Non-conventional Methods of Gas Turbine Engine ...

EDITORIAL BONAVENTURIANA

Non-conventional Methods of Gas Turbine Engine Efficiency Improvement Max

Min Max

Min Rafael Mauricio Cerpa Bernal Ph.D. • COLECCIÓN FACULTAD DE INGENIERÍA •

12

Rafael Mauricio Cerpa Bernal Ph.D. Profesor Titular Director grupo de investigación AeroTech


Bogotá, 2016

"A mi papá Rafael en el cielo".

Cerpa Bernal, Rafael Mauricio Non-conventional methods of gas turbine engine efficiency improvement / Rafael Mauricio Cerpa Bernal. – Bogotá : Editorial Bonaventuriana, 2016. 130 p. : il. col., tablas. -- (Colección facultad de ingeniería ; 12) Incluye referencias bibliográficas. ISBN: 978-958-8928-14-2 1. Turbinas de gas -- 2. Motores de reacción – 3. Termodinámica CDD. 621.433


Non-conventional Methods of Gas Turbine Engine Efficiency Improvement Colección Facultad de Ingeniería • Número 12 Universidad de San Buenaventura Colombia © Editorial Bonaventuriana, 2016 Universidad de San Buenaventura Carrera 9 N.º 123-76, oficinas 602-603 PBX: 57 (1) 629 5955 www.usb.edu.co Bogotá - Colombia Rector: Fray José Wilson Téllez Casas, o.f.m. Coordinador editorial: Anatael Garay Álvares Jefe Unidad de Publicaciones: Luis Alfredo Téllez Casas Diseño y diagramación: Luis Orlando Ferrucho Bran Aviso Legal El autor es responsable del contenido de la presente obra. Prohibida la reproducción total o parcial de este libro por cualquier medio, sin permiso escrito de la Editorial Bonaventuriana. Derechos reservados de la Universidad de San Buenaventura isbn: 978-958-8928-14-2

Tiraje: 120 ejemplares Depósito legal: se da cumplimiento a lo estipulado en la Ley 44 de 1993, Decreto 460 de 1995 y Decreto 358 de 2000. Impreso en Colombia - Printed in Colombia.

INTRODUCTION......................................................................................................................... 9 CHAPTER 1. PRINCIPLES OF GAS TURBINE ENGINES OPERATION AND IMPROVEMENTS....13 1.1

Brayton Cycle.......................................................................................................................................13

1.2

Humphrey Cycle.................................................................................................................................15

1.3

Wave Rotor Cycle Designs And Thermodynamics.........................................................16

1.4

Unsteady Combustion.....................................................................................................................18

1.5

Research Project of Topping Unit..............................................................................................20

CHAPTER 2. THERMODYNAMIC ANALYSIS...............................................................................................25 2.1

Thermal Calculations of the Baseline Engine......................................................................25

2.2

Thermal Calculation of Base Line Engine Enhanced by Wave Rotor...................28

2.3

Thermal Calculations of Base Line Engine Modified with a Constant volume Combustion Chamber.............................................................................32

2.4

Thermal Cycles Results Comparison......................................................................................36

2.5

Initial Combustion Stoichiometric Calculations................................................................38

CHAPTER 3. CALCULATIONS OF A BASE LINE ENGINE ENHANCED WITH WAVE ROTOR.....41 3.1

Base Line Engine Enhanced by Wave Rotor - Flow and Stress Calculations.......41

3.1.1 Wave Rotor Flow Analysis..............................................................................................41

3.1.2 Wave Rotor Structural Analysis...................................................................................57

Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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CHAPTER 4. BASE LINE ENGINE MODIFIED WITH CONSTANT VOLUME COMBUSTION CHAMBER - FLOW CALCULATIONS...................................................63 4.1

Quasi – Steady Calculations.........................................................................................................63

4.1.1 Filling and Purging Stages (phases)............................................................................63

4.1.2 Ignition Stage..........................................................................................................................66

4.1.3 Exhaust Stage.........................................................................................................................73

CHAPTER 5. WAYS TO PRODUCE TORQUE UNDER UNSTEADY FLOW CONDITIONS (HIGH PRESSURE UNSTEADY TURBINE DESIGN SIMULATIONS)........................................................................................81 5.1

Reference Values.................................................................................................................................81

5.2

High Pressure Unsteady Turbine Geometry Design......................................................87

5.2.1 Model 1.....................................................................................................................................90

5.2.2 Model 5.....................................................................................................................................93

5.2.3 Model 6.....................................................................................................................................95

5.2.4 Model 8.....................................................................................................................................97

5.3

Simulation of the Rotating Combustion Chamber Cycle.........................................103

5.3.1 Unsteady Expansion Simulations.............................................................................107

5.3.2 Filling and Scavenging Process...................................................................................111

5.4

Cycle Simulation of the Model................................................................................................113

REFERENCES............................................................................................................................. 129

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Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12

The information presented in the book is the result of the research project “Construction and numerical analysis using CFD of the Wave Rotor applied in a jet engine I, II and III (2011-2013)” sponsored by Universidad de San Buenaventura Bogotá in cooperation with Warsaw University of Technology. The book also includes the results of the Ph.D thesis of the author, developed at Warsaw University of Technology. The main aim of this study is to prove that it is possible to improve the operation of the turbine engine by the use of unconventional methods utilizing unsteady flow properties. The particular aim of this research project is to modify a turbojet engine by application of unconventional wave compression unit to increase the total engine pressure ratio and use of pulse combustion chamber for further increase of pressure ratio. In a typical Brayton cycle, it is possible to observe that the combustion is realized at constant pressure; that in a real cycle, the pressure at the turbine inlet is lower than the pressure of the combustion chamber inlet; reduced by some losses at the combustor. Investigations effort is concentrated on modifications of the normal cycle, and realization of the combustion process at constant volume. Realization of combustion at constant volume can create an increase of the pressure and temperature inside of the combustion chamber.The unsteady nature of the process is the main problem of considered solution. The turbine has to operate in these conditions. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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In the first years of the twenty century, projects of the pressure wave exchangers (PWE) or the wave rotors (WR) were started. The pressure wave exchanger is a machine in which energy is transferred directly from one gas to another. The wave rotor uses unsteady waves to produce steady streams of gas, for which the stagnation pressure can be higher than the input stream stagnation pressure (Piechna, 2005). Wave rotors are the most famous wave devices used to improve the performance of vehicle engines and other propulsion systems. They are typically used as topping (supercharging) units. Wave rotors do not use mechanical components, such as pistons, to compress the fluid. Instead, the pressure rise is obtained by generating compression waves in appropriate geometries. It has been proved that for the same inlet and outlet Mach numbers, the pressure gain in time dependent flow devices can be much greater than in steady flow devices (Pezhman & Muller, Gas Dynamic Design Analysis of Charging Zone for Reverse Flow Pressire Wave Superchargers, 2003). The wave rotor is a non-steady flow device that uses shock waves to pressurize fluids by transferring energy from a high-pressure flow to a low-pressure flow. The wave rotor consists of many axial channels arranged around the axis of a cylindrical drum, usually driven by an external motor. Chambers (channels) are periodically connected through ports located on the steady casing with containers including gas at different pressure. For gas turbine engine applications, the wave rotor employs the hot, high pressure exhaust gas from combustion chamber to generate a shock wave that compresses the cooler, lower pressure air received from the compressor (Pezhman, Nalim, & Muller, A Review of Wave Rotor Technology and its Applications, 2006). The wave combustor is a device similar to a wave rotor and the combustion occurs inside the rotor channels. This combustion is realized in a constant volume and produces a pressure rise during combustion, unlike a typical combustion chamber used in gas turbine engines. A wave rotor acting as a pressure exchanger can be used (together with a conventional combustor) as a topping unit to enhance the performance of a gas 10


turbine engine. Fundamental thermodynamics and detailed simulations indicate a possible substantial pressure gain between the compressor and the turbine. Wave rotor devices for gas turbine applications have been studied extensively to improve engine efficiency, including research test-rigs and numerical simulation. Alternatively, pressure gain could be obtained using an internal-combustion wave rotor (ICWR or PDE). In ICWR case, combustion occurs sequentially within the wave channels. Each channel is being periodically charged and discharged as it rotates past properly-sized and timed inlet and outlet ports. By accomplishing combustion in the rotor, the external combustor needed in a pressure-exchanger topping cycle is eliminated. The significant performance advantage is retained, as well as the considerable, but technologically addressable, thermal and sealing challenges. In most designs, premixed air-fuel mixture is selectively introduced into the axially rotating straight chambers through the inlet manifold, but fuel injection from the stator end plate is also possible. A spark igniter or a hot gas injection duct initiates the deflagration or detonation waves. As in other wave rotors without combustion, shock and expansion waves are generated as the channels experience sudden opening and closing at the inlet and outlet ends.The process repeats itself in each cycle, with high-pressure gas being continuously supplied to the turbine(s). It is possible to have more than one gas dynamic cycle per revolution, which improves mechanical load balancing, but may complicate ducting (Nalim & Kerem, 2003).


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5.1.

Brayton Cycle

The Brayton cycle was first proposed by George Brayton for use in the reciprocating oil-burning engine that he developed around 1870.Today, it is used as cycle describing operation of gas turbines where both the compression and expansion processes take place in rotating machinery. Gas turbines usually operate in an open cycle, as shown in Fig. 1. Fresh air at ambient conditions is drawn into the compressor, where its temperature and pressure are raised. The high pressure air proceeds into the combustion chamber, where the fuel is burned at constant pressure.The resulting high-temperature gases then enter the turbine, where they expand to the atmospheric pressure while producing power. The exhaust gases leaving the turbine are thrown out (Cengel & Boles, 2002).

Figure 1. Brayton cycle. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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The pressure – volume and the temperature – entropy diagrams, show the typical turbojet engine operation; where the basic fourth process of operation are showed in the fig. 2 and 3.

Figure 2. Pressure – volume diagram Página 16 – imagen 6

Página 54 – 55 – 56 – Figuras 34 y 35 Figure 3. Temperature – entropy diagram.

The following information explains the behavior of the air and gas inside of the turbojet engine: 1-2 Air enters to the compressor, where the pressure and temperature are raised. (Isentropic compression in a compressor) 2-3 Fuel is mixed with air, and a combustion process is realised (constantpressure heat addition) 14


3-4 Exhaust gases enter to the turbine and an expansion is realised (isentropic expansion in a turbine) 4-1 The exhaust gases leaving the turbine are thrown out (constant-pressure heat rejection)

5.2.

Humphrey Cycle

The Humphrey cycle is a thermodynamic cycle similar to the pulse detonation engine cycle. It may be considered to be a modification of the Brayton cycle in which the constant-pressure heat addition process of the Brayton cycle is replaced by a constant-volume heat addition process (Heiser & Pratt, 2002). Ideal Humphrey cycle consists of 4 processes:

Figure 4. Humphrey cycle.

Figure 5. Humphrey cycle p-v and T-s diagrams. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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The fig. 5 shows the pressure – volume and temperature – entropy diagrams; the following processes are developed inside the turbojet engine: 1. Reversible, adiabatic (isentropic) compression of the incoming air. During this step, the temperature and pressure of the incoming air is increased, by the compressor. 2. Constant-volume heat addition. Heat is added while the gas is kept at constant volume. In most cases, Humphrey cycle engines are considered open cycles, which means that the specific volume (or density) remains constant throughout the heat addition process. Heat is usually added by combustion. 3. Reversible, adiabatic (isentropic) expansion of the gas. During the process incoming gas is expanded by the turbine. 4. Constant-pressure heat rejection. Heat is removed from the working fluid while the fluid remains at constant pressure. In open-cycle engines this process usually represents expulsion of the gas from the engine. The main advantage of a Humphrey cycle is the higher pressure ratio. Disadvantage is related to periodic operation of constant volume combustion chamber.

5.3.

Wave Rotor Cycle Designs And Thermodynamics

Two basic wave rotor cycle designs, termed as four-port through flow (TF) and four-port reverse flow (RF) cycles can be considered. They may provide identical topping and overall performance enhancement, but they differ substantially in their internal processes. The four-port TF wave rotor is often used to top gas turbine engine as illustrated in Fig. 6a. Because its better inherent self-cooling feature, which is essential for the high gas temperatures in gas turbine applications. In the TF configuration, for both driving gas and air, the inlet ports are located on one side of the rotor and the outlet ports are located on the other side of the rotor. Thus, the hot gas and, in particular, the relatively cold air travel through the full length of the rotor, which explains 16


the self-cooling feature. However, detailed fluid flow investigations suggest that approximately 30 to 50 percent of burned gas is recirculated to the combustion chamber in TF configuration (Pezhman & Muller, Gas Dynamic Design Analysis of Charging Zone for Reverse Flow Pressire Wave Super chargers, 2003). Página 16 – imagen 6

Figure 6. Four port through flow (a) Reverse flow wave rotor Página 54 – 55 – 56 – Figuras 34 y 35 (b) (Pezhman & Muller, Gas Dynamic Design Analysis of Charging Zone

for Reverse Flow Pressire Wave Superchargers, 2003).

The internal process can be described as follows. In the wave rotor channels, the hot driving gas leaving the combustion chamber compresses the air coming out of the compressor. After the additional compression of the air in the wave rotor, it is delivered into the combustion chamber. Then the burned gas pre-expanded inside wave rotor is scavenged toward the turbine and the channels are reconnected to the compressor outlet, allowing fresh pre-compressed air to flow into the wave rotor channels. The pre-expanded gas entering the turbine from the wave rotor can have the same temperature as the gas would have in a conventional arrangement without the wave rotor. However, the gas pressure is higher than the compressor exit pressure by the pressure gain obtained in the wave rotor (Pezhman & Muller, Gas Dynamic Design Analysis of Charging Zone for Reverse Flow Pressire Wave Superchargers, 2003). Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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Figure 7. Schematic T-s diagrams for a gas turbine baseline engine and the most common implementation case of a topping wave rotor. (Piechna, Cerpa, Muller, Pezhman, & Marcin, 2010).

The general advantage of using a wave rotor becomes apparent when comparing the thermodynamic cycles of baseline and wave rotor-enhanced engines, in accordance with the state numbering in Fig. 7. It shows schematic T-s diagrams of the baseline engine and the corresponding wave-rotor-topped engine. The wave rotor implementation shown is the one most commonly discussed in the references. It is evident that both gas turbines are operating with the same turbine inlet temperature and compressor pressure ratio while the turbine inlet total pressure of the topped cycle is higher than that of the baseline engine. Since the heat addition is the same for both cycles, the waverotor-topped engine produces more work resulting in a higher cycle efficiency (Piechna, Cerpa, Muller, Pezhman, & Marcin, 2010).

5.4.

Unsteady Combustion

The cycle is envisioned for use as topping cycles in gas turbine engines. The combustion occurs sequentially within the wave channels, each channel being periodically charged and discharged as it rotates past properly sized inlet and outlet ports. By accomplishing combustion in the rotor, the external combustor normally needed in a wave rotor topping cycle is eliminated along with the associated ducting, some of which may be exposed to very high temperatures. 18


Figure 8. Temperature – entropy diagram (Pezhman & Muller, Gas Dynamic Design Analysis of Charging Zone for Reverse Flow Pressire Wave Superchargers, 2003).

This concept is related to the earliest working gas turbines, which had valved, pulsating combustion chambers and no compressor, relying entirely on the pressure produced by confined combustion to drive the turbine. The notion of a wave rotor with internal combustion first appeared in the 1950’s, and interest resumed in the 1990’s. Contemporary studies of pulsed detonation engines are of related interest (Nalim & Kerem, 2003). Different types of constant volume combustion chambers models applied in turbojet engines have been developed. Some examples are pulse detonation chambers, wave disc engine (radial flow), and internal combustion wave rotor (ICWR - axial flow). Recently, there has been significant progress in the development of pulsed detonation engines (PDE) for direct thrust application, and they have also been considered for gas turbine enhancement. More so than other pulsed combustors with a single-chamber, the PDE delivers a highly unsteady flow to the turbine. Although multi-chamber PDE designs have been developed for thrust applications, there remains significant unsteadiness in velocity, pressure, and temperature of the outflow that may be unacceptable for utilization in a turbine (Nalim & Kerem, 2003). Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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5.5.

Research Project of Topping Unit

A turbojet engine was designed at Universidad de San Buenaventura Bogotá: by Green Energy GIMOC (AeroTech) research group. It was led by Pachón Diego; Mondragon Cesar, Escobar Arnold and Cerpa Rafael. The main idea was to create a turbojet engine in modular structure. First configuration includes also a heat exchanger (Fig. 9), but it is possible to disassemble it and get a typical turbojet engine; it is feasible make a new assembly that includes a wave topping unit. (Fig. 20)

Figure 9. Engine stations (Escobar, Cerpa, Pachón, & Mondragón, 2012).

The Fig. 9 shows the engine stations: 1. Compressor inlet 2. Compressor outlet 3. Turbine inlet 4. Turbine outlet 5. Combustor inlet 6. Heat Exchanger outlet hot fluid 1 – 2 The pressure and temperature of the incoming air is increased by a centrifugal compressor. 20


2 – 5 The air temperature is increased by a heat exchanger. 5 – 3 Fuel is mixed with the air and a combustion process is produced (Constant pressure) 3 – 4 Exhaust gases are expanded in the turbine 4 – 6 Exhaust gases from the turbine go through the pipes in the heat exchanger. The table 1 gives the main operational parameters of the turbojet engine. Table 1. Technical Data Value

Parameter

Th

289 K

Ambient temperature

Ph

75190 Pa

Ambient pressure

TIT

1073 K

Turbine inlet temperature

Πc

3,25

Pressure ratio

ṁ

0,128Kg/s

Air flow rate

The turbojet engine showed (Fig. 9) will be used as a baseline engine. The research will study the effects caused exchanging the combustion chamber by a wave rotor and wave combustor. So the combustion will be realized at constant volume. This internal combustion wave rotor will have some special characteristic of operation, as will be explained below.

Figure 10. Baseline engine. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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Fig. 10 shows the baseline arrangement of the engine and its temperature – entropy diagram. As is possible to observe, this engine has a typical constant pressure combustor applied in aero engines. The compressor is driven by the turbine; so both of these components have the same rotational speed. However the aim of this investigation is to present some modification in the baseline engine in order to improve the engine thermal efficiency, specific fuel consumption, and the power produced by the turbo machinery.

Figure 11. Baseline engine modified by a wave rotor.

Fig. 11 shows a base line engine modified with a wave rotor used as a topping unit. It is evident that both gas turbines are operating with the same turbine inlet temperature and compressor pressure ratio, while the pressure at the inlet of the turbine using a topped cycle is higher than that the baseline engine. Since the heat addition is the same for both cycles, the wave-rotor-topped engine produces more work resulting in higher cycle efficiency. (Piechna, Cerpa, Muller, Pezhman, & Marcin, 2010)

Figure 12. Baseline engine modified by a constant volume combustion chamber.

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Fig. 12 gives a brief explanation of the baseline engine modified with an internal combustion wave rotor (constant volume combustion chamber). This model will be studied on the research project; then let us make a thorough explanation of the new cycle. The engine consists of a compressor, internal combustion wave rotor, high pressure unsteady turbine, and steady or low pressure turbine. The low pressure turbine drives the compressor; then these both will rotate at the same rotational speed. The wave combustor will be connected with an electrical motor, giving the optimal, relatively very low, rotational speed of operation. Moreover, some part of the flow inside the ICWR will be unsteady; this flow will pass through a special turbine (high pressure unsteady turbine) to increase the power produced by the engine. The high pressure unsteady turbine will produce additional power in comparison with the baseline engine. According to the theory, 30% of the main flow will pass through to the high pressure unsteady turbine; the other 70% of the flow will directly discharge to the low pressure turbine. Also it will receive the stream of gas from the high pressure unsteady turbine outlet. In Fig. 13, a wave diagram for the internal combustion wave rotor is shown.The processes start with air coming from the compressor. The air acts as a piston and forces the exhaust gases to leave the wave combustor to the low pressure turbine. If the turbine port is closed at the correct time, a compression wave will be produced, hereby increasing the pressure of the air from the compressor. After this process, fuel will be injected and the wave channels closed. Then an ignition will be forced by one or various ignition sources, increasing the pressure and temperature inside the channel (constant volume combustion).The flame propagation speed has to be taken into account, because the importance of ensure the totally combustion of the air-fuel mixture. After combustion, an expansion process started. A small exit port is open and creates some expansion waves, the exhaust gases are conduced to the high pressure unsteady turbine in a quasi-steady expansion process. Pressure and temperature inside the combustion chamber is falling down with time of outflow. After lowering the pressure inside the combustion chamber to the level slightly lower than Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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the compressor the exit port will be fully opened; and the exhaust gases will leave the wave combustion to the low pressure turbine and the combustion chamber will be refilled by the fresh air compressed by the compressor.

Figure 13. Wave diagram for the internal combustion wave rotor.

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5.1.

Thermal Calculations of the Baseline Engine

Figure 14. Baseline engine (Piechna & Marcin, Design of micro - turbojet engine intended to be supercharged by wave rotor, 2007).

Input Parameters Table 2. Initial Parameters Baseline Engine Parameter

Value

C

Speed

0

TH

Ambient temperature (Bogotá – Colombia)

289 [K]

Rair

PH

Ambient pressure (Bogotá – Colombia)

75190[Pa]

Air constant

287 [J/kgK]

k

Air specific heat ratio

1,4 This table continues on next page ––>


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Parameter

Value

Gas specific heat ratio

1,33

Lt

Stoichiometric air fuel ratio

15,6

Calorific value

49,82 [MJ/kg]

Tt3


1073 [K]

Compressor pressure ratio

3,25

ηC

Isentropic compressor efficiency

0,76

Combustion efficiency

0,95

ηT

Isentropic turbine efficiency

0,72

Inlet diffuser efficiency

0,99

kg Wu πc t

ξcc

σWL

A thermodynamic and gas dynamics calculations were carrying out. Table 3 gives the engine parameter results. Table 3. Gas dynamics and thermal calculations results baseline engine P1t

Lec P2t

Parameter

Value

Compressor inlet pressure

74438 [Pa]

Compressor work

136,9[kJ/kg]

Compressor outlet pressure

241924 [Pa]

T2t

Compressor outlet temperature

425[K]

α

Excess air coefficient

4,06

P3t

Turbine inlet pressure

232247 [Pa]

Turbine work

141,9[kJ/kg]

T4t

LeT-C

Turbine outlet temperature

951 [K]

πT-C

Turbine expansion ratio

2

P4t

Turbine outlet pressure

116289[Pa]

C5

Outlet velocity

472 [m/s]

P5t

Outlet pressure

75190 [Pa]

T5t

Outlet temperature

856 [K]

Outlet density

0,30 [Kg/m3]

m

Mass flow rate

0,36 [Kg/s]

Kj

Specific thrust

479,3 [N/kgs]

K

Thrust

172 [N]

SFC

Specific Fuel consumption

0,12 [Kg/Nh]

ηth

Thermal efficiency

0,14

ρ5t

Note: (Cerpa, y otros, 2010) (Cerpa, Piechna, Escobar, & Rico, 2011)

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Thermal and gas dynamics calculations of the turbojet baseline engine gives the possibility to plot a pressure – volume (Fig 15) and Temperature – Entropy (Fig 16) diagrams.

Figure 15. Baseline engine P-V diagram (Cerpa, Piechna, Escobar, & Rico, 2011)

Figure 16. Baseline engine T-s diagram (Cerpa, Piechna, Escobar, & Rico, 2011).

Fig. 15 and 16; show the pressure – volume and temperature – entropy diagrams in the baseline engine. At process (1-2) pressure and temperature increase on the compressor; at process (2-3) heat addition on the combustion is realised. Pressure decrease due to the flow losses is observed (2-3) in the pressure – volume diagram, because the efficiency of the combustor chamber was taken into account. At process (3-4; 4-5) pressure and temperature decreases on the turbine and outlet nozzle. It can be observed an irreversible process on T-S diagram (1-2; 3-4-5), because the calculation takes into account the components losses. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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5.2. Thermal Calculation of Base Line Engine Enhanced by Wave Rotor

Figure 17. Baseline engine enhanced by wave rotor (Piechna & Marcin, Design of micro - turbojet engine intended to be supercharged by wave rotor, 2007).

Input Parameters Table 4. Initial parameters base line engine enhanced by wave rotor C TH PH Rair k kg Lt Wu Tt3 πc

η tC ξcc ηT σWL T4F πwr ηT

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Parameter Speed Ambient temperature (Bogotá – Colombia) Ambient pressure (Bogotá – Colombia) Air constant Air specific heat ratio Gas specific heat ratio Stoichiometric air fuel ratio Calorific value Turbine inlet temperature Compressor pressure ratio Isentropic compressor efficiency Combustion efficiency Isentropic turbine efficiency Inlet diffuser efficiency Combustion chamber outlet temperature Wave rotor pressure ratio Wave rotor efficiency

Value 0 289 [K] 75190[Pa] 287 [J/kgK] 1,4 1,33 15,6 49,82 [MJ/kg] 1073 [K] 3,25 0,76 0,95 0,72 0,99 1120 [K] 1,45 0,8


A thermal and gas dynamics calculations were carrying out. Table 5 gives the results of the base line engine enhanced by wave rotor. Table 5. Gas dynamics and thermal calculations results baseline engine enhanced by wave rotor P1t T1t Lec P2t T2t P3f T3f α P4f P5f LeT-C T6f πT-C P6f C7f P7f T7f Ρ7f m Kj K SFC ηth

Parameter Compressor inlet pressure Compressor inlet temperature Compressor work Compressor outlet pressure Compressor outlet temperature Combustion chamber inlet pressure Combustion chamber inlet temperature Excess air coefficient Combustion chamber outlet pressure Turbine inlet pressure Turbine work Turbine outlet temperature Turbine Expansion ratio Outlet turbine pressure Outlet velocity Outlet pressure Outlet temperature Outlet density Mass flow rate Specific thrust Thrust Specific Fuel consumption Thermal efficiency

Value 74438 [Pa] 289 [K] 136,9 [J/Kg] 241924 [Pa] 425 [K] 350789 [Pa] 485,4 [K] 4,1 336758 [Pa] 254020 [Pa] 141,9 [KJ/Kg] 951 [K] 2 125644 [Pa] 519 [m/s] 75190 [Pa] 836 [K] 0,31 [Kg/m3] 0,35 [Kg/s] 527 [N/Kgs] 189 [N] 0,10 [Kg/Nh] 0,17

Note: (Cerpa, Piechna, Escobar, & Rico, 2011).

Table 5 gives the results of the gas dynamics and thermal calculation analysis of the base line engine enhanced by Wave Rotor. It is possible to compare recent results with the results shown on the Table 3. Using a Wave Rotor as a topping unit the specific thrust and thrust was increased by 11%, thermal efficiency increase by 24%; and finally the specific fuel consumption decreases by 11%. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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Figure 18. Baseline engine and base line engine enhanced by wave rotor, p-v diagram (Cerpa, Piechna, Escobar, & Rico, 2011).

Figure19. Baseline engine and base line engine enhanced by wave rotor, T-s diagram (Cerpa, Piechna, Escobar, & Rico, 2011).

P-V and T-s diagrams of the base line engine enhanced by wave rotor are shown in the figures 18 and 19. The process represented in the p-v and T-s diagrams can be described with the following information: 30


1-2

Increase of temperature and pressure in the compressor.

2-2’ Increase of temperature and pressure in the wave rotor (unsteady compression due to shock waves inside the rotor). 2’-3’ Combustion. 3’-4’ Expansion in the wave rotor (unsteady expansion due to expansion waves inside the rotor). 4’-5’ Expansion in the turbine. 5’-5 Expansion in the nozzle. The wave rotor compression work is equal to the wave rotor expansion work. Thus the temperature increase from point 2 to 3 in the baseline engine and from point 2´ to 3´ in the wave-rotor topped engine is the same. This leads to the same heat addition for both engines. However, the specific shaft work of the topped engine is higher than that of the baseline engine due to the pressure gain across the wave rotor (p4´>p3). Therefore, the overall thermal efficiency for the topped engine is higher than that of the baseline engine.The inherent gas dynamic design of the wave rotor compensates for the combustor pressure loss from point 2´ to 3´, so the compressed air leaving the wave rotor is at higher pressure than the hot gas entering the wave rotor at point 3´. (Akbari & Muller, 2003) (Pezhman & Muller, Gas Dynamic Design Analysis of Charging Zone for Reverse Flow Pressire Wave Superchargers, 2003). For the wave rotor implementation described in Fig. 11, the pressure ratio of the compressor is kept unchanged, so the physical compressor of the baseline engine can also be used for the wave-rotor-enhanced engine provided the mass flow is kept approximately the same. The pressure in the combustion chamber of the enhanced engine is increased by the compression ratio of the wave rotor. This may require modifications to the structure of the combustion chamber and to the fuel injection system. The heat addition in the combustor is the same as for the baseline engine, but it takes place after the energy exchange in the wave rotor, hence the heat addition starts at a higher temperature. Thus, the combustion end temperature is even higher than that of the baseline engine, possibly requiring additional thermal enhancement of the combustor structure. The turbine of the topped engine might need to be Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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adapted to efficiently utilize the higher pressure ratio. The turbine inlet temperature, however, is the same as that of the baseline engine (Piechna, Cerpa, Muller, Pezhman, & Marcin, 2010).

5.3.

Thermal Calculations of Base Line Engine Modified with a Constant volume Combustion Chamber

Figure 20. Base line engine modified with a constant volume combustor.

Input Parameters Table 6. Initial parameters engine modified with a constant volume combustion chamber Parameter

Value

m

Mass flow rate

0,359 [Kg/s]

Cp

Specific heat at constant pressure

1005 [J/KgK]

TH

Ambient temperature (Bogotá – Colombia)

289 [K]

PH

Ambient pressure (Bogotá – Colombia)

75190[Pa]

Tt3


1500 [K]

Rair

Air constant

287 [J/KgK]

Cv

Specific heat at constant volume

717[J/KgK]

πc

Pressure Ratio

3,25

k

Air specific heat ratio

1,4

v

Volume

2,49e-4 [m3]

A simple thermal analysis was carried out to obtain the parameters in the engine modified with constant volume combustion chamber. The subscript used in following calculation is according to the figure 20. 32


Table 7. Gas dynamics and thermal calculations results baseline engine modified with a constant volume combustion chamber Parameter

Value

Compressor inlet pressure

74438 [Pa]

T1t

Compressor inlet temperature

289 [K]

Compressor outlet pressure

244367,7 [Pa]

T2t

Compressor outlet temperature

405,3 [K]

High pressure turbine inlet pressure

904292,9[Pa]

P1t P2t P3f

T3f

High pressure turbine inlet temperature

1500 [K]

Low pressure turbine inlet pressure

244367,7 [Pa]

T4f

Low pressure turbine inlet temperature

1032,1[K]

Outlet pressure

75190 [Pa]

T5f

Outlet temperature

737 [K]

Thermal efficiency

0,28

P4f P5f

ηth

Thermal results of the turbojet engine modified with constant volume combustor (Table 7) allow the possibility to prepare a pressure – volume and Temperature – Entropy diagrams

Figure 21. Baseline engine modified with a constant volume combustion chamber p-v diagram.

Fig. 21 shows the P-V diagram of the turbojet modified with the constant volume combustion chamber. As was explained previously one of the purposes Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

33

of the investigation is to change the normal combustion chamber operating at constant pressure (Brayton cycle) using a novel combustion chamber that will operate at constant volume. On the P-V diagram is possible to observe an isentropic compression at the compressor, generating temperature and pressure increase (compression 1-2). The heat will be added at constant volume, increasing the pressure and the temperature inside of the combustor (constant volume combustion 2-3). The first expansion takes place in the high pressure unsteady turbine, (expansion 3-4). A second expansion, where the pressure and temperature decrease is developing in the turbine and nozzle (expansion 4-5). The pressure at the engine outlet achieves the atmospheric pressure. It’s possible to observe the differences between the Brayton cycle (constant pressure combustion), and Humphrey cycle (constant volume combustion), where the cycle working at constant volume has more area in the sketch (Figure 21). It means that the engine modified has more available power. But the new cycle generates an increase in the maximum temperature of operation. Also a special turbine has to be designed to take advantage of the unsteady flow produced in the constant volume combustor. Fig. 21 shows the pressure ratio developed in the combustion. The maximum pressure and the temperature in the combustor will be 3.7 times the pressure and temperature at the compressor outlet.

Figure 22. Baseline engine modified with a constant volume combustion chamber T-s diagram.

34


Fig. 22. Shows the T-s diagram of the turbo engine modified with the constant volume combustion chamber. In the diagram it is possible to observe the isentropic compression and expansion in the compressor and turbine (compression 1-2 and expansion 4-5). As the heat addition is produced at constant volume, the pressure and the temperature will rise (constant volume combustion 2-3), followed by the unsteady and steady expansion in the turbines (expansion 3-4). Figure 22 shows that using constant volume combustion in a turbo engine produce greater power than the values obtained in a typical Brayton cycle (constant pressure combustion). T-s diagram of Brayton cycle has drawn a constant pressure lines (isobars). In the constant pressure combustion cycle the temperature rises through these isobaric lines. Using constant volume combustion it will not happen, due to the increase of pressure and temperature in the heat addition process.

Figure 23. Baseline engine modified with a constant volume combustion chamber p-s diagram.

Fig. 23. Shows the p-s diagram of the turbo engine modified with the constant volume combustion chamber. The process explanation is similar as T-s and p-v diagram, and also shows the advantages of the new cycle. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

35

5.4.

Thermal Cycles Results Comparison

The thermal efficiency is a measure of the performance developed by a machine that uses thermal energy. In other words, it is the ratio between the useful output of a device and the input, in energy terms. For a thermal efficiency, energy to the system is heat and the output is mechanical work, heat, or both. The engine used in the project, is a heat engine, it transform the thermal energy, heat (Qin) into mechanical energy, the energy is in another words work (Wout), also it is possible to obtain some heat (Qout), because some part of the energy is not converted. Some engineering application uses the Qout to heat other adjacent fluids, but in this case the heat will be rejected to the environment. Taking into account the last explanation, and applying the thermodynamic laws is possible to obtain the next equations:

Qin = Wout + Qout h th =

Wout Qin

h th =

Qin � Qout Q = 1 � out Qin Qin

The heat depends of the temperature and the specific heat. Brayton cycle works with specific heat at constant pressure, but as the modified engine works at constant volume then is necessary to use specific heat at constant volume. Taking into account the last equations it is possible to calculate the thermal efficiencies in the proposed engines: Table 8. Thermal efficiency of the engine variants

36

Engine

Thermal Efficiency

Base Line Engine

0.14

Base Line Engine Enhanced by Wave Rotor

0.17

Base Line Engine modified with a constant volume combustion chamber

0.28


Fig.24 shows a comparison of the thermal efficiency between the base line engine, base line engine enhanced by wave rotor, and base line engine modified with a constant volume chamber.The thermal efficiency using constant volume combustion is greater than the thermal efficiency developed by a combustion chamber operating at constant pressure in both cases (base line engine, and base line engine enhanced by wave rotor). It is also possible to realize, that by using a wave rotor, the thermal efficiency of the turbojet engine can be increased. Using a constant volume combustion chamber the thermal efficiency is twice increased in comparison with the base line engine; and using a wave rotor the thermal efficiency increases by 21% in comparison with the base line engine.

Figure 24. Thermal efficiency comparison.

Figure 25. Fuel consumption comparison. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

37

It is possible to contrast in the Figure 25 the fuel consumption in different cycle’s variants. It is noticed that a cycle using a constant volume combustion chamber decreases the fuel consumption by 29% whereas engine enhance with a wave rotor decreases a fuel consumption by 16,61%

Figure 26. Summary of the base line engine modifications advantages.

To evaluate the performance enhancement of the base line engine using wave rotor and constant volume combustor, a thermodynamic approach is used to calculate the theoretic performance expressed by: overall thermal efficiency, specific fuel consumption (SFC) and fuel consumption of wave rotor and constant volume combustor engine. Predicted values are summarized in Fig. 26. A significant performance enhancement of 100% and 21% for thermal efficiency, and a 29 % and 16,6% reduction in the fuel consumption is estimated for the engine enhanced by constant volume combustor and wave rotor.

5.5.

Initial Combustion Stoichiometric Calculations

The fuel that will be supplied to the combustion chamber is propane, then: 38


C 3 H8 + a(O 2 + 3.76N 2 ) ↔ bCO 2 + cH 2 O + dN 2 C 33 H88 + a(O + dN 2 5(O22 ++3.76N 3.76N22))↔ ↔bCO 3CO22 ++cH 4H2 O 2 O + 18,8N 2 C H + 5(O + 3.76N ) ↔ 3CO + 4H O + 18,8N 2 C = 12 C H H 3= 18 C = 12 ((12)(3) + (8)(12)) = 44 Kg fuel H =1 ((12)(3) + (8)(12)) = 44 Kg fuel

3 2 2 2 3 8 8 Mass of the fuel and air are estimated2 as follows

5(O 2 + 3.76N 2 ) O = 16 5(O 2 + 3.76N 2 ) N = 14 O = 16 5((16)(2) + 3.76((14)(2)) = 686,4Kg air N = 14 5((16)(2) + 3.76((14)(2)) = 686,4Kg air 686,4Kg aire Kg air ⎛A⎞ = = 15,6 ⎜ ⎟ 44 Kg fuel Kg Fuel ⎝ F ⎠ stech 686,4Kg aire Kg air ⎛A⎞ = = 15,6 ⎜ ⎟ 44 Kg fuel Kg Fuel ⎝ F ⎠ stech

m air ⋅ i air +η cc ⋅m f ⋅ HCV = m eg ⋅ i eg m eg = m air + m f m air ⋅ i air +η cc ⋅m f ⋅ HCV = m eg ⋅ i eg m eg = m air + m f m air ⋅ i air +η cc ⋅m f ⋅ HCV = (mair + m f ) ⋅ i eg η =1 mccair ⋅ i air +η cc ⋅m f ⋅ HCV = (mair + m f ) ⋅ i eg

Figure 27. Combustion chamber diagram.

η cc = 1m air (ieg − i air ) m = To f getηthe real air – fuel ratio, it is necessary to make an energy balance cc HCV − i eg m (i air eg − i air ) taking m f = into accountJ the Figure 27. Energy balance will depreciate incomplete i eg =imperfect 740870,6 η cc HCVcombustion − i eg and losses. The next calculations were carried out Kg in the engine modified with constant volume combustor, to shows how to J J icalculate eg = 740870,6 the excess i air = 290963,5 Kg air coefficient. The procedure can be repeated in the other variants. Kg J J i air = 290963,5 HCV = 49822000 Kg Non-conventional Methods of KgK Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D. 39 J HCV = 49822000 KgK Kg m air = 0,359

686,4Kg aire Kg air ⎛A⎞ = = 15,6 ⎜ ⎟ 44 Kg fuel Kg Fuel ⎝ F ⎠ stech

m air ⋅ i air +η cc ⋅m f ⋅ HCV = m eg ⋅ i eg m eg = m air + m f m air ⋅ i air +η cc ⋅m f ⋅ HCV = (mair + m f ) ⋅ i eg η cc = 1 mf =

m air (ieg − i air ) η cc HCV − i eg

J Kg J = 290963,5 Kg

i eg = 740870,6 i air

HCV = 49822000

m air = 0,359

mf =

J KgK

Kg s

Kg 0.359(1740 870,6 − 290963,5) = 0.0032 (1⋅ 49822000) − 1740870,6 s

m air 0,359 ⎛A⎞ = = 109 ⎜ ⎟ = 0,0032 ⎝ F ⎠ real m f

⎛A⎞ ⎜ ⎟ 109 ⎝ F ⎠ real α= = = 6,9 15.6 ⎛A⎞ ⎜ ⎟ ⎝ F ⎠ stoich

40


5.1.

Base Line Engine Enhanced by Wave Rotor - Flow and Stress Calculations

3.1.1 Wave Rotor Flow Analysis Understanding the particulars of complex non-steady flows, and reasonable application in the construction of many devices can simplify their schemes, increase durability, reduce costs of production, increase performance and efficiency.The major benefit of the application of unsteady – flow phenomena in flow machines construction is their potential to generate much greater pressure increases than those obtained in steady state flow devices (Piechna,Wave Machines, Models and Numerical Simulation, 2005).

Figure 28. Comparison of compression ratio caused by shock wave (unsteady process - pp ) with isentropic p compression (steady process p ) (Piechna, Wave Machines, Models and Numerical Simulation, 2005). 2

1

0


41

Comparison between the pressure increase generated by shock wave and possible isentropic compression of a gas having the same Mach number is shown in Figure 28. It may be noticed that fluid with the same flow velocity can be compressed much more strongly in a non – steady way than in a steady process (Piechna, Wave Machines, Models and Numerical Simulation, 2005). To understand the simulation results it is necessary to know the physical principles of a pressure wave rotor operation. To explain the idea of pressure wave supercharger. Piechna (Piechna,Wave Machines, Models and Numerical Simulation, 2005) considered a device consisting of a pipe closed on both sides by valves which connected the pipe with vessels containing two different gases of different pressures. The valve located on the left end of the pipe sequentially connects the pipe with the vessel containing of propellant gas of high pressure or with a vessel with low pressure exhausted gases. The valve located on the right side of the pipe connects the pipe with a vessel in which a compressed gas is stored or with a vessel containing a low pressure gas that is to be compressed. Figure 29 shows a wave diagram with the position of all the ports.The compression process starts from an initial state (0) in which the pipe is filled with a gas of low pressure at zero velocity. In this phase of the process both pipe ends are closed. If we connect the left side of the pipe with port A having a gas of higher pressure (HPgas – propellant gas) we generate a pressure wave (a) traveling in the pipe at the local speed of sound. Behind this pressure wave gas has a higher pressure (1) and moves right with velocity some 3-4 times smaller than the speed of the pressure wave. (Piechna,Wave Machines, Models and Numerical Simulation, 2005) On the left side the inflow of the propellant gas into the pipe and motion of the contact surface between the propellant and compressed gas (called the working gas) occur. If the right valve is opened at the moment when the pressure wave reaches it and the compressed gas (working gas) enters the compressed gas vessel, an inflow of the compressed gas into the vessel (state 2 in port C) is observed. This process is accompanied by the reflection of the compression wave (b) and it proceeds until the contact surface approaches the right ends of the pipe. Because we do not want to store the propellant gas, but rather the working gas, it is neces42


sary to close the right valve before the contact surface can cross it. Unfortunately, the compression wave (b) reflected on the right side, which moves left, disturbs flow on the left side. To avoid this effect, the left valve should be closed earlier. However, this causes reflection (c) and after while it creates a disturbance in the flow near the right side valve. Closing the right valve at the right moment stops the gas flow. Now, the pipe is (almost) filled with the high pressure propellant gas. Opening the connection on the left side of the area with low pressure (port B), an expansion wave in the pipe (d) is generated.The waves travel right and we observe the motion of the gas in a leftward direction. In this way the propellant gas is taken out of the pipe. If port D is open at the appropriate moment (when the expansion wave (d) arrives near the right end of the pipe) the low pressure gas inflow appears due to gas inertia ((5) Figure 29 left part). For some time the gas motion to the left is observed and it is accompanied by several reflections (e, f, g, h, i). The gas that is to be compressed (working gas) fills the pipe and the exhausted propellant gas leaves it at the left end. When the pipe is completely filled by the working gas, both valves should be closed and the process can be repeated. The propellant gas always has a high temperature and because of this the left pipe side is called the hot side whereas the right side is cold (Piechna, Wave Machines, Models and Numerical Simulation, 2005).

Figure 29. Wave diagram for basic device configuration and state plane (Piechna, Wave Machines, Models and Numerical Simulation, 2005). Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

43

In each area in the physical plane bounded by the compression (a, b, f, h) or expansion (c, d, e, i) waves, flow parameters (pressure and velocity) exists shown by appropriate points in the state plane (Piechna, Wave Machines, Models and Numerical Simulation, 2005). To star t the computational fluid dynamic simulation of the wave rotor applied in the base line engine, a one dimensional calculation had to be carried out. After tests conducted by Piechna Janusz using software called “Pressure Wave Rotor Simulation Program” the next operational parameters were found: Number of ports located on left side: 2 PORT A Open Time:

5

Close Time:

14

Stag, Pressure:

350000

Stag. Temperature:

1200

Radius: 150 PORT B Open Time:

25

Close Time:

80

Stag, Pressure:

256000

Stag. Temperature:

1073

Radius: 0 Number of ports located on right side:

2

PORT C Open Time: 44

10


Close Time:

18

Stag, Pressure:

350000

Stag. Temperature:

503

Radius: 60 PORT D Open Time:

31

Close Time:

88

Stag, Pressure:

200000

Stag. Temperature:

441

Radius: 0 Cell Length:

90

Time of single Cycle

3600 [microsec]

Rgas 287 Fricx1000 5 Wall temp

400

Total number of cell

50 (double port set)

Rotor radius (mean)

45

Disk thickness

5

Heat Release rate

10000

Axial cell height

10

Number of port sets 2 Number of iterations 100 Using the results given above, a two dimensional model was developed, to be simulated using CFD tools. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

45

Figure 30. Pre – processor generation.

Figure 30 shows the pre – processor generation of the model. Once the specification of the flow problem is known, we can turn our attention to build a computer model. The first part is a geometry and mesh generation. To develop such elements GAMBIT software was used. GAMBIT gives also the option to generate the boundary conditions of the model. As the set of channels has motion in Y direction, it is necessary to use an interface condition between steady and movable parts of the model. Also pressure inlet and pressure outlet conditions were utilized to recreate the flow behaviour coming from the combustor and compressor and the flow leaving channels to the combustor and turbine. 46


Table 9. Boundary conditions specified in FLUENT PORT A (pressure inlet – gas from combustor) Pressure

336758 Pa

Temperature

1120 K

PORT B (pressure outlet – to turbine) Pressure

Depends of the simulation case

Temperature

1073 K

PORT C (pressure outlet – to combustor) Pressure

350789 Pa

Temperature

503 K

PORT D (pressure Inlet – air from compressor) Pressure

241924 Pa

Temperature

441 K

Once the model is meshed and it’s boundary conditions defined, next step to follow is to import the model to FLUENT, check grid consistency and define flow model components and boundary conditions; before to start the calculation. It is expected, that inside the channels of the wave rotor formation and propagation of pressure and shock waves in presence of contact surfaces and heat transfer to the channels walls will be simulated. It is assumed that the flow in the channels is unsteady and fluid is treated as compressible, ideal gas. The following models were applied in the 2D and 3D Simulations of the wave rotor: Compressible Flow Model: Compressibility effects are taken into account when the flow has high velocity or when it suffers large pressure variations. When considering compressible flows, variation of the gas density with pressure has a significant impact on the flow velocity, pressure, and temperature. Compressibility effects had to be considered or omitted on the basis of the Mach number. Let’s remember the following information: Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

47

M 5,0

Hypersonic flow

If the Mach number is higher than 0,3 compressibility effects become to be important; because change of density is higher than 5%. If it exceeds the unit, a supersonic flow can be produced generating a shock wave that can impact the flow pattern significantly. Once can noticed that the compressibility effects enable generation of the shock waves inside the wave rotor channels, and it effects. The flow is treated as unsteady ideal gas flow. In FLUENT a pressure-based solver, time transient and variable density of the air, as ideal gas options, were selected. Also energy equation has to be turned on. The boundary conditions well-posed in a compressible flow at the inlet and outlet are: Pressure_inlet, Mass_flow_inlet and Pressure_outlet. That´s why a pressure inlet and outlet condition were used in the model (Figure 30) Turbulence Model: Conceptual chart showed above gives the main characteristics of the turbulence models. It can be conclude that no single turbulence model is universally accepted as being superior of all classes of problems. Then is advisable take into account the physics of the model, the level of accuracy expected in the simulation, the available computational resources, and the experience of previous wave rotor simulations (Cerpa, Numerical analysis of the untypical effects in a wave topping unit for a small turbojet, 2009) (Piechna, Cerpa, & Muller, Numerical Analysis of untypical effects in a wave topping unit for a small turbojet, 2010) (Piechna, Cerpa, Muller, Pezhman, & Marcin, Numerical Analysis of the wave topping unit for small turbojet, 2010)(Piechna, Cerpa, Muller, Pezhman, & Marcin, Numerical Analysis of the wave topping unit for small turbojet, 2010) (Cerpa, Vargas, Rico, Piñeros, & maldonado, 2013) to select the turbulent model for the simulation. 48


Chart. 1. Turbulent models (ANSYS , 2012).

According with the last information Spallart-Allmaras turbulent model was selected for the simulation process. Sliding Mesh Model: When a time-accurate solution for rotor – stator interaction is desired a proper boundary conditions on the interface between steady and moving grid should be used. The user must use the sliding mesh model to compute the unsteady flow field.The moving mesh model is the most accurate method for simulating flows in moving reference frames, but also the most computationally demanding (ANSYS , 2012). According with the wave rotor theory, the rotor channels move through the ports, and then it is necessary to create a special boundary condition to connect the channels with the ports or valves of the model.Then an interface boundary condition was used in the model. (Figure 30).


49

50


Port A

Port B

Port C

Port D

Port A

Port B

Port C

Port D

Port A

Port B

Port C

Port D

Port A

Port B

Port C

Port D

Port A

Port B

Port C

Port D

Port A

Port B

Port C

Port D

c. Pressure at Port B= 4000Pa

d. Pressure at Port B = 6000Pa

e. Pressure at Port B = 8000Pa f. Pressure at Port B = 10000Pa

g. Pressure at Port B= 14000 Pa

58

Figure 31. Contours of static pressure in the wave rotor (Cerpa, Vargas, Rico, Piñeros, & Maldonado, Construcción y análisis numérico utilizando CFD "FLUENT" de la operación de un rotor de ondas aplicado a un motor a reacción fase II, 2012)

Figure 31. Contours of static pressure in the wave rotor (Cerpa, Vargas, Rico, Piñeros, & Maldonado, Construcción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción fase II, 2012).

b. Pressure at Port B = 2000Pa

b. Pressure at Port B = 2000 Pa c. Pressure at Port B= 4000Pa d. Pressure at Port B = 6000Pa e. Pressure at Port B = 8000Pa f. Pressure at Port B = 10000Pa g. Pressure at Port B= 14000 Pa

Port C

Port D

a. Pressure at Port B = 0 Pa


Port A

Port B


51


Port A

Port B



Port C

Port D

Port A

Port B

Port C

Port D

Port C

Port A

d. Pressure at Port B = 6000Pa

e. Pressure at Port B = 8000Pa

Port A

Port B

Port C

Port D

Port A

Port B

Port C

Port D

f. Pressure at Port B = 10000Pa

g. Pressure at Port B= 14000

f. Pressure at Port B = 10000Pa g. Pressure at Port B= 14000 Pa

Port D

Port B

d. Pressure at Port B = 6000Pa e. Pressure at Port B = 8000Pa

Port C

Port D

Pa

59

Figure 32. Contours of static temperature in the wave rotor (Cerpa, Vargas, Rico, Piñeros, & Maldonado, Construcción y análisis numérico utilizando CFD "FLUENT" de la operación de un rotor de ondas aplicado a un motor a reacción fase II, 2012)

Figure 32. Contours of static temperature in the wave rotor (Cerpa, Vargas, Rico, Piñeros, & Maldonado, Construcción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción fase II, 2012).


Port A

Port B


Port C

Port A


Port D

Port B

Figure 31 gives contours of pressure in the wave rotor. The process begins in the bottom part of the figure, where the channel(s) is closed at both ends and contains low-temperature and low-pressure air. When the inlet gas port is open (port A), the rotor channels are exposed to a high-pressure inlet gas arrived from the combustion chamber.The high-pressure gas starts compressing the low-pressure air in the channel by generating compression waves. These compression waves form a stronger shock wave running through the channel. As the shock wave reaches the right end of the channel (port C), a reflected shock wave is generated, compressing the air further. This reflected compression wave propagates from the right to the left side of the channel. The compressed air leaves the channel by the opening of the high-pressure air outlet port (port C). Before the reflected wave meets the left end of the channel, the inlet gas port closes. By closing port A, an expansion wave originates from the upper inlet edge and propagates from the left to the right. This wave can be seen in the Figure 31 also. To finish the charging process, the doubled-compressed air is stopped by closing port C. At this moment another shock wave is generated at the upper corner of the outlet port traveling through the channels toward the left end wall. This wave brings the channel flow to rest. Opening the air inlet port terminates the high-pressure (charging) operating cycle of the wave rotor. In the low-pressure process (scavenging), the fluid is purged from the rotor channels to the turbine through the exhaust port (port B) employing expansion waves that allow ingestion of a fresh low-pressure air into the rotor channels through air inlet port (port D) (Piechna, Cerpa, Muller, Pezhman, & Marcin, Numerical Analysis of the wave topping unit for small turbojet, 2010). Figure 32 illustrates the temperature distribution in the channels. Typical for the RF wave rotor configuration, the fresh air enters and exits at the same end of the rotor (port C and port D - right side - air side) while the burned gas enters and exits the rotor at the other end (port A and port B - left side – gas side). Gradual mixing at the contact surfaces is visible. It is clearly shown that the hot gas never reaches the other end of the rotor. As a result, the air side of the rotor is relatively cool while the gas side of the rotor is relatively hot. It is important to avoid the entry of residual gas to the burner when the process starts a new loop (Piechna, Cerpa, Muller, 52


Pezhman, & Marcin, Numerical Analysis of the wave topping unit for small turbojet, 2010). The Figure 31 and 32 show the results obtained in the 2D wave rotor simulation; Figures 31 (a, b, c, d, e, f, g) are the results of the pressure distribution obtained in the simulations changing the pressure at the turbine inlet (port B). As was explained above , the shock wave is travelling from the port A to the port C. when the shock wave arrives to port C a reflection is produced and the shock wave will be returned to the port B. The reflection wave will travel to the left part and will disturb the flow in the left side of the rotor. If the port B is opened will create a new expansion wave travelling to the port D and this wave will create some reflections. The main difference between results is that increasing the inlet turbine pressure (port B); the flow disturb created in the left side by the reflection wave will also increase.Then it is possible to conclude that increasing the pressure in the Port B the flow disturbance on the left side will affect the operation and the performance of the wave machine, generating the possibility to keep some residual gas into the rotor channels, and in the new loop this gas will enter into the combustor. The Figures 32 (a, b, c, d, e, f, g) depicted the results of the temperature distribution obtained in the simulations changing the pressure at the turbine inlet (port B). Temperature distribution diagrams determine the maximum effective pressure to be increased on the port B. It is expected that no revers flow will be seen. In the contours of the simulation the cold and hot side of the wave rotor are well defined and is possible to differentiate it. As was explained in the previous pages it is important to ensure that propellant gas must leave the rotor through the port B. Some studies presented in the references indicate that 5% of the compressor exit pressure is the maximum increase of the pressure in the port B to avoid that some revers of the residual gas occur and enter to the combustor. This theory could be tested in the simulations obtained in the Figure 32. According two dimensional simulations it is possible to confirm theory propounded in thermodynamic analysis (Fig. 19) and conclude that the pressure at the turbine inlet can be increased by 5% using an engine enhanced by wave rotor in comparison with baseline engine. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

53

Two dimensional calculations determine the operational pressure at the inlet of the turbine (port B). Taking into account this information, a three dimensional calculations were worked out.

Figure 33. 3D Pre – Processor generation.

Three dimensional geometry, boundary condition and mesh generation were developed using GAMBIT. The boundary conditions are specified in the Figure 33. It is possible to observe the rotor and the fourth ports of the wave rotor (port A - gas from combustor; port B - gas to turbine; port C - air to combustor, port D – air from Compressor). Figure 33 gives an idea of the mesh used in the three dimensional model. Due to the wave rotor geometry, in this case a structural mesh was applied.

a.

54

b. Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12

c. Figure 34. 3D Contours of static pressure in the wave rotor.

Figure 34 presents the simulation results of the wave rotor model in 3D. Figure 34a shows the beginning of the process. Channels are filling through por t A with gas of high pressure and temperature (combustor chamber inlet). A shock wave is generated, travelling from the por t A toward por t C. Shock wave arrives at por t C and it is opened generating a ver y strong reflection of the wave. The compressed air is going into the por t C. As it is possible to obser ve in the Figure 34a the reflection wave is ver y strong and it generates a disturbance of the gas near to the por t A. Figure 34b depicts the phase when por t B is open on the left side of the rotor (turbine inlet) an expansion wave inside the channel is generated.The wave travels to the right side of the channel and is possible to observe the motion of the gas in a leftward direction. In this way the propellant gas is taken out of the channel to the turbine. If por t D (compressor outlet) is open at the appropriate moment, the low pressure gas inflow appears due to gas inertia. Also in the figure 36c is possible to observe several wave reflections generating scavenging process. Combustion gases leave the rotor through por t B. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

55

a.

b.

c. Figure 35. 3D Contours of static temperature in the wave rotor.

Three dimensional temperature distributions are shown in Figures 35 (a, b, c). Figure 35a shows the outer surface of the wave rotor. It has an expected temperature distribution. It is possible to observe the hot and the cold sides of the wave rotor. The gas from the compressor left the rotor through port B (to turbine). Figure 35b shows the high temperature gas leaving the rotor through the port B. Let´s remember the importance to ensure the total gas scavenging process.The inner surface of the wave rotor has a different temperature distribution in comparison to the outer surface. It is possible to observe 56


that the flows begin to detach from the final part of the port B, producing that some quantity of the combustion gas kept inside the rotor. The phenomenon enounced above is generated due to the centrifugal force and Coriolis effect which are produced by the high rotational speed of the wave rotor, increasing the effects generated by the centrifugal force. (Piechna, Cerpa, & Muller, Numerical Analysis of untypical effects in a wave topping unit for a small turbojet, 2010) shows an investigation of untypical effects in a wave topping unit for a small turbojet. The importance of the Coriolis forces is defined by the Rossby number. The Rossby number is the ratio of inertial to Coriolis forces. A small Rossby number signifies a system which is strongly affected by Coriolis forces, and a large Rossby number signifies a system in which inertial forces dominate. It is possible to conclude that due to the high rotational speed of the wave rotor some part of the gas will remains inside the channels of the rotor. It can produce some problems in the combustion process.The process can be shifted or avoided reducing the rotational speed of the wave rotor or increasing the inner radius of the rotor.

3.1.2 Wave Rotor Structural Analysis An investigation of the structural analysis using finite elements methods of a wave rotor applied in a turbojet engine (Girón & Morales, 2010) was carried out by Universidad de San Buenaventura Bogotá and some results are shown below:


57

Figure 36. Structural analysis using finite elements methods of a wave rotor applied in a turbojet engine (Girón & Morales, 2010).

Universidad de San Buenaventura Bogotá, in order to continue developing new technologies applied in turbojet engines sponsored during three years 58


the design and construction of the wave rotor enounced in the investigation. Results obtained in the figure 36 and in the (Girón & Morales, 2010) were helpful in order to define the components material, dimensions, thickness of the channels and other important information to be taken into account in a construction process.


59

Figure 37. Wave rotor construction process (Cerpa, Vargas, Rico, Piñeros, & maldonado, COnstrucción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción Fase III, 2013).

One model of wave rotor was built, and it was the main problem to choose the optimum manufacturing process.Taking into account the wave rotor design characteristics, a casting process was one of the best options. But due to manufacturing cost this option was discarded. Then a block of stainless steel was machined using chucking machine to create the external and internal surface of the ports and rotor. Also an EDM and CNC process was carrying out to generate the holes in the channels and ports. Also a polished of the surface was made. Figure 37 show the manufacturing process. Finally the wave rotor was assembled to the base line engine (Figure 38); and some operational test will be carried out by Green Energy GIMOC (AeroTech) research group. 60


Figure 38. Engine test bench Universidad de San Buenaventura Bogotá (Cerpa, Vargas, Rico, Piñeros & Maldonado, Construcción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción Fase III, 2013).


61

5.1.

Quasi – Steady Calculations

Figure 39. Constant volume combustor operation sketch.

Figure 39 is a sketch of the constant volume combustion chamber operation; during one revolution will take place twice the 5 stages showed in the figure 39. Step Number 1: The channel is filling by the air coming from the compressor, and by the fuel. The exhaust gases from the previous cycle are pushed out. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

63

Step Number 2: The channel is closed on both sides, and a spark will start the ignition. Step Number 3: (compression and Heat Addition) As the channel is closed, the combustion will be at constant volume, then the pressure and temperature increases inside the channel. Step Number 4: The combustion is finished and the temperature and pressure inside the channel have the maximum values. Step Number 5: Exhaust Stage; the channel is open but the outflow is realised through a small area in comparison with the inlet area. It guaranties a quasisteady outflow conditions from the chamber with lowering pressure. The gas flow goes to the high pressure unsteady turbine. Some initial calculations (1D simulation) may be applied to find the correct geometry and operational parameters inside of the constant volume combustion chamber; but some operational requirements and limitations has to be taken into account before to start the calculations. Requirements

64

»»

Rotational Speed

»»

Channel Geometry

»»

Pressure Difference inside the channel (Filling stage).

»»

Maximum Temperature and Pressure inside the channel.

»»

∆t Steady.

»»

∆t Unsteady

»»

Location of each port (compressor; high pressure unsteady turbine; low pressure turbine).

»»

Combustion time

»»

Unsteady time. Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12

Limitations »»

Maximum permissible temperature by the material.

»»

Flame propagation speed.

»»

Angle of each port; or Port localization.

»»

Scavenging time.

»»

Velocity inside the channel

»»

Time of burning.

»»

Reduction in the outlet area (unsteady expansion – exhaust Stage).

One of the most important limitations is the maximum operational temperature; it is restricted by the material. In considered combustion chambers is usually utilized stainless steel with some coatings, increasing resistance to higher temperature and oxidation. Most austenitic steels, with chromium contents of at least 18%, can be used at temperatures up to 870°C. Most martensitic and ferritic steels have lower resistance to oxidation and hence lower useful operating temperatures. An exception to this is the ferritic grade 446 - this has approximately 24% chromium, and can be used to resist scaling at temperatures up to 1100°C (ASM, 2010) Table 10. Maximum service temperatures in dry air, based on scaling resistance Grade

Intermittent (°C)

Continuous (°C)

304

870

925

309

980

1095

310

1035

1150

410

815

705

420

735

620

430

870

815

2111HTR

1150

1150

Note: (ASM, 2010). Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

65

4.1.1 Filling and Purging Stages (phases) The stage starts when the channel is filled by the air coming from the compressor, and by the fuel. Also a purging stage is developed at the same time, because air coming from the compressor pushes the combustion gas to the turbine, like a piston through the channel.

Figure. 40. Filling and scavenging process. Página 67 In Fig. 40 a filling and scavenging process inside the channels of the wave rotor isError: shown; it’s possible to observe that the air from the compressor acts as a An application in Excel and Matlab was developed to calculate the values denoted above,

piston, pushing the hot gases to the turbine; but it is not a simple method; a were inletthe is constant is some delta differential pressures ( p(∆P) inlet − p outlet )to pressure has be studied. createdThe topressure scavenge fluid tobecause turbine. Because of that it wasofnecessary some a main an operational parameter the engine.toInmake any case the calculations mean density,to airhave velocity and idea of the air and gas behaviour inside of the internal combustion wave rotor. scavenging time change according to the value of pressure assumed at the outlet of the channel, results of this study are shown below.

66

Some parametric studies have to be made to have an idea of the process changing some operational parameters. If a pressure differential is created all parameters are modified inside the channels. Corrección: Hay que quitar “and MatLab.” Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12 Página 129 Error: Quitar todas las refercnicas.

The question is, how much time is required to remove the exhaust gases and refill the chamber by the fresh air. This time is dependent on the available pressure difference between the inlet and outlet chamber cross-section. »»

Pressure Inlet → Air coming from the compressor.

� ΔP� Δp = pinlet − p outlet »» Pressure Outlet → Pressure of the Gas at the turbine.

p »» ΔP→ �p = p inlet � p outlet � Density cold Fluid � Density of air coming from the compressor ρ coldfluid = in RT pinlet r coming from the compressor ρ = coldfluid→ Density of air coming from the compressor »» Density cold Fluid RTinlet pinlet (Fig.42) (Fig.42) rom the compressor ρ coldfluid = RTinlet p »» Density hot Fluid → Density gastotothe thecompressor compressor ρ hotfluid = outlet (Fig.40) � Density hot Fluid � Density ofof gas RToutlet p the compressor ρ hotfluid (Fig.40) = outlet (Fig.40) RToutlet p ρ + ρ coldfluid sor ρ hotfluid = outlet»» (Fig.40) Density → density Mean density hotcold gas air. andρ cold= air.hotfluid � outlet MeanMean Density � Mean betweenbetween hot gas and RT mean ρ + ρ coldfluid 2 n hot gas and cold air. ρ mean = hotfluid ρ hotfluid + ρ coldfluid 2 2 �P d cold air. ρ mean = » » Velocity → Flow velocity propagation V = 2ΔP � Velocity 2� Flow velocity propagation V� = ρr 2 ΔP V= m »» Area → Cross section area A = ρ • r ×V m mean � Area � Cross section area »» Side Length → Length A of=the cross ρ mean ⋅ Vsection area (square)

»» Time → Time that will take the air in cross the channel. Scavenging Time. � Side Length Length of the cross section area (square) L ;� where L is the length of the channel t= tion area (square) V L � Time � Time will take air in cross channel. »» Volume →that Volume of thethe channel. Vol = the AChannel ×L Scavenging Time. t = V ; wh uare) L cross the channel. Scavenging Time. t = ; where V L isapplication the length the channel L ofExcel and MatLab was developed to calculate the values annel. ScavengingAnTime. t = in; where V some delta pressures ( p inlet � p outlet ) were studied.The presdenoted above, � Volume � Volume of the channel. Vol = AChannel ⋅ L sure inlet is constant because is an operational parameter of the engine. In l = AChannel ⋅ L any case the mean density, air velocity and scavenging time change according to the value of pressure assumed at the outlet of the channel, results of this L An application Excel and Matlab was developed to calculate the values denoted above, so study are in shown below.

eloped to calculate the values denoted above, some delta pressures (p ) were studied. The pressure inlet constant Non-conventional Methods Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpais Bernal Ph.D. 67because is inlet −ofpGas outlet lculate values inlet denoted d. The the pressure is above, constantsome because is an operational parameter of the engine. In any case the mean density, air velocity and scaveng ssure inlet is constant air because an scavenging case the mean velocityis timedensity, change according toand the value of pressure assumed at the outlet of the channel, results

Mean Density (Kg/m3) Mean Density (Kg/m3)

Mean Density vs. Delta P 1,35 1,34 1,33

Mean Density vs. Delta P

1,32 1,35 1,31 1,34 0

5000

10000 15000 20000 25000 Delta P (Pa)

1,33

1,32 Figure 41. Mean density vs. ΔPressure ( p inlet − p outlet ) 1,31 0 5000 10000 15000 20000 25000 Delta P (Pa)

gure 41 shows the variation of the main density inside the channel dependent on the ΔPressure

nlet pressure – outlet pressure), let’s that( the cold fluid (air coming p inlet � p outlet ).of the Figure 41. Mean remember density vs. ΔPressure Figure 41. Mean density vs. ΔPressure ( pdensity inlet − p outlet )

om the compressor) always be the same; the pressure the hotdepenfluid (gas to turbine Figure 41 showswill the variation of the and mainifdensity inside theofchannel dent on the ΔPressure (inlet pressure – outlet pressure), let’s remember that

decreased the density of theofgas will decrease. Then channel the mean density decreases if the Δ gure 41 shows thedensity variation thealso main inside on the ΔPressure the of the cold fluid (airdensity coming from thethe compressor)dependent always will be

the same; and if the pressure of the hot fluid (gas to turbine) is decreased the ressure is increased. nlet pressure – outlet pressure), let’s remember that the density of the cold fluid (air coming

density of the gas also will decrease. Then the mean density decreases if the Δ Pressure is increased. om the compressor) always will be the same; and if the pressure of the hot fluid (gas to turbine

decreased the density of the gas also will decrease. Then the mean density decreases if the Δ

Velocity vs. Delta P

ressure is increased.

68 gure 42 shows

Velocity (m/s)

Velocity (m/s)

200 150 100 50 200 0 150 0 100

Velocity vs. Delta P 5000

10000 15000 20000 25000 Delta P (Pa)

Figure 5042. Estimated air velocity inside the channel vs. ΔPressure. Figure 42. Estimated air velocity inside the channel vs. ΔPressure 0 Universidad de San Buenaventura, sede Bogotá • Colección de Ingeniería n.º 12 the developed estimated velocity inside the Facultad channel 0 5000 air10000 15000 20000 25000 versus ΔPressure

Delta P (Pa)

essure – outlet pressure); taking into account the equation of the flow velocity Figure 42. Estimated air velocity inside the channel vs. ΔPressure

(inle

2ΔP / ρ .It is

Figure 42 shows the developed estimated air velocity inside the channel versus (inlet pressure – outlet pressure); taking into account the equation velocity inside ΔPressure the channel. The mean density decreases also if the ΔP increases, then an of the flow velocity 2�P / r .It is possible to conclude that any increase in the pressure (ΔP) will also the air velocity inside the channel. ncrease in the ΔP valuedifference will increase theincrease air velocity inside the channel. The mean density decreases also if the ΔP increases, then any increase in the ΔP value will increase the air velocity inside the channel.

Time vs. Delta P 0,01 Tíme (s)

0,008 0,006 0,004 0,002 0

0

5000

10000 15000 20000 25000 Delta P (Pa)

Figure 43. Scavenging time vs. ΔPressure.

Figure 43. Scavenging time vs. ΔPressure

Figure 43 shows the variation of the scavenging time according to some Δ pressure values; as was shown in the Figure 42. If the pressure difference is Figure 43 shows the variation of the scavenging time according to some Δ pressure values; increased the velocity of the air inside the channel also increases, then the time taken by cross thedifference channel willisbe reduced. the velocity of the air insid was shown in the Figure 42.theIf fluid the to pressure increased

he channel alsoThe increases, then the timemade takenwith by the fluid∆P tovalues, cross has theachannel parametric calculations different purpose will to be reduced. choose the scavenging time and the pressure in the channel outlet or (low

The parametricpressure calculations made with different ∆P values, has a purpose to choose th turbine inlet). The next are the parameters selected by the author:

scavenging time and the pressure in the channel outlet or (low pressure turbine inlet). The ne »»

Inlet Pressure: 241924 Pa.

»»

ΔP: 4838,4Pa.

are the parameters»»selected by the author: Outlet Pressure: 237085,5 Pa.

»» Cold Fluid Density: 1,9 kg/m3. nlet Pressure: 241924 Pa.

Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D. Outlet Pressure:Non-conventional 237085,5 Pa.

ΔP: 4838,4Pa.

Cold Fluid Density: 1,9 kg/m3.

69

»»

Hot Fluid Density: 0,76 kg/m3.

»»

Fluid velocity inside the channel: 85,1m/s

»»

Port Area: 0,00315m2.

»»

Channel Length: 0,24 m.

»»

Time: 0,002819 s.

The scavenging and filling process are realised simultaneously in the same time (Figure 40) ; So calculated the time of this process, will be possible to determine the opening and closing time of the ports (air from the compressor, scavenging gas to the turbine). Table 11. Constant volume combustor RPM calculation Angle

Time (s)

RPM

10°

2,819e-3

591

20°

2,819e-3

1182

30°

2,819e-3

1773

40°

2,819e-3

2364

50°

2,819e-3

2955

60°

2,819e-3

3546

70°

2,819e-3

4137

80°

2,819e-3

4728

90°

2,819e-3

5319

In the Figure 39 a phases of constant volume combustion chamber operation were explained. Taking into consideration this information is possible to understand that the filling and scavenging process cannot be realised at rotor rotation angles greater than 90°. It’s why the Table 11 indicates the RPM´s of the constant volume combustion chamber including the filling and scavenging time and the location of the ports (angles) in the coordinate system. The data chosen by the author were selected taking into account the manufacturing process, materials, and operation of the component: 70


Filling process starts at

0°

Filling process finishes at

30°

Time 0,002819 s RPM´s 1773 Parametric analysis allowed finding the timing of the scavenging process. Each pressure difference (∆p = Pressure Inlet – Pressure outlet) has a different speed of propagation of the contact surface of air-gas inside the channel.Taking into account these velocities, a rpm calculations was made (table 11). This calculation is based on some assumptions and takes into account also physical restrictions. For example the angle was varied from 0° - 180°, this angle indicates the rotation of the combustion chamber until the end of scavenging process of the steady flow to the turbine was reached. A correct physical result has to be obtained in an angle below 90°. All this data was taking into account to obtain the operational rotational speed and the first approximation of the constant volume combustor geometry.

4.1.2 Ignition Stage The combustion process is a complex process; and in the first approximation, let us consider just three variant involved in the combustion process, the fuel, the flame propagation speed and the number of ignition sources.

Figure 44. Ignition sources location variants.

Figure 44 shows a sketch of distribution of the number of ignition sources inside the chamber. For reduction of the combustion time, the idea to have in the chamber more than one source, is applied. It’s important to remember that the channel is closed and the combustion will be at constant volume; then if it’s possible to have various spark plugs then the combustion will take less time and the angle required to burn all fuel will decrease. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

71

Some studies made concluded that is important to reduce the time of combustion, to obtain smaller leakage and thermal losses in this process. Then having multiple ignition sources the combustion takes less time and smaller leakages and thermal losses will be produced. In a project realised in a laboratory by Warsaw University of Technology have been tested different kinds of fuel. Taking into consideration that the base line engine operates with propane; some result was extracted of this research project called: Experimental investigation on flame propagation of hydrogen + air, methane + air and propane + air stoichiometric mixtures in a small size constant volume combustor (l=20 cm); by Galvis Felipe. Results of investigation showed the flame propagation speed: 9,6 m/s. A parametric study was conducted to determine the changes in time and in location of the port depending on the number of ignition sources inside the channel. The flame propagation speed combined with the rotational speed selected; was used to make a new calculation, to find the time that will takes the combustion process, and the rotation that will suffers the rotor channels while this process is completed. The results depend of the number of ignition sources that will be used in the model. It’s possible to observe the results in the figure 45. Increasing the number of ignition sources, the time to complete the combustion inside of the channel will be lower. RPM vs. Combus>on Angle 900

1 Igni1on Source

Combus>on Angle°

800 700

2 Igni1on Sources

600 3 Igni1on Sources

500 400

4 Igni1on Sources

300 200

6 Igni1on Sources

100 0

0

2000

4000 RPM

6000

8 Igni1on Sources Technical Limita1on Angle

45. RPM vs. angle required to burn fuel(necessary (necessary to limit to reasonable Figure 45. RPM Figure vs. angle required to burn thethe fuel to solution limit solution torange) reasonable range).

72

4.1.3 Exhaust Stage


The next step is to find the gas behaviour inside the channels in the expansion process. The exhaust stage starts with the channel closed including gas of high pressure and temperature. Then the channel outlet is partially open and an expansion process is carried out. Depending on

4.1.3 Exhaust Stage The next step is to find the gas behaviour inside the channels in the expansion process. The exhaust stage starts with the channel closed including gas of high pressure and temperature. Then the channel outlet is partially open and an expansion process is carried out. Depending on the pressure values two phases of the outflow are expected. Initially at high pressure ratio a chocked flow exists limited by the Mach number 1 on the outlet cross-section. Later subsonic outflow is expected. The expansion process finishes, when the pressure in combustion channel reaches slightly higher value than the air pressure from the compressor (Figure 40). Generated expansion wave by opening the outlet port reduces the pressure inside channel and enable the filling process. Then a filling and purging process starts (paragraph 4.1.1). While the scavenging could notisbecarried performed; the port that connects the channels the low turbine is process out, then the flow velocity, Mach number in thewith outlet sidepressure of the channel and the mass flow decreases but it cannot achieve values close closed andbe theperformed; process concludes. could not then the port that connects the channels with the low pressure turbine is to zero because a scavenging process could not be performed; then the port Considering theprocess above concludes. explanation; the following critical flow and subsonic flow equations have closed and the that connects the channels with the low pressure turbine is closed and the process to be usedconcludes. in the the above calculations of the exhaust stage: critical flow and subsonic flow equations have Considering explanation; the following to be used in the of the exhaust stage: Considering thecalculations above explanation; the following critical flow and subsonic 2 flow have to be used in uthe ⎛ kRT ⎞calculations of the exhaust stage: dp equations k −1 out = + out ⎟⎟ αβρ out u out A out ⎜⎜ dt V 22 ⎠ ⎝ k −1 ⎛ kRTout u out ⎞ dp k − 1 ⎟ = + αβρ out u out A out ⎜⎜ dt V k −1 2 ⎟⎠ ⎝ Critical Flow Equations

Critical Flow Equations

Critical Flow Equations T * c *2 2 = 2 = = 0,8333 T0 c 0 k + 1 * *2 T c 2 = kk+1 = 0,8333 * = 2 p T0 = ⎛c 0 2 ⎞k + 1= 0,5283 ⎜ ⎟ p 0 ⎝ k + 1⎠ k * p ⎛ 2 ⎞ k +1 =⎜ ⎟ = 0,5283 p 0* ⎝ k + 1⎠ 1 ρ ⎛ 2 ⎞ k −1 =⎜ ⎟ = 0,6339 ρ 0 ⎝ k + 1⎠ 1 ρ * ⎛ 2 ⎞ k −1 =⎜ ⎟ = 0,6339 Subsonic Equations ρ 0 ⎝ k + 1Flow ⎠ Methods Non-conventional of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

Subsonic Flow Equations T0 k −1 2 = 1+ M T 2 T0 k k −1 2 p = 1⎛ + k − 1M ⎞ k −1

73

1

ρ * ⎛ 2 ⎞ k −1 =⎜ ⎟ = 0,6339 ρ 0 ⎝ k + 1⎠ Subsonic Flow Equations

Subsonic Flow Equations T0 k −1 2 = 1+ M T 2 k

p 0 ⎛ k − 1 2 ⎞ k −1 M ⎟ = ⎜1 + p ⎝ 2 ⎠ 1

ρ 0 ⎛ k − 1 2 ⎞ k −1 M ⎟ = ⎜1 + ρ ⎝ 2 ⎠

Mmax

k −1 ⎡ ⎤ 2 ⎢⎛ P0 ⎞ k = ⎜ ⎟ − 1⎥ ⎥ k − 1 ⎢⎝ P ⎠ ⎣ ⎦

ρw =

p0 RT0

1 1

⎛ k − 1 2 ⎞ k −1 Mw ⎟ ⎜1 + 2 ⎝ ⎠

⎛ 82 ⎜ kRT 1 0 ⎜ u w = Mw a w = Mw a 0 = M w 1 k −1 2 ⎜ Mw ⎛ k −1 2 ⎞2 ⎜ 1+ Mw ⎟ ⎜1 + 2 ⎝ 2 ⎝ ⎠ 2 πD Q = ρwuw 4 p3 p2 = T3 T2

1

⎞2 ⎟ ⎟ ⎟ ⎟ ⎠

The aim of the following calculation was to determine the changing parameters (pressure, velocity, temperature, density,was mass and Mach number) parameters inside The aim of the following calculation to flow determine the changing (pressure, the channel during the expansion process period. The optimal time of the velocity, temperature, mass flow (Filling-purging) and Mach number) inside the search. channel during the expansion process anddensity, of the scavenging process were expansion process period. The optimal time of the expansion process and of the scavenging

Both times calculated are important, because give out the first approximation (Filling-purging) process were search. of the location of the valves or ports that connect the rotor channels with the Bothpressure times calculated areturbine, important, out the approximation of the location of high unsteady lowbecause pressuregive turbine andfirst compressor. the valves or ports that connect the rotor channels with the high pressure unsteady turbine, low

The following figures were calculated using critical and subsonic flow equations: pressure turbine and compressor.

74

Universidad San Buenaventura, sede Bogotá •and Colección Facultad de Ingeniería n.º 12 The following figures weredecalculated using critical subsonic flow equations:

600000

1000000

500000 Pout (Pa)

P_v (Pa)

800000 600000 400000

p_v vs. t

200000

pref

0

0

400000 300000 200000 100000 0

0,0002 0,0004 0,0006 0,0008

0

0,0002

Time (s) Figure. 46.46. Pressure inside thethe channel vs. time Figure. Pressure inside channel vs. time

500000

800000 600000 600000 500000

P* vs. t p_v vs. t

300000 200000 400000 200000 0 200000 100000 0

pref Pout vs. t 0,0002 0,0004 0,0006 0,0008

Time (s) 0 0 0 0,0002 0,0004 0,0006 0,0008 0 0,0002 0,0004 0,0006 0,0008 Time (s) the channel vs. time Figure. 46. Pressure inside Tíme (s)

06 0,0008

annel vs. time

pref P* vs. t Pref

800000 200000 100000 600000 0 400000 0

47.Sta 0Figure 0,0002

Figure 47.Static outlet pressure vs.vs. time Figure 47.48.Static outlet pressure time Figure Critical pressure vs. time

Figure

Pref 0,0008

200000 600000 400000 0 200000 0

0

0,0002

0,0004

0,0006

0,0008

Tíme (s) 0

1000000 Pressure (Pa)

Pressure (Pa) P* (Pa)

P* vs. t

84

P vs. Time

600000 1000000 400000 800000

P* vs. t P_out Pref p*

800000 600000 400000 200000 0

P_v

0

0,000

Pref

0,0002 0,0004 0,0006 0,0008 Figure 48. Critical Figure 48. Critical pressure pressurevs. vs.time time. Tíme (s)

Figur

Figure 49.Efficiency Pressures vs. time • Rafael Mauricio Cerpa Bernal Ph.D. Non-conventional Methods of Gas Turbine Engine Improvement

84 84

0,0002

200000 0

P* vs. t

re vs. time

400000 1000000 300000

Pout (Pa)

P* (Pa) Pout (Pa) P_v (Pa)

600000

400000 600000 400000

pref

Po

P_v vs. t Pout vs. t

1000000

p_v vs. t

Figure 47.Sta

Pressure (Pa)

t

06

Po

P_v vs. t

75

Time (s)

nel vs. time

Figure 47.Static outlet pressure vs. time

P vs. Time

Pressure (Pa)

1000000

P* vs. t Pref

800000 600000

P_out

400000

p*

200000

P_v

0,0008

0

Pref 0

0,0002

0,0004

0,0006

0,0008

Tíme (s) Figure 49. Pressures Pressures vs. Figure 49. vs. time time.

vs. time

M_v vs. t

84

T_

1,2 0,8

T_out (K)

M_v vs. t

1 0,6 0,4

M_v vs. t

0,2 0

0

0,0002 0,0004 0,0006 0,0008

1400 1200 1000 800 600 400 200 0

0

0,0002 0,0

Tíme (s)

Tím

,0008

1400 1200 2000 1000 800 1500 600 400 1000 200 500 0 0

Figure 51. Stat

T_out vs. t T_v vs. t 1000 800 u(m/s)

M_v vs. t

T_out (K) T_v (Pa)

Figure Mach inside channelvs.vs. time Figure 50.50. Mach inside thethe channel time.

T_out vs. t t_v vs. t 0 0

600 400 200

0,0002 0,0004 0,0006 0,0008

0

Tíme (s) 0,0002 0,0004 0,0006 0,0008

0

0,00

Tíme (s) Figure51. 51.Static Statictemperature temperature outlet Figure outlet vs. vs. time time.

hannel vs. time

76

Figure 52. Temperature inside the channel vs. time Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12

u vs. t 1000

85

Fi

Tíme (s)

T

Figure 50. Mach inside the channel vs. time

Figure 51. S

T_out vs. t 1400 1200 1000 800 2000 600 1500 T_out vs. t 400 200 1000 0 t_v vs. t 0500 0,0002 0,0004 0,0006 0,0008 Tíme (s) 0 0 0,0002 0,0004 0,0006 0,0008

08

800

nel vs. time

u(m/s)

M_v vs. t

1000

T_v (Pa)

T_out (K)

T_v vs. t

0

Figure 52.52. Temperature inside Figure Temperature insidethe thechannel channelvs. vs.time. time

85

1000

u(m/s)

800

t_v vs. t

600 400

u vs. s

200 0

008

0

0,0002 0,0004 0,0006 0,0008 Time (s)

Figure53. 53.Velocity Velocityvs. vs. time time. Figure

annel vs. time

Kine%c Energy Kine%c Energy [m2/s2]

85 800000 700000 600000 500000 400000 300000 200000 100000 0

100% Area

0

400 200

Tíme (s) outlet vs. time Figure 51. Static temperature

u vs. t

600

0,0002 0,0004 0,0006 0,0008 Tíme (s)

Figure 54. Figure 54.Kinetic Kineticenergy energy vs. vs.time. time Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D. 77 To obtain the Figures 46 – 54, it was necessary to use the equations listed above. An application

made in Matlab and Excel was developed; where was possible to find the behaviour of the gas in the expansion state inside the channel. A numerical method was used to get such parameters

0

0,

To obtain the Figures 46 – 54, it was necessary to use the equations listed above. An application made in Matlab and Excel was developed; where was possible to find the behaviour of the gas in the expansion state inside the channel. A numerical method was used to get such parameters results. Then an iteration process was carried out, this calculations finished when the velocity achieve values less than zero. A time step after 103 iterations was obtained (6,94 μs), Fist calculations assume the channel area at the outlet equal to the inlet channel area. Some calculations were performed reducing the outlet channel area in 75%, 50% and 25%, just to have softer or weak unsteady expansion (the results were presented in the next pages). Figure 49 shows results comparison of the Figures 46, 47, 48, it is important to observe that the pressure inside the channel starts at the maximum pressure achieved in the process (905000 Pa), and an expansion will be produce till obtain the reference pressure. When it value is achieved the fluid will be steady. Gas flow can be scavenge to the baseline turbine, it´s important to take into account that the unsteady fluid is just exploited and transformed in torque by the high pressure unsteady turbine (the simulations of this turbine model will be shown in the next chapter). Figure 50 and 53 shows the results obtained of the Mach and velocity inside the channel. It was observed that the Mach number in the unsteady expansion always is 1, because of that the process is critical. After some time the expansion starts to be subsonic.

800000 700000 600000 500000 400000 300000 200000 100000 0

Kin

100% Area

0

0,0002 0,0004 0,0006 0,0008

Kine%c Energy [m2/s2]


Kine%c Energy 800000 600000 400000 200000 0

Tíme (s)

T

Figure 55. Kinetic time area) (100% area). Figure 55. Kinetic energy energy vs. timevs. (100%

78

0 0,00020,00

Figure 56. Kinetic


Kin

800000 600000

2/s2]

2/s2]

Kine%c Energy 800000 700000 600000

Kine%c Energy Kine%c Energy

100% Area

0,0008

800000 700000 800000 600000 500000 600000 400000 300000 400000 200000 100000 200000 0 0 0 0,0002 0,0004 0,0006 0,0008 0 0,00020,0004 Tíme 0,0006 (s) 0,0008 0,001

Kin Kine%c Energy [m2/s2]

Kine%c Energy [m2/s2] Kine%c Energy [m2/s2]

ergy

100% Area 75% Area

800000 600000 400000 200000 0

0 0,00020,

Time (s) Figure 55. Kinetic energy vs. time (100% area) Figure56.56.Kinetic Kineticenergy energyvs.vs.time time(75% (75%area) area). Figure

0% area)

Figure 56. Kinet

Kin

Kine%c Energy

Kine%c Energy Energy Kine%c

800000


Kine%c Energy [m2/s2] Kine%c Energy [m2/s2] Kine%c Energy [m2/s2]

rgy ergy

800000 800000

700000 600000

600000 600000

400000 500000

400000 400000

100% Area

200000 300000 200000 100000 00 0,0005 0,001 000 0,0002 0,00040,0006 0,00080,0015 0,001 0 0,001 0,003 Time (s)0,002

200000

50% Area

,0008

0,0015

50% Area 25% Area

75% Area

800000 700000 600000 500000 400000 300000 200000 100000 0

0

0,0

Time (s)

Time (s)

Figure Kinetic energy time (50% area). Figure 57. Kinetic energy vs. time (50% area) Figure 56.57. Kinetic energy vs.vs. time (75% area) Figure 58. Kinetic energy vs. time (25% area)

0% area)

0% area)

Figure 58. Kin

Kine%c Energy 88

50% Area

0,0015


ergy 800000 700000 600000 500000 400000 300000 200000 100000 0

88

25% Area

0

0,001

0,002

0,003

Time (s)

0% area)

Figure Kinetic energy energy vs. vs. time time (25% (25% area) Figure 58. 58. Kinetic area).


88

79

Figure 59. Kinetic energy vs. time (parametric study).

The figure 55 – 58, shows the results of the variation of kinetic energy in time on the outlet of the channel. Some variations in the outflow area was made (outlet area = 100% inlet area; outlet area = 75% inlet area; outlet area = 50% inlet area; outlet area = 25% inlet area). The results of case study presented in Figure 59 shows that if the outlet area is decreased the expansion time will increase and the expansion process is weaker. It helps to have better fluid characteristics in the high pressure unsteady turbine, because the gas flow can be converted more easily into torque, but it has a problem related with the reduction of the area because some part of the energy will be lost. It is possible to notice higher values of kinetic energy if the outlet area has also higher values; but the expansion time is too small to extract all energy of the fluid and be converted in power by turbine. In order to produce a smooth expansion process but also generate a largest amount of energy to be converted in work by the high pressure unsteady turbine; it was decided to have a weak unsteady expansion process, although the kinetic energies losses may be higher, it´s better do not give a high kinetic energy, and deliver to the turbine a fluid easier to be converted to torque. According last conclusions the variants with 50 and 25 percent of the area were chosen.

80


5.1.

Reference Values

Figure 59 shows the available kinetic energy inside the channels when the quasi-steady expansion starts.The energy can be used to accelerate the turbine and produce work. It was decided to have an outflow area equal to the 50% of the inlet area of the channel. Subpart 2.5.2 study the way to produce the maximum power by the proposed model. Several simulations are carried out modifying some design parameters (geometry, velocity of the rotor blades of the turbine and velocity of the ICWR). There’s necessary to find a reference value which doesn’t vary depending of the model or arrangement to be selected in subpart 5.2. Use of constant volume combustion process in a turbojet engine generates problem of gas expansion from constant volume, which means variable pressure and temperature inside volume and variable outflow velocity. In such conditions Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

81

it is difficult to find reference values for further analysis of different expansion conditions. Because of thatand an untypical reference values have section. During this time velocity temperature of expanded gasbeen are proposed. constant. So those

parameters have been proposed to be a reference values for following investigations. During unsteady expansion process parameters on the outlet are constant in a time instance required for expansion wave to pass the length of the section. During time velocity and ofofexpanded gas SoSothose section. Duringthis time velocity andtemperature temperature expanded gasare areconstant. constant. those chamber and return tothisthe outlet cross-section. During this time velocity and Figure 60 shows the physical plane (x-t) used for depicting propagations of waves along the temperature of have expanded gas are So those parameters have been parameters been proposed toto beconstant. a reference values forfor following investigations. parameters have been proposed be a reference values following investigations. proposed to be a reference values for following investigations. a ref t x vs. chamber. X = Dimensionl Dimensionl ess form ofoftofwaves Zwaves = (along ) . After form of x (= ) (x-t) Figure shows thethephysical plane propagations Figure6060ess shows physical plane (x-t)used usedforfordepicting depicting propagations L thethe L used for depicting propagations of wavesalong Figure 60 shows the physical plane (x-t) aat t xx chamber. chamber. vs.Dimensionl . After as ess form of Dimensionl ess form oft tZ = (= (ref ref)channels Z = Dimensionl ess x (x=(outflow vs. . )After along the chamber. = Dimensionl ess form = ) )vs. analyze different options, itX Xwas decided toform useofofthe velocity from the ICWR LL LL After analyze different options, it was decided to use the outflow velocity from analyze different analyze differentoptions, options,it itwas wasdecided decidedtotouse usethetheoutflow outflowvelocity velocityfrom fromthetheICWR ICWRchannels channelsasas reference value the expansion the in ICWR channels asanalysis. reference value in the expansion analysis. reference value inin thethe expansion analysis. reference value expansion analysis.

Figure 60.60.Schematic expansion waves diagram Figure Schematic expansion waves diagram

Figure Schematic expansion expansion waves Figure 60.60.Schematic wavesdiagram. diagram Figure Figure6161shows showsa astate statediagram diagramused usedforforpresentation presentationofofgas gasstate state(velocity (velocityand andpressure) pressure) corresponding ininphysical planes, it’s expansion process corresponding tozones zones physical planes, where it’sobserved observed expansion processfrom fromthethe Figure 61 shows a tostate diagram used forwhere presentation ofthethe gas state (velocity and pressure) corresponding to zones inpressure physical planes, where it’s observed state 1 to state 2.2. Diagram represents thethe pressure ratio but defined byby thethe speeds ofof sound. state 1 to state Diagram represents ratio but defined speeds sound. the expansion process from the state 1 to state 2. Diagram represents the Figure 61 shows a state diagram used for presentation of gas state (velocity and pressure) pressure ratio but k defined by the speeds of sound. −1k −1 2⎞k 2 k ⎛ ⎞ ⎛ a1a1 ⎜in⎜pk1physical p corresponding to zones planes, where it’s observed the expansion process from the = = �11⎟ ⎟ ⎜ p⎜ p2 k ⎟ ⎟ a a ref ref ref ⎝� ⎝ ref⎠ ⎠ a1 � p = � 1 ÷represents the pressure ratio but defined by the speeds of sound. state 1 to state 2. Diagram �p ÷ a ref � ref �

82

a1 ⎛⎜ p1 ⎞⎟ = a ref ⎜⎝ p ref ⎟⎠

k −1 2k

92 • Colección Facultad de Ingeniería n.º 12 Universidad de San Buenaventura, sede 92 Bogotá

Values obtained after the combustion (p,T, ρ) are found in the state number 1 (Fig. 61). And the values achieved after the unsteady expansion are located in the state number 2. As was decided the reference value selected is the outflow velocity (u2), the figure 61 gives information about the way to calculate such velocity.

Figure 61. Schematic A-U diagram for unsteady expansion.

The following gas dynamics calculation is performed to find the velocity reference value: p1= 904293 Pa p2=pref= 244367,7 Pa Tref= 1032 K a

A= a A = aaref A = a ref a ref u U= u U = auref U = a ref a ref A 2 � A1 k -1 = ± k -1 A A � 2 1 U2 � U A A11 = ± k2- 1 U2 � U1 = ± 2 U2 � U1 2 Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D. a A 1 = a1 a A 1 = aref11 A 1 = a ref a ref a A 2 = a2 2

83

a ref A 2 � A1 k -1 =± �U A A1 k -1 U22 � 1 = ± 2 U2 � U1 2 a A1 = 1 a A 1 = a ref1 a ref a A2 = 2 a A 2 = a ref2 According a ref with the Figure

According with the Figure a 2 = a ref A2 = 1 U1 = 0 A 2 � A1 = �

k -1 (U2 � U1 ) 2

� P1 a A1 = 1 = � a ref � �Pref A 2 � A1 = �

k �1

1.4 �1

�2k � 904293 �2(1.4) ÷ = 1.2055 ÷ = �244367,7 ÷ � � �

k -1 (U2 � U1 ) 2

1 � 1.2055 = �

1.4 - 1 (U2 � 0) 2

U2 = 1.02 a ref = kRT = 1.4 ×287

a ref = 643

U2 =

J ×1032K KgK

m s

u2 aref

u2 643 m u2 = 656 s

1.02 =

84


A gas dynamic calculation gives the value of the flow velocity (Fig. 62). In further analysis a reference torque or force is required. Because of that, torque or force generated in ideal turbine was calculated and used as a reference value. As was explained above, kinetic energy can be used to accelerate the turbine and produce force.The force produced by the turbine can be estimated from the momentum equation, and some trigonometric calculations.

Figure 62. Triangle of velocities.

In the blade operation, it´s assumed that the flow coming from the stator nozzle is tangent to the geometry of the pressure side of the blade (Fig. 63). The turbine velocity is selected according the information presented in subpart 5.3 (150 m/s); also α is equal to 19° according of the blade geometry design. Taking into account triangle of velocities (Fig.62). It´s possible to find the resultant velocity tangent to the leading edge of the blade: c 2 = a 2 + b 2 � 2ab ×cosC c 2 = (656) 2 + (150) 2 � 2(656 ×150) ×cos161 c = 638914 m c = 799 s Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

85

Figure 63. Triangle of velocities.

If the resultant velocity is calculated also the relative velocity component in blade motion direction (Fig. 62) can be calculated.

cosa =

u relative u2

u relative = cosa ×u 2 u relative = cos19 ×656 = 620.3

m s

The force generated by the blade can be determined with the relative vemomentum has mass magnitude and momentum direction; theisfollowing calculations release the force generated locity and the flow. The the product of the mass flow and velocity of the object. In this case the momentum has magnitude and by single turbine blade: direction; the following calculations release the force generated by single turbine blade: •

Fref = (u relatuve − (−u relative )) ⋅ m kg m m + 620.3 ) ⋅ (0.359 ) s s s = 445.4N

Fref = (620.3 Fref 86


The force calculated above will be used as a reference value for calculation of the force coefficients in subpart 2.5.2, continue the following equations:

The force calculated above will be used as a reference value for calculation of coefficients in subpart 2.5.2, continue the following equations: The force calculated above will be used as a reference value for calculation of the force coefficients in subpart 2.5.2, continue the following equations:

Force coefficien t =

Fi Fref

Preference = Fref ⋅ u turbine Power coefficien t = 5.2.

Fcoefficeint⋅ ⋅ u turbine Preference

High Pressure Unsteady Turbine Geometry Design

A simulation process will be implemented to optimize the first geometry estimation calculated on the chapter 4. One dimensional model results are taken into account to generate a two dimensional model. Even 2-D model requires simplifications. 5.2 Highsome Pressure Unsteady Turbine Geometry Design

Outflow from process the combustion was realized in a way alA simulation will be chamber implemented to optimize the guaranty first geometry estimation most steady type of expansion process. Duration of expansion is determined on the thetop chapter 4. Oneof dimensional results are into account to gener by parameters gas at the endmodel of combustion, andtaken cross-section of the outlet.model. Rotation angle, rotorrequires containing combustion chambers, dimensional Even 2-Dofmodel some simplifications. realized during the expansion process, depends on the rotational speed. Gas stream leaving the combustion chamber had to be finally expanded in steady expansion nozzles. Geometrically such nozzles can be distributed on the steady casing on part of arch having described angle. To fully expand gas 98 from combustion chamber, angle of rotation of rotor containing combustion chamber should be lower than arch angle with steady expansion nozzles located in casing. Rotation speed of rotor containing combustion chamber can be controlled to reach expected expansion angle. Due to limited area possible to be used for steady nozzles distribution, only part of the turbine blade system can be operated simultaneously. A problem Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

87

is known as turbine partial admittance. Such configuration forced generation of unsteady flows through the turbine blades. Optimal speed of turbine blades depends on the gas velocity at the exit of the steady expansion nozzles. Because of that, rotational speeds of rotor containing combustion chamber and turbine had to be different. For simulation of the process of expansion and torque generation some simplifications have been done. Axisymmetric configuration of the considered device was exchanged to plane x-y configuration.(Figure 64). Scheme of considered geometry was presented in Fig 64. Each combustion chamber expands it’s contents reducing in time stagnation pressure and temperature. Because of that external stream of expanded gases has variable parameters: velocity, temperature and density. Turbine extracting mechanical power from such stream had to have untypical geometry. Figure 64 shows the simplification process in which the model simulated in FLUENT is obtained. First simulation has been limited to the expansion process; and how it´s produced torque. As was commented above, the flow accelerates in the stator channels (stator nozzle) producing the generation of unsteady flows through the turbine blades. The simulation process starts with rotor channels closed on both sides and filled with high pressure and temperature gas (after constant volume combustion). Stator nozzle port is open and an expansion process is generated (let’s remember that the rotor channels move forward in X direction).The gas coming from the rotor is accelerated and expanded in the nozzle channels and delivered to the turbine, where an unsteady flow can be generated through the blades. The high energy of the flow discharged to the turbine is used by the turbine to produce power. It was assumed a fully expansion inside steady nozzle, so the turbine is of action type. The channel between blades has constant cross-section as is observed in the figure 64. 88


Figure 64. 2D simulation model.

The aim of the next simulations was to find the best geometrical arrangement of the component, to reach the maximum torque generated by the turbine. As Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

89

a parametrical study will be carry out, and due to limited computational time resources, the simulation only includes 1 cycle, and results of the expansion process. Set of different options and arrangements were simulated and the results are shown below; eight cases were proposed (but just the results of the models 1, 5, 6 and 8 are presented).

5.2.1 Model 1

90

Model number 1

Contours of static pressure [Pa]

Contours of static temperature [K]

Contours of velocity magnitude [m/s]


Contours of Mach number

Pathlines colored by velocity magnitude [m/s]

Figure 65. Simulation results case 1.

Figure 65 shows geometry and the boundary conditions of the model number one. In this case the stator has only 2 nozzles. Both stator channels are connected directly with the high pressure unsteady turbine. A convergent nozzle was applied to accelerate the flow coming from the rotor channels; a temporarilly free jet effect will be produced and the turbine has to operate with unsteady flow. Turbine mid-blade channels in this type of turbine contains the gas in steady state, in relation to blades, before passing in front of steady nozzles, so gas had to be accelerated by the gas incoming from steady nozzles. After passing the zone of steady nozzles gas in mid-blade area had to be decelerated to zero velocity. High pressure unsteady turbine takes advantage of the high energy fluid delivered by the nozzle, and part of the energy it’s converted into power. In the considered model interface type boundary conditions were created. One connects the rotor channels - stator nozzle. The second connects the stator nozzle - high pressure unsteady turbine. Figure 65 also presents the results of the simulation. The contours of pressure, velocity, temperature and Mach number are released. Presented pathlines, because of unsteady flow conditions, should be treated only as illustrative. Pathlines calculated in following time instances would have different shapes. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

91

The following data and parameters have been used in the simulation: Initial pressure inside the channel

904292 Pa.

Initial temperature inside the channel

1500 K

Pressure at Outlet

237085 Pa

Temperature at Outlet

1023 K

Rotor Channels speed (moving mesh - X direction) 29 m/s Turbine blades speed (moving mesh - X direction)

150 m/s

After the 2D model simulations, two coefficients can be taken out to check the possible torque and power produced by the turbine. The first one it’s a force coefficient, which is a dimensionless coefficient that quantify the force generated by the turbine. This force coefficient takes into account the force produced in single blade and it is calculated using FLUENT, this value is divided by the force reference value (described in subpart 5.1).The second is the power coefficient, relating the power calculated during simulation with reference power. Both coefficients identify the energy developed by any proposed and considered model. If the power coefficient has low values the energy produced by the turbine will be also small. According with the expansion process theory present in the subpart (4.1.3), can be conclude in the accordance with the simulation results (Figure 61), that the stator nozzles cannot fully expand the gas inside the rotor channels to achieve the same pressure value of the air from the compressor. One can notice a strongly non-uniform temperature distribution inside the turbine channels resulting from the unsteady type of flow process. Mach number distribution also indicates local non-uniformities. Mach number distribution shows that inside the turbine channels, locally and temporarily, the Mach number is higher than 1 (1.65). High velocity flow is produced because the static temperature is relatively high in the suction side of the turbine blades; also a free jet effect (high velocity) is produced by the stator nozzle affecting such region of the blade. 92


Velocity distribution and pathlines indicate flow separation in some parts of the channel between neighboring blades. Table 12. Case 1 simulation results CASE 1 SIMULATION RESULTS Force coefficient

Power coefficient

0.196

0.196

Taking into account the weaknesses of developed first model; a set of models were proposed and studied.

5.2.2 Model 5

Model number 5





93

Contours of mach number



The figure 66 shows a new model based on the last variants; the main difference was the modification in the number of nozzles and the connection area between the stator nozzles and high pressure unsteady turbine.The height and length of this area has to be as small as possible to prevent the losses inside this connection and also to reduce some reflections detected inside of this area, resulting in energy losses in the channel. The same initial values as used on the model 1 were applied on the case 5. Table 13. Case 5 simulation results CASE 5 SIMULATION RESULTS Force coefficient

Power coefficient

0.57

0.57

After analysis of the results obtained in the simulations (Figure 66); let us conclude about these calculations: The mean power coefficient value is the highest one obtained in last set of simulations. The turbine operation is not affected by the high velocity, because the flow inside the blade channels has Mach number less than 0,8 (transonic flow). Su94


personic flow is detected in the stator nozzle discharge due to the temporally free jet effect through the channels. The pressure distribution (Fig. 66) shows higher pressure values in the suction side of the leading edge of the blade than the pressure side of the blade. Physically it is incorrect; and the flow in this section produces a large amount of losses. A normal operation of the turbine is detected after the middle section of the blade; where the pressure is higher in the pressure side. It was possible to observe the scavenging process of the fluid inside the combustion rotor channels; delivering the gas to the high pressure unsteady turbine. Due the problems presented on the clearance between the stator nozzles and the turbine, a new model without the connector was proposed. The idea is to connect directly the stator nozzles with the high pressure unsteady turbine; but also the modification includes a small space to stabilize the flow delivered to the turbine. Because it seemed, that possibility of flow improvements of considered geometry have been exhausted a new flow configuration was tested.

5.2.3 Model 6

Model number 6



95






Analyzing pressure distributions at the outlet of the turbine blades presented in Figures 65-66, were detected a higher pressure values compared with the thermal calculations of the cycle in the subpart 2.3. A new concept was applied to extract the energy left in the outflow of the high pressure unsteady turbine. A recirculation channel was added to the last model (Fig. 66). The gas at the outlet of the turbine blades has remaining enthalpy to be used, then such gas is directed back to the turbine though recirculation channel. The same initial values as used on the case 1 were applied on the case 6. 96


Table 14. Case 6 simulation results CASE 6 SIMULATION RESULTS Force coefficient

Power coefficient

1.21

1.21

Table 14 gives the force and power coefficient obtained in the model 6. As was expected the mean values are higher than in the other variants. It was produced by double gas pass through the turbine. A small clearance was left in the stator channels discharge to avoid the problem of direct deliver the jet flow to the turbine blades. The flow in the clearance (stator nozzle outlet – turbine Inlet) is supersonic. Inside the channels the flow has Mach number values below 1, therefore turbine operation cannot be strongly affected by the gas velocity. The pressure distribution in Figure 67; confirms the solution of the problem presented earlier in the pressure difference between the suction and pressure side. In the recent model always the pressure in the pressure side is equal or higher than the pressure presented in the suction side. Last variant (Fig. 67) applied in the geometry of the model, gives the better results, reaching the operational limits of the turbine given by theory.

5.2.4 Model 8

Model number 8



97






A final model was proposed (Fig. 68). The outlet of the recirculating channel was moved in X direction, to bring closer it to the stator nozzles (Figure 68) and realize a smooth transition of flow parameters between stages. The aim of the model 8 is override the effect caused when the difference in the pressure distribution at both side of the blade channels it’s too high. The same initial values used on the case 1 were applied on the case 8. Table 15. Case 8 simulation results CASE 8 SIMULATION RESULTS

98

Force coefficient

Power Coefficient

1.37

1.37


Taking into account the simulations results depicted in the figure 68; let us analyze these results »»

The gas from stator channels crossing the high pressure unsteady turbine is recirculating to the turbine again. As it was expected, the power coefficient achieves the maximum value obtained in all simulation cases.

»»

It is possible to conclude that the idea applied in the new model to avoid the big pressure differences between the blade channels was reasonable and successful. The mean power coefficient increases; and the pressure losses due to the pressure difference between the turbine blades decreases.

»»

The maximum Mach number presented on the modes is lower than 1. The complete operation of the model is not affected by the fluid velocity and temperature.

»»

Analyzing pathlines (Fig.68). It´s possible to observe between the recirculation channel and turbine connection a free jet flow applied in the leading edge of the blade. It produces negative values in force coefficient. It can be concluded case 8 is not the optimal one, because has some geometrical problems in the recirculation channel and stator nozzle.

To better understand the flow conditions and ways of power generation, variation of the force coefficient in time for considered case were monitored and depicted in figures below.

Figure 69. Study of the model cases 1-5 (force coefficient vs. time). Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

99

Figure 70. Study of the model cases 6-8 (force coefficient vs. time).

Figures 69 and 70 show a comparison of force coefficient variation for the cases simulated in FLUENT. It gives the variation of the force coefficient versus time. The comparison gives an idea of how the gas affects the turbine blades operation. Figures 69 and 70 give the results of the mean force coefficient value in the models simulated. The main goal is to tr y to use as much as possible energy from the gas coming from the rotor channels to produce power. The model analysis gives impor tant information about the gas behavior ; and how the unsteady fluid affects the operation of the turbine. Also shows, how can be used the unsteady flow to produce torque or power. Figures 69 and 70 also present the stator nozzle location. There is possible to detect zones where negative values are presented. It is caused by the unsteady effects presented during the expansion process; also jet flow is affecting the suction side of the blade generating inconvenient operation of blade (Fig.71).

100


a. Contours of static temperature [K]

b. Contours of velocity magnitude [m/s]

c. Contours of velocity magnitude [m/s] Figure 71. Problems detected on the blades.

Free jets is a temporally effect presented in the stator nozzle discharge. Flow from the rotor channels is expanded in the stator nozzle and deliver to the high pressure unsteady turbine; momentarily as rotating phenomena (Fig.71 c) a Laval nozzle is produced, generating a variation in flow parameters. Figure 71. Shows free jet effect applied in the leading edge of the blade. It is the physical reason of negative values of force and power coefficients. Flow velocity from stator nozzles has to be tangent to the blade, but in the simulations can be detected some operation problems where unsteady effects in partial admittance affect the suction and pressure side of the blade.


101

The model number 8 increases mean power coefficient in comparison to the first obtained by seven times, it means torque or power produced by the turbine is increased seven times; achieving the maximum possible value with the operational conditions established in the subparts (2,1 ; 2,2; 2,3 and 2,4). It also means that the development of the turbine unit geometry is critical to power generation by pulse internal combustion devices.

Figure 72. Study of the model cases (mean force coefficient value).

Figure 73. Study of the model cases (power coefficient value).

102


CFD FLUENT is used to simulate the unsteady expansion process (subpart 4.1.3). Also gives an idea about the ways to use an unsteady flow to produce power by an axial turbine. The last 2D simulation results confirm the aim of the research. It is possible to increase the power produced by the engine, changing the typical arrangement in a Brayton cycle using a constant volume combustion chamber. Also the results are in accordance with the thermal and gas dynamic calculations performed in the sections 2,2 and 2,3. Finally these simulations helped to determine the possibility of extract energy of an unsteady flow using a new version of stator nozzles and rotor blades configuration.

5.3.

Simulation of the Rotating Combustion Chamber Cycle

The calculations of the eight turbine unit models were carried out to determine the most effective arrangement of the unit geometry (rotor channels - nozzle channels - high pressure unsteady turbine) to produce the maximum power. According with the results of the studied cases (Fig. 73), the geometr y the number eight was chosen for fur ther analysis. But in such simulations the following operational parameters were not studied deeply: »»

Optimal velocity of the turbine rotor blades.

»»

Optimal velocity of the ICWR (internal combustion wave rotor) combustion rotor channels.

To determine the enhanced velocity of the high pressure unsteady turbine and the rotor channels, a cases analysis was conducted. Where the high pressure unsteady turbine velocity (U velocity (Fig. 61)) is changed from 50 m/s to 250 m/s. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

103

Figure 74 shows the triangle of velocity for the high pressure unsteady turbine used in the project. The gas enters to the nozzle channels with some pressure, temperature and velocity (C1). It is expanded in the nozzle channels and leaves with a velocity C2 at an angle α2. (rotor blade inlet angle β2) is chosen to suit the direction of the gas velocity V2 relative to the blade at the inlet. Let´s remember that β2 and V2 are found by vectorial subtraction of the blade speed U from the absolute velocity C2. Inside the rotor blades the gas is changing the flow direction and delivers to the low pressure turbine with relative velocity V3 at angle β2.

Figure 74. Turbine triangle of velocities.

According to sketch in Figure 74. It´s possible to observe the impor tance of blade speed U in a turbine design. However the optimal value of the blade velocity in the high pressure unsteady turbine is not known; so, several simulations of the final model were develop changing the blade speed from 50 m/s – 200 m/s, trying to find the velocity where the maximum power its produced by the turbine. 104


Figure 75. Force coefficient vs. rotor blade velocity.

Figure 76. Power coefficient vs. rotor blade velocity.

Table 16. Rotor blade speed – force coefficient – power coefficient Rotor Blade Speed [m/s]

Force Coefficient

Power Coefficient

50

-4.4

-1.46

75

1.4

0.7

100

1.9

1.3


105

Rotor Blade Speed [m/s]

Force Coefficient

Power Coefficient

125

1.3

1.1

150

1.2

1.2

175

0.8

1

200

0.7

0.9

250

0.3

0.5

The results obtained in the cases analysis, shown in the Fig. 75, 76, determined the value of the rotor blade optimal speed. The maximum power coefficient values on the study were noticed when the rotor blade speed achieved values between 100 – 150 m/s. The optimal rotor speed has to be located within this range. Velocity of 150 m/s is selected because the jet effect detected on the blades and temporally unsteady effects are weaker than the presented in the variants using 100 m/s and 125 m/s. Having calculated the optimal speed of the turbine rotor blade; we focus our attention to find the optimal velocity of the ICWR (internal combustion wave rotor) rotor channels. It velocity depends of the unsteady expansion and scavenging process. A time calculation of this process where carried out in subpart 4.1.1. Based on such results some simulations were developed to check one dimensional calculation.

Figure 77. Two dimensional sketch of the wave combustion chamber.

Figure 77 presents a sketch of one cycle of the process. It starts when the channels are closed on both sides and combustion (at constant volume) is 106


finished increasing the pressure and temperature inside the combustion channel. Then the connection with the stator nozzles is opened and an expansion process starts through the stator nozzles. Expansion wave is generated after opening combustion chamber side to steady state low pressure turbine. After while, when the expansion wave will reach the compressor side of combustion chamber the fresh air push out the exhaust gas finalizing scavenging and refilling process. The air from the compressor acts as a piston removing the gas from the channel. When the combustion gas left the ICWR channels both ports are closed (From compressor side and turbine side). Also is possible to observe on the figure 86 that two cycles of combustion, scavenging and filling are realized per one rotor revolution. One dimensional calculation present the basic operational parameters of the wave rotor combustion, also give the first approximation of the geometry of the model. But it was a simple estimation; two dimensional simulations has to be performed to understand the behavior of the fluid in the cycle and determine the optimal speed of the the ICWR rotor channels

5.4.1 Unsteady Expansion Simulations Simulations presented in the previous chapter used model of unsteady expansion but explanation were concentrated on the torque generation but not on the expansion process. In present chapter investigation was concentrated on the unsteady process of expansion. The operational parameters obtained in thermal calculations subpart 2.3 have been applied as boundary conditions in 2-D simulations. Table 17. Turbojet engine modified with constant volume combustion chamber PARAMETER Compressor Outlet Pressure Compressor Outlet Temperature High Pressure Unsteady Turbine Inlet Pressure

VALUE 244000 Pa 405 K 905000 Pa


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PARAMETER

VALUE

High Pressure Unsteady Turbine Inlet Temperature

1500 K

Low Pressure Turbine Inlet Pressure Low Pressure Turbine Inlet Temperature

237000 Pa 1032 K

Table 17 gives the operation values of the engine enhanced with ICWR. The pressure and the temperature after the combustion achieves 905000 Pa and 1500 K, to apply such results a patch option in the channels was applied in FLUENT.

Figure 78. p_v vs time.

Unsteady expansion, starts when the combustion is finished inside the channel and the stator nozzle port (connection with the high pressure unsteady turbine) is open, an unsteady expansion is generated. Gas dynamics calculations give the main idea of the fluid motion during the unsteady process. Calculations presented in chapter 4 have been performed with assumption of uniform pressure distribution inside the combustion channel. Due to ratio of channel length to width about 6 to 10, wave effects had to be taken into account. The real pressure distribution inside the combustion channel is not uniform. Generally, it was assumed that due to the chocking effect of the outlet (outlet 108


cross-section area is only 50% of channel cross-section) the expansion process will be of quasi-steady type with some wave effects inside channel.Taking into account the last information a two dimensional simulation was carried out; to get the main characteristics of the unsteady expansion process, and utilize the operation of the model according with the values obtained from the gas dynamics studies of the baseline engine enhanced by ICWR.With the dropping pressure inside combustion channel also the outlet velocity is reduced and can reach the level not usable for the torque generation (Fig 78). Because of that after lowering pressure inside combustion chamber to some prescribed level gas delivery to the turbine is cut out. But inside combustion channel gas is left with pressure slightly higher than in the inlet to the low pressure turbine (Fig 78 “Pwork”).

Figure 79. Single channel unsteady partial expansion simulations (contours of static pressure [Pa]).

In Fig. 79 have been presented case with relatively high pressure left inside the combustion chamber after two stage expansion in the high pressure turbine. To improve the expansion process number of expansion nozzles has been increased two times. In first four nozzles gas is expanding to relatively high Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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outlet pressure to realize two step expansions on the turbine blades. Gas left inside the combustion chamber has enough energy to be expanded in a single pass through the turbine. Such a case is presented in Fig. 80 and 81.

Figure 80. Single channel unsteady full expansion simulations (contours of static pressure [Pa]).

Figure 81. Single channel unsteady full expansion simulations end phase (contours of static pressure [Pa]).

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Stator nozzle arrangement (Fig.79, 80) left part of gas with remaining pressure that can be used to produce torque. Unsteady process finishes when the pressure inside the channel is slightly higher than reference pressure (Fig. 78), several simulations were performed to find the optimal number of stator nozzles to guarantee the totally expansion of the gas until achieves work pressure. Many simulations were made, modifying the number and geometry of the nozzle channels. Hence the final model has 9 stator channels instead 4 (first calculation fig, 79-81). Also the angles of the stator nozzles were changed to improve delivery process of flow to the turbine blades. The next step is to study the filling and scavenging process of the ICWR channels.

5.4.2 Filling and Scavenging Process Determination of the operational limits of the model requires some more steps. The last subparts were focused in the quasi-steady expansion process. The following simulation shows the filling and scavenging process of the ICWR channels.

Figure 82. Filling and scavenging process (contours of CO2 mass fraction). Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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To simulate the filling and scavenging process the initial configuration was taken from the gas dynamics calculations. Concentration of CO2 was chosen as indicator of the presence of the fresh air from compressor to determine the successful of the scavenging process. Also, likely the geometry of the ports has to be changed during the simulations to guarantee the totally scavenging of the combustion gas inside the channels. It is possible to notice in the Fig. 82(D) that some part of the combustion gas remaining inside the channel. To solve the operational problems detected in the filling and scavenging process (Fig. 82); a new modification in the geometry was applied. It consists in change the direction of the air from the compressor; also the port that connects the channel with the baseline turbine was moved leftward to produce an expansion wave, which improves scavenging process of the gas inside the ICWR channel. A final model (Fig 83) proposed is simulated to test the last assertions. Figure 83 gives an idea of the behavior of the gas inside the channel if the direction of the air coming from the compressor is changed.

Figure 83. Filling and scavenging process with improved inlet (contours of static temperature [K]).

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Figure 83 checks the behaviour of the gas inside the channels, after application modifications presented above. It is possible to observe that the problems presented on the previous simulation (Fig. 83) were almost removed. Some part of the gas remain inside the channel but it will be tested again when a full set of channels are simulated. Estimation of the rotor rotation velocity strongly depends on the length of the combustion process which is not modeled in presented investigation. Instead of that, some assumption related to combustion process and it is final state parameters have been done. Due to that, velocity assumed in the ICWR channels was not the optimal. The main parameter considered to find the operational velocity of the ICWR channels was the full expansion to high pressure turbine and scavenging of the gases inside the channels to low pressure turbine. (Fig. 81-82) Table 18 gives the design data of the wave rotor combustor after the two dimensional analysis carried out in FLUENT. Table 18. Design data of the wave rotor combustor DESIGN DATA OF THE INTERNAL WAVE ROTOR COMBUSTOR Cycles per revolution RPM

2 1553

Channel Velocity

29 m/s

Time per one revolution

0,0386 s

Internal radio of the rotor

0,17825 m

External radio of the rotor

0,15425 m

5.4.

Cycle Simulation of the Model

Taking into account results of investigations presented in subchapter 5.2 determining the operational parameters and fluid characteristics inside the channel across the wave rotor combustion chamber; a final configuration of the model was developed. This model includes all components of the rotorturbine unit. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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According simulations and calculations performed in the last sub-chapters, the operational and geometrical parameters of design in the turbojet engine modified with wave rotor were found. In figure 84 have been shown a CAD model of the components added to the baseline engine to produce combustion at constant volume. There is the possibility to observe the unit arrangement, and the way to connect the different components. The aim to create a three dimensional model is show the engine assembly and the component construction feasibility. However such types of elements are not easy to construct due it operation parameters and the small clearance and limits of the unit components. Figure 85 shows a two dimensional model based in the engine arrangement presented in Fig. 84. Two dimensional model is developed to simulate one revolution of the ICWR and components; where will be possible to observe the complete operation of the model in 1 cycle. Preprocessing task was made using the software GAMBIT.The geometry, mesh and specified the boundary conditions were generated on this software (Fig. 86).

Figure 84. 3D model of the baseline engine modified with constant volume combustor.

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Figure 85. 2D model of the baseline engine modified with constant volume combustor. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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Figure 85 give the idea of the two dimensional model. It describes the optimal geometr y selected to be simulated and also the mesh used on the process. In the rotor channels and por ts a square mesh were selected. In the nozzle channels, recirculation channel and turbine blades a triangular mesh was used because the complex shape presented in the geometr y. Probably it is possible to get some problems if a quadrilateral mesh is selected. Table 19. Mesh information MESH INFORMATION

116

Cells

398752

Nodes

266735


Figure 86. Meshing and geometry of the model.

Figure 85 and 86 shows the pre – processor generation of the model (baseline engine modified with constant volume combustor). Once the specification of the flow problem is known, we can turn our attention to build a computer model. The first part is a geometry and mesh generation. To develop such elements GAMBIT software was used. GAMBIT gives also the option to apply suitable boundary conditions to the model. Let´s start introducing the following assumptions applied in the developed model: »»

The combustion process inside the channel it´s not simulated.To obtain the operating conditions (pressure and temperature) inside the ICWR channels after the combustion a patch option will be used in FLUENT.


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»»

The operational speed of the ICWR channels is 29 m/s according with the results shown in the chapter 5.

»»

The operational speed of the high pressure unsteady turbine blades is 150 m/s according with the results shown in the chapter 5.

»»

The geometry showed on the Figure 81 was used taking into account all process involved in the model operation (baseline engine modified with constant volume combustor), and according with the simulation and calculation results presented in chapters 4 and 5.

»»

The model (baseline engine modified with constant volume combustor) contains only topping part of the engine. Will be simulated with the following components: the internal combustion wave rotor channels, stator nozzles, high pressure unsteady turbine and Low Pressure turbine connections. It is due to the modification of the baseline engine. Let´s remember that the modified engine has the same compressor and turbine; that’s why it is not necessary to simulate such components.

The model shown in the figure 85, has two rotating components (ICWR channels and high pressure unsteady turbine), these components in 2 dimensional model have a moving velocity on X direction. Therefore, it was necessary to use a set of interface boundary condition to connect the components of the model (see fig 85 to check the interfaces created). The pressure inlet condition is used to deliver air to the model, with the operational pressure and temperature increased by the compressor. Also pressure outlet condition was used to allow the scavenging process of the flow to the low pressure turbine. The following physical assumptions were applied in the 2D Simulations of model (baseline engine modified with constant volume combustor): Compressibility effects are taken into account because is expected that the flow in the nozzle channels and high pressure unsteady turbine blades has high velocity and temporarily Mach numbers higher than 1. 118


Taking into account that flow and especially boundary layer in almost all channels were developed in unsteady way a Spallart-Allmaras turbulent model was selected for the simulation process. Due to inclusion of terms sensing distance of the centre of mesh volumes from the wall, and correcting the turbulence influence on the flow parameters this model is robust in considered applications.

Fig. 87. Cycle simulation of the model (contours of static pressure [Pa]. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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Figure 88. Cycle simulation of the model (contours of static temperature [K].

In figure 87 have been shown contours of static pressure distribution during the process. It starts when the ICWR channels are filled with high pressure and high temperature gas (Fig 87–left side). ICWR channels are moved rightward with constant velocity. After assumed time, the end of combustion process is simulated by patch application inside the combustion chamber constant values 120


of final combustion pressure and temperature. Then the stator nozzle port (Fig. 81) is open and an expansion process starts. The pressure will decrease along the stator until achieve the pressure slightly higher than the pressure of the air coming from the compressor. When this pressure is reached, the nozzle channels port is closed. Now the ICRW channel is close in both sides with a pressure value slightly higher than the air delivered by the compressor.The low pressure turbine port (Fig. 81) is open and an expansion wave is produced traveling from the bottom to the top of the channel, (Figure 88). The port containing air from the compressor is open and the filling – scavenging process starts inside the ICWR channels. As was explained above the air coming from the compressor acts as a piston; it pushes out the combustion gas from the channel (Fig 88). When the scavenging process finalizes the low pressure turbine port it´s closed. Once more the ICWR channels are closed on both sides containing air – fuel mixture. Then the combustion process is carried out increasing the temperature and pressure inside the channels (combustion process is not simulated on the model. The operating conditions are applied using a patch option – fig. 87 and 88). Then the process starts again. (take into account that per 1 cycle, two process “combustion – unsteady expansion –steady expansion” are carried out) Figure 88 shows the contours of static temperature during the process. It starts when the ICWR channels are filled with high temperature gas (Fig 88 – left side).Then ICWR channel is connected with the high pressure unsteady turbine stator port and unsteady expansion begins. The temperature will decrease along the channels due to expansion process developed by the stator nozzles and high pressure unsteady turbine blades. Unsteady expansion will finish when the pressure inside the channel is slightly lower than air from compressor, then the connection with the compressor is open, and the air coming from the compressor starts to fill the channels and push out the combustion gas from the channel (Fig 88). Combustion gas inside the channels is represented by high temperature values. It is seeing a scavenging process where air from the compressor acts like a piston scavenging the gas form the channels to the low pressure turbine (Fig 40). When the scavenging process finalizes the low pressure turbine port is closed. Again the ICWR Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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channels are closed, then the combustion process is carried out increasing the temperature and pressure inside the channels (combustion process it is not simulated on the model, proper ,operating conditions are applied using a patch option). Then the process starts again. (take into account that per 1 cycle, two process “Combustion – unsteady expansion –steady expansion” are carried out)

Fig. 89. Contours of Mach number.

122


Figure 90. Pathlines of the model (baseline engine modified with constant volume combustor).

Figure 89 shows the contours of Mach number. It is possible to observe high values of Mach number on the stator nozzles and close to the turbine blades walls. The maximum values are presented in the junction between the stator nozzles and the high pressure unsteady turbine blades. High pressure unsteady Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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turbine will utilize the energy from the fluid delivered by the nozzle channels to produce power. Figure 90 shows the path lines of the gas passing turbine blades. Also is possible to observe the behavior or direction of the gas inside the turbine and how it is scavenged from the rotor channels. Additionally it’s possible to notice the flow path inside the recirculating channels, that re–connect a par t of the high pressure unsteady turbine outlet with the high pressure unsteady turbine inlet. The thermal, gas dynamic calculations and simulation results let us conclude that it is possible to modify the base line engine with an internal combustion wave rotor, to increase the power generated by the engine and it’s thermal efficiency, and reduce the fuel consumption. Also such simulations expose the advantages and dis advantages of use unsteady flows to produce power. Computational fluid dynamic tools are able to expose the advantages and disadvantages of use unsteady flow to produce power. The aim of the research project was to test out the following theories: 1. The use of pressure wave exchanger increases the performance of baseline engine. 2. The use of pulse combustion chamber increases the performance in comparison with baseline engine. Taking into account the results it is possible to conclude: »»

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Performed thermodynamic calculations of baseline engine enhanced with pressure wave exchanger and pulse combustion chamber confirms the theory of the performance increasing implementing pressure wave exchangers and unsteady pulse combustion chamber in turbo engines. Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12

»»

The use of pressure wave exchanger applied to baseline engine “PowerGeneration X-01” increases the thrust by 11.4%, thermal efficiency by 15.3, and reduce the specific fuel consumption by 11.2% and fuel flow by 16.6%.

»»

The use of pulse combustion chamber applied to baseline engine “PowerGeneration X-01” increases the thrust by 104.1%, thermal efficiency by 11.7, and reduce the specific fuel consumption by 29% and fuel flow by 49.5%.

»»

In the performed simulations of pressure wave exchanger and pulse combustion chamber all factors seemed to be important to develop a correct physical results were taken into account. But not all factors were studied, as heat transfer and combustion problems, which can be analyse in future investigations.

»»

The results of thermodynamic analyses performed for the baseline engine topped by wave rotor and base line engine modified with constant volume combustor; show an increase of the overall efficiency and specific work on the baseline engine. Also, in both engine variants the fuel consumption has been decreased.

»»

The thermal, gas dynamic calculations and simulation results let us conclude that it is possible to modify the base line engine with an internal combustion wave rotor, to increase the power generated by the engine and it’s thermal efficiency, and reduce the fuel consumption. Also such simulations expose the advantages and disadvantages of use unsteady flows to produce power.

»»

Hypothesis, that devices using transient processes can be used to improve the performance of gas turbine engines, was confirmed by both, thermodynamic calculations, as well as the numerical simulations showing physical evidence of realizing them.

»»

1D simulation and thermodynamic calculations give the baseline parameters, which can be used to obtain an initial geometry of the models,


125

where the opening time of the channels can be found as well operational parameters of the engine variants.

126

»»

2D and 3D simulations have complex flow behaviour. Modelling a complex simulation, such as the flow inside a series of passages can take several man-months and computing time to complete. This was one of the project limitations, due to that it was necessary to assume some typical flow features to decrease the simulation process time.

»»

One-dimensional and multi-dimensional numerical models are developed to simulate unsteady flow in the wave rotor and around the high pressure unsteady turbine blades. The results agree well with predicted in the wave rotor and constant volume combustor theory. In the wave rotor simulation three-dimensional flow features were identified: strong skewing of the interface between hot and cold gases in the radial direction due to Coriolis accelerations induced by rotation, and also distortion of moving compression waves that create a complex flow wave pattern. In the constant volume combustor, two- dimensional model flow features were identified, where an optimal geometry and operational parameters were found after several simulations.

»»

Two–dimensional studies applied in the baseline engine modified with constant volume combustor, release that any modification in the geometrical and operational parameters of the model can increase or decrease the power produced by the engine.

»»

The relative velocity from the stator nozzles was treated as the reference value in order to obtain the force and power coefficient, which determine the relationship between the force developed by the blade in the simulations and in gas dynamic calculations; also determining the power produced by the turbine blades.

»»

Two-dimensional simulation of the engine modified with constant volume combustion detects a temporally free jet effect presented in the stator nozzle discharge. It is generated momentarily due the interaction of the Universidad de San Buenaventura, sede Bogotá • Colección Facultad de Ingeniería n.º 12

stator nozzle and high pressure unsteady turbine producing Laval nozzle geometry (stator nozzle and turbine blades), then strongly variation of the flow parameters is detected in the model.


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Akbari, P., & Muller, N. (2003). Performance improvement of small gas turbines through use of wave rotor topping cycles. Proceedings of Asme turbo expo 2003. ANSYS . (2012). ANSYS FLUENT User´s guide. ASM. (2010). ASM Metals Handbook. Cengel, Y., & Boles, M. (2002). Thermodynamics an Engineering approach. Mc Graw Hill. Cerpa, R. (2009). Numerical analysis of the untypical effects in a wave topping unit for a small turbojet. Warsaw: Faculty of power and aeronautical engineering - Warsaw University of Technology - M.Sc Thesis. Cerpa, R., Escobar, A., Girón, A., Morales, L., Guzman, O., López, A., & Bolívar, N. (2010). Construcción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción Fase I. Bogotá: Universidad de San Buenaventura. Cerpa, R., Piechna, J., Escobar, A., & Rico, M. (2011). Cálculos térmicos y de dinámica de gases de un turbojet “Power Generation X-01”, modificado con un rotor de ondas. INGENIUM. Cerpa, R., Vargas, S., Rico, M., Piñeros, C., & Maldonado, D. (2012). Construcción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción fase II. Bogotá: Universidad de San Buenaventura. Cerpa, R.,Vargas, S., Rico, M., Piñeros, C., & maldonado, D. (2013). COnstrucción y análisis numérico utilizando CFD “FLUENT” de la operación de un rotor de ondas aplicado a un motor a reacción Fase III. Bogotá: Universidad de San Buenaventura. Non-conventional Methods of Gas Turbine Engine Efficiency Improvement • Rafael Mauricio Cerpa Bernal Ph.D.

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Escobar, A., Cerpa, R., Pachón, D., & Mondragón, C. (2012). Diseño y COnstrucción de una turbina de gas para generación de baja potencia (TGBP) con ciclo regenerativo a partir de un turbo cargador. Revista Ciencia y Poder Aéreo. Girón, A., & Morales, L. (2010). Análisis estructural mediante elementos finitos de un rotor de ondas para el power generation X-01. Bogotá: Universidad de San Buenaventura - Aeronautical Engineering - B.Sc Thesis. Heiser, W., & Pratt, D. (2002). Thermodynamic Cycle of Pulse Detonation Engines. Journal of Propulsion and Power Vol. 18. Nalim, R., & Kerem, P. (2003). Internal combustion wave rotors for gas turbine engine enhancement. Proceedings of the International Gas Turbine Congress, 6. Pezhman, A., & Muller, N. (2003). Gas Dynamic Design Analysis of Charging Zone for Reverse Flow Pressure Wave Superchargers. ICES 2003-690. Pezhman, A., Nalim, R., & Muller, N. (2006). A Review of Wave Rotor Technology and its Applications. ASME Joint od Engineering for gas turnines and Power, 18. Piechna, J. (2005). Wave Machines, Models and Numerical Simulation. Warsaw: Oficyna Wydawnicza Politechniki Warszawskiej. Piechna, J., & Marcin, S. (2007). Design of micro - turbojet engine intended to be supercharged by wave rotor. Warsaw: Master thesis Faculty of power and aeronautical engineering - Politechnika Warszawska. Piechna, J., Cerpa, R., & Muller, N. (2010). Numerical Analysis of untypical effects in a wave topping unit for a small turbojet. INGENIUM, 9. Piechna, J., Cerpa, R., Muller, N., Pezhman, A., & Marcin, S. (2010). Numerical Analysis of the wave topping unit for small turbojet. Proceedings of ASME Turbo Expo - Power fro Land, sea and air, 9.

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Este libro se terminó de imprimir en la Unidad de Publicaciones de la Universidad de San Buenaventura, sede Bogotá, el día 19 de marzo de 2016.

Los resultados de investigación presentados en el presente libro fueron obtenidos de los proyectos “construcción y análisis numérico utilizando CFD de un rotor de ondas aplicado en un motor a reacción I,II y III” patrocinados por la Universidad de San Buenaventura Bogotá en cooperación con la Universidad Politécnica de Varsovia. El objetivo principal del estudio es comprobar la posibilidad de mejorar la operación de un motor a reacción con uso de métodos no convencionales de operación (flujo inestable). En el estudio se modificó un motor turborreactor base con dos diferentes sistemas, en el primero se implementó una sección adicional con un rotor de ondas, que actúa como una etapa de compresión y en el segundo caso se retiró la cámara de combustión convencional y se incorporo una nueva con combustión a volumen constante, dicha modificación también requirió de la adición de una etapa adicional de turbina para extraer la entalpia del fluido. El objetivo de la modificación del motor base es el de reducir el consumo específico de combustible, el flujo de combustible, además de aumentar la potencia de salida y la eficiencia del ciclo del motor a reacción estudiado. ISBN 958-8928-14-2 C.I. n.o 12 ISBN 958-8928-14-2 C.I. n.o 12

9 789588 928142

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9 789588 928142

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Diseño e impresión: Unidad de Publicaciones de la Universidad de San Buenaventura, sede Bogotá