provided by the airframer.

In the developed software, there is a possibility of varying any of the two design
point inputs by determining the initial value, final value and steps of iteration.
Corresponding cycle result in each step will be shown in a carpet plot. The default
output graph is the specific fuel consumption versus the shaft power and the
parameters represented by the axes can be altered by the user of the software. In
addition, it is possible to use the design modes of the rotating components, which
gives the user a much more realistic approach than assuming constant component
37
efficiencies. Sample screenshots of the parametric design mode in the developed
software is presented in the Appendix B.

Sample input parameters of the parametric design calculation are shown in Figure
2.5.

Figure 2.5 - Sample input parameters of parametric design calculation

The related output is shown in Figure 2.6.

Figure 2.6 - Output of parametric design module with given input in Figure 2.5

There are very small differences between the results of the developed software with
“GasTurb” which can be seen in Figure 2.7.

38
Figure 2.7 – Results of parametric study example in the same graph

39
40
 CHAPTER 3

3 COMPONENT DESIGN PERFORMANCE ESTIMATIONS

Component performance estimation is a required feature of a preliminary design tool.

The reason is that the component efficiencies should be estimated properly in order
to start from a suitable cycle. In this chapter, how the component performances are
estimated is explained starting from the compressor. The main outputs of the
developed component performance estimation modules can be seen in Figure 3.1.

Figure 3.1 – Main outputs of the developed component performance estimation modules

41
3.1 Compressor Design Mode

Reference [2] is used for the calculation of the compressor design parameters with
the velocity triangle nomenclature stated in Figure 3.2.

Figure 3.2 - Velocity triangle nomenclature of compressor [3]

3.1.1.1 Inputs

Inputs of the compressor design module are as follows:

i) Total pressure
ii) Total temperature
iii) Tip speed
iv) Radius ratio
v) Mach number

3.1.1.2 Calculation procedure

The static temperature at the inlet of the compressor can be found as

(3.1)

42
where M is the Mach number of the working fluid. Similarly, the static pressure at
the inlet of the compressor is

( ) (3.2)

While the density of air can be calculated by using the equation of state for a perfect
gas,

(3.3)

where is the density of the working fluid. Corresponding inlet area of the
compressor is then:

(3.4)

and the required tip diameter of the inlet of the compressor is

√ (3.5)

where is the tip diameter, is the axial velocity and is the hub to tip ratio.

Resulting rotational speed with these parameters can be found by

(3.6)

where is the impeller speed at the tip.

The main output of this mode, which is the rotational speed of the HP Spool, is
finally found by applying the above calculations via Equations (3.1) to (3.6).
Furthermore, with assuming that there are no inlet guide vanes and the flow enters
axially into the compressor, inlet blade height and relative Mach number at the tip
can be calculated at the inlet of the compressor by using the following equations. The
axial velocity is assumed to be constant everywhere at the inlet. Its value can be
found by:

√ (3.7)

43
Then, the relative velocity at the tip of the inlet of the compressor can be calculated
by

√ (3.8)

where is the relative velocity at the tip. Finally, Mach number at the tip of the
compressor inlet is

(3.9)
√

Resulting rotational speed is used in other calculations in the design module of the
software if this mode is on.

3.2 Compressor Efficiency Calculation Mode

In the developed software, there are two types of efficiency estimation modes, which
are for axial and radial compressors. It is a design choice to construct a turboshaft
engine with axial or radial compressors or combining both. Different methods are
used in the calculation of these types of compressors.

3.2.1 Axial Compressor

Axial compressor efficiency estimation is presented in reference [25]. Additionally,

tip clearance effect is simulated by inputting the percentage change in compressor
efficiency with the clearance at last stage. Default value for this change is given as
2% in reference [9] and it is a user defined value.

3.2.1.1 Inputs

Inputs of this module are the followings:

i) Total to total pressure ratio of compressor

ii) Corrected air flow at inlet of compressor
iii) Number of stages
iv) Loss correction factor : Depending on technology level
v) Mach number at exit of compressor
vi) Compressor exit hub to tip radius ratio
vii) Last stage tip clearance

44
 viii) % Compressor Change for % Clearance

3.2.1.2 Calculation procedure

The unit of the corrected air flow that is used in this module is British units and
denoted by . Pressure ratio of each compressor stage is

(3.10)

where is the pressure ratio of each compressor stage. Polytropic efficiency is

given by

i) for pr 2 (3.11.a)

for pr 2 (3.11.b)

where is the polytropic efficiency which is not modified with respect to size and
tip clearance.

If the tip clearance input is ‘0’, the software does not consider the tip clearance losses
with the additional modification explained above and uses the experimental
correlation in reference [25]. The sizing of the compressor can be taken into account
by using

(3.12.a)
for <10 or >=1.5

for <1.5 (3.12.b)

for >10 (3.12.c)

where is the modification of polytropic efficiency with the effect of size. If the
tip clearance is not equal to zero, then

(3.13)

45
By definition,

(3.14)

(3.15)

where is the polytropic efficiency of the compressor and is the loss

correction factor.

After the polytropic efficiency is found, it is a straightforward procedure to find the

isentropic efficiency of the compressor by using the Equation (2.29). The tip
clearance effect is included by the following formula,

(3.16)

where cer is compressor efficiency decrease rate with clearance, rtc is relative tip
clearance ( the tip clearance divided by the last stage blade height) and is the
isentropic efficiency of the compressor without including the effect of tip clearance.
Validation of this study with the experimental data is available in reference [25].

3.2.2 Centrifugal Compressor

Centrifugal compressor efficiency estimation is from reference [26] and the software
gives an additional output of the expected pressure ratio for the designed centrifugal
compressor from the inputted fundamental geometric parameters. It is the user’s
option to update input pressure ratio or not.

3.2.2.1 Inputs

The inputs required for the calculation of the centrifugal compressor efficiency can
be given as follows:

i) Actual mass flow rate of air at inlet of compressor

ii) Total temperature and pressure at inlet of compressor
iii) Stage number (One or two stages)
iv) Type of diffuser (Vaned or vaneless)
v) Impeller tip radius
vi) Second compressor impeller tip radius (If available)

Air station numbers for only this sub-function is stated at Table 3.1.

46
 Table 3.1 - Air Stations used in centrifugal compressor efficiency estimation

Station Location

0 Compressor Inlet

1 First Centrifugal Compressor Exit

2 Second Centrifugal Compressor Exit (If available)

3.2.2.2 Calculation procedure

The density, volumetric flow rate and the compressor blade exit tip speed with the
assumption of constant tip height is calculated by using

(3.17)

̇
(3.18)

And

(3.19)

respectively. In the above equations, is the volumetric flow rate and N is the
rotational speed of impeller in revolution per minutes.

After calculating the stage flow coefficient by using

(3.20)

the work input coefficient and the head coefficient of stage are calculated by
empirical formulas given in reference [26] as

( ) (3.21)

and

(3.22)

47
Respectively. In the above equations, is the stage flow coefficient, is the work
input coefficient and is the head coefficient of stage. In addition, the subscript VD
denotes vaned diffuser.

For a compressor with vaned diffuser, polytropic efficiency is calculated by

(3.23)

For a compressor with vaneless diffuser, polytropic efficiency is calculated by

(3.24)

whereas subscript VLD denotes the vaneless diffuser.

For vaned diffuser type, the enthalpy rise can be calculated by

(3.25)

Similarly, the enthalpy rise for vaneless diffuser type compressor can be calculated
by

(3.26)

Finally, the estimation of the pressure ratio of the compressor is found by

( ) (3.27)

If available, the same procedure is applied for the second compressor. The inputs of
the second compressor are determined from the results of the first compressor. These
formulations are obtained from a number of experiments carried out as mentioned in
reference [26].

3.3 Turbine Efficiency Calculation Mode

The developed software gives an idea about the velocity triangles in the turbine
stages by assuming symmetrical triangles (Turbine reaction ratio=0.5) and it
estimates the efficiency by using these triangles as in reference [27]. Stage loading,
flow factor, exit angles and exit Mach numbers are also calculated for the detailed
analysis of the turbine section. This provides the designer an estimation of the stage

48
number, which is a very important parameter with regards to cost and weight of the
turbine design. Furthermore, cooling feature is embedded into the code from
reference [28] and this leads user to have an idea about the first rotor mean metal
temperature. It should be noted that this temperature is one of the essential
considerations in gas turbine design since the determination of the cooling air is
completely dependent on this value and the cycle calculations considerably changes
with the amount of cooling air for HP turbine. Velocity triangle nomenclature is the
same as the one in Figure 3.2.

Air station numbers for only section 3 are stated at Table 3.2.

Table 3.2 - Air Stations used in turbine efficiency estimation

Station Location

1 Turbine First Stage Stator Inlet

2 Turbine First Stage Rotor Inlet (Stator Exit)

3 Turbine First Stage Rotor Exit

4 Turbine Last Stage Stator Exit (Rotor Inlet)

5 Turbine Last Stage Rotor Exit

3.3.1 HP Turbine Efficiency Calculations

3.3.1.1 Inputs

In order to estimate the HP turbine efficiency, the following input parameters are
required:

i) Total temperature and pressure at station 41

ii) Required turbine power
iii) Mass flow rate of bleed air
iv) Total temperature of bleed air
v) Rotational speed of high speed spool
vi) Fuel to air ratio
vii) Actual mass flow rate of working gas at station 41
viii) Number of stages
49
 ix) First HPT rotor inlet diameter
x) Last HPT rotor inlet diameter ( For more than one stage of HPT )
xi) Exit radius ratio
xii)
xiii) Loss factor (0.3-0.4)
xiv) First rotor cooling constant

3.3.1.2 Calculation procedure

3.3.1.2.1 Velocity Triangles

First of all, the expected turbine power should be known in order to calculate the
velocity triangles. This can be calculated by

̇ ̇ (3.28)

It should be noted that, HP turbine efficiency estimation is an iterative process.

Initially, the efficiency of the turbine is assumed and the pressure ratio of the turbine
corresponding to that efficiency is found. After calculations, the efficiency is updated
and this process continues up to a point where the difference between the guessed
and calculated efficiencies is less than 0.001. Additionally, the tangential component
of the exit velocity is assumed at first and compared with the calculated value by the
Euler turbine equation. This requires another iterative process and continues until the
velocity difference of 0.01.

Calculating the exit tangential speed of the turbine last stage at mean radius as

(3.29)

The pressure ratio of each stage is

(3.30)

where is the pressure ratio of each stage and n is the number of axial stages in
HPT.

Calculating the exit tangential speed of the turbine first stage at the mean radius as

50
 (3.31)

Updating the reduced pressures at station 3 and 5 of the turbines can be updated as

(3.32)

(3.33)

The properties of the gas at station 3 can now be updated by using the reduced
pressure.

The tip radius of the last stage exit can be found by

(3.34)

So that the hub radius is

(3.35)

The exit area can be found by

(3.36)

The axial velocity at the last rotor of the turbine can be found by continuity equation
as follows,

̇
(3.37)

where is the mass flow rate through HPT.

An iterative process should be carried out by using Equations (3.29) to (3.37) to

evaluate the static temperature of stations until the calculated turbine mass flow rate
value is equal to the input mass flow rate value. With this iteration, static temperature
of station 5 is found.

The absolute velocity at station 5 can be found by

√ (3.38)

The corresponding Mach number and the static temperature can be found with this
obtained velocity by formulas,
51
 (3.39)
√

(3.40)

After finding , the static pressure can be found by

( ) (3.41)

Now, it is possible to find the density of the gas at station 5 as

(3.42)

Finally, the gas flow rate can be found by

̇ (3.43)

Since are known, now it is possible to construct the velocity triangle at

station 5 by using the following relations,

(3.44)

√ (3.45)

(3.46)

(3.47)

where is the absolute flow angle, is the relative flow angle and subscript
denotes the whirl component of the corresponding velocity.

After these calculations, there is sufficient information to calculate to the parameters

at station 4. The calculation of enthalpy at turbine station 4 is done by

(3.48)

52
where is the degree of reaction of turbine to be designed. The gas properties are
then evaluated by using the evaluated enthalpy.

The velocity triangles, may now be calculated as follows,

(3.49)

(3.50)

√ (3.51)

√ (3.52)

where is the ratio of the exit axial velocity to the average axial velocity of the
stage.

Since velocity and air properties are known, it is possible to calculate the Mach
number and the pressure at station 4 as

(3.53)

(3.54)

With the available values, it is possible to construct the velocity triangle at station 3
as

(3.55)

(3.56)

(3.57)

(3.58)

With the assumption of symmetrical velocity triangles, all the necessary parameters
are found in order to be used in the Euler turbine equation for updating the tangential
velocity as iteratively until the difference between its successive values is 0.01.

53
 ̇ ̇

(3.59)

The parameters of station 2 are calculated by the values of station 3 similar to the
calculation of station 4 from the values of station 5.

3.3.1.2.2 Cooling Effects

Cooling effectiveness is calculated by using reference [28] as

̇
(3.60)
̇

where is the cooling effectiveness and is the rotor cooling constant. The
resulting metal temperature is then,

(3.61)

where is the cooling air temperature which is equal to the compressor exit total
temperature. is the HPT First rotor inlet relative total temperature and calculated
by using

(3.62)

The next step is the calculation of the outputs of interest which are the HPT first
rotor inlet relative temperature, the HPT first stage flow factor ( ), the HPT
first stage loading ( ), the HPT exit Mach number ( the HPT exit flow
angle ( , the HPT cooling effectiveness ( and the HPT first rotor blade
metal temperature ( .

3.3.1.2.3 Efficiency Estimation

This efficiency estimation is provided by Ref [27] with the inputs of HPT velocity
triangles. The isentropic efficiency of the stage is

(3.63)

54
where is the isentropic efficiency of the stage, swp is the speed-work
parameter and is a constant to be calculated. The swp is defined as

(3.64)

where the subscript i represents the inlet station of the considered rotor and the
subscript e specifies the exit station of the considered rotor. The constant A can be
calculated as

(3.65)

where K is the loss factor, is Reynolds number at the rotor and and are the
defined constants in order to calculate the turbine efficiency. The constants and
are calculated as

For the rotor

for 0 swp 1 (3.66)

For the stator

i) For single or first stage

for 0 swp 1 (3.67)

ii) For intermediate stages

for 0 swp 0.5 (3.68a)

and
(3.68b)
for 0.5 swp 1

The constant is calculated for both the rotor and the stator as

For Single or First Stages

for 0 swp 0.5 (3.69a)

for 0 swp 0.5 (3.69b)

For Intermediate or Last Stages

55
 for 0 swp
(3.70a)
0.5

for 0.5 swp 1 (3.70b)

Similarly, the constant is calculated for both the rotor and the stator as

for 0 swp 0.5 (3.71a)

for 0.5 swp 1 (3.71b)

The dynamic viscosity (Pa·s) is calculated by using the Sutherland’s relation [5] at
the turbine inlet with the following formula,

(3.72)

where is the dynamic viscosity. Calculating the Reynolds Number at the rotor by

̇
(3.73)

where is the mean radius of the first stage of the interested turbine.

Finally, the total turbine stage isentropic efficiency can be calculated via following
formula,

(3.74)

As mentioned before, this is an iterative process and continues until the efficiency
found gets very close to the guessed value (previous result). The resulting stage flow
factor and the stage loading is plotted in Smith chart [29] to give an insight to the
designer that is whether the designed turbine is feasible and efficient or not for the
designed configuration of the cycle.

Validation of this study with the experimental data is available in reference [27].
Sample turbine efficiency mode output GUI is presented in Appendix B.

56
3.3.2 Power Turbine Efficiency Calculations

All of the calculations are similar to the HP Turbine calculations except that the
pressure ratio of the power turbine is evaluated by using Equation (2.33).

3.4 Combustor Design Mode

The combustor efficiency estimation is from reference [5] and the software gives an
idea about the combustor design parameters such as loading, intensity and residence
time. In addition, with the parameters found in this mode, the software updates the
burner efficiency in the design calculations for better approximation of the cycle
towards reality.

3.4.1.1 Inputs

For the estimation of the combustion efficiency,

1) Actual mass flow rate at station 3.1,

2) Total temperature and total pressure at station 3.1,
3) Combustor mean radius,
4) Combustor height,
5) Combustor length,
6) Combustor average Mach number and
7) Fuel to air ratio are required.

3.4.1.1.1 Combustion Efficiency

3.4.1.2 Calculation Procedure

The radius of the tip and hub of the combustion chamber can be calculated by

(3.75)

and

(3.76)

respectively. Then the volume of the combustor is

(3.77)

57
where is the length of the combustion chamber. The loading, intensity and
residence time for the combustor can be evaluated as

(3.78)
( )

(3.79)
( )

(3.80)

Where L is the loading of the combustor, I is the combustion intensity and is the
residence time. The resulting combustion efficiency can be found by

(3.81)

where is the combustion efficiency. It should be noted that, since and therefore
fuel to air ratio ( f ) changes, combustion calculations are repeated three times. In the
software, these calculations are performed three times for this purpose and the values
are updated accordingly.

58
 CHAPTER 4

4 OFF-DESIGN PERFORMANCE ESTIMATION

After determining the design point of the turboshaft engine, it is important to

estimate and examine how the engine behaves at different operating points within the
aircraft operating envelope. This is a must since the capability of the engine to cope
with the defined missions should be examined by the engine manufacturer while
developing the cycle of the engine in the preliminary design phase. In the actual case,
compressor and turbine maps are not determined at this point of the engine design
phase. In order to estimate the performance, there are some techniques to estimate
the maps of the components which can be used to determine the performance at the
desired operating point. One of these techniques, namely map scaling, is used in this
thesis.

4.1 Map Scaling

In the map scaling method, reference maps are used and scaled for off-design
calculations. The pressure ratio, efficiency and mass flow values of the maps should
be scaled to the design values of the engine to be designed.

The scaling factor used in the pressure ratio is [30]

(4.1)

For mass flow and efficiency, the following scales are used,

̇
̇ ̇ (4.2)
̇

59
 (4.3)

where subscript d denotes the design value of the engine to be designed, md denotes
the design value of the reference maps and m denotes the value of interested point for
scaling at the reference maps.

Reference maps for the components are selected as the ones in reference [9]. As the
compressor reference map, NASA TM 101433 compressor map is used. For the HPT
reference map, high work low aspect ratio turbine of NASA TM83655 is used.
Finally, AGARD two stage turbine map is used for the power turbine.

Furthermore, the reference map for the compressor changes to a different map when
the centrifugal compressor type is selected in the software. For this reason, a two-
stage centrifugal sample engine map is digitized and embedded into the software
from reference [31]. This conversion of maps is necessary because although the same
progress is carried out thermodynamically for both types, each type has different
operating characteristics which lead to very different engine parameters in the off-
design matching. To illustrate the difference, characteristics of both types are as
shown in Figure 4.1.

Figure 4.1 - Performance characteristics of axial and centrifugal compressors [32]

Centrifugal compressor characteristics are flatter than axial flow compressor

characteristics at constant speed in the pressure ratio versus flow graph. Hence, in
centrifugal compressors, the flow can be decreased much more with respect to axial

60
ones without reaching the surge line. Furthermore, the efficiency of an axial
compressor is higher than a centrifugal compressor in an operation within the normal
range of designs [4].

After determining the rotating component maps, it is then required to match these
components. The engine operates at one point for the given fuel input and the
determination of the ‘non-dimensional thermodynamic’ operating point is fully
dependent on these component maps. Constraints that force the engine to operate at
this single point for the given fuel are work and flow compatibility equations. To
illustrate, the flow that passes through the compressor and the turbine is strongly
connected to each other whereas the power required to drive the compressor is
provided by the extracted power from the working fluid at the turbine.

4.2 Beta-Line Technique

Before matching, new maps, formed for the components, are tabulated for the usage
in the developed computer software. To provide a precise reading, “beta-line”
technique is used in which mass flow, efficiency and pressure ratios for the specified
speeds are tabulated with respect to their betas. Beta lines are arbitrary lines which
are placed nearly equally spaced and parallel to surge line in the compressor map.
After this point, created maps are tabulated as three matrices carrying corrected mass
flow, total pressure ratio and isentropic efficiency data to be used in the developed
software [5]. The surge line beta value is equal to 1 whereas the lowest line beta
value is equal to 0. The region in between these two lines are divided into equal
sections (the mostly preferred section number is 20) and named as their respective
beta value that is interpolated linearly between 1 and 0. The map presentation and the
respective tabulation of the data can be seen in Figure 4.2.

61
 Figure 4.2 - Compressor map and beta lines

In turbine maps, linear interpolation between the map points is used. The beta value
is determined by setting the upper most point at that speed equal to 1 whereas the
lower most point beta value is set to zero. Interpolation for the interested point is
done between these three points.

4.3 Component Matching in Off-Design Calculations

The thermodynamic matching type model is used in the software. This is a universal
form of the steady state design models and is commonly referred to as a deck. Once
the maps of the components are fixed by setting the geometrical specifications of the
components, it is possible to represent the performance of the engine at all on and off
design conditions. For a given engine operating condition, the operating point at each
map is also unique for the designed components [5]. In other words, unique maps of
the unique components are matched to each other for a unique operating point of the
engine.

In the component matching, there are four independent variables and four errors that
can arise from mismatching of the rotating components. These variables are the
compressor beta value, the turbine inlet temperature, the high pressure turbine beta
value and the power turbine beta value. Errors that have to be minimized are the high
pressure turbine flow difference (should be equal to the expected flow rate through
62
the compressor), the high pressure turbine work difference (should be equal to the
expected work required to rotate the compressor), the power turbine flow difference
(should be equal to the expected flow rate through HPT) and lastly the exhaust
pressure ratio. A certain total pressure is required to force the exit mass flow with the
exit total temperature through the given exit area while the back pressure is equal to
ambient pressure [9]. Hence, the last error is the difference between the required
pressure ratio and the actual one in the iteration. It should be noted that the power
turbine speed is set as constant in off-design (i.e. in a helicopter application it is a
requisite). As the main input for the off-design calculations, the relative high
pressure spool speed is selected. For the given spool speed, the operating point is
fixed at the compressor map with the input of beta value of the compressor. In
addition, the corrected speed (N/√ ) is fixed for the HP turbine with the knowledge
of the turbine inlet temperature. After setting the beta value of the HP turbine in the
map, the operating point of the HP turbine is fixed as well. With the determination of
this operating condition, the power turbine inlet temperature is fixed which results in
the fixed corrected speed of the power turbine. Lastly, the beta value for the power
turbine is put into the code to fix the power turbine operating point. At this point, the
problem is how to reach a solution. Iterations begin with initial guesses of the four
independent parameters mentioned above and iterations are updated with the
Newton-Raphson iteration method. This method calculates the Jacobians and updates
these parameters accordingly. This process goes on until the square of the sum of the
errors decreases up to

The algorithm for the off-design calculations are presented in Figure 4.3.

63
 Figure 4.3 - Off-design matching algorithm

4.4 Changing Parameters at Off-Design

Some of the design point input parameters should be modified since the engine is
operating in various mass flows in its operating envelope. In order to apply this
necessary modification, pressure losses in the burner and the exit duct are assumed to
be changing proportional to the corrected mass flow rate such as in reference [9]. In
addition, the burner efficiency is also updated with the comparison of the burner
loadings of the design and the interested off-design point is obtained in the same way
as in reference [9].

The burner loading is defined as

(4.4)

Where is the air mass flow in the combustor, is the pressure at the inlet of
the combustor in bars, is the combustor inlet temperature in K and is the
combustor volume in . The burner efficiency can be estimated by the formula
from reference [28],

(4.5)

where and b is the burner part load constant. In the developed

software, the burner part load constant is taken as 1.6 which is the default value Ref
[9].

64
4.5 Operating Lines

Solving numbers of spool speed operation at off-design will result in operating points
for steady state operation in each of the component maps. Linking these points to
each other gives the operating line of the components of the engine.

Some samples of off design operation results of the developed code are shown in
Figure 4.4 to Figure 4.6.

Figure 4.4 – Sample output of operating line in compressor map in the developed code

65
 Figure 4.5 – Sample output of operating line in HP turbine map in the developed code

Figure 4.6 – Sample outputs of operating line in power turbine map in the developed code

In Table 4.1, the sample outputs of the operating lines of the developed software and
GasTurb are compared while resulting power outputs are presented in Table 4.2. It
can be seen that the results are nearly matched with each other.

66
 Table 4.1- Comparison of results of the developed software and GasTurb for given sample inputs
Relative Developed Code Gasturb Absolute % Diff
Speed m PRc Tt4 m PRc Tt4 m PRc Tt4
0.75 1.87 6.05 1190 1.8800 6.07 1187 0.53 0.41 0.23
0.8 2.25 7.46 1217 2.2540 7.46 1214 0.18 0.00 0.22
0.85 2.63 8.99 1270 2.6310 8.99 1272 0.04 0.08 0.16
0.9 2.97 10.45 1333 2.9650 10.44 1331 0.17 0.04 0.16
0.95 3.25 11.74 1387 3.2450 11.72 1384 0.15 0.16 0.27
1 3.50 12.99 1445 3.5000 13.00 1450 0.00 0.08 0.33
1.05 3.66 14.12 1545 3.6630 14.09 1544 0.08 0.23 0.08
MEAN 0.16 0.14 0.21

Table 4.2 - Operating line power output comparison of the developed Software and GasTurb11
Relative Developed Code Gasturb Absolute Difference
Speed POWER (kW) %
0.75 151.2 153.2 1.2
0.8 259.4 259.2 0.1
0.85 395.1 396.0 0.2
0.9 541.6 540.5 0.2
0.95 677.8 673.8 0.5
1 815.6 818.5 0.4
1.05 957.4 955.7 0.2
MEAN 0.4

To sum up, after using the same reference maps with GasTurb, the results of the
developed code are in close agreement with the results of GasTurb, which shows that
the written code is operating correctly and ready to be used in engine on and off
design (steady operation) performance estimations.

4.6 Handling Bleed Effects

The handling bleed effect is introduced into the developed software and can be
switched on in the off-design and transient calculations. It is modeled as the air flow
which is taken from the discharge air at the compressor without affecting the main
flow. Required inputs for scheduling the handling bleed module are:

i) Closed above the corrected speed

ii) Open below the corrected speed
iii) Maximum handling bleed (kg/s)
iv) Minimum handling bleed (kg/s)

The handling bleed is widely used in the gas turbine applications due to its beneficial
effects over the compressor surge phenomenon. Using the handling bleed valves in

67
low speed operation is necessary since it moves the operating line down in the
compressor performance maps. The reason is that the mass flow rate is increased
when the valves are opened and hence the surge margin is increased. To illustrate,
the sample operating lines with and without handling bleeds are shown in Figure 4.7
(the darker operating line is the one that the handling bleed effect is active):

Figure 4.7 - Handling bleed effect on operating line

68
 CHAPTER 5

5 SIMULATION OF INLET DISTORTION EFFECTS

The two main influences of the inlet distortion in gas turbines are on the stability of
the compression system and propulsion system performance due to the compressor
efficiency degradation and the control system action in the engine [33]. The effects
of the control system, in order not to stall the compressor, are widely investigated in
the literature such as in reference [34] . However, since the main interest of the
software is not the control system, the compressor efficiency degradation and the
resulting performance changes in the turboshaft engine are considered in the
software.

Methodology of the inlet distortion part of the software follows mainly reference
[33] and the results then will be compared with the commercially available tool
GasTurb11. It should be noted that, the coupling factor is not considered in this
thesis since the main interest is the turboshaft engine. Because these engines are
small gas turbines, there are no serially connected low and high pressure compressors
in general.

5.1 Methodology

The parallel compressor theory was first proposed by Pearson [35] and it is the
common method in modelling the inlet distortion. The main idea of this theory is that
two different streams in the compressor is assumed to be working at the same time
and matched with each other to have the same exit static pressures. Inlet properties of
the each flow can be modeled by the definitions in reference [36].

The compressor map is divided into parts for the parallel compressor operation and
new maps are required for each section of the compressor. In order to create new

69
maps, same maps with the only difference of corrected mass flows are used for each
section. The design point corrected mass flow rate of the distorted part is calculated
by the user input angle divided by 360 degrees and multiplied with the whole design
point mass flow rate of the compressor. The remaining corrected mass flow is the
design point of clean section of the compressor used. New betas are defined in each
map and the Newton- Raphson iteration is performed with five parameters and five
constraints. The new constraint is that the static pressures at each compressor section
exit must be the same. In the developed software, Mach number of 0.2 is the default
value at the exit of the compressor and the static pressure is calculated by this value
and the total pressure for each section is found via the related compressor maps.

Before all calculations, the aerodynamic interface plane (AIP) should be defined just
before the inlet of the compressor. In order to calculate the properties there, the
compressor design module calculations should be made before.

The static pressure at the inlet of the compressor can be found by the following
formula,

(5.1)
( )

where is the static pressure.

In the compressor design mode calculations, the hub radius, , and the tip radius,
can be found. Using these values, the area at the aerodynamic interface plane, ,
can be calculated by

(5.2)

The compressor inlet area is then calculated by

(5.3)

The velocity at the inlet of the compressor is then

(5.4)

Assuming constant density, the velocity at AIP can be calculated as

70
 (5.5)

5.1.1 Pressure Distortion:

The pressure distortion coefficient is defined to take the inlet distortion into account
and it is an input value from the user to calculate the inlet station properties of the
compressor and it adjusts the magnitude of the pressure distortion.

(5.6)

where is the pressure distortion coefficient. In addition, is the average

pressure and is the pressure at the distorted section.

Using , can be calculated by using Equation (5.6). It is assumed that the

total temperature does not change when the pressure distortion is applied. After
finding the same static pressures for the exit at the same corrected speeds for each
flow rate in the compressor, the average values are set depending on the actual mass
flow rates and then the cycle calculation is performed.

5.1.2 Temperature Distortion:

Similar to the pressure distortion coefficient, the temperature distortion coefficient is

an input that the user can change the intensity of the temperature distortion. By
definition,

(5.7)

where denotes the temperature distortion coefficient.

Additional definition in reference [9] is used in the developed software for the
calculation of the temperature with the input of the temperature distortion coefficient,

( )
(5.8)
( )

where is the circumferential extent of the distortion in degrees.

71
After finding , the corrected speed of the distorted section is updated and
the iterational process goes on until the same static pressures for the compressor exit
is found, as mentioned before. Again, the average values are set depending on the
actual mass flow rates.

5.2 Sample Results and Comparison with GasTurb11

For the temperature and pressure distorted inlet, a sample input and output in the
developed software is presented in Figure 5.1.

Figure 5.1- Inlet distortion output of the developed software

In this figure, –dis affix denotes the distorted section properties whereas –clean affix
denotes the clean section properties. The darkest point in the compressor map
belongs to the distorted section whereas the rightmost dark point shows the operating
point of the clean part of the compressor. Furthermore, the point in between is the
average working point of the compressor. As expected, the pressure ratio is higher in
the distorted section in order to reach the same static pressure at the exit with starting
from a much lower pressure value at the inlet.

A sample output of GasTurb11 for the same inputs is shown in Figure 5.2.

72
 Figure 5.2 - GasTurb11 output with inlet distortion

It is concluded from the results that there is a maximum difference of 0.5 % which is
an acceptable value for the inlet disturbance model. The main concern of this inlet
distortion model is the effect on the performance of the turboshaft. Because of this,
the results of the developed software and GasTurb11 with and without the
disturbance shaft powers and specific fuel consumptions are presented in Table 5.1 in
order to see the degradation of the performance with inlet distortion.

Table 5.1 - Inlet distortion effect on performance

Without Distortion With Distortion

Developed Shaft Power (kW) 879.37 820.13

Software SFC (kg/kWh) 0.3002 0.3040

Shaft Power (kW) 880.7 817.2

GasTurb 11
SFC (kg/kWh) 0.3005 0.3042

It can be seen from the results that, moderate inlet distortion inputs (DT=0.1 and
DC=1 taken in sample) result in nearly 7 percent of loss in the shaft power, which
can be evaluated as a significant loss.

73
74
 CHAPTER 6

6 TRANSIENT PERFORMANCE ESTIMATION

On and off designs of a system can give outputs on state changes. If one needs to
determine how the engine and its outputs react to varying inputs (such as fuel input),
dynamic analysis of the turboshaft engine is required. This means that a modification
is required on the steady state model in order to get the transient model of the engine.
This can be accomplished by taking the polar moment of inertia into account while
establishing the power balance between the compressors and turbines. It is obvious
that more fuel is required during accelerations than that for steady state design point.
For decelerations, less fuel is required in the same sense [9].

In accelerations, there is an additional power on the high speed spool due to the
increased fuel input. In other words, the power output of the HP turbine exceeds the
power that required to drive the compressor, auxiliaries and mechanical losses.
Conversely, the power output of the HP turbine decreases and becomes insufficient
to drive compressor, auxiliaries and mechanical losses due to the decreased fuel flow
rate in decelerations. To take these effects into account, unbalanced power, , is
introduced to the work compatibility equation of the compressor and the gas
generator turbine in order to demonstrate the effect of transients as in the following
formula,

̇ ̇ (6.1)

It should be noted that the unbalanced power is negative in deceleration type

transients. Newton-Raphson Method is used to guess the unbalanced power (UP) in
the HP spool. In addition to the off-design matching, the desired fuel flow (WF) is
matched with the addition of the guessed unbalanced power in the gas generator
spool (similar to the effect of power offtake) at the initial spool speed. The iteration
75
is completed when the two fuel values are matched and the unbalanced power
(results in acceleration or deceleration) is found. After this matching, calculations in
the current time step are carried out and the code moves on to the next time step. It
should be noted that the fuel pump is modeled with a response with first order time
lag.

The spool acceleration is calculated as

(6.2)

then the new spool speed is obtained by Euler integration as

(6.3)

where is the spool speed in rpm, is the polar moment of inertia of the HP spool in
, is the HP spool acceleration rate in rpm/s and is the time step.

The algorithm that explains the transient process in the developed code is given in
Figure 6.1.

Figure 6.1 - Transient matching algorithm

The iteration process continues until the magnitude of the unbalanced power
decreases to 0.01. After that, the new steady state operating point is reached with the

76
desired fuel value and the operation path of the transient performance estimation is
plotted in the component maps. In addition, the following plots are obtained from the
developed code:

i) Burner exit temperature versus time elapsed

ii) Turbine rotor inlet temperature versus time elapsed
iii) Power turbine inlet temperature versus time elapsed
iv) Gas generator spool speed versus time elapsed
v) Unbalanced power versus time elapsed
vi) Fuel flow rate versus time elapsed

The sample output is shown in Figure 6.2 and Figure 6.3.

Figure 6.2 - Sample output of transient performance on component maps

77
 Figure 6.3 - Sample output of transient performance - output figures of Tt4 and Ncorr

There are differences between the results of the developed software and GasTurb 11
which can be seen in Figure 6.4. The difference between the results of these two
softwares is mainly due to the different models used for the fuel pump. It can be seen
in the temperature versus time elapsed graph given in Figure 6.4 that the increase in
the temperature is more rapid in the developed software. This result cannot be
interpreted as incorrect since the modeling of the fuel injection may differ from each
other.

Figure 6.4 - Comparison of Tt4 and GG spool speed of GasTurb11 and the developed software

In the developed software, the formula used in the creation of the first order time lag
model for the fuel pump is
78
 ( ) (6.4)

where is the fuel flow rate at initial state of transient, is the fuel flow rate at
final state of transient, is the fuel pump time constant and is the elapsed time after
initialization of transient.

6.1 Heat Soakage Model

In transient estimations, there are two phenomena that significantly affect the engine
performance, namely the heat soakage and volume packing (dynamics). There are
large heat fluxes between the operating gas and the metal parts of the engine
especially at the inlet of the HP turbine [13] . This results in a considerable variation
in the engine performance and the operating gas temperature. The latter effect,
volume packing, can be seen in the transient operation of the engine. The reason is
that the mass flow at the inlet of a volume (such as a duct) is not equal to that of the
exit of that volume during transient operation as the pressure and temperature (hence
density) changes with respect to time. However, in order to introduce these effects,
detailed geometrical and metallurgical data of the engine of interest or some
empirical relationships that fits well to transient behavior of a specific engine are
required. According to reference [5], Reynolds and Prandtl numbers dominantly
affect the heat transfer coefficients and these coefficients are difficult to evaluate
accurately. Hence, empirical correlation factors can be applied to match the model
with the engine test data. Since the main interest of this thesis is generating a tool for
a generic turboshaft engine, a basic heat soakage model is implemented in the code
and the volume dynamics effects are not considered.

The heat transfer between the metal and the gas can be found by the following
formula,

(6.5)

where is the heat transfer coefficient between the operating gas and the metal
part, is the area of where the heat transfer occurs, is the operating gas
temperature and is the temperature of the metal part of the engine in between
engine air stations 4 and 4.1.

In the developed software, this effect is modeled with the inputs of:
79
  Heat Transfer Constant
 Heat Soakage Time Constant

The maximum heat transfer between the gas and the metal is found by the following
formula,

(6.6)

where is used for the approximation of hA of the engine stations 4 and 4.1
and is the difference between the maximum gas temperature at the initial time
and the steady-state gas temperature. The mentioned maximum gas temperature
corresponds to the temperature that could be reached if the effects of the fuel pump
and the heat soakage models are not included. Then approximation of the heat
transfer is calculated by the following 1st order time lag formula,

(6.7)

where t is the time elapsed after initiation of the transient performance and is
the heat soakage time constant which is an input from the user. Sample results with a
heat soakage model can be seen in Section 7.2 in Figure 7.1 to Figure 7.2.

80
 CHAPTER 7

7 COMPARISON OF THE DEVELOPED SOFTWARE RESULTS WITH

THE LITERATURE

In addition to the comparison of the results of the developed software with the
commercial tool GasTurb 11, comparison with the engine data available in the
literature will enhance the reliability of the software. This also shows the progress of
the software and the possible applicable improvements in it. The steady state
performances are expected to well match with experimental data whereas small
variations in the transient performance results may be acceptable due to two main
error sources. The first one is the control system that maintains the power turbine
speed at 100% relative speed. In the developed software, no control model is defined
and it is assumed that the power turbine always operates at a constant relative speed
during the transients. The second one is the absence of the volume dynamics and the
coarse modelling of the heat soakage effect. The developed software is a generic
performance estimation tool and these effects are very much dependent on the
specific data of the engine of interest. The consideration of the application of these
effects is discussed in the future work section.

7.1 Steady – State Performance Comparison

The steady-state performance estimation results of the software are compared with
the available performance data of LHTEC CTS800-4N in FAA Certification in
reference [37]. The engine is modeled with the developed software in the design
mode with the help of some literature data as in reference [31]. In addition, the
compressor map used in the off-design calculations is the digitized version of the
compressor map in the same paper [31] whereas the turbine maps are the default
maps in the software as mentioned in the map scaling section of this thesis. The

81
values of the shaft power and power turbine inlet temperature (PTIT) are presented in
Table 7.1 with the HP Spool Speeds given in reference [37].

Table 7.1 - Comparison of certification data of LHTEC CTS800-4N with model in the developed software
Developed
FAA Difference (%)
Engine Software
N(rpm)
Ratings Power PTIT Power
Power(kW) PTIT(K) PTIT(K)
(kW) (K) (kW)
30 sec OEI 46681 1208 1251 1197 1249 0.89 0.18
2 min OEI 45556 1108 1201 1104 1206 0.38 0.40
COEI 44576 1014 1158 1008 1163 0.64 0.45
Takeoff 44576 1014 1178 1008 1163 0.64 1.26
Max Cont 43983 955 1134 943 1135 1.32 0.07
AVERAGE 0.78 0.47

Average differences of 0.78 % and 0.47 % in the power and power turbine inlet
temperatures respectively, show that the model matches well with the certification
data and the software can be used in the estimation of the on and off design
performance of the CTS800-4N engine.

7.2 Transient Performance Comparison

The transient performance estimation capability of the developed software is

compared with the simulation results of reference [13]. In this reference paper, there
is a comparison of a developed real time model of the T700 engine of General
Electric with the NASA Lewis simulation. The latter simulation is also validated
with the NASA Lewis experimental test engine and referenced in the same paper.
The models mentioned in this paper are embedded with the heat sink and volume
dynamics approximations with the constants developed specifically for the T700
engine. In reference [38], the digitized T700 engine map is available and this map is
used in the transient performance estimation in the developed software. The transient
scenario used in this comparison is that the fuel flow of the engine is increased from
400 lbm to 775 lbm per hour (step increase). Resultant turbine inlet temperatures and
the relative spool speeds are given in Figure 7.1 and Figure 7.2.

82
 3000
2900
2800
2700
2600
Tt41 ( R )

2500
2400
2300
2200
2100
2000
0 1 2 3 4 5
t(s)

Figure 7.1 - HP turbine inlet temperature versus time elapsed

2250

2150

2050

1950

1850
Tt45 ( R )

1750

1650

1550

1450

1350

1250
0 1 2 3 4 5
t(s)

Figure 7.2 - Power turbine inlet temperature versus time elapsed

83
There are some deviations mainly due to the different heat soakage and volume
dynamics approaches in between the simulation models. The constructed models are
developed in 100% corrected speed at the developed software, and then gas generator
speed values are reduced to nearly 90% of the corrected speed in the off-design
calculation module. In this kind of preliminary design calculations, the important
examination of the transient applications are the initial and final points of the
transient scenario. In other words, if the initial and final parameters (steady-state
values with considering the elapsed time after initiation of the transient) of the
transient scenario match well with real application results, this software can be
categorized as sufficient for preliminary design transient estimations. The difference
at the initial part of the transients is caused by the differences in the approximations
of the off-design performances of the engine. However, it is seen that there are not
any huge differences in these parts in between simulation models. In the two figures
above, there are differences in temperature values at some portions of the transients.
However, as mentioned before, these variations are due to the different modeling of
the heat soakage and volume dynamics in between the models and are not considered
in the cycle design phase of the turboshaft engine.

However, as expected, similar trends in transient performances can be seen in Figure

7.1 and Figure7.2. In addition, properties at steady state performances (i.e. at t = 0 s
and t = 5 s) nearly match with each other, which implies that the developed model
matches well with the engine. Furthermore, the effect of the heat transfer to the
engine walls can be seen in the models In the developed model without heat soakage
effect, the temperature values are a bit higher at the first part of the transient. After
consideration of this effect and the implementation of the model of the heat soakage,
the results match more with the available data in the literature as seen in the same
figures.

84
 CHAPTER 8

8 CONCLUSIONS AND FUTURE WORK

8.1 Conclusion

The purpose of this thesis is to develop a computer software to carry out on and off-
design performance predictions of a turboshaft engine along with the dynamic
analysis. With these abilities of the developed software, the cycle of the engine can
be designed in an optimum way to accomplish the previously defined missions for
the aircraft.

The design point (on-design) engine performance analysis starts with the design
choices. The importance of the preliminary design is usually high because when the
calculations proceed further, it may be hard to revive those initial steps in the design
of an engine. Therefore, the design point calculations are needed to be carried out
carefully and lots of different designs should be compared with each other to find the
optimum cycle design of a turboshaft engine. With this aim, firstly the design point
and the parametric study modes of the software are developed in order to compare
the design points which satisfy the requirements of the engine and select the
optimum one. Inside these modes, there are options for efficiency estimations for the
components of the turboshaft. These options result in better approximations of real
cycles in different pressure ratios, rotational speeds etc. In order to check the
accuracy of the developed tool, the results of the software are compared with the
results of the commercial product Gasturb11 for the same conditions and inputs. The
deviations in results are only 0.1-0.2%, indicating a high accuracy has been obtained.

The software should also carry on the off-design analysis in order to find out whether
the designed engine is capable of overcoming every mission in its defined mission
profiles or not. The reference compressor and turbine maps have been used in the
85
off-design performance calculations with the technique of map scaling. Iterations for
the component matching are carried out by the Newton-Raphson parameter updating
method. The operating line of the engine can be investigated in this mode. In
addition, the handling bleed and the inlet distortion effect can be simulated in the off-
design mode. These effects are important in application because operating lines
differ from each other significantly if these effects are taken into consideration and it
should be noted that these effects may result in varying the fundamental parameters
of the engine design during the preliminary studies. In addition to the comparison of
the results with Gasturb11, the LHTEC CTS800-4N is modeled in the developed
software and the off-design results are compared with its certification data. It is seen
that the results match well and off-design model is validated satisfactorily.

In the transient model of the turboshaft engine, the fuel pump is modeled with a
delay and the heat soakage effect is introduced whereas the power turbine speed is
kept constant. With the knowledge of how much additional fuel is exerted and the
value of the inertia of the gas generator spool, corresponding behavior of the
designed engine can be seen in component maps as an output. In addition, change in
some important parameters of the designed engine with time can be seen in the main
screen of the transient mode of the developed software. The results are compared
with the commercially available tool Gasturb11 and presented in the related chapter.
Furthermore, the GE T700 turboshaft model is developed in the software and a
sample transient scenario is applied. The results are then compared with the available
literature data and it is proved that acceptable levels of accuracy are reached.

To conclude, a computer software that can model the turboshaft engine with features
of design, off-design and transient performance estimation is developed for the use of
performance engineers. The reliability of the developed software is also validated
with comparison to the available literature data and the available commercial
software Gasturb 11.

8.2 Future Work

Although the developed software has reached to an agreement with the available
engine data, there are some points to be improved.

86
Firstly, the iteration time may be shortened by improving the Newton – Raphson
iteration scheme with the Broyden update model. Since there are small differences in
the off-design simulation times, shorter time targets can be reached especially in
transient matching.

Secondly, the control algorithm for the power turbine may be embedded into the
code. By changing gas generator speeds of the designed turboshaft engine, in real
applications, the engine control responses to keep the power turbine speed constant.
However, after the initial application of the fuel, there will be fluctuations in the
power turbine speed, which is not the case in the model in the software developed.

Another possible improvement is that the mean line analysis may be introduced to
the software for a more detailed design of the turboshaft engine. The compressor and
turbine 1D mean-line codes will be useful for the determination of the main gas path
and the estimation of the pressure ratios in addition to the efficiency levels. However,
it is seen in the literature that, instead of using these codes, fundamental efficiency
estimation modes as in the developed software may be sufficient for the estimation of
the cycle design performance.

Lastly, there may be an additional mode for the detailed modeling of the heat
soakage and volume dynamics effects which can be used to update the resulting
behavior of the engine in transients as in reference [13]. This can be done by
introducing the detailed inputs required for the detailed simulation of the engine
transients.

87
88
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Two-Stage Centrifugal Compressor," Journal of Turbomachinery, ASME, 1995.

[32] R. H. Aungier, Axial-Flow Compressors - A Strategy for Aerodynamic Design

and Analysis, New York : ASME Press, 2003.

[33] J. Kurzke, "Effects of Inlet Flow Distortion on the Performance of Aircraft Gas
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 Distorted Inflow Conditions in: Engine Response to Distorted Inflow
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Royal Aeronautical Society, vol. 63, pp. 415-416, 1959.

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CERTIFICATE DATA SHEET," 2012.

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 APPENDIX A

NEWTON-RAPHSON ITERATION METHOD

One of the most widely used root finding methods is the Newton-Raphson iteration
method.

Figure A.1 – Newton-Raphson method

This method is derived from the geometrical interpretation of Figure A.1. The slope
at can be found by

(A.1)

After rearranging,

(A.2)

This formula is called the Newton-Raphson formula [39]. In words, this method uses
the tangent of the equation at the first point to find the root of the interested equation.
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After numbers of iterations, the root can be found as long as the second derivative of
the equation at any iteration point is not equal to zero.

In the developed software, since there are many equations linked together, taking the
derivative of the equation is not a feasible way to reach a solution. Rather than this,
step increases are applied to variables separately and the differences in errors are
examined. To illustrate:

At first, assume the beta value of the compressor is equal to 0.5 and the
corresponding four errors are 0.2, 0.1, 0.3 and 0.05. It is assumed that the beta value
of the compressor is increased to 0.52 and the corresponding errors changes to 0.25,
0.15, 0.25, and 0.03. The new beta value of the compressor is found by the procedure
explained below.

At first, Jacobians should be found,

(A.3)

(A.4)

(A.5)

(A.6)

The next step is to find how much change is required for beta by (assuming zero
errors in other error parameters for only this example)

(A.7)

where A is the matrix of derivatives and the B matrix contains the error values. The
X matrix gives how much change in the examined variable is needed.

Different than this sample procedure, all variables affect the errors so that this
procedure should be applied simultaneously for all variables by constructing the
matrices and all of the variables updated accordingly in one calculation step of the
off-design iterations.

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 APPENDIX B

SCREENSHOTS OF THE DEVELOPED SOFTWARE

Figure B. 1 - TEImep home page

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Figure B. 2 - TEImep turbine module

Figure B. 3 - TEImep parametric study

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Figure B. 4 - TEImep operating line sample result

Figure B. 5 - TEImep transient sample screenshot

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Figure B. 6 - Transient sample map result

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