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THE CONSTRAINT ANALYSIS OF A 250 kW MICROTURBINE

GENERATOR

By: Avnish Garg

Final YearB.Eng. in Electromechanical Engineering

Aston UniversityBirmingham, U.K.

Report prepared for:Dr. J. HillSchool of Engineering and Applied ScienceAston UniversityBirmingham, U.K.

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ACKNOWLEDGMENTS

I am indebted to my parents, my family for their trust and support. I am highly

grateful to my supervisor, Dr. J. Hill for his keen interest in my work and his generous

support throughout the duration of this project. His encouragement and motivation

spurred me onto greater heights. His valuable comments, suggestions, criticisms

inspired me to give off my best and improve the quality of my project at every step.

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SYNOPSIS

This project involves the development of a constraint (technical and economic) analysis for a

250 kWe microturbine engine as means for electric power generation. Various design

parameters have been identified and quantified in order to determine the economic viability

and performance characteristics of a 250 kW microturbine system. Microturbines are small-

scale distributed generation systems based on a similar technology to large-scale gas turbine

power plants but they work at low pressure ratios.

The key technical differences between a microturbine and a gas turbine are that most

microturbines (usually) use centrifugal (or radial flow) turbomachinery instead of axial

turbomachinery and a recuperator (heat exchanger) instead of a regenerator. A parametric

cycle analysis for the ideal and actual unrecuperated (simple) and recuperated gas turbine cycle

(known as the Brayton Cycle) has been carried out in order to evaluate the influence of

recuperation on the performance and fuel consumption of the microturbine. Effects on various

design and performance parameters have been analyzed while keeping the other input

parameters constant. Effects of different component efficiencies, pressure ratios and turbine

inlet temperatures on the overall efficiency, fuel costs and other design parameters have been

discussed. An effort has been made to determine optimum operating conditions for a 250 kW

microturbine system.

An attempt has been made to define the range of configurations and key design parameters that

are able to fulfil the requirements for a 250 kWe microturbine engine, hence defining the

design space. Key technical limitations of microturbines have been addressed and solutions for

these problems have been discussed. Current applications of microturbine systems have been

studied and possible future applications have been proposed.

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CONTENTS

Synopsis1 Introduction 52 Components of a Microturbine 6

2.1 Compressor 72.1.1 Centrifugal (or Radial Flow) Compressor 92.1.2 Axial Flow Compressor 11

2.2 Radial and Axial Flow Turbines 122.3 Combustion Chamber 142.4 Heat Exchanger 15

2.4.1 Regenerator 162.4.2 Recuperator 16

2.5 Other Components 183 Cycle Analysis 19

3.1 Ideal Simple Brayton Cycle 193.2 Ideal Brayton Cycle with Heat Exchange 283.3 Actual Simple Brayton Cycle 313.4 Actual Brayton Cycle with Heat Exchange 393.5 Electric Power Output and Shaft Power Required 433.6 Fuel Consumption and Costs 44

4 Conclusion 485 Nomenclature 506 References 527 Figures 548 Graphs 56

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1. INTRODUCTION

In the recent decades, many factors have contributed to the development and usage of

distribution generation technologies, such as microturbines, as a means to reduce load

on large power plants globally. Newfound awareness about pollution control

measures and emission-free power generation has made distributed generation a

necessity. Rising fossil fuel prices, depletion of fossil fuels and ever-increasing

electricity consumption have led to a situation of ‘energy crises’ and necessitated the

development of and research into alternative sources of energy such as bio-fuels and

refuse (both industrial and domestic). Recent energy legislations such as the Kyoto

Protocol which limit the levels of carbon dioxide and other atmospheric pollutants for

various sectors have spurred on this development. Microturbines are just one of these

means of distributed generation which are bound to fulfil these future energy needs of

the world.

A Microturbine Generator may be described as a stationary gas turbine power plant

which predominantly produces on-site electric power (prime-mover application)

which has a design electric output rating in the range of about 25 kWe to 500 kWe a

(Shane, 2002, p. 29) while conventional gas turbines are usually classified as those

which have outputs of greater than about 500 kWe. Salient features of microturbines

which make them appealing to customers include fuel flexibility, low toxic emissions,

compactness and modularity. One of the chief advantages of microturbine generators

is their simple design because of which they can be used for a large number of

applications by just making a few design modifications. Other possible applications of

microturbine include Combined Heat and Power (CHP), Hybrid Electric Vehicles

(HEV) and Heating, Ventilation & Air Cooling (HVAC) although development of

microturbines for these applications is currently in its initial stages.

a There is no complete consensus about the classification of a gas turbine as a microturbine or a conventional gas turbine among various cited sources. Hence, a broad range of values of electrical power outputs from various models has been mentioned by the author.

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2. COMPONENTS OF A MICROTURBINE

A 250 kWe microturbine has been discussed in this study due to the feasibility of

manufacture of its components. In microturbines with lower electric power outputs,

the machinability of the components reduces greatly and tendency of flaws increases,

thereby reducing the overall efficiency of the microturbine and increasing need of

maintenance and repair. Hence, a mid-range microturbine generator seems to be an

appropriate model for this study.

The key components of a typical microturbine are as follows (Stares and Mabbutt,

2002, pp. 67-72, Hamilton, 2003, p. 6-11):

a) Compressor (typically single-stage centrifugal type)

b) Turbine (typically single-stage radial flow type)

c) Combustion Chamber

d) Recuperator

Other components include the electric generator, bearings, power conditioning

systems, nozzles, and fuel filtration, metering and injection systems. These

components have not been analysed in this study. Additional components can be

added to the microturbine depending on the application of the system.

The microturbine generator (usually referred to as microturbine) works on principles

similar to larger gas turbines but is distinguishable from them with regard to a number

of technical aspects. Like large gas turbines, the thermodynamics of microturbines are

based on the Brayton cycle. The compressor and the turbine are mounted on a single

shaft along with the electric generator. Twin bearings support the shaft. The single

moving part of the single shaft design reduces the need for maintenance and enhances

overall reliability and durability.

The compressor compresses incoming atmospheric air. This air is then preheated in

the recuperator (only used in cycles with heat exchange) using heat from the exhaust

gases. The heated air from the recuperator is mixed with fuel in the combustion

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chamber which increases the temperature, velocity and volume of the gas. The turbine

extracts work from the hot exhaust gases, thereby generating shaft power. This shaft

power drives the compressor and rotates the electric generator (which converts this

mechanical power to electric power). The frequency of this electric power can be

modified as per the requirements using power electronics systems.

The recuperated cycle is typically a popular choice (when disregarding the cost of the

recuperator) for microturbines because of its ability to achieve high thermal

efficiencies at low compression pressure ratios and its suitability to radial flow

turbomachinery. Currently, most microturbines work at low turbine inlet temperatures

of about 900°C and compression pressure ratios of about 4:1 (Pullen et al., 2002, p.

87). At such low pressure ratios, the thermal efficiencies of unrecuperated

microturbines are relatively low. Hence, the use of the recuperator is as such essential

for viable power generation.

2.1 COMPRESSOR

Gorla and Khan (2003, p. 6) describe a Compressor as a turbomachine which

performs work on a compressible working fluid (usually air, in the case of gas

turbines) by reducing its volume and then allowing it to gradually expand. This

process imparts kinetic energy to the fluid in the impeller and increases its internal

temperature and pressure energy in the diffuser. The kinetic energy imparted to the

working fluid forces the air through the nozzle to make the fluid suitable for efficient

combustion of the fuel.

Though many types of compressors are in use nowadays, the two major types of

compressors used in gas turbines (and microturbines) are the Centrifugal (or Radial

Flow) Compressor and the Axial Flow Compressor. According to Pullen et al. (2002,

p. 90), centrifugal compressors and mixed-flow compressors (hybrid of centrifugal

and axial flow compressors) are popular choices for compressors in microturbine

generators “on grounds of efficiency and development costs” at low temperature and

pressure conditions.

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The ratio of the pressure at compressor exit to the pressure at compressor inlet

(usually atmospheric pressure in the case of gas turbines) is known as the

compression pressure ratio (Π) and plays an important role in the performance of the

microturbine system.

Centrifugal compressors are better suited for microturbines than axial ones due to the

following reasons (Energy Nexus Group, 2002, p. 3; Håll, 2002a, pp. 1-2;

Saravanamuttoo et al., 2001, p. 182):

a) Since microturbines need to use small turbomachinery, intricate designing, which

is an essential feature of axial compressors, is not feasible. Centrifugal

compressors are usually relatively more efficient at low pressure ratios (at which

microturbines work) due to their uncomplicated design, robustness and

insensitivity to flaws.

b) Centrifugal compressors can achieve higher pressure ratios per stage. This reduces

the number of stages and the size of the compressor significantly. Since size of

components is a critical factor for microturbines, centrifugal compressors are a

popular choice. Hence, centrifugal compressors in microturbines are usually

single stage models.

c) Centrifugal compressors can handle small volumetric flows with reasonably high

component efficiency. In the case of microturbines, blade height would be too

small to be practical for axial flow compressors.

d) In the size range of microturbines, centrifugal compressors offer minimum surface

and end wall losses thereby providing optimum efficiency.

Currently, the technology for centrifugal compressors is less developed than axial

compressors as the former had not found many applications before the advent of

microturbines. The complex design of the diffuser in centrifugal compressors reduces

their ease of manufacture. Another problem faced by centrifugal compressors is their

susceptibility to formation of deposits of particulate matter as this leads to corrosion

and reduction in durability of the compressor.

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According to Stares and Mabbutt (2002, p. 68), compressor materials for

microturbines vary from cast iron and aluminium to stainless steel. Other robust

materials such as titanium and nickel alloys (such as Inconels, Monels and Nimonics)

can be used to provide better durability to the compressor.

2.1.1 CENTRIFUGAL (OR RADIAL FLOW) COMPRESSOR

According to Saravanamuttoo et al. (2001, p. 152-4) and Gorla and Khan (2003, p.

143-4), a centrifugal compressor basically consists of a rotating impeller (within a

stationary casing), which imparts a high velocity (with both radial and tangential

components) to the fluid, and a stationary diffuser (“a series of fixed diverging

passages”) which decelerates the air with a consequent increase in static pressure

(diffusion).

In a centrifugal compressor, air enters the impeller eye and is spun at a high velocity

by the vanes on the disc of the impeller, (thereby imparting a “centripetal

acceleration” and increased static pressure to the compressed air) and leaves and

enters the diffuser via the tip of the impeller. Usually, centrifugal compressors are

designed such that about half of the rise in static pressure of the air occurs in the

impeller and the remainder takes place in the diffuser.

According to Gorla and Khan (2003, p. 150), the basic purpose of the diffuser is to

reduce the velocity of the air which leaves the compressor and enters the combustion

chamber, thereby ensuring “efficient combustion of the fuel” while maintaining high

levels of static pressure in the air. Since air has a natural tendency to break away from

the walls of the diverging passage and flow back in the direction of pressure gradient,

it loses some of the static pressure developed in the impeller and the diffuser due to

formation of ‘Eddy Currents’. The angle of divergence of the passages in the diffuser

should not exceed a certain design value to limit stagnation pressure loss (∆pb).

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Saravanamuttoo et al. (2001, pp. 163-4) state that to carry out the diffusion process in

as short a length as possible and to control the flow of the working fluid effectively,

the fluid leaving the impeller is divided by fixed diffuser vanes. During part-load

operation of the gas turbine, the flow direction varies with mass flow rate ( m ) and

pressure ratio (Π), thereby reducing the part-load efficiency of the gas turbine.

Usually, only large gas turbines use variable-angle diffuser vanes to adjust the flow

direction effectively over a wider range of operating conditions as incorporation of

this type of vanes increases the size and complexity of the system.

After leaving the diffuser vanes, the working fluid may be delivered to a volute and

then to the combustion chamber (via a heat exchanger, if used). A number of small

industrial gas turbines avoid using the diffuser vanes and instead use the volute alone

in order to reduce the compressor size.

Actual compression work done on the air and rise in pressure is affected by the

number of diffuser vanes (in terms of ‘slip’ factor σ), impeller tip speed (U);

‘windage’, disc friction and casing losses (in terms of power input factor ψ) and

compressor inlet temperature T1 (Saravanamuttoo et al., 2001, pp. 155-7; Gorla and

Khan, 2003, pp. 148-150).

According to Gorla and Khan (2003, pp. 145-6), the impeller tends to undergo high

stress forces. Curved blades (forward-curved and backward-curved) tend to straighten

out due to these centrifugal forces and bending stresses are set up in the vanes. Radial

blades are free from bending stresses and are “somewhat easier to manufacture than

curved blades”. Increased mass flow rate does not change the pressure on radial

blades but forward-curved blades can achieve higher pressure ratios.

Centrifugal stresses developed in the impeller of the single-stage centrifugal

compressor (usually using light alloys such as aluminium) limit the impeller tip speed

U to about 460m/s and the pressure ratio to about 4:1. According to Bullin (2002, p.

2), microturbine generators operate at pressure ratios of typically 4:1. Hence, it may

be inferred that centrifugal compressors are well-suited for them.

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Currently, higher impeller tip speeds can be used with high-strength alloys such as

titanium or stainless steel and pressure ratios of 8:1 can be achieved but unsuitability

for mass production and low efficiencies associated with single-stage compressors act

as a deterrent to their popularity and increase costs. Additional losses in static

pressure and efficiency occur in compressors due to stalling (breakaway of flow) of

stages, surging (complete breakdown of continuous steady flow) and choking (of

mass flow at various stages) (Saravanamuttoo et al., 2001, pp. 155-7; Pullen et al.,

2002, p. 90; Gorla and Khan, 2003, p. 153-55, 187).

2.1.2 AXIAL FLOW COMPRESSOR

According to Saravanamuttoo et al. (2001, p. 182), “the axial flow compressor

consists of a series of stages, each stage comprising of a row of rotor blades followed

by a row of stator blades. The working fluid is initially accelerated by the rotor blades,

and then decelerated in the stator blade passages wherein the kinetic energy

transferred in the rotor is converted to static pressure. The process is repeated in as

many stages as are necessary to yield the required overall pressure ratio.”

In essence, the components of the axial compressor are somewhat analogous to the

centrifugal compressor where the rotor blades replace the impeller and the stator

blades replace the diffuser. The flow of the working fluid is axial (in the direction of

the axis of the compressor) to the axis of rotation (of the blades) as compared to the

radial (centripetal) direction of fluid flow in the centrifugal compressor.

As the pressure increases in the direction of flow, the volume of working fluid

decreases. The height of the blades is decreased along the axis of the compressor to

keep the axial velocity of the fluid approximately constant for each stage. The fluid is

directed at the correct angle onto the first stage by a row of inlet guide vanes. As the

number of stages (N) in the axial compressor increases, the overall pressure ratio

which can be achieved by it increases (Saravanamuttoo et al., p. 187).

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Saravanamuttoo et al. (2001, p. 188) state that a high stagnation temperature rise

reduces the number of stages for a given pressure overall pressure ratio. In order to

ensure this, the following features need to be incorporated in the axial compressor – (a)

high blade speed; (b) high axial velocity; and (c) high fluid deflection in rotor blades.

The blade speed is limited by blade stresses and adverse pressure gradient and

aerodynamic considerations combine to limit axial velocity and fluid deflection.

According to Gorla and Khan (2003, pp. 187-8) one of the important characteristics of

the axial flow compressor is its ability to achieve high pressure ratios at good

efficiency. Modern axial flow compressors can provide efficiencies of 86-90%. Since

large gas turbines work at high pressure ratios and are not affected significantly by the

size of turbomachinery, axial compressors are suitable for such turbines. Axial

compressors (especially multi-stage) are unsuitable for microturbines since

compactness of turbomachinery is a very important requirement.

2.2 RADIAL AND AXIAL FLOW TURBINES

Gorla and Khan (2003, p. 283) describe a turbine as a machine which extracts kinetic

energy from hot expanding gases leaving the combustion chamber, converting this

kinetic energy into shaft power to drive the compressor and the engine accessories. A

reduction in pressure ratio of the expanding gases also takes place in the turbine.

In essence, a turbine has just the opposite function to a compressor which performs

work on the fluid to increase the pressure on it. The basic purpose of the turbine is to

extract as much work as possible from the fluid so as to provide acceptable levels of

power drive the compressor. There are many similarities between the design and

features of turbines and compressors. Turbines, like compressors, can be classified as

axial, radial or mixed according to the type of fluid flow being used. Axial flow

turbines work on similar principles as axial flow compressors.

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According to Saravanamuttoo et al. (2001, pp. 366-7), in the radial flow turbine, fluid

flow with high tangential velocity is directed inwards and leaves the rotor with as

small a whirl (almost axial) velocity as practicable near the axis of rotation. Though

the radial flow turbine has similar components as the centrifugal compressor, a ring of

nozzle vanes replace the diffuser vanes. According to Gorla and Khan (2003, pp. 307-

8), a diffuser is usually used at the exit of the turbine to reduce velocity of exhaust

gases to a negligible value.

According to Håll (2002b, p. 6-8), since the turbine is at the hot end of the gas turbine

engine and is expected to run at high speeds, its blades undergo a number of stresses

such as centrifugal stress, bending stresses, creep, mechanical and thermal fatigue

which can lead to mechanical failure of the blades. In order to ensure durability of the

turbine blades in microturbines, the temperature of the expanding gases (Turbine Inlet

Temperature T3) is limited to a ‘metallurgical limit’. Pullen et al. (2002, p. 91) state

that both radial and axial tip clearances need to be controlled in radial flow turbines

leading to mechanical design failure.

Energy Nexus Group (2002, p. 2) states that in order to obtain optimum overall

efficiency, it is advantageous to operate the expansion turbine at the highest practical

temperature consistent with economic materials and to operate the compressor with

inlet airflow at as low a temperature as possible. According to Dr. J.L. Hill (personal

communication, November 9, 2005), due to advancement in materials technology, it

is possible to increase the turbine inlet temperature, compression pressure ratio and

the efficiency of the microturbine by using high-temperature alloys such as Inconels,

Monels and Nimonics. The main barrier to large-scale use of these materials in

microturbines is the high cost involved.

Gorla and Khan (2003, pp. 307-8) and Pullen et al. (2002, p. 91) assert that the main

advantages of radial flow turbines are that they are compact and can run at high

speeds (to extract greater amount of shaft power). They are particularly efficient when

dealing with small mass flows (as in microturbines) though for larger mass flows,

axial flow turbines are preferable. A single stage in a radial flow turbine can accept a

high-pressure ratio. Most of the reasons for radial flow turbines in microturbines are

the same as those for centrifugal compressors.

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According to Dambach et al. (2002, pp. 101, 106), another reason for using single-

stage radial flow turbines in microturbines is that they suffer less from tip-leakage

loss as compared to equivalent (usually multi-stage) axial flow turbines. The tip-

leakage loss for an axial flow turbine can be about four times greater than that for a

centrifugal turbine. The tip speed for a centrifugal turbine is significantly greater than

that for an equivalent axial flow turbine. Higher tip speeds enable larger work in

single-stage radial flow turbines than is obtained in single-stage axial flow turbines

and reduce tip leakage and clearance losses.

Pullen et al. (2002, p. 91) suggest the use of mixed flow turbines in microturbine

generators as they are capable of higher mass flow rates than their radial counterparts

for the same expansion pressure ratio (p3/p4) and due to their increased compactness

and efficiency.

Saravanamuttoo (2001, p. 7) states that when operational flexibility is required in the

gas turbine, an additional free (or power) turbine may be used in order to enhance the

efficiency of the system. In the opinion of the author, although a power turbine may

be suitable for larger gas turbines, it is undesirable to use it in a microturbine engine

as it would increase the size and cost of the unit significantly without any appreciable

change in efficiency.

2.3 COMBUSTION CHAMBER

The fuel (either in its original form or after gasification in the gasifier) undergoes

combustion (in the presence of air supplied by the compressor) in the combustion

chamber. Combustion in gas turbines is a continuous process initiated by an electric

spark, and thereafter continued by the self-sustaining flame. A number of types and

configurations of combustion chambers are used in gas turbine engines depending

upon the requirements of the engine (Saravanamuttoo et al., 2001, p. 266).

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Due to the high temperatures involved in the combustion of fuels, the combustion

chamber has to be highly resistant to mechanical and thermal breakdown. In recent

times, combustion efficiency of the chamber has gained great importance as efficient

combustion of the fuel reduces pollutants such as oxides of carbon (CO2 and CO),

nitrogen (NOx) and unburned hydrocarbons (UHC). Hence, the current goal in

combustion chamber design is to utilise as much of the given fuel as possible

(complete combustion), i.e. attainment of almost 100% combustion efficiency

(Saravanamuttoo et al., 2001, pp. 267-9).

With the advent of various bio-fuels and waste gases as fuels and due to the

introduction of stringent environment protection legislations globally, the need for

better combustion chamber design has become imperative. It may be inferred from

Saravanamuttoo et al. (2001, pp. 266-8) and Shepherd (1960, p. 234-6) that annular

and cannular combustion chambers are well-suited for microturbine engines because

of their compactness and simplicity of design. Bullin (2002, p. 5) suggests the use of

catalysts in the combustion process as an alternative to conventional combustion may

boost the overall efficiency of the microturbine.

2.4 HEAT EXCHANGER

According to Shepherd (1960, p. 5), the basic purpose of a heat exchanger is to reduce

fuel supply for a given required temperature rise by utilizing the heat in the exhaust

gases to raise the temperature of the working fluid immediately after compression.

Eastop and Croft (1990, p. 44-45) classify heat exchangers into three broad categories:

recuperative, regenerative and evaporative. Recuperative heat exchangers (or

recuperators) and regenerative heat exchangers (or regenerators) are commonly used

types of equipment for heat transfer in gas turbines.

Cengel and Turner (2005, p. 374) assert that heat exchangers are suitable for gas

turbines only when the turbine exit temperature T4 is greater than the compressor exit

temperature T2 else heat will flow in the reverse direction (to exhaust gases). Since

gas turbines operating at high pressure ratios (usually in the case of large gas turbines)

encounter this situation frequently, heat exchangers are rarely used there. Hence, heat

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exchangers are more suitable for microturbines which inherently work at low pressure

ratios.

2.4.1 REGENERATOR

According to Eastop and Croft (2002, p. 181-2), in a regenerator, the hot and cold

fluids pass alternately across a matrix of material of considerable specific heat

capacity; the material is heated by the hot fluid and then cooled by the cold fluid,

thereby making the heat transfer process cyclic in nature. The matrix may be kept

stationary or made to rotate through the hot and cold fluids. According to Shepherd

(1960, p. 250-67), though a regenerator is advantageous with respect to power-to-

weight ratio, excessive leakage losses (of working fluid) make them unsuitable for

long-term use in industrial applications like microturbines. Regenerators are difficult

to manufacture due to the machinability issues associated with (especially in the case

of small regenerators, which could be used for microturbines) and brittleness (which

leads to cracking) of the ceramic materials which are usually used.

2.4.2 RECUPERATOR

Shepherd (1960, p. 250-1) describes a recuperator as a heat exchanger in which heat is

transferred across a solid (usually metallic) wall between the hot and cold fluids. In

the case of recuperated microturbines, the function of a recuperator is to extract heat

from the gas turbine exhaust gases in order to preheat the air used in the combustion

process, and thereby reduce the amount of fuel used to reach operating temperature

(Bullin, 2002, p. 3). Stares and Mabbutt (2002, p. 69) state that predominantly

recuperators used in microturbines are “metallic of a matrix or honeycomb-type

construction”. Recuperated microturbines are more popular than their unrecuperated

counterparts in industrial applications.

According to Bullin (2002, p. 8-10), stainless steel primary surface recuperators are a

popular choice for heat exchange in microturbines currently while research is being

carried out on alternative recuperator design utilizing brazed fin and plate technology.

In primary surface recuperators, the plates are not bonded together. They are instead

welded together around the edge, and are clamped together thus allowing for thermal

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expansion without the transmission of high stresses to the joints (as is the case with

brazed recuperators). This tends to increase reliability and durability due to reduced

probability of thermal stress failure and consequential leakage of fluids. It can further

be inferred that the box-shaped recuperator is a well-suited type of recuperator for

microturbines due to its high effectiveness and comparatively low capital costs.

According to Stares and Mabbutt (2002, p. 69), chief design constraints for

recuperators are the need for cost-effectiveness and high thermal effectiveness ε.

Long-term recuperator performance is dependent on the type of fuel and thermal

cycling history. Since recuperators work at the hot end of the microturbine, efforts are

being made to reduce the formation of thermal fatigue (leading to mechanical failure)

in the recuperator material. Since recuperators are usually comprise of robust

materials such as stainless steels and high temperature alloys, they are usually

preferred to regenerators (which use brittle materials such as ceramic) for use in

microturbines.

According to Dr. J.L. Hill (personal communication, November 9, 2005), a major

problem faced by recuperators in microturbines running on refuse-based fuels or

biomass is the formation of deposits of unburned particulate matter on the honeycomb

structure, thereby leading to accelerated corrosion of the recuperator material and

reduced effectiveness of the recuperator. High temperatures at the hot end further

contribute to this corrosion process. Hence, efficient combustion of the fuels is an

essentiality for efficient recuperation of heat from exhaust gases. High temperature

alloys are well-suited materials for recuperators but their cost-effectiveness currently

makes them impractical for large-scale manufacture of microturbine generators.

Borbely and Kreider (2001, p. 280) state that the use of recuperators in microturbines

limits the amount of recovered heat which could be used for CHP applications such as

water heating and space heating.

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2.5 OTHER COMPONENTS

According to Energy Nexus Group (2002, p. 5), single-shaft microturbines contain

digital power controllers to convert the high frequency Alternating Current produced

by the electric generator into usable electricity. The high frequency Alternating

Current is rectified to Direct Current, inverted back to 60 or 50 Hz AC, and then

filtered to reduce harmonic distortion. This is a critical component in the single-shaft

microturbine design and represents significant design challenges, specifically in

matching turbine output to the required load. Most microturbine power electronics are

generating 3-phase electricity.

The shaft of the microturbine is typically supported on two bearings. According to

Pullen et al. (2002, p. 93-4), although conventional oil bearings are extremely durable,

they are only suitable if the shaft has a low diameter and large clearances to reduce

excessive losses. Leakage of oil is another problem associated with this type of

bearing. Magnetic bearings and air bearings are new alternatives but are cost-effective.

According to Saravanamuttoo (2001, p. 36-7), a gasifier can be attached to a

microturbine when the fuel (solid or liquid) being used contains high levels of

impurities (usually vanadium and sodium, which may cause corrosion of the turbine).

The purpose of the gasifier is to transform a fuel such as poor-quality coal or heavy

oil into a clean gaseous fuel. The usage of gasifier along with a microturbine plant

gives potential for power generation using virtually any waste material (such as solid

refuse or liquid slurry).

The nozzle design (convergent, divergent or convergent-divergent) and performance

also affects the overall performance of the microturbine system to some extent as

choking losses occurring in the nozzle reduce thermal efficiency of the system.

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3. CYCLE ANALYSIS

The basic working principles of a microturbine are the same as those for gas turbines.

Both are forms of heat engines which can be simply described using the First and the

Second Law of Thermodynamics. Gas turbines are basically engines which convert

chemical energy into mechanical energy and finally into electrical and heat energy (in

Combined Heat and Power installations). The following sections contain a

thermodynamic analysis of the Brayton Cycle, both unrecuperated and recuperated.

The key difference between the ideal analyses and the actual analyses is the fact that

the former does not take into account efficiencies of the components. Other

modifications such as reheating and intercooling can be made to the cycle but these

modifications will not be discussed in the study as they are not used by microturbines

currently.

3.1 IDEAL SIMPLE BRAYTON CYCLE

According to the Cengel and Turner (2005, pp. 367-8), the ideal Brayton Cycle is a

gas power cycle which is composed of four internally reversible processes:

Process 1-2 Isentropic compression

Process 2-3 Isobaric heat addition

Process 3-4 Isentropic expansion

Process 4-1 Isobaric heat rejection

In the analysis of the ideal simple cycle, the following air-standard assumptions are

being made (Saravanamuttoo et al., 2001, pp. 45-6; Shepherd, 1960, p. 27):

a) Processes 1-2 (compression) and 3-4 (expansion) are both adiabatic (processes

involving no heat transfer) and reversible in nature.

b) There are no losses in any of the components during the thermodynamic cycle.

20

c) The properties of the working fluid (such as density and molecular weight) used in

the cycle remain constant throughout the thermodynamic cycle, thereby

suggesting that the working fluid is a perfect gas.

d) The specific heat capacities at constant pressure (cP) and at constant volume (cV)

and the heat capacity ratio (γ) of the working fluid are constant throughout the

thermodynamic cycle.

e) Complete (perfect) combustion of the fuel is taking place in the combustion

chamber.

f) No leakage occurs in the system, thereby emphasising that the mass flow of the

working fluid is constant throughout the cycle.

g) The mass of the fuel is negligible.

h) The compressor inlet pressure is equal to the turbine exit pressure, thereby

emphasizing that there are no pressure losses during the course of the cycle.

Using the Steady Flow Energy Equation for a single-stream system, the cycle

efficiency of the Brayton Cycle can be obtained. Due to the assumptions being taken,

the energy balance for the system (Cengel and Turner, 2005, pp. 542-3) may be

written as follows:

ieieieoutin zzguuhhmWQ ..

2

1. 22 … (1)

inQ is the rate of heat supply to the system

outW is the rate of work done (shaft work, in this case) by the working fluid

m is the mass flow rate of the working fluid

21

hi and he are the enthalpies b of the working fluid at the inlet and exit states

respectively

ui and ue are the average flow velocities of the working fluid at the inlet and exit states

respectively

g is the acceleration due to gravity

zi and ze are the elevations of the inlet and exit states

If equation (1) is divided by the mass flow rate m , the following expression will be

obtained:

ieieieoutin zzguuhh

m

W

m

Q ..

2

1 22

… (2)

In the case of an ideal gas turbine, it may be assumed that the difference between the

elevations of the inlet and exit points of the working fluid is negligible, i.e. ∆z ≈ 0,

and that the change in kinetic energy of the working fluid between the inlet and is

negligible, which implies that ∆u ≈ 0 (since it has already been stated that the mass

flow remains constant throughout the cycle in assumption ‘f’ above). If QmQin

and WmWout , equation (2) may be modified as follows:

ieoutin hhWQ … (3)

(derived from Cengel and Turner, 2005, pp. 542-3)

It can be clearly seen that equation (3) is a form of the ‘First Law of

Thermodynamics’ according to which the “total energy of the system during a process

is equal to the difference between the total energy entering the system and the total

energy leaving the system during the process” (Cengel and Turner, 2005, p. 159).

b All work (W) and heat (Q) quantities used in the calculations have been expressed as energy divided by mass flow of air. Another assumption which is being made throughout the analysis is that the mass

flow rate of the fuel ( fm ) is negligible as compared to the mass flow rate of air ( am ) used in the

system. Hence, it may be assumed that afa mmm .

22

If equation (3) is applied to the various processes of the ideal Brayton Cycle, the

following expressions will be obtained (Cengel and Turner, 2005, p. 368;

Saravanamuttoo et al., p. 46):

CWhhW 2121 Work done by compressor on working fluid … (4)

inQhhQ 2332 Heat supplied to system … (5)

TWhhW 4343 Work done on turbine by working fluid … (6)

outQhhQ 1414 Heat emitted from system … (7)

For any thermodynamic cycle, the thermal efficiency ηth can be described as:

in

netth Q

W

suppliedheat

outputnet work … (8)

(Cengel and Turner, 2005, p. 227)

In the case of a Brayton Cycle, the net work done by the system (Wnet) is the sum of

the work done on the compressor (WC) and the work done by the turbine (WT):

21432143 hhhhWWWnet … (9)

(Saravanamuttoo et al., 2001, p. 46)

By substitution of Wnet and Qin from equations (9) and (5) into equation (8), the

thermal efficiency of the Brayton Cycle may be obtained as:

23

2143, hh

hhhhBraytonth

(Saravanamuttoo et al., 2001, p. 46)

23

Since Tch P . for a gas in equilibriumc, the above equation (Saravanamuttoo et

al., 2001, p. 47) may be re-arranged as follows:

23

2143, .

..

TTc

TTcTTc

P

PPBraytonth

Since it is being assumed that the specific heat capacity at constant pressure of the

working fluid remains constant, the above equation may be arranged as follows:

23

1243, TT

TTTTBraytonth

… (10)

Since processes 1-2 (compression) and 3-4 (expansion) are assumed to be isentropic,

it can be said that (Saravanamuttoo et al., 2001, p. 47):

1

1

2

1

2

p

p

T

T and

1

4

3

4

3

p

p

T

T

Since pressure losses are negligible, pressures at various points of the cycle may be

related as 4312 pppp constant. Here, the constant may be represented by Π and

is known as the pressure ratio.

4

3

1

2

p

p

p

p … (11)

1

4

3

1

2

T

T

T

T … (12)

(Saravanamuttoo et al., 2001, p. 47; Cengel and Turner, 2005, p. 368)

Therefore,

1

12 .TT and

1

43 .TT

c All temperatures used for calculations are in K (absolute) although in actual practise, °C is a popular unit for temperature. K = °C + 273

24

Substitute T2 and T4 in equation (10):

1,

11Braytonth … (13)

(Hodge, 1955, p. 160; Cengel and Turner, 2005, p. 368)

In equation (13), it may be noted that the ideal Brayton Cycle efficiency is

independent of inlet or exit temperatures. It is only dependent on two factors, namely

the pressure ratio of the system (Π) and the heat capacity ratio (γ) of the working fluid

(which represents the atomicity of the working fluid as mono-atomic, di-atomic, etc.).

Therefore, in an ideal scenario, if the pressure ratio of the system is increased, the

thermal efficiency of the system increases. An interesting point which may be noted is

that if the working fluid is compressed to an infinite pressure ratio, the system tends to

become 100% efficient, i.e. 1lim , Braytonth .

The values for the Ideal Brayton Cycle Efficiency for pressure ratios of 1 to 40 have

been calculated and plotted in Graph (1). The value of γ is taken to be 1.4 for dry air.

It can be seen that the value of efficiency keeps increasing continuously along with

the pressure ratio. It may also be noted that for a unity pressure ratio (which implies

that no compression of the working fluid is taking place); the efficiency of the cycle is

zero, which means that no positive work output can be obtained from the gas turbine.

Another significant quantity which affects the feasibility of a gas turbine is the

Specific Work Output. It is a major factor deciding the size of a gas turbine power

plant for a given power. The specific work output can be determined by modifying

equation (9) for net work output into a non-dimensional form as follows

(Saravanamuttoo et al., 2001, p. 47):

1

2

1

4

1

3

1

1. T

T

T

T

T

T

Tc

W

P

net

25

1

12 .TT and

13

4

TT may be substituted into the expression above:

1

1

1

1

3

11

3

1

.1.

1

. T

TT

TT

T

Tc

W

P

net

1

1

1

3

1

11.

. T

T

Tc

W

P

net … (14)

(derived from Saravanamuttoo et al., 2001, p. 47; Hodge, 1955, p. 160)

In equation (14), it may be observed that the Specific Work Output of the cycle is

dependent on the Compressor Inlet Temperature (T1) and Turbine Inlet Temperature

(T3) along with pressure ratio and heat capacity ratio unlike the cycle efficiency that is

independent of temperature. Since T1 is the ambient temperature and is not under

human control, the only factors which can susceptible to human intervention in this

case are the pressure ratio (Π) and the turbine inlet temperature (T3).

In practice though, T3 can only be increased up to a certain limit as the metallic

turbine blades, being at the hot end of the gas turbine, undergo mechanical failure due

to the generation of thermal and mechanical ‘creep’ (both of which complement each

other) by the high temperatures present in the turbine region of the gas turbine. This

limit on the turbine inlet temperature is known as the ‘metallurgical limit’ and has

affected the demand of gas turbines and microturbines as power generation equipment

adversely. Research is being carried out in order to manufacture turbine blades with

high-temperature alloys which can tolerate high turbine inlet temperatures as higher

values of T3 will increase the specific work output from the gas turbine substantially

(Saravanamuttoo et al., 2001, pp. 47-8).

26

Currently, excessive costs of high-temperature alloys act as a barrier to the

manufacture of turbine blades for microturbines from these materials though there is a

future possibility of such a revolution taking place once the benefits related to use of

high-temperature alloys for microturbine blades exceed their costs and the demand for

microturbines increases.

Graph (2) shows the values of Specific Work Output under the following conditions:

γ = 1.4 (for dry air)

1T 15°C (288K)

3T from 500°C (773K) to 1500°C (1773K) at increments of 50°C

from 1 to 40 at increments of 1

The pressure ratio (Πopt) for optimum specific work output for a given compressor

inlet temperature and turbine inlet temperature can be calculated by differentiating

equation (16) with respect to Π as follows:

011

1..

1

11

3

1

T

T

Tc

W

optP

net

01

.1

11

3

opt

opt

T

T

1

3

21

T

Topt

12

1

3

T

Topt … (15)

(Saravanamuttoo et al., 2001, p. 47-8)

27

In order to obtain the optimum specific value for any given values of T1 and T3, Πopt

can be substituted from equation (15) into equation (14):

2/1

1

32/1

1

31

3

1

11

1.. T

T

T

TT

T

Tc

W

optP

net

2

1

3

1

1.

T

T

Tc

W

optP

net … (16)

(derived from Saravanamuttoo et al., 2001, p. 48)

The optimum values of pressure ratios and corresponding specific work outputs have

been tabulated in represented by a straight line on Graph (2). The value of γ = 1.4 for

dry air has been used. The reason for the decrease in specific work output after an

increase is that at higher compression pressures, the effect of the pressure ratio

dominates over the effect of the temperature ratio (ratio of T3 and T1). According to

Cengel and Turner (2005, p. 39), this leads to a need for compromise between specific

work output and efficiency. If the specific work output is low then the larger mass

flow (leading to a larger gas turbine unit) is required to obtain the same power output.

28

3.2 IDEAL BRAYTON CYCLE WITH HEAT EXCHANGE

This is a modification of the simple Brayton Cycle where an ideal heat exchanger

(with an effectiveness of 100%) is added to the system. In this case, T5 and T6 are

equal to equal to T4 and T2 respectively. Therefore, exhaust heat from process 4-6 can

be completely transferred to process 2-5 after compression (1-2), thereby conserving

the fuel which would have otherwise been required to raise the temperature of the

working fluid from T2 to T4. The net work output is not affected by the addition of a

heat exchanger but the heat supplied to the system (Qin) reduces from 23 hh to

53 hh and the heat emitted by the system (Qout) reduces from 14 hh to

16 hh (Saravanamuttoo et al., 2001, pp. 48-9; Cengel and Turner, 2005, 374-5).

In addition to the assumptions stated for the simple Brayton Cycle earlier, an

additional assumption applicable to the heat exchange cycle is that the heat exchanger

used in the system in a countercurrent flow heat exchanger which performs ‘complete

heat exchange’. So, the “temperature rise on the cold side is maximum possible and

exactly equal to the temperature drop on the hot side” (Saravanamuttoo et al., 2001, p.

46; Cengel and Turner, 2005, p. 374-5).

Using equations (5), (8) and (9), the thermal efficiency of the ideal Brayton Cycle

with Heat Exchange will be:

53

2143, hh

hhhhHEth

… (17)

(Saravanamuttoo et al., 2001, p. 48)

Here, h5 can be obtained from the expression for the effectiveness (ε) of a heat

exchanger which is:

24

25

hh

hh

(Cengel and Turner, 2005, p. 375)

29

2245 . hhhh … (18)

Substitute h5 into from equation (18) into equation (17):

2243

2143,

. hhhh

hhhhHEth

… (19)

Since an ideal heat exchanger is being used in this case, ε = 100%:

43

2143, hh

hhhhHEth

(derived from Saravanamuttoo, 2001, p. 48)

Since Tch P . for a gas in equilibrium, the above equation may be re-arranged as

follows:

43

2143, .

..

TTc

TTcTTc

P

PPHEth

, or

43

12, 1

TT

TTHEth

Since the processes are isentropic,

1

12 .TT and

1

34

TT can be

substituted into the above equation:

1

33

1

1

1,

.1

TT

TTHEth

30

1

3

1

, 1

TTHEth

… (20)

(Saravanamuttoo et al., 2001, p. 48-9; Cengel and Turner, 2005, p. 375)

From equation (20) and Graph (3), it may be deduced that HEth, reduces if there is an

increase in pressure ratio and increases if there is an increase in the turbine inlet

temperature. Contrary to the efficiency of the simple cycle, the efficiency of the heat

exchange cycle decreases with an increase in pressure ratio after an initial increase.

Similar to specific work output, thermal efficiency of the heat exchange cycle also

increases up to an optimum value and then decreases due to the dominance of the

pressure ratio over the temperature ratio. According to Saravanamuttoo (2001, p. 49),

at higher pressures than

1

.2

1

13 /

TT [equation (15)], the heat exchanger starts

to cool the air leaving the compressor, thus reducing the overall thermal efficiency.

Hence, it may be inferred that a heat exchange Brayton Cycle is most efficient at low

pressure ratios and reduces the fuel consumption of the gas turbine, thereby making it

a good substitute to the simple Brayton Cycle at low pressure ratios.

The values of efficiency of the ideal Brayton Cycle with Heat Exchange for the

following parameters have been plotted on Graph (3):

ε = 100%

γ = 1.4 (for dry air)

1T 15°C (288K)

3T from 500°C (773K) to 1500°C (1773K) at increments of 50°C

from 1 to 40 at increments of 1

As the net work output for a heat exchange cycle is the same as the simple cycle, the

specific work output also remains the same [equation (16)]. Hence, Graph (2) for

specific work output applies to the heat exchange cycle as well.

31

3.3 ACTUAL SIMPLE BRAYTON CYCLE

The actual Brayton Cycle has much lower efficiencies than the ideal cycle because it

uses real components (compressor and turbine) which have efficiencies lower than

100% due to the presence of number of component losses such as friction and

turbulence. Most of the assumptions stated for ideal systems earlier do not apply to

actual systems. Other combustion losses (due to incomplete combustion of fuel),

mechanical losses (due to bearings, auxiliaries, etc.) and loss of heat to surroundings

further reduce the efficiency of the cycle. Leakage losses can reduce the mass flow

rate of air and fuel considerably. The main reason for low actual cycle efficiencies is

that under actual conditions, the thermodynamic processes become irreversible.

Pressure losses in the system during constant pressure (ideally) heat addition and heat

rejection processes also contribute to these discrepancies. Other types of losses may

also occur in the system but these are usually ignored (Saravanamuttoo et al., 2001,

pp. 53-66; Shepherd, p. 27, 47-49). The changes in ideal assumptions have been listed

below:

a) All processes are irreversible in nature as some amount of energy is lost to the

environment.

b) Components losses are being considered during the thermodynamic cycle. Hence,

the efficiencies of the compressor (ηC), turbine (ηT) and other components are not

100%. Also, mechanical efficiency (ηm) is less than 100%.

c) The properties of the working fluid used in the cycle do change throughout the

thermodynamic cycle, but they are being assumed constant during the actual cycle

calculations.

d) Different values for constants such as specific heat capacity at constant pressure

(cP) and the heat capacity ratio (γ) are being considered for air during compression

processes 1-2a and for combustion gases during expansion processes 3-4a. For

more accurate results, these values are expected to vary with temperature.

Dry air: cP,a = 1.005 kJ/kg.K, γa = 1.40

Combustion gases: cP,g = 1.148 kJ/kg.K, γg = 1.33

32

e) Incomplete combustion of the fuel is takes place in the combustion chamber with

an efficiency ηB.

For the actual cycles, the letter ‘a’ will be used to differentiate between actual and

isentropic parameters. The actual Compressor Exit Temperature (T2a) is higher than

the isentropic Compressor Exit Temperature (T2) and the actual Turbine Exit

Temperature (T4a) is higher than the isentropic Turbine Exit Temperature (T4). Due to

these changes in the turbine exit temperature and compressor exit temperature, the

area under the curve reduces from Area (1-2-3-4-1) to Area (1-2a-3-4a-1). Since the

area under the T-s curve represents net work done by the system, this reduction in

area (under the curve) reduces the net output and thermal efficiency of the gas turbine

system (Thomson, 1949, pp. 39-41).

Now, the energy equations (4), (5), (6) and (7) will change to:

aa hhW 2121 Work done by compressor on working fluid … (21)

aa hhQ 2332 Heat supplied to system … (22)

aTaa WhhW ,4343 Work done on turbine by working fluid … (23)

aoutaa QhhQ ,1414 Heat emitted from system … (24)

Mechanical losses occur during transmission of power mainly due to bearing friction

and windage in the ducts. So, the net work done by the compressor changes to

maaC hhW 21, where aCW , is actual turbine work which is required to drive the

compressor divided by mass flow and m is the mechanical transmission efficiency

for transmission of power from the turbine to the compressor (Saravanamuttoo et al.,

2001, p. 66). An assumed value of %99m has been used in the calculations.

33

Now, the net work done by the system (Wnet) [equation (9)] will change to:

m

aaaCaTanet

hhhhWWW

21

43,,,

… (25)

(derived from Saravanamuttoo et al., 2001, p. 75)

Similarly, due to incomplete combustion of the fuel in the combustion chamber, the

heat needed by the system increases and the combustion efficiency (ηB) is lower than

100%. Therefore, the heat supplied by the fuel becomes:

B

aain

hhQ

23

,

… (26)

An assumed value of %98B has been used in the calculations.

Fixed values for Specific Heat Capacity (cP) and Heat Capacity Ratio (γ) have been

used in the design calculations but in reality, they vary with temperature changes and

changes in chemical composition of the working fluid due to internal combustion,

though these effects are usually negligible (Saravanamuttoo et al., 2001, p. 66-8). For

more accurate results, property tables or charts for gases may be used to obtain

enthalpy values at each temperature.

Equation (11) for pressure ratio is valid only for the ideal Brayton cycle. According to

Saravanamuttoo et al. (2001, p. 61-3), in the actual cycle, 4

3

1

2p

pp

p due to the

presence of pressure losses in the various components and ducting. In the combustion

chamber, a loss in stagnation pressure bp occurs due to the aerodynamic resistance

of flame-stabilizing and mixing devices. An assumed value of %2 bp compressor

delivery pressure has been used in the calculations. The turbine inlet pressure changes

from 23 pp (ideal case) to

223 1.

p

ppp b

a .

34

The turbine exit pressure remains the same, i.e. 44 pp a . So the pressure ratio at

expansion changes to:

24

2

4

3 1.'p

p

p

p

p

p b

a

a

Since p4 = p1 and 1

2

p

p, the equation may be re-modelled as follows:

1.

1.'p

pb … (27)

(derived from Saravanamuttoo et al., 2001, p. 61-3)

The expressionsd for Compressor Efficiency ( C ) and Turbine Efficiency ( T ) are as

follows:

aaP

P

aaC

CC TTc

TTc

hh

hh

W

W

2121,

2121,

21

21

, .

).(

… (28)

4343,

4343,

43

43,

.

).(

TTc

TTc

hh

hh

W

W

P

aaPa

T

aTT

… (29)

(Cengel and Turner, 2005, p. 373; Saravanamuttoo et al., 2001, p. 56)

For actual cycles, the specific heat capacity changes according to the temperature. In

equations (28) and (29), the numbers in the subscript of cP represent the process for

which the energy is being calculated.

d Isentropic efficiencies are being used in this case although polytropic efficiencies may be used when dealing with multi-stage turbomachinery.

35

By assuming aPaPP ccc ,21,21, and a (i.e. constant Pc and are being

assumed for the compression processes) in equation (29) and substituting

1

12 .TT from equation (12), actual Compressor Exit Temperature can be

determined. aPc , and a are the specific heat capacity and heat capacity ratio for dry

air during the compression process:

C

a

a

a TT

11.

1

12 … (30)

(Saravanamuttoo et al., 2001, p. 57)

By assuming gPaPP ccc ,43,43, and g (i.e. constant Pc and are being

assumed for the expansion processes) in equation (29) and substituting

1

'34 /TT from equation (12) and (27), actual Turbine Exit Temperature can

be determined. gPc , and g are the specific heat capacity and heat capacity ratio for

exhaust gases during the expansion process.

g

g

b

TTa

p

p

TT

1

1

34

.1.

1. … (31)

(Saravanamuttoo et al., 2001, p. 57)

Now, equations (25) and (26) can be re-modelled as follows:

B

aaPgPain

TcTcQ

2,3,

,

.. … (32)

(Cengel and Turner, 2005, p. 368)

36

m

aaPagPanet

TTcTTcW

21,

43,,

… (33)

(Saravanamuttoo et al., 2001, p. 75)

Substitute T2a and T4a from equations (29) and (30) in equations (32) and (33)

respectively:

C

a

a

aPgPB

ain TcTcQ

11....

11

1,3,, … (34)

(derived from Cengel and Turner, 2005, p. 368)

C

a

a

aPm

g

g

bTgPanet Tc

p

pTcW

1

1,

1

13,,

1..

1

.1.1... … (35)

(derived from Saravanamuttoo et al., 2001, p. 47; Cengel and Turner, 2005, p. 368)

Substitute anetW , and ainQ , in equation (8) in order to determine the actual cycle

efficiency:

C

a

a

aPgPB

C

a

a

m

aPg

g

bTgP

aBraytonth

cT

Tc

c

p

p

T

Tc

1

,1

3,

1

,

1

11

3,

,,

11...

1

1.

.1.1...

… (36)

(derived from Saravanamuttoo et al., 2001, p. 47; Cengel and Turner, 2005, p. 368)

According to Hodge (1955, pp. 102-3), if the compressor efficiency and the turbine

efficiencies for a simple cycle are numerically equal then the turbine efficiency would

have a greater effect on the thermal efficiency and specific work output of the cycle.

This occurrence can be accounted for by the fact that “the whole expansion work (WT)

37

is affected by turbine efficiency (ηT) while the compressor efficiency (ηC) only affects

the results of the work (WC) used internally, which, for all positive values of overall

efficiency, is a smaller quantity”.

Graphs (4a-f) describe the effect of changing compressor efficiencies on the thermal

efficiency of the actual Brayton Cycle. The following parameters have been used in

the graphs:

γa = 1.4 (for dry air)

γg = 1.33 (for combustion gases)

cP,a = 1.005 kJ/kg.K (for dry air)

cP,g = 1.148 kJ/kg.K (for combustion gases)

1T 15°C (288K)

3T from 500°C (773K) to 1500°C (1773K) at increments of 50°C

from 1 to 40 at increments of 1

ηC from 70% to 95% at increments of 5%

ηT = 85%

ηB = 98%

ηm = 99%

p1 = 1 bar

∆pb = 2% compressor delivery pressure

In each of these graphs, it can be observed that thermal efficiency increases with

increasing turbine inlet temperatures. If each of the graphs is observed, it can be

inferred that increasing compressor efficiencies increase the thermal efficiency of the

cycle. If cycle efficiencies are compared in Graphs (4a) and (4f) at turbine inlet

temperature 1500°C and at a pressure ratio of 4:1, it can be seen that an increase of

25% in the compressor efficiency increases the overall efficiency by only 2.66%. In

Graph (4f), it can be observed that for the given parameters, the thermal efficiency at

turbine inlet temperature of 1500°C (and at a pressure ratio of 4:1) is 6.57% higher

than thermal efficiency at 500°C. Since these differences are not very large, it may be

inferred that at low pressure ratios, the thermal efficiency of the cycle is not affected

38

significantly by increasing turbine inlet temperatures and thus, unrecuperated are not

viable for operation at low pressure ratios.

Graphs (5a-f) show the effect of changing turbine efficiencies on the thermal

efficiency of the cycle of the Brayton Cycle. The same parameters have been used as

for Graphs (4a-f) except the compressor and turbine efficiencies. In this case:

ηC = 85%

ηT from 70% to 95% at increments of 5%

The observations with respect to the thermal efficiency and turbine inlet temperatures

are similar to those for Graphs (4a-f). While comparing Graphs (4f) and (5f), it may

be observed that the thermal efficiencies at T3 = 1500°C and Π = 4, the efficiency in

the former case is 21.53% and in the latter case is 24.32%. This shows that the effect

of the turbine efficiency on the cycle efficiency is greater than the effect of the

compressor efficiency. Hence, methods to improve turbine efficiency need to be

researched to achieve greater cycle efficiencies for the microturbine.

If cP = cP,g is assumed for the complete cycle then according to equations (14) and

(35), the specific work output will become:

Cm

a

a

gP

aPg

g

bT

gP

anet

c

c

p

p

T

T

Tc

W

.

1.

.1.1.

.

.

1

,

,

1

11

3

1,

, … (37)

(derived from Saravanamuttoo et al., 2001, p. 47; Hodge, 1955, p. 93)

39

3.4 ACTUAL BRAYTON CYCLE WITH HEAT EXCHANGE

The actual Brayton Cycle with Heat Exchange is basically a modification of the actual

Brayton Cycle (simple) which includes a real heat exchanger [with effectiveness (ε)

less than 100%]. In this case, only a part of the exhaust heat is transferred from

process 4a - 6 to process 2a - 5 as some of the energy is dissipated from the system

during heat transfer.

The net work output (Wnet,a) will remain the almost the same as that in the simple

actual cycle with a small difference because of additional pressure losses in the heat

exchanger. Since a real heat exchanger is being included in the system, pressure

losses [other than stagnation pressure losses (Δpb) in the combustion chamber] occur

in it due to friction in the passages on the air-side (Δpha) and the gas-side (Δphg) of the

heat exchanger (Saravanamuttoo et al., 2001, p. 61-3). Assumed values of %3 hap

compressor delivery pressure and 04.0 hgp bar have been used in the calculations.

The turbine inlet pressure changes from 23 pp to

222,3 1.

p

p

p

ppp hab

hexa .

The turbine exit pressure changes from 14 pp to hghexa ppp 1,4 . So, the

pressure ratio at expansion becomes:

hg

hab

hexa

hexa

pp

p

p

p

p

p

p

1

11

,4

,3 ..1.

'' … (38)

Now, T2a remains the same as that in equation (32) but T4a changes to:

g

gT

Thexa TT

13,4

''1. … (39)

(derived from Saravanamuttoo et al., 2001, p. 75)

40

Here, h5 can be obtained from the expression for the effectiveness (ε) of a real heat

exchanger which is:

ahexa

a

hh

hh

2,4

25

… (40)

(Cengel and Turner, 2005, p. 375)

aahexa hhhh 22,45 . … (41)

Since, heat energy supplied to the system (Qin,a) is h3 – h5, it can be expressed as:

B

aahexahexain

hhhhQ

22,43

,,

. … (42)

Since Tch P . , equation (45) can be re-modelled as follows:

B

aaPhexagPhexain

TcTTcQ

1.... 2,,43,

,, … (43)

If equation (43) is subtracted from equation (32), it can be observed that the heat

supplied to a heat exchange cycle (Qin,a,hex) reduces by an amount Qin,a,red as compared

to heat supplied to the simple cycle (Qin,a) such that:

aaPhexagPB

redain TcTcQ 2,,4,,, ..

… (44)

Substitute T2a and T4a,hex from equations (30) and (39) into equations (33) and (42) to

obtain Wnet,a and Qin,a:

1.

.

.''1...

1

1,1

3,,,a

a

Cm

aPg

g

TgPhexanet

TcTcW

… (45)

(derived from Saravanamuttoo et al., 2001, p. 75)

41

1.

11.

.''1..1.

.1

1,1

3,,,

C

a

a

B

aPg

g

TB

gPhexain

TcTcQ

… (46)

(derived from Saravanamuttoo et al., 2001, p. 75; Cengel and Turner, p. 368)

Substitute Wnet,a and Qin,a from equations (45) and (46) into equation (8) to obtain the

thermal efficiency for the actual Brayton Cycle with heat exchange:

C

a

a

B

aP

g

g

hg

hab

TB

gP

a

a

Cm

aP

g

g

hg

hab

TgP

hexth

Tc

pp

p

p

p

p

Tc

Tc

pp

p

p

p

p

Tc

1

1,

1

1

113,

1

1,

1

1

113,

,

11.

1....1.

1..1..

1..

...1.

1...

… (47)

(derived from Saravanamuttoo et al., 2001, p. 75; Cengel and Turner, p. 368)

Graphs (6a-f) show the effect of changing heat exchanger effectiveness on the thermal

efficiency of the recuperated Brayton Cycle. Thermal efficiencies have been plotted

using the same parameters as Graphs (4a-f) with a few differences as stated below:

ηC = ηT = 85%

ε from 70% to 95% at increments of 5%

42

In each of these graphs, it can be observed that thermal efficiency increases with

increasing turbine inlet temperature. If each of the graphs is compared, it may be

inferred that increasing heat exchanger effectiveness increases the thermal efficiency

of the cycle. An important observation which can be made from these graphs is that

the peak of each of the curves (at low pressure ratios) rises significantly with

increasing heat exchanger effectiveness but the rest of the curve is virtually unaffected.

If Graphs (6a) and (6f) are compared for Π = 40 and T3 = 1500°C, the cycle efficiency

increases by a mere 0.72% whereas for Π = 4 and the same temperature, it increases

by 19.47%. The reason for this phenomenon is the cooling which takes place in the

system (due to the heat exchanger, as described earlier) at pressure ratios higher than

the optimum pressure ratio. At Π = 4 and T3 = 1500°C, Graphs (5d) and (6d) give

cycle efficiencies of 20.67% and 47.41% respectively. This difference of 26.74% in

the thermal efficiency shows the clear advantage of using a heat exchanger for low

compression pressure ratios of 4:1.

This argument can be further supported by Graph (7), in which at Π = 4 and T3 =

900°C, the simple cycle has a thermal efficiency of 18.02% and that of the

recuperated cycle is 36.37%, i.e., a twofold increase (approximately), thereby

exhibiting the beneficial recuperative effect of heat exchange on the cycle efficiency

at low pressure ratios.

If cP = cP,g is assumed for the complete cycle then according to equations (14) and

(35), the specific work output will become:

Cm

a

a

gP

aP

g

g

hg

hab

T

gP

hexanet

c

c

pp

p

p

p

p

T

T

Tc

W

.

1.

..1.

1..

.

1

,

,

1

1

11

1

3

1,

,, … (48)

(derived from Saravanamuttoo et al., 2001, p. 47, 75; Hodge, 1955, p. 113)

43

3.5 ELECTRIC POWER OUTPUT AND SHAFT POWER REQUIRED

The gas turbine produces shaft power. It can be connected to an electric generator in

order to convert this shaft (mechanical) power into electric power. Some amount of

this power is lost during this conversion (mechanical to electrical). Thus, the

efficiency of the electric generator is always lower than 100%.

Suppose the electric power output of a plant is PE, then the shaft power that has to be

produced by the gas turbine has to be higher than the rated electric power (PE) of the

plant due to power losses in the generator. The required shaft power (PM) may be

calculated by using the following expression:

E

EM

PP

kW … (49)

ηE is the efficiency of the electric generator and its value is being assumed to be 95%

for the calculations.

If the number of hours for which the system runs annually is AH, then total energy (ET)

which needs to be generated by the gas turbine in order to work at full load per annum

is:

AHPE MT . … (50)

44

3.6 FUEL CONSUMPTION AND COSTS

Mass flow rate of air ( am ) required for a power plant of shaft power PM under the

given conditions can be determined using the following equation:

net

Ma W

Pm … (51)

(Saravanamuttoo et al., 2001, p. 75)

It may be inferred from Saravanamuttoo et al. (2001, pp. 47-76) that the heat supplied

to the system (simple and heat exchange cycle) is the product of the fuel-air ratio fa

and the net calorific value of the fuel, fpnetQ ,

e. Therefore, for the fuel air ratio for the

system becomes:

fpnet

ain

a

fa Q

Q

m

mf

,

,

… (52)

The mass flow rate of fuel ( fm ) can be calculated using equation (52).

Another important parameter which can be used to express the performance of an

actual gas turbine cycle is the Specific Fuel Consumption (SFC), i.e., fuel mass flow

required divided by net work output. According to Saravanamuttoo et al. (2001, p. 71),

it may be defined in terms of the thermal efficiency of the cycle as follows:

net

a

fpnetth W

f

QSFC

,

1

in kg/kJ … (53)

It may be observed that for constant cycle efficiency, an increase in the net calorific

value of the fuel reduces the specific fuel consumption of the gas turbine. This means

that if a better fuel [in terms of net calorific value] is used, lesser quantity of the fuel e Net Calorific Value

fpnetQ , is the heat released by the complete combustion per unit of fuel

combusted (under ideal conditions) at constant pressure. It excludes the latent heat of the H2O vapour as this heat cannot be utilized by a gas turbine (Saravanamuttoo et al., 2001, p. 71).

45

has to be used. The SI unit of SFC is ‘kg/J’ but usually electric power is expressed in

‘kWh’. Usually, calorific values of fuels are expressed in ‘kJ/kg’ and SFC is

expressed in ‘kg/kWh’. Hence, the equation may be restructured to obtain SFC in

‘kg/kWh’ as follows:

fpnetth Q

SFC,

3600

in kg/kWh … (54)

If the cost of the fuel is given in pence per litre (in this case, the fuel being used is

kerosene, which is liquid) then the unit of fpnetQ , which will have to be used is

‘kWh/l’. This quantity is dependent on the temperature of the fuel and the source of

the fuel although these differences are usually neglected for the ease of calculation. In

this case, the unit of SFC changes to ‘l/kWh’.

When comparing the SFC for the simple cycle [Graph (8a)] with the SFC for the heat

exchange cycle [Graph (8b)], it can be seen that at T3 = 1500°C and Π = 4, SFC in the

former case is 0.48 l/kWh and in the latter case is 0.21 l/kWh. This shows that that the

addition of a heat exchanger reduces the fuel consumption considerably (by almost

half, in this case) at low pressure ratios. In both cases, an increase in the turbine inlet

temperature reduces the specific fuel consumption.

According to Spiers (1961, p. 270), the net calorific value of kerosene is 1.45 therm

per U.K. Gallon at 15.5°C.

1 therm = 29.3071 kWh (Spiers, 1961, p. 16)

1 U.K. Gallon = 4.54596 l (Spiers, 1961, p. 12)

Hence, the net calorific value of kerosene at 15.5°C in kWh/l will become:

3479.9, fpnetQ kWh/l

46

Due to improvements in fuel technology, this quantity may have increased slightly.

Hence, the author is assuming an approximate value for fpnetQ , as 10 kWh/l in the

calculations.

Total Fuel Consumption (FT) for the system may be obtained by using equations (50)

and (54):

TT ESFCF (l) … (55)

If the cost of the fuel (in £/l) is CF, then the total fuel costs (in £) can be calculated as

follows:

100,FT

totalF

CFC

(£) … (56)

The cost of fuel required (in l) to produce 1 kWh of electricity using the gas turbine

system can be calculated using the following expression:

fpnetthE

F

E

totalFkWhF Q

C

AHP

CC

,

,,

3600

… (57)

The fuel costs of the simple cycle have been plotted in Graph (9). In this case, it can

be clearly seen that increasing turbine inlet temperatures can reduce fuel costs

considerably although this increases equipment and maintenance costs as high turbine

inlet temperatures reduce durability of the hot-end components of the microturbine (as

discussed earlier). Hence, a cost-benefit balance needs to be made between turbine

inlet temperatures and component material costs. At low pressure ratios, the fuel costs

are virtually unaffected by differences in T3 but at higher pressure ratios, the costs

increase considerably on the reduction of T3.

47

Similar trends can be observed for fuel costs of the recuperated cycle [Graphs (10a-c)]

but at lower pressure ratios, the recuperated cycle has lower fuel costs than the simple

cycle. At T3 = 1500°C and Π = 4, the fuel cost for the simple cycle is about 18 p/kWh;

while for the heat exchange cycle with heat exchanger effectiveness 75%, 85% or

95%, the fuel costs are about 9, 8 and 6 p/kWh, thereby exhibiting a clear economic

advantage (in terms of fuel cost) of the recuperated cycle.

48

4. CONCLUSION

The objective of the project was to perform a constraint analysis of microturbine

engine with an electrical output 250 kWe and to analyse the conditions and parameters

for which a recuperated cycle (used in most models of microturbine generators) is

best suited for microturbine generators of the given size range. It can be inferred from

the study that at low pressure ratios of about 4:1, the recuperated cycle can provide

lower fuel costs than its unrecuperated counterpart. It is desirable to obtain higher

turbine inlet temperatures in order to increase thermal efficiency of the microturbine

system.

Graphs (11a-c) show the ratio of fuel costs of the simple cycle to those of the

recuperated cycle (with a heat exchanger of effectiveness 75%, 85% or 95% added to

the system). It can be seen that for a turbine inlet temperature of 1500°C, the fuel cost

ratio is greater than 1 in all cases, thereby indicating that the recuperated cycle is

better (in terms of fuel cost) than the simple cycle for all pressure ratios in the range

of 1 to 40. Up to a pressure ratio of 5, the recuperated cycle is definitely better (in

terms of fuel cost) than the simple cycle for turbine inlet temperatures as low as

500°C.

Key technical features which need to be improved upon in order to make microturbine

generators more viable and popular are better and cheaper materials for hot-end

components such as the recuperator and the turbine; achievement of better component

efficiencies leading to better overall efficiencies of greater than 40% and reduction of

toxic emissions. Improved gasification technology can lead the microturbine to such a

stage where it can run on virtually any fuel. The use of microturbines in trigeneration

is a future possibility.

49

Though microturbines have only captured a number of niche markets, the scope of

improvement is unlimited as technologies associated with microturbines are

improving rapidly and because mainstream sources of energy are facing extensive

depletion with little or no chance of recovery. The author believes that microturbines

could replace large power plants all over the world and every house could have its

own power generation unit.

If time had permitted, then more intensive research could have been carried out about

relating the microturbine system. An off-design analysis could be carried out for the

various components of the microturbine. Suitable turbine designs could be explored

and ascertained to provide better turbine efficiencies. An intensive study of

engineering materials applicable to microturbines (especially for the hot-end

components) could be accomplished. A more comprehensive economic analysis could

be performed to ascertain capital costs and operation & maintenance costs for the

microturbine system.

50

5. NOMENCLATURE

AH number of hours (annual)

CF fuel cost

cP specific heat at constant pressure

ET total energy

fa fuel-air ratio

FT total fuel consumption

g acceleration due to gravity

h specific enthalpy

m mass flow rate

m mass flow of fluid

∆p pressure loss

p absolute pressure

P power

Q heat transfer rate

Qin heat supplied per unit mass flow

Qnet, p net calorific value at constant pressure

SFC specific fuel consumption

T absolute temperature

u flow velocity

W specific work

z elevation from reference plane

γ ratio of specific heats

ε effectiveness of heat exchanger

η efficiency

Π compression pressure ratio

Π’, Π’’ expansion pressure ratios for actual cycles

51

Suffixes

1 , 2, 3, etc. reference planes

a dry air

b, B combustion chamber

C compressor

E electrical

e exit

f fuel

g combustion gases

HE, hex heat exchange

i inlet

m, M mechanical

opt optimum

red reduced

T turbine, total

th thermal

52

6. REFERENCES

Borbely, A. and Kreider, J.F. eds. (2001), Distributed Generation: The Power

Paradigm for the New Millennium, 1st ed., Boca Raton: CRC Press.

Bullin, A. (2002), An Introduction to Micro-turbine Generators. In: Moore, M.J., ed.,

Micro-turbine Generators, 1st ed., London: Institution of Mechanical Engineering.

Cengel, Y.A. and Turner, R.H. (2005), Fundamentals of Thermal-Fluid Sciences, 2nd

ed., London: Tata McGraw-Hill.

Dambach, R., Hodson, H.P. and Huntsman, I. (2002), Tip-leakage Flow: A

Comparison between Axial and Radial Turbines. In: Moore, M.J., ed., Micro-turbine

Generators, 1st ed., London: Institution of Mechanical Engineering.

Eastop, T.D. and Croft, D.R. (1990), Energy Efficiency for Engineers and

Technologists, 1st ed., Essex: Longman Group.

Energy Nexus Group (2002), Technology Characterization: Microturbines [Online].

Available: http://www.epa.gov/chp/pdf/microturbines.pdf [2005, November 30].

Gorla, R.S.R. and Khan, A.A. (2003), Turbomachinery: Design and Theory, 1st ed.,

New York: Marcel Dekker.

Håll, U. (2002a), Centrifugal Compressors, Lecture Notes to Cohen, Rogers and

Saravanamuttoo, Gas Turbine Theory, Chapter 4 [Online]. Available:

http://www.tfd.chalmers.se/~ulfh/gas_turb_h/crsohbilder/crs4en.pdf, [2006, April 2].

Håll, U. (2002b), Turbines, Lecture Notes to Cohen, Rogers and Saravanamuttoo, Gas

Turbine Theory, Chapter 7 [Online]. Available:

http://www.tfd.chalmers.se/~ulfh/gas_turb_h/crsohbilder/crs7en.pdf [2006, April 2].

53

Hamilton, S.L. (2003), Microturbine Generator Handbook, 1st ed., Oklahoma:

Pennwell Corporation.

Hodge, J. (1955), Cycles and Performance Estimation (Gas Turbine Series Vol. 1),

London: Butterworths Scientific Publications.

Pullen, K.R., Martinez-Botas, R. and Buffard, K. (2002), Design Problems in Micro-

turbine Generators. In: Moore, M.J., ed., Micro-turbine Generators, 1st ed., London:

Institution of Mechanical Engineering.

Saravanamuttoo, H.I.H., Rogers, G.F.C. and Cohen, H. (2001), Gas Turbine Theory,

5th ed., Harlow: Pearson Education.

Shane, T. (2002), Analysis of Micro- and Mini- turbine Competitive and Supply

Markets in Europe. In: Moore, M.J., ed., Micro-turbine Generators, 1st ed., London:

Institution of Mechanical Engineering.

Shepherd, D.G. (1960), Introduction to the Gas Turbine, 2nd ed., London: Constable

and Company.

Spiers, H.M., ed. (1961), Technical Data on Fuel, 6th ed., London: British National

Committee.

Stares, I.J. and Mabbutt, Q.J. (2002), Design Reliability of Micro-turbines. In: Moore,

M.J., ed., Micro-turbine Generators, 1st ed., London: Institution of Mechanical

Engineering.

Thomson, W.R. (1949), The Fundamentals of Gas Turbine Technology, 1st ed.,

London: Power Jets Limited.

54

7. FIGURES

Ideal Simple Brayton Cycle

Ideal Brayton Cycle with Heat Exchange

55

Actual Simple Brayton Cycle

Actual Brayton Cycle with Heat Exchange

56

8. GRAPHS

1 Effect of Π on Thermal Efficiency of Ideal Brayton Cycle

2Effect of T3 and Π on Specific Work Output of Ideal Simple Cycle and Cycle with Heat

Exchange

3 Effect of T3 and Π on Efficiency of Ideal Brayton Cycle with Heat Exchange

4a Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 70%, ηT = 85%

4b Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 75%, ηT = 85%

4c Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 80%, ηT = 85%

4d Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 85%

4e Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 90%, ηT = 85%

4f Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 95%, ηT = 85%

5a Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 70%

5b Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 75%

5c Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 80%

5d Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 85%

5e Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 90%

5f Variation in Efficiency of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 95%

6a Variation in Efficiency of Heat Exchange Cycle T3 and Π at ε = 70%

6b Variation in Efficiency of Heat Exchange Cycle T3 and Π at ε = 75%

6c Variation in Efficiency of Heat Exchange Cycle T3 and Π at ε = 80%

6d Variation in Efficiency of Heat Exchange Cycle T3 and Π at ε = 85%

6e Variation in Efficiency of Heat Exchange Cycle T3 and Π at ε = 90%

6f Variation in Efficiency of Heat Exchange Cycle T3 and Π at ε = 95%

7Variation in Efficiency of Actual Brayton Cycle and Heat Exchange Cycle (ε = 85%)

with Π at T3 = 900°C, ηC = ηT = 85%

8a Variation in SFC of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 85%

8bVariation in SFC of Actual Heat Exchange Cycle with T3 and Π at ηC = ηT = 85% and ε

= 85%

9 Variation in Fuel Cost of Unrecuperated Microturbine with T3 and Π at ηC = ηT = 85%

10aVariation in Fuel Cost of Recuperated Microturbine with T3 and Π at ηC = ηT = 85%, ε

= 75%

10bVariation in Fuel Cost of Recuperated Microturbine with T3 and Π at ηC = ηT = 85%, ε

= 85%

57

10cVariation in Fuel Cost of Recuperated Microturbine with T3 and Π at ηC = ηT = 85%, ε

= 95%

11aVariation of Fuel Cost Ratio (Simple/ Recuperated) with T3 and Π at ηC = ηT = 85%, ε

= 75%

11bVariation of Fuel Cost Ratio (Simple/ Recuperated) with T3 and Π at ηC = ηT = 85%, ε

= 85%

11cVariation of Fuel Cost Ratio (Simple/ Recuperated) with T3 and Π at ηC = ηT = 85%, ε

= 95%

58

Gr. 1 - Effect of Pressure Ratio on Ideal Cycle Thermal Efficiency

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

γ = 1.4

Eff

icie

ncy

η %

ηth tends to 100% for all Turbine Inlet Temperatures at Π = ∞

At Π = 1, ηth = 0% due to absence of compression or expansion work

59

Gr. 2 - Effect of Turbine Inlet Temperature and Pressure Ratio on Specific Work Output of Ideal Simple Cycle and Cycle with Heat Exchange

0.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Spe

cifi

c W

ork

Out

put

T3 = 500°C

T3 = 1500°COptimum Specific Work OutputT1 =15°C

γ = 1.4

Spe

cifi

c W

ork

Out

put W

/CP

.T1

Increasing Turbine Inlet Temperature T3

60

Gr. 3 - Effect of Turbine Inlet Temperature and Pressure Ratio on Efficiency of the Ideal Brayton Cycle with Heat Exchange

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

T1 =15°C

γ = 1.4ε = 100%

T3 = 1500°C

T3 = 500°C

Increasing Turbine Inlet Temperature T3Eff

icie

ncy

η %

61

Gr. 4a - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 70% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 70%ηT = 85%

Eff

icie

ncy

η %

T3 = 1500°C

T3 = 500°C

62

Gr. 4b - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 75% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 75%ηT = 85%

Eff

icie

ncy

η % T3 = 1500°C

T3 = 500°C

63

Gr. 4c - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 80% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 80%ηT = 85%

Eff

icie

ncy

η % T3 = 1500°C

T3 = 500°C

64

Gr. 4d - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 85%

Eff

icie

ncy

η % T3 = 1500°C

T3 = 500°C

65

Gr. 4e - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 90% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 90%ηT = 85%

Eff

icie

ncy

η % T3 = 1500°C

T3 = 500°C

66

Gr. 4f - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 95% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 95%ηT = 85%

Eff

icie

ncy

η %

T3 = 1500°C

T3 = 500°C

67

Gr. 5a - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 70%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 70%

Eff

icie

ncy

η %

T3 = 1500°CT3 = 500°C

68

Gr. 5b - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 75%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 75%

Eff

icie

ncy

η %

T3 = 1500°C

T3 = 500°C

69

Gr. 5c - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 80%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 80%

Eff

icie

ncy

η % T3 = 1500°C

T3 = 500°C

70

Gr. 5d - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 85%

Eff

icie

ncy

η % T3 = 1500°C

T3 = 500°C

71

Gr. 5e - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 90%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 90%

Eff

icie

ncy

η %

T3 = 1500°C

T3 = 500°C

72

Gr. 5f - Variation in Efficiency of Actual Brayton Cycle with Turbine Inlet Temperature and Pressure Ratio at ηC = 85% ηT = 95%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = 85%ηT = 95%

Eff

icie

ncy

η %

T3 = 1500°C

T3 = 500°C

73

Gr. 6a - Variation of Efficiency of Heat Exchange Cycle with Pressure Ratio and Turbine Inlet Temperature at ε = 70%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

ηC = ηT = 85%ε = 70%

T3 = 500°C

T3 = 1500°C

74

Gr. 6b - Variation of Efficiency of Heat Exchange Cycle with Pressure Ratio and Turbine Inlet Temperature at ε = 75%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

ηC = ηT = 85%ε = 75%

T3 = 500°C

T3 = 1500°C

75

Gr. 6c - Variation of Efficiency of Heat Exchange Cycle with Pressure Ratio and Turbine Inlet Temperature at ε = 80%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

ηC = ηT = 85%ε = 80%

T3 = 500°C

T3 = 1500°C

76

Gr. 6d - Variation of Efficiency of Heat Exchange Cycle with Pressure Ratio and Turbine Inlet Temperature at ε = 85%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

ηC = ηT = 85%ε = 85%

T3 = 500°C

T3 = 1500°C

77

Gr. 6e - Variation of Efficiency of Heat Exchange Cycle with Pressure Ratio and Turbine Inlet Temperature at ε = 90%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

ηC = ηT = 85%ε = 90%

T3 = 500°C

T3 = 1500°C

78

Gr. 6f - Variation of Efficiency of Heat Exchange Cycle with Pressure Ratio and Turbine Inlet Temperature at ε = 95%

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

ηC = ηT = 85%ε = 95%

T3 = 500°C

T3 = 1500°C

79

Gr. 7 - Variation in Efficiency of Actual Brayton Cycle and Heat Exchange Cycle (ε = 85%) with Π at T3 = 900°C, ηC = ηT = 85%

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Eff

icie

ncy

η %

Thermal Efficiency of Heat Exchange Cycle

Thermal Efficiency of Simple Cycle

80

Gr 8a - Variation in SFC of Actual Brayton Cycle with T3 and Π at ηC = 85%, ηT = 85%

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

SF

C l/

kWh

T3 = 1500°C

T3 = 500°C

81

Gr 8b - Variation in SFC of Actual Heat Exchange Cycle with T3 and Π at ε = ηC = ηT = 85%

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

SF

C l/

kWh

T3 = 500°C

T3 = 1500°C

82

Gr. 9 - Variation in Fuel Cost of an Unrecuperated Microturbine with T3 and Π at ηC = ηT = 85%

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Fue

l Cos

t p/k

Wh

T3 = 500°C

T3 = 1500°C

83

Gr. 10a - Variation in Fuel Cost of Recuperated Microtubine with T3 and Π at ε = 75%

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Fue

l Cos

t p/k

Wh

T3 = 500°C

T3 = 1500°C

ηC = ηT = 85%ε = 75%

84

Gr. 10b - Variation in Fuel Cost of Recuperated Microtubine with T3 and Π at ε = 85%

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Fue

l Cos

t p/k

Wh

T3 = 500°C

T3 = 1500°C

ηC = ηT = 85%ε = 85%

85

Gr. 10c - Variation in Fuel Cost of Recuperated Microtubine with T3 and Π at ε = 95%

0

20

40

60

80

100

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

Fue

l Cos

t p/k

Wh

T3 = 500°C

T3 = 1500°C

ηC = ηT = 85%ε = 95%

86

Gr. 11a - Variation of Fuel Costs Ratio (Simple/ Recuperated) with Turbine Inlet Temperature and Pressure Ratio at ε = 75%

0

1

2

3

4

5

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = ηT = 85%ε = 75%

Fue

l Cos

t Rat

io

T3 = 1500°C

T3 = 500°C

87

Gr. 11b - Variation of Fuel Costs Ratio (Simple/ Recuperated) with Turbine Inlet Temperature and Pressure Ratio at ε = 85%

0

1

2

3

4

5

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = ηT = 85%ε = 85%

Fue

l Cos

t Rat

io

T3 = 1500°C

T3 = 500°C

88

Gr. 11c - Variation of Fuel Costs Ratio (Simple/ Recuperated) with Turbine Inlet Temperature and Pressure Ratio at ε = 95%

0

1

2

3

4

5

0 5 10 15 20 25 30 35 40

Pressure Ratio Π

ηC = ηT = 85%ε = 95%

Fue

l Cos

t Rat

io

T3 = 1500°C

T3 = 500°C