exergy analysis of the revolving vane expander - ua...

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Exergy Analysis of The Revolving Vane

Expander

Keywords:

Exergy; Revolving vane; Expander; Optimization; Refrigeration

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Abstract

This report presents an exergy analysis of the Revolving Vane (RV) expander. Exergy, also known as

availability, is the maximum amount of useful work that can be derived from a substance in bringing

it to an equilibrium state with the environment. The application of exergy analysis is beneficial to the

study of the RV expander as it incorporates the first and second law of thermodynamics, which

makes the analysis of efficiency more comprehensive.

The objectives of the report are to evaluate the sources of irreversibilities or exergy destruction

within the expander during operation and to identify the optimum working conditions of the

expander. The sources of exergy destruction are identified as throttling of fluid, heat transfer

between fluid and expander solid mass, mixing of inflow fluid with bulk fluid in control volumes, and

friction between moving components.

The working principles of the RV expander are formulated using mathematical modelling and the

operation of the expander is simulated using a computer code in Matlab programming language. The

working fluid selected is air. The model accounts for the geometrical configuration, valve flow,

thermodynamic properties of the working fluid, and leakages within the expander. The exergy

analysis model is then applied to identify and quantify the various sources of exergy destruction. The

second-law efficiency of the expander under the benchmark operating conditions is 30.0%.

A parametric study is conducted to evaluate the optimum working conditions of the RV expander.

The parameters which are varied are suction reservoir pressure, rotational speed, and rotational

inertia of the cylinder. At each parametric study, one of the parameters is varied while keeping the

others constant. By comparing the second-law efficiencies of each parametric study, the result

shows that the expander is desirable to operate at high suction reservoir pressure, low rotational

speed and low inertia of cylinder.

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Contents

Abstract .................................................................................................... 2

List of Tables: ................................................................................................. 6

List of Figures: ................................................................................................ 7

Chapter 1: Introduction ................................................................................. 8

1.1 Background ................................................................................................................................... 8

1.2 Objectives...................................................................................................................................... 9

1.3 Scope ............................................................................................................................................. 9

Chapter 2: Literature Review ....................................................................... 11

2.1 Carbon dioxide as a potential refrigerant ................................................................................... 11

2.2 Revolving Vane Expander............................................................................................................ 12

2.3 Exergy analysis of refrigeration systems ..................................................................................... 13

Chapter 3: Review of Theory ....................................................................... 15

3.1 First law of thermodynamics ................................................................................................ 15

3.1.1 Energy balance equations ............................................................................................. 15

3.2 Second law of thermodynamics ............................................................................................ 17

3.3 Defining Exergy ........................................................................................................................... 18

3.3.1 Exergy Reference Environment ..................................................................................... 18

3.3.2 Concept of Dead State ......................................................................................................... 18

3.3.3 Equation of exergy as a property in a closed system ........................................................... 19

3.4 Flow Exergy ................................................................................................................................. 20

3.5 Exergy balance in a closed system .............................................................................................. 21

3.6 Exergy balance of control volumes ............................................................................................. 22

3.7 Second-law Efficiency ................................................................................................................. 22

Chapter 4: Working principles of the Revolving Vane Expander .................. 25

4.1 Components of Revolving Vane Expander .................................................................................. 25

4.2 Operation of the Revolving Vane Expander ................................................................................ 26

4.3 Mathematical modelling of the Revolving Vane Expander......................................................... 27

4.3.1 Geometrical model .............................................................................................................. 27

4.3.2 Thermodynamic model ........................................................................................................ 28

4.3.3 Suction and discharge ports flow model.............................................................................. 30

4.3.4 Heat transfer model ............................................................................................................. 30

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4.3.5 Friction model ............................................................................................................... 32

4.4 Irreversibility modelling .............................................................................................................. 36

4.4.1 Exergy destruction by heat transfer .................................................................................... 36

4.4.2 Exergy destruction by throttling of inflow fluid ................................................................... 37

4.4.3 Exergy destruction by fluid mixing ....................................................................................... 38

4.4.4 Exergy destruction by friction ....................................................................................... 39

Chapter 5: Simulation and exergy analysis .................................................. 40

5.1 Introduction .......................................................................................................................... 40

5.2 Simulation procedure ........................................................................................................... 40

5.3 Simulation results ................................................................................................................. 43

5.3.1 Mass and mass flow rates ............................................................................................. 45

5.3.2 Temperature, heat transfer rates and pressure ........................................................... 46

5.3.3 Leakage ......................................................................................................................... 49

5.3.4 Frictional power loss ..................................................................................................... 49

5.4 Exergy destruction rates ....................................................................................................... 50

5.4.1 Exergy destruction due to throttling ............................................................................. 50

5.4.2 Exergy destruction rates due to fluid mixing ................................................................ 51

5.4.3 Exergy destruction rates due to heat transfer .............................................................. 52

5.4.4 Exergy destruction rates due to friction ....................................................................... 53

5.4.5 Overall exergy destruction ............................................................................................ 54

Chapter 6: Parametric study ........................................................................ 56

6.1 Introduction .......................................................................................................................... 56

6.1.1 Suction reservoir pressure ............................................................................................ 56

6.1.2 Rotational speed of rotor .............................................................................................. 57

6.1.3 Inertia of cylinder .......................................................................................................... 57

6.2 Effects of variation of suction reservoir pressure ................................................................. 57

6.2.1 Heat transfer with variation of suction pressure .......................................................... 58

6.2.2 Throttling with variation of suction reservoir pressure ................................................ 59

6.2.3 Fluid mixing with variation of suction reservoir pressure ............................................ 61

6.2.4 Friction with variation of suction reservoir pressure .................................................... 61

6.2.5 Overall analysis of exergy destruction due to variation in suction reservoir pressure 61

6.3 Effects of variation of rotational speed ................................................................................ 63

6.3.1 Heat transfer with variation of rotational speed .......................................................... 63

6.3.2 Throttling with variation of rotational speed ............................................................... 64

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6.3.3 Fluid mixing with variation of rotational speed ............................................................ 65

6.3.4 Friction with variation of rotational speed ................................................................... 65

6.3.5 Overall analysis of exergy destruction due to variation in rotational speed ................ 66

6.4 Effects of inertia of cylinder .................................................................................................. 67

6.4.1 Heat transfer with variation of inertia of cylinder ........................................................ 68

6.4.2 Throttling with variation of inertia of cylinder.............................................................. 68

6.4.3 Fluid mixing with variation of inertia of cylinder .......................................................... 68

6.4.4 Friction with variation of inertia of cylinder ................................................................. 69

6.4.5 Overall analysis of exergy destruction due to variation in cylinder inertia .................. 69

Chapter 7: Conclusion and further studies ................................................... 72

7.1 Further studies ...................................................................................................................... 73

References 75

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List of Tables:

Table 1: List of operating conditions ..................................................................................................... 44

Table 2: Summary of average exergy destruction rates ....................................................................... 55

Table 3: Suction valve opening angle according to suction pressure [4] .............................................. 58

Table 4: Exergy destruction with variation of suction pressure ........................................................... 58

Table 5: Mass flow rate with variation of suction pressure .................................................................. 60

Table 6: Second-law efficiency with variation of suction pressure ...................................................... 62

Table 7: Exergy destruction with variation of rotational speed ........................................................... 63

Table 8: Mass flow rate with variation of rotational speed .................................................................. 65

Table 9: Second-law efficiency with variation of rotational speed....................................................... 67

Table 10: Exergy destruction wtih variation of inertia of cylinder ....................................................... 67

Table 11: Vane friction loss due to different cylinder inertia ............................................................... 69

Table 12: Second-law efficiency with variation of cylinder inertia ....................................................... 70

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List of Figures:

Figure 1: T-s graph of CO2 transcritical cycle [8] .................................................................................. 12

Figure 2: Energy balance for closed system .......................................................................................... 16

Figure 3: Energy balance for control volume ........................................................................................ 17

Figure 4: Example of a system in dead state[20] .................................................................................. 19

Figure 5: Front sectional view of RV expander [12] .............................................................................. 25

Figure 6: Side sectional view of the RV expander [12] ......................................................................... 26

Figure 7: The operating process of the RV expander [12] .................................................................... 27

Figure 8: The schematic of a Revolving Vane Expander [11] ................................................................ 28

Figure 9: Free body diagram of cylinder [5] .......................................................................................... 33

Figure 10: The real (a) and approximated locations of contact force [5] ............................................. 33

Figure 11: The triangle ACR with the forces shown [5] ........................................................................ 33

Figure 12: Endface friction model [5] ................................................................................................... 35

Figure 13: Journal bearing illustration [11] ........................................................................................... 36

Figure 14: Model for exergy analysis of heat transfer .......................................................................... 37

Figure 15: Model for exergy analysis of throttling ................................................................................ 38

Figure 16: Model of exergy analysis for fluid mixing[18] ...................................................................... 39

Figure 17: Model for exergy analysis of friction ................................................................................... 39

Figure 18: Algorithm of simulation ....................................................................................................... 41

Figure 19: Suction control volume analysis .......................................................................................... 42

Figure 20: Discharge control volume analysis ...................................................................................... 42

Figure 21: Mass of suction and discharge control volumes .................................................................. 45

Figure 22: Mass flow rates of suction and discharge flow .................................................................... 46

Figure 23: Temperature of fluid in suction and discharge control volumes ......................................... 47

Figure 24: Heat transfer rates of fluid in suction and discharge control volumes ............................... 48

Figure 25: Pressure of fluid in suction and discharge control volume .................................................. 48

Figure 26: Total leakage mass flow rate ............................................................................................... 49

Figure 27: Frictional power loss ............................................................................................................ 50

Figure 28: Exergy destruction rates due to throttling .......................................................................... 51

Figure 29: Exergy destruction rates due to fluid mixing ....................................................................... 52

Figure 30: Exergy destruction rates due to heat transfer ..................................................................... 53

Figure 31: Exergy destruction rates due to friction .............................................................................. 54

Figure 32: Breakdown of exergy destruction ........................................................................................ 55

Figure 33: Densities of fluid in suction control volume ........................................................................ 59

Figure 34: Entropy difference for variation of suction reservoir pressure ........................................... 60

Figure 35: Second-law efficiency for variation of suction reservoir pressure ...................................... 62

Figure 36: Fluid velocities for variation of rotational speed ................................................................. 64

Figure 37: Cylinder angular acceleration for variation of rotational speed .......................................... 66

Figure 38: Second-law efficiency for variation of rotational speed ...................................................... 67

Figure 39: Overall exergy analysis for variation of inertia of cylinder .................................................. 70

Figure 40: Second-law efficiency for variation of inertia of cylinder .................................................... 71

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Chapter 1: Introduction

1.1 Background

In the 21st century, the rise in energy consumption and rapidly depleting natural resources in the

world has caused an increased awareness in many countries to re-evaluate their energy policies.

Industries and scientific community are also looking at developing more energy-efficient devices and

optimizing efficiencies of current technologies.

The refrigeration, heating and air-conditioning (RHA) systems involve processes which consume

great amount of energy. According to Omer[1] in 2008, about 40% of the world annual energy

consumption is used for provision of building-related facilities such as lighting, heating and air-

conditioning. In Singapore, according to a report from Ministry of Trade and Industry [2] in 2007,

about 50% of the household electricity consumption is due to air-conditioning and refrigerators.

Hence, there is a great need to better evaluate the energy efficiency of devices in the RHA systems

and continually improve upon the products.

Expanders have been proposed recently to improve the energy efficiency of RHA systems [3]. It

recovers the expansion power at the expansion device that is usually lost. In conventional systems,

expanders can increase COP by 15% [3] while in a trans-critical CO2 system it is even more effective

with COP increase of up to 25% [3]. In order to achieve maximum result, the expander needs to be

highly efficient as well. In 2008, a novel highly energy efficient expander mechanism, called the

Revolving Vane expander, was introduced [4].

Until now, the energy analysis makes use of the first law of thermodynamics to evaluate the

efficiency of the device. The first law deals with the concept of conservation of energy and asserts

that energy can neither be created nor destroyed. However, the first law does not provide

information on the detailed breakdown of energy lost in different components [5]. As such, a better

approach known as exergy analysis is introduced.

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Exergy, also known as availability, is the maximum amount of useful work that can be derived from a

substance in bringing it to an equilibrium state with the environment [6]. In addition to the first law,

exergy analysis also uses the second law of thermodynamics, which deals with the concepts of

quality of energy as well as entropy of a system. As exergy is a property of the system, the exergies

of the fluid before and after the cycle can be quantified. The loss will then be the reduction in total

exergy of the system [6]. Exergy analysis can thus allow a better understanding of thermodynamic

systems.

1.2 Objectives

This paper shall evaluate the efficiency of the novel Revolving Vane Expander using techniques of

the exergy analysis.

Using mathematical modelling of the Revolving Vane Expander, computer simulations will be carried

out to identify and quantify the thermodynamic properties of the device during operation. A

detailed exergy analysis can then be obtained from the data. The eventual outcome of this paper is

to determine the optimal operating conditions of the expander.

1.3 Scope

The scope of the project is listed as such:

- To gain a better understanding of the first and second law of thermodynamics

- To understand the concept of exergy and its application to evaluating efficiency of

thermodynamic devices

- To understand the working principles of the Revolving Vane Expander

- To identify and quantify the irreversibilities involved in the processes during operation of the

Revolving Vane Expander

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- To conduct a parametric study on factors that affect the exergy efficiency of the Revolving

Vane Expander

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Chapter 2: Literature Review

2.1 Carbon dioxide as a potential refrigerant

In the recent decades, environmental concerns over the use of synthetic refrigerants have escalated.

The production and emission of chlorofluorocarbons (CFCs) have been regulated under the Montreal

Protocol [7] in 1987. The refrigeration, heating and air conditioning industry are forced to switch

over to ‘ozone-friendly’ chlorine-free substances as refrigerants. Later in 1997, with the aim to

reduce global warming, the Kyoto Protocol calls for the reduction in emission of two groups of

refrigerants, i.e. hydro-fluorocarbons and per-fluorocarbons [8].

In response to the problems of global warming and ozone depletion, Lorentzen and Pettersen [9]

proposed to revive the usage of carbon dioxide as a potential future refrigerant in 1993. Carbon

dioxide is abundant in nature and being a natural-occurring gas, it poses less environmental impact

than that of the synthetic refrigerants. One way of measuring impact to the environment is the

global warming potential (GWP), which is an index that relates the potency of a greenhouse gas to

the carbon dioxide over a 100-year period. Common refrigerants such as the R-134a has a GWP of

1300, which means that one molecule of R-134a has a potency of 1300 times to that of carbon

dioxide [10]! Carbon dioxide as a refrigerant possesses excellent thermodynamic behaviour and is

safe to use as it is non-toxic and incombustible [11].

However, the use of carbon dioxide as a refrigerant poses its difficulties as well. Carbon dioxide has a

low critical temperature of 31.1°C and high critical pressure of 7.38 MPa [10]. In places where the

ambient temperature is higher than this critical temperature, the refrigeration system needs to run

in a trans-critical cycle, as shown in Figure 1. A typical refrigeration cycle comprises the compressor,

condenser, expansion valve and evaporator. However, in a trans-critical carbon dioxide system, the

condenser is replaced by a gas cooler.

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The large operational pressure range causes a large throttling loss at the expansion valve, causing

low energy efficiency for the carbon dioxide refrigeration cycle. To overcome this problem,

Lorentzen [11] proposed to replace the expansion valve with an expander to recover the energy lost

due to throttling.

Figure 1: T-s graph of CO2 transcritical cycle [8]

2.2 Revolving Vane Expander

In principle, an expander is a device similar to a compressor but operates in an opposite direction. In

the refrigeration cycle, a compressor takes in shaft power from the motor to do work on the

refrigerant and increases its pressure. However, an expander takes in high-pressure refrigerant and

the refrigerant does work on the expander to provide shaft power. This shaft power generated can

be used to reduce the motor load in running the compressor and hence, increases the COP of the

system [12].

Robinson and Groll [3] have shown that the introduction of an expander can indeed increase the

COP of the carbon dioxide refrigerant system by up to 25%. This provides evidence of the capacity to

make the trans-critical carbon dioxide refrigeration system to be of comparable efficiency to a

conventional R-22 system.

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There are many different mechanisms available for an expander design, such as rolling piston,

reciprocating, rotary screw, scroll and rotary vane [13]. The new design of Revolving Vane

mechanism was introduced by Teh and Ooi [14] in 2006 as a compressor. In this design, the cylinder

is allowed to rotate together with the rotor, resulting in lower frictional losses at the rubbing

surfaces due to lower relative velocities.

Subiantoro and Ooi [15] adopted the revolving vane mechanism for expander applications. This

Revolving Vane Expander is thus the main subject of exergy analysis for this project.

Although the motivation of the Revolving Vane Expander is to improve on the efficiency of carbon

dioxide refrigeration systems, it is highly applicable for conventional systems too. Robinson and Groll

[3] reported a 15% increase in the efficiency of a conventional R-12 system that uses an expander.

2.3 Exergy analysis of refrigeration systems

Ahamed et al. [5] compiled exergy analysis of various parameters for vapour compression

refrigeration cycle. Effects of refrigerant as contribution to exergy efficiency are evaluated too. R-

600a, R-410a and R-1270 show great potential according to energy and exergy efficiency of the

system[5]. From the study of Saidur et al. [16] on exergy analysis of the residential sector in

Malaysia, it was found that 33% of exergy loss occurred in the vapour compression system which

consisted of refrigeration and air-conditioning.

Kalaiselvam and Saravanan [17] conducted exergy analysis on scroll compressors working with R-22,

R-407 and R-717 as refrigerant. They discovered that exergy losses increased with the increase in

suction and discharge temperature of the compressor. Recommendations of compressor discharge

and suction temperature to be within 65 °C and 14°C respectively are made.

McGovern et al. [6] developed an analysis technique that uses the exergy of a gas to quantify the

shaft power wastage in a scroll and rotary compressors. He summarized the losses in a compressor

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to be mainly contributed by throttling at valves, mechanical friction, leakage, heat transfers and re-

expansion of compressed gases. By employing equations of irreversibilities for the different

components, he was able to quantify that the major losses in the compressor are due to throttling

(12%), leakage (40%) and friction (24%).

McGovern and Harte [18] performed an exergy analysis for an open reciprocating compressor which

used R-12 refrigerant. The article showed that results from computer simulations of compressors

can be readily utilised to provide an understanding for design optimization. Instantaneous rates of

exergy destruction for the different components were quantified and compared in graphical forms.

The major irreversibilities are found to be throttling (53.7%), friction (12.5%) and internal convection

(18.7%).

Lee [19] worked on screw liquid chillers to quantify the exergy destruction of the different

components and identify the potential for each component to improve the overall energy efficiency

of the system. He reported that the compressor possessed the highest potential to increase

efficiency, followed by the condenser, then the evaporator. By identifying the components of higher

exergy destruction, engineers can focus their attention to the components which matter most.

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Chapter 3: Review of Theory

Exergy analysis uses both the first and second law of thermodynamics, hence a good understanding

of these are required. In this chapter, a review on the first and second law is briefly discussed,

followed by the detailed discussion of the concept of exergy.

3.1 First law of thermodynamics

The first law of thermodynamics deals with the conservation of energy principle. It provides a basis

for interaction between various forms of energies in a system. It states that energy can neither be

created nor destroyed during a process, but can change forms [20].

Energy can be transferred in or from a system in three forms: heat, work and mass flow. Energy

interactions take place at the system boundary as they cross it. When dealing with a fixed mass or a

closed system, only heat and work transfer take place.

3.1.1 Energy balance equations

The general energy balance equation for any system undergoing a thermodynamic process is

expressed as:

(3.1)

The rate form of equation is expressed as:

(3.2)

For a closed system, the heat transfer to the system and work done by the system are taken as

positive quantities. Figure 2 shows the energy balance in a closed system. The energy balance

equation is expressed as:

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(3.3)

where:

Q is the quantity of heat transfer to or from the system (J)

W is the quantity of work done to or from the system (J)

is the change in internal energy of the system (J)

is the change in kinetic energy of the system (J)

is the change in potential energy of the system (J)

Figure 2: Energy balance for closed system

For a steady-state control volume, energy interactions occur at the system boundary due to mass

flow transfer too. As mass flow carries energy to or from the system, the energy balance equation

needs to be modified.

When fluid is pushed in or out of a control volume, energy transfer known as flow work occurs. The

flow work for per unit mass of fluid is expressed as:

(3.4)

Thus, the total specific energy of a flowing fluid is expressed as:

(3.5)

Since specific enthalpy is h= Pv + u, the above equation can be expressed as:

Energy

transfer by

heat, Q

Boundary work

done by

system, W

Closed system: Fixed mass

Change in internal energy,

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(3.6)

Figure 3 shows the energy balance for a control volume. The general energy balance equation for a

control volume can thus be expressed as:

(3.7)

Figure 3: Energy balance for control volume

3.2 Second law of thermodynamics

The second law of thermodynamics states that processes occur in a certain direction. A process does

not occur unless it satisfies both first and second law of thermodynamics. The second law deals with

the concept of quality of energy. The term entropy of a system is needed to have a better

understanding of a system.

Entropy is a measure of the degree of orderliness in a system. A good comparison of entropy can be

seen in that of solids and gases. In solids, the molecules within a substance vibrate about their

equilibrium positions and cannot move relative to one another. Hence their positions can be

Control volume

Change in energy,

Energy inflow by

mass, (m )in Energy outflow by

mass, (m )out

Energy transfer

by heat, Q

Work done by

system, W

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predicted with a good degree of certainty and thus possess low entropy. Whereas molecules in a gas

move about randomly with frequent collisions, thus harder to predict their positions. This leads to

high entropy.

3.3 Defining Exergy

As mentioned previously, exergy, also known as availability, is the maximum theoretical work that

can be derived from a substance in bringing it to an equilibrium state with the environment [21].

Exergy is closely related to the state of a system of interest, as well as the condition of the

environment.

3.3.1 Exergy Reference Environment

Any thermodynamic system will have to operate within surroundings of some kind. It is important to

distinguish between the reference environment and a system’s immediate surroundings. In

considering the exergy concept, the immediate surroundings are where the intensive properties

such as temperature and pressure may vary during interactions with the system; whereas the

reference environment is the larger portion of surroundings at a distance, where the intensive

properties are unaffected by the process involving the system and the surrounding.

In this paper, the reference environment shall be considered to be at temperature of 30°C and

having an atmospheric pressure of 1 bar.

3.3.2 Concept of Dead State

If the state of a fixed quantity of matter in a closed system deviates from that of the environment,

an opportunity exists for work to be obtained. However, as the state of the system moves towards

that of the environment, the opportunity is reduced; finally all opportunity is lost when the system

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comes into equilibrium with the environment. Thus, the state of the system is known as the dead

state when it is in thermodynamic equilibrium with the environment [21]. Figure 4 shows an

example of a system in dead state.

Figure 4: Example of a system in dead state[20]

3.3.3 Equation of exergy as a property in a closed system

With the concepts of reference environment and dead state defined, the exergy of a closed system,

X, at a specific state is given by the expression

(3.8)

where , respectively, are the values of internal energy (J), volume (m3),

temperature (K) and entropy (J/K) of the system at dead state, i.e. in equilibrium with the reference

environment[21].

In a stationary system, the potential and kinetic energy can be excluded. Thus, the expression

becomes

(3.9)

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The exergy change of a closed system is simply the difference between final and initial exergies of

the system:

(3.10)

where the subscripts 0, 1 and 2 represent the state of reference environment, initial and final states

of the system respectively.

Some important aspects of exergy concept are listed as follows [21]:

Exergy is a measure of the departure of the state of a system from that of the environment.

Once the reference environment is specified, a value can be assigned to exergy as shown

above. Therefore, exergy can be regarded as a property of the system.

The value of exergy cannot be negative. If the state of the system deviates from that of the

environment, the system would be able to change its condition spontaneously toward the

dead state. Thus the potential of work for the system is always zero or positive.

Exergy is not conserved but is destroyed by irreversibilities. The concept of irreversibility

shall be discussed in the later sections.

3.4 Flow Exergy

The Flow Exergy concept is important for the control volume form which is used for the Revolving

Vane Expander analysis. It is necessary to account for the exergy transfer accompanying flow work.

The flow work on the control volume is PV and the work done against the atmosphere is PoV [21].

Together, the exergy transfer for flow work is shown as:

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(3.11)

Hence, Flow Exergy, E, consists of both the exergies of a closed system and a flow work system,

(3.10)

since the definition of enthalpy, H, is U + PV.

3.5 Exergy balance in a closed system

In a closed system, exergy transfer can occur through work and heat interactions with its

surroundings. Where irreversibility is present within the system during the process, entropy will be

generated and this results in exergy destruction [21].

Exergy transfer by heat transfer is expressed as:

(3.11)

where represent the quantity of heat transfer at a particular temperature , measured in Kelvin.

Exergy transfer accompanying work is expressed as:

(3.12)

Exergy destruction due to irreversibilities in the system is expressed as:

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(3.13)

By assuming positive heat transfer to the system and work done by the system, the exergy balance

for a closed system can be expressed as:

(3.14)

3.6 Exergy balance of control volumes

While the exergy balance of a closed system is useful, many work devices deal with flow work and

the concept of control volumes is needed. In control volumes, mass flow occurs across boundaries.

Mass flow itself transfers exergy in and out of the control volumes. Hence, the exergy balance

expression is modified[21]:

(3.15)

3.7 Second-law Efficiency

Using the first law of thermodynamics, concepts such as thermal efficiency and coefficient of

performance give us a measure of the performance of systems. They are sometimes defined as first-

law efficiencies and do not clearly illustrate the best possible performance of the system [20].

The thermal efficiency of a heat engine is given by the expression:

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(3.16)

where:

is the net work output of the engine (J),

is the amount of heat supplied to the engine (J) and

is the amount of heat rejected by the engine (J).

Refrigerators and heat pumps take in heat from a low-temperature space and reject heat to higher

temperature heat sink. The coefficient of performance (COP) is defined as [20]:

For refrigerator:

(3.17)

For heat pump:

(3.18)

where is the net work input to the system (J).

Second-law efficiency, nII, is defined as the ratio of actual thermal efficiency to the maximum

possible thermal efficiency[20].

For heat engines, the second-law efficiency is

(3.19)

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For work-producing devices, second-law efficiency can also be expressed as the ratio of the useful

work output to the maximum possible (reversible) work output:

(3.20)

This expression is applicable to processes in turbines and expanders as well as to cycles.

For cyclic devices such as refrigerators and heat pumps, the second-law efficiency can also be

expressed in terms of COP:

(3.21)

In a more general definition for devices that are not intended to produce or consume work, the

second-law efficiency of a system can be expressed as [20]:

(3.22)

Note that the exergy can be supplied or recovered as various form such as heat, work, kinetic

energy, potential energy, internal energy and enthalpy.

The second-law efficiency range from zero (complete destruction of exergy) to one in the best case

(no destruction of exergy). Due to the definition of second-law efficiency, the value cannot exceed

100%. The value of the second-law efficiency will give us a better understanding than the first-law

efficiency on how much the work potential of the system is utilised. It also serves as a good

comparison across similar devices.

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Chapter 4: Working principles of the Revolving Vane Expander

4.1 Components of Revolving Vane Expander

The Revolving Vane Expander is used for exergy analysis in this report. Figure 5 shows the front

sectional view and Figure 6 shows the side sectional view of the Revolving Vane Expander. The

expander consists of a cylinder and a rotor that are encased in a stationary casing. The vane is fixed

to the rotor. The suction port is situated at the cylinder, while the discharge port is situated at the

rotor. Since the suction port revolves due to the rotation of cylinder, the inlet pipe is connected to

the casing, which acts a reservoir for the suction port. The discharge port runs through the rotor

shaft, which rotates but does not revolve. Therefore, it can be connected to a discharge reservoir

first or coupled directly to the discharge pipe [15].

Figure 5: Front sectional view of RV expander [12]

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Figure 6: Side sectional view of the RV expander [12]

4.2 Operation of the Revolving Vane Expander

The Revolving Vane expander consists of the suction chamber, discharge chamber and vane slot

chamber. Each complete cycle takes two revolutions. The operating process of the Revolving Vane

Expander is illustrated in Figure 7.

Figure 7a shows the start of suction and discharge. The suction valve is first open. Due to high

pressure fluid in the suction reservoir, the pressure difference across the vane pushes the vane to

move in the direction of increasing the volume of suction chamber and reducing volume of discharge

chamber. This causes high-pressure fluid to flow into the suction chamber, while low-pressure fluid

to leave the discharge chamber, as shown in Figure 7b.

At a designated point, the suction valve is then closed, as shown in Figure 7c. This marks the end of

the suction process and the beginning of the expansion process. Since fluid can no longer enter the

suction chamber, further increase in volume of the suction chamber causes the working fluid to

undergo expansion, as shown in Figure 7d. After one complete revolution, the suction chamber

becomes the discharge chamber and the fluid in the discharge chamber is ejected after the second

revolution. The process then repeats itself.

27

Figure 7: The operating process of the RV expander [12]

4.3 Mathematical modelling of the Revolving Vane Expander

During the operating process of the expander, the working fluid undergoes changes in properties,

such as the pressure, temperature, density and entropy changes. Processes of thermodynamics, fluid

mechanics and heat transfer will take place between the working fluid and the expander itself too.

The suction flow, discharge flow and internal leakages will be crucial for a good understanding of the

working processes too. It is thus important to model these changes and processes to get an accurate

picture of the operating process of the Revolving Vane Expander.

4.3.1 Geometrical model

The Revolving Vane Expander can be divided into 3 distinct control volumes for analysis, namely the

suction chamber, discharge chamber and vane slot. Figure 8 shows an illustration of the 3 control

volumes and the associated components[12].

28

Figure 8: The schematic of a Revolving Vane Expander [11]

As the expander rotates, the volumes of the suction and discharge chambers change. For the suction

chamber, the volume can be calculated geometrically using equation[12]:

(4.1)

For the discharge chamber,

(4.2)

4.3.2 Thermodynamic model

As the refrigerant fluid enters the suction port, it will undergo changes in thermodynamic properties

due to the change in volume of the suction chamber. In order to evaluate the properties of the fluid,

the REFPROP subroutine [22] is used. REFPROP contains formulae for the equations of states of

many refrigerants. By inputting the states of the fluid, such as pressure and temperature, the other

properties such as internal energy, specific volume, enthalpy and entropy are easily obtainable using

the REFPROP subroutines.

29

From the first law of thermodynamics, the conservation of energy within a control volume,

neglecting potential energy due to insignificant change of height, is given by the expression:

(4.3)

where:

is the mass of fluid in the control volume (kg)

is the specific internal energy of fluid in the control volume (kJ/kg)

is the rate of heat energy input to the working fluid in the control volume (kW)

is the rate of work done by the fluid in the control volume (kW)

and are the specific enthalpies of inflow and outflow fluid respectively (kJ/kg)

and

are kinetic energies of inflow and outflow fluid respectively (kJ/kg)

and

are mass rates of inflow and outflow fluid respectively (kg/s)

The rate of change of the working fluid properties in the different chambers are given by the

following equations[15]:

For the temperature of the fluid,

(4.4)

For the rate of change of pressure of fluid:

30

(4.5)

For the rate of change of mass of fluid in a control volume:

(4.6)

4.3.3 Suction and discharge ports flow model

For the flow of fluid through the suction or discharge port, it is approximated as a steady one-

dimensional adiabatic flow through an orifice. In order to factor in reduction in effective flow area,

friction and turbulence, a coefficient of discharge, , is added. The value of can be approximated

to be around 0.7 to 0.85 [23].

(4.7)

where:

is the coefficient of discharge

is the area of orifice opening (m2)

is the specific enthalpy of fluid at the upstream (kJ/kg)

is the specific enthalpy of fluid at the downstream, assuming isentropic flow (kJ/kg)

4.3.4 Heat transfer model

In each of the 3 separate chambers, heat transfer can occur between the working fluid and the

chamber walls. The heat transfer in each chamber can be modelled according to Newton’s law of

cooling by convection. Due to the significantly higher thermal mass of the expander solid as

31

compared to the working fluid, the wall temperature is assumed to be uniform and average

temperature of suction and discharge chamber.

(4.8)

The heat transfer coefficient, h, can be calculated from the Nusselt number correlation proposed by

Liu and Zhou[24]:

(4.9)

where Re is the Reynolds number of the fluid and is expressed as:

(4.10)

and Pr is the Prandtl number of the working fluid and is expressed as:

(4.11)

where:

is the density of fluid (kg/m3)

is the velocity of free stream (m/s)

is the hydraulic diameter of a non-circular duct (m)

is the kinematic viscosity of fluid (Ns/m2)

is the specific heat capacity of fluid (kJ/kg.K)

is the thermal conductivity of fluid (W/m.K)

32

4.3.5 Friction model

Friction is one of the important factors affecting the performance of the expander. Due to relative

velocities of the moving components, friction is generated between the rubbing surfaces. For the

Revolving Vane Expander, the main sources of frictional losses are [4]:

Vane side

Endfaces

Shaft bearings

4.3.5.1 Vane side friction

For the vane side friction, the force between the cylinder surface and normal of the vane side is to

be considered. The free body diagram of the cylinder is shown in Figure 9. The vane is assumed to be

of a rectangular geometry of width . The centre of mass of the cylinder is assumed to be at the

centre of the rotation at point C, while that of the rotor at point R. The summation of torques acting

at the cylinder, , includes the torques caused by the shafting bearings and endface frictions,

which will be discussed later in this chapter. A torque gain is assumed to be positive, while torque

loss is assumed to be negative.

In order to simplify the analysis, the vane side force is assumed to be at point A instead of point B, as

shown in Figure 10. The assumption does not affect the accuracy of the solution to a large extent

due to the fact that the width of vane is much smaller as compared to the main dimensions of the

expander[4].

33

Figure 9: Free body diagram of cylinder [5]

Figure 10: The real (a) and approximated locations of contact force [5]

Figure 11: The triangle ACR with the forces shown [5]

The normal force of the vane side acting on the cylinder is expressed as:

34

(4.12)

where:

is the product of rotational inertia and angular acceleration of cylinder (N)

is the coefficient of friction between the vane side and cylinder

The frictional power loss due to vane side friction is the product of the vane contact force, friction

coefficient and vane sliding velocity, which is expressed as:

(4.13)

4.3.5.2 Endface friction

There are gaps between the endfaces of the rotor and cylinder. These gaps are lubricated by oil and

during operation of the expander, friction due to fluid shear exists because of relative velocity of the

rubbing components. Such flow can be approximated by Couette flow. The fluid shear due to the

vane endface is neglected due to its comparatively smaller areas as compared to that of the rotor.

In this case, the oil lubricant in the gaps is assumed to have a constant viscosity, . The endface gaps,

, are assumed to be uniform and constant throughout. It is also assumed that the gaps are small

enough such the pressure effect to the fluid flow is insignificant [4].

35

Figure 12: Endface friction model [5]

The torque due to rotor is expressed as:

(4.14)

The torque due to cylinder is expressed as:

(4.15)

The power loss due to endface friction is expressed as:

(4.16)

4.3.5.3 Bearing friction

Bearings are needed to support the rotating shafts. In this study, journal bearings are used. The

frictional losses are approximated using the Mobility Method by Booker[25] to analyze the

dynamically loaded journal bearing. The frictional loss is assumed to be due to shear of oil film and

due to hydrodynamic film pressure.

36

Figure 13: Journal bearing illustration [11]

The power loss due to bearing friction is expressed as:

(4.17)

where

.

4.4 Irreversibility modelling

In order to evaluate the exergy destruction within the expander during its operation, the expander

suction and discharge chambers will be used as boundaries of the control volume. Within the

system, there are unsteady inflow of fluid into the suction chamber and outflow of fluid from the

discharge chamber. The various processes of exergy destruction will be analysed in this section.

4.4.1 Exergy destruction by heat transfer

When heat is produced at a temperature above the temperature of the surroundings, the heat can

be transferred to a heat engine to produce useful work. However, heat is a form of disorganised

37

energy and not the entire energy can be converted into work. Hence, there will be exergy

destruction or loss of work potential during the heat transfer process.

Figure 14 shows the model used for heat transfer exergy analysis. The irreversibility or exergy

destruction due to heat transfer can be expressed as [18]:

(4.18)

where:

is the temperature of the surroundings (K)

is the temperature of the fluid in the system (K)

is the temperature of the solid surface (K)

Figure 14: Model for exergy analysis of heat transfer

4.4.2 Exergy destruction by throttling of inflow fluid

In a control volume analysis, the pressure of the fluid entering a control volume will be different

from that of the bulk fluid already in the system. The fluid can be modelled as undergoing adiabatic

throttling when it possesses a higher pressure and enters a system at a lower pressure.

Figure 15 shows the model used for exergy analysis of adiabatic throttling. The irreversibility due to

adiabatic throttling can be expressed as [18]:

Fluid in suction or

discharge control

volumes

Temperature

Solid mass of expander

Temperature

Heat transfer at expander

wall surface,

Surrounding temperature,

38

(4.19)

where:

is the specific entropy after throttling and is evaluated at the pressure of the bulk fluid in

the system and at enthalpy .

Figure 15: Model for exergy analysis of throttling

4.4.3 Exergy destruction by fluid mixing

Irreversibility due to fluid mixing occurs when the inflow fluid possess a different temperature to

that of the bulk fluid in the system. In the fluid system, the inflow fluid receives or rejects heat over a

range of temperature, while the bulk fluid in the system receives or rejects heat at a constant

temperature.

Figure 16 shows the model to be used in exergy analysis for the mixing of an incoming flow with fluid

already in the system. Figure 16a shows the irreversible mixing process, and it can be replaced with

figure 16b where irreversible heat transfer occurs between the incoming fluid and bulk fluid already

in the system.

Bulk fluid in control volume

Inflow fluid at rate,

Initial pressure, Pi

Initial enthalpy, hi

Initial entropy, si

Throttled fluid, with conditions at:

Bulk fluid pressure, P

Enthalpy,

New entropy,

39

Figure 16: Model of exergy analysis for fluid mixing[18]

The exergy destruction due to fluid mixing can be expressed as [18]:

(4.20)

4.4.4 Exergy destruction by friction

During operation, the moving components within the expander rub against one another with

relative speeds. In order to overcome the frictional forces, some work is needed. The amount of

work supplied will eventually be dissipated as heat to the components. The heat produced from

friction can be a form of potential work as discussed in section 4.4.1.

The model used for exergy analysis of friction is shown in figure 17. The exergy destruction rate

associated with a rate of friction work that is dissipated as heat transfer to a mass at temperature Tk

can be expressed as [18]:

(4.21)

Figure 17: Model for exergy analysis of friction

Temperature of

solid mass, Heat transfer at

interfaces,

Rubbing surfaces

Work input to overcome

friction,

Surrounding

temperature,

40

Chapter 5: Simulation and exergy analysis

5.1 Introduction

In this chapter, simulation of the operation of the Revolving Vane Expander will be carried out. The

exergy analysis will be applied to identify the different sources of exergy destruction within the

expander.

The working fluid selected for the operation of the expander will be air. Air is chosen because

experimental work by Subiantoro [4], which was used for verification, utilised air.

5.2 Simulation procedure

Using the theoretical models of the Revolving Vane Expander set up in Chapter 4, the expander

simulation is carried out to observe its behaviours. A computer code was developed in Matlab

programming language. The REFPROP routines [22] were incorporated into the code to provide the

thermophysical properties of the working fluid. The simulation code consists of five main blocks:

Geometrical model

Thermodynamics and heat transfer

Dynamics and friction

Internal leakages

Exergy destruction

The simulation code requires an iterative approach. The mass flow rate of the expander is taken as

the parameter for convergence check because internal leakage is the main cause of fluctuations in

the simulation data. The mass flow rates of the consecutive iterations are compared for convergence

check and convergence is considered to be achieved when they differ by less than 1%. Otherwise,

41

the iteration is repeated to obtain new internal leakage data[4]. Figure 18 shows the algorithm of

the simulation.

If not satisfied If satisfied

Geometry Model

Establish kinematics properties

for one complete cycle

Thermodynamics and Heat Transfer model

Establish thermodynamics properties for

suction chamber and discharge chamber

separately

Dynamics and Frictional model

Establish dynamics and properties for one

complete cycle. Determine frictions at each

component

Leakage model

Determine leakage from suction

chamber to discharge chamber

Check

converge

nce

criterion

Reset time End

Exergy destruction

Throttling

Fluid mixing

Heat transfer

Exergy destruction

Friction

Exergy destruction

Throttling

Fluid mixing

Figure 18: Algorithm of simulation

42

Finally, after convergence is acquired, the exergy destruction model is applied to the data recorded.

The exergy analysis can be broken down to the suction and discharge control volumes, separately.

The exergy destruction rates due to the different components can be computed and put into

comparison. Figures 19 and 20 show the summary of exergy destruction taking place in the suction

and discharge control volume respectively.

Figure 19: Suction control volume analysis

Figure 20: Discharge control volume analysis

Discharge Control Volume

- Friction exergy

destruction

- Heat transfer exergy

destruction

Inflow through leakages:

-Throttling exergy destruction

-Fluid mixing exergy

destruction

Outflow through

discharge port:

-Throttling exergy

destruction

-Fluid mixing exergy

destruction

Suction Control Volume

- Friction exergy

destruction

- Heat transfer exergy

destruction

Inflow through suction port:

-Throttling exergy destruction

-Fluid mixing exergy destruction

Leakages to

Discharge

Control Volume

43

5.3 Simulation results The simulated expander operating conditions and dimensions are listed in Table 1.

Operating conditions

Angular velocity of rotor 3000 rev/min

Suction reservoir temperature 25 ºC

Suction reservoir pressure 800000 Pa

Discharge reservoir temperature 25 ºC

Discharge reservoir pressure 101325 Pa

Rotor dimensions and parameters

Radius of rotor 0.029 m

Length of rotor (or length of the expander) 0.025 m

Rotating inertia of rotor 0.00021 kg·m2

Cylinder dimensions and parameters

Radius of cylinder 0.035 m

Rotating inertia of cylinder 0.00281 kg·m2

Non-loaded radial clearance gap between the rotor and the cylinder 15 ×10-6 m

Vane dimensions and parameters

Length of vane 0.016 m

Width of vane 0.004 m

Friction coefficient between vane and vane slot 0.15

Suction ports dimensions and parameters

Radius of suction ports 0.0032 m

Depth of suction ports 0.029 m

Number of suction ports 3

Opening angle of suction valve 84º

44

Coefficient of discharge of suction ports 0.7

Discharge ports dimensions and parameters

Radius of discharge ports 0.0023 m

Depth of discharge ports 0.029 m

Number of discharge ports 3

Coefficient of discharge of discharge ports 0.7

Endfaces dimensions and parameters

Viscosity of lubricant 0.0034 Pa·s

Width of endface gap 10 × 10-6 m

Rotor shaft bearings dimensions and parameters

Radius of rotor shaft bearings 0.0125 m

Length of rotor upper shaft bearing 0.04 m

Length of rotor lower shaft bearing 0.02 m

Radial clearance of rotor shaft bearings 15 × 10-6 m

Distance between upper rotor shaft bearing to rotor 0.0325 m

Distance between lower rotor shaft bearing to rotor 0.0225 m


Cylinder shaft bearings dimensions and parameters

Radius of cylinder shaft bearings 0.0246 m

Length of cylinder upper shaft bearing 0.01 m

Length of cylinder lower shaft bearing 0.01 m

Radial clearance of cylinder shaft bearings 12.5 × 10-6 m

Distance between upper cylinder shaft bearing to cylinder 0.0175 m

Distance between lower cylinder shaft bearing to cylinder 0.0175 m


Table 1: List of operating conditions

45

5.3.1 Mass and mass flow rates

Figure 21 shows that the mass of fluid in the suction control volume increases as fluid flows in from

the suction port when the suction valve is opened. The peak is reached at about 70mg. At the end of

one revolution, the suction control volume becomes the discharge control volume, thus the mass of

fluid is the same for the end of suction cycle and start of discharge cycle. When the suction valve is

closed at about 2.3 radians, the mass in the suction control volume continues to decrease gradually

due to leakages from the suction to discharge control volume.

Figure 21: Mass of suction and discharge control volumes

The mass flow rates of fluid are shown in Figure 22. The suction mass flow rate increases rapidly

initially due to the increase in area of the flow from the opening of the suction valve. While suction

flow is restricted to the opening of suction valve, discharge flow occurs almost throughout the entire

cycle. The rapid fluctuations of the suction mass flow rate between rotor angle of 1.0 to 1.5 radians

occur due to the fluctuations in area of valve opening, density and enthalpy of fluid in the suction

control volume.

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

Mass (

mg)

Rotor angle (rad)

Mass of fluid

Suction control volume

Discharge control volume

46

Figure 22: Mass flow rates of suction and discharge flow

5.3.2 Temperature, heat transfer rates and pressure

Figure 23 shows the temperature of fluid in the suction and discharge control volumes. The suction

control volume experiences a large variation of temperature change in a cycle, whereas that of

discharge control volume is almost constant. For the suction control volume, the temperature of

fluid increases rapidly at the start of cycle due to increase in pressure from the suction process.

Temperature then falls due to heat transfer to the solid mass and subsequently decreases rapidly

when the expansion process starts. Temperature of fluid in the discharge control volume is fairly

constant as it is does not undergo the suction or expansion processes, and is mainly affected by heat

transfer between the fluid and the solid mass.

0 1 2 3 4 5 6-15

-10

-5

0

5

10

15

20

25

30

Rotor angle (rad)

Mass f

low

rate

(g/s

)

Mass flow rate

Suction flow rate

Discharge flow rate

47

Figure 23: Temperature of fluid in suction and discharge control volumes

In Figure 24, it shows that the heat transfer rate is much higher for suction control volume due to

the larger temperature difference between the temperature of fluid and solid mass. A negative rate

indicates heat transfer from the fluid and a positive rate indicates heat transfer to the fluid. The

suction control volume experiences high heat transfer rate from the fluid to the solid mass at the

initial stage as it has a much higher fluid temperature than the solid mass. But the heat transfer

reverses when the expansion process starts and the fluid temperature drops below the solid mass

temperature. The sudden drop of heat transfer rate at the end of the suction cycle is due to the

Reynolds number falling rapidly to zero.

0 1 2 3 4 5 6-20

0

20

40

60

80

100

Rotor angle (rad)

Tem

pera

ture

(C

)

Temperature of fluid in control volume



48

Figure 24: Heat transfer rates of fluid in suction and discharge control volumes

Figure 25 shows the pressure of the control volumes. As fluid flows into the suction control volume,

the pressure equilibrates with the suction reservoir at 800 kPa and subsequently falls when the

expansion process starts. The fluid is found to be under-expanded as the fluid pressure at the end of

the expansion cycle is higher than that of the discharge reservoir, which is maintained at 101 kPa.

This is caused mainly by the heat transfer from the solid mass to the fluid in the suction control

volume during the expansion process, as the increase in temperature maintains the fluid pressure

even though its volume increases.

Figure 25: Pressure of fluid in suction and discharge control volume

0 1 2 3 4 5 6-800

-600

-400

-200

0

200

400

600

800

1000

1200

Rotor angle (rad)

Heat

transfe

r ra

te (

W)

Heat transfer rate



0 1 2 3 4 5 60

100

200

300

400

500

600

700

800

900

Rotor angle (rad)

Pre

ssure

(kP

a)

Pressure of fluid in control volume



49

5.3.3 Leakage

Figure 26 shows the leakage mass flow rate from the suction to discharge control volume. The

leakage mass flow rate increases as the pressure difference between the suction and discharge

control volumes becomes larger. The leakage is peaked when the rotor angle is about 2 radians

when the pressure difference between suction and discharge control volumes is highest. As

compared to the suction and discharge mass flow rates, the leakage mass flow rate is significantly

lower. The volumetric efficiency, which is the ratio between the real flow rate and ideal flow rate

(with no internal leakage), is 89.1%.

Figure 26: Total leakage mass flow rate

5.3.4 Frictional power loss

Figure 27 shows the frictional power loss due to the different components in the expander. It is

noted that the vane frictional loss dominates because the operating pressure is low and hence, the

inertial effect is dominant.

0 1 2 3 4 5 6-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Rotor angle (rad)

Mass f

low

rate

(g/s

)

Total leakage mass flow rate

50

Figure 27: Frictional power loss

5.4 Exergy destruction rates

5.4.1 Exergy destruction due to throttling

Figure 28 shows the breakdown of exergy destruction rates due to throttling. As discussed in

Chapter 4, exergy destruction due to throttling is expressed as:

(4.19)

The main determining factors for the exergy destruction are the mass flow rate and entropy

difference between the inflow fluid and bulk fluid already in the control volume. The highest exergy

destruction occurs in the suction control volume at rotor angle 0.5 radian when the mass flow rate

and entropy difference are highest.

For the discharge flow, exergy destruction due to throttling is dominated by the discharge mass flow

rate as the entropy of discharge fluid is very near to that of the discharge reservoir. Thus the exergy

destruction rate peaks at about rotor angle 0.9 radian when the corresponding discharge mass flow

rate is highest.

For exergy destruction due to leakage, both the mass flow rate and entropy difference are important

for consideration. The highest exergy destruction rate occurs at rotor angle 2 radians, which

0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

Rotor angle (rad)

Pow

er

(W)

Frictional power loss

Endface

Cylinder bearing

Rotor bearing

Vane

51

corresponds to the highest leakage mass flow rate and large pressure difference between suction

and discharge control volumes.

It is interesting to note that exergy destructions due to leakage and discharge are of comparable

values, even though that the leakage flow rate is significantly smaller than that of discharge flow

rate. This is mainly because the pressure difference is much larger for the leakage flow as compared

to that of the discharge flow, resulting in larger entropy difference for leakage flow.

Figure 28: Exergy destruction rates due to throttling

5.4.2 Exergy destruction rates due to fluid mixing

Figure 29 shows the breakdown of exergy destruction rates due to fluid mixing. As discussed in

Chapter 4, exergy destruction due to fluid mixing is expressed as:

(4.20)

The main factors affecting the exergy destruction due to fluid mixing are the mass flow rates,

entropy difference and enthalpy difference between the inflow fluid and bulk fluid in the system.

Once again, the exergy destruction due to suction fluid dominates for the case of fluid mixing. This is

due to the significantly larger flow rate and entropy difference. The contributions of exergy

destruction due to fluid mixing from the leakage and discharge flow are considered to be negligible.

0 1 2 3 4 5 60

500

1000

1500

Rotor angle (rad)

Exerg

y d

estr

uction r

ate

s (

W)

Exergy destruction rates due to throttling

Suction

Leakage

Discharge

52

Figure 29: Exergy destruction rates due to fluid mixing

5.4.3 Exergy destruction rates due to heat transfer

Figure 30 shows the breakdown of exergy destruction rates due to heat transfer. As discussed in

Chapter 4, exergy destruction due to heat transfer is expressed as:

(4.18)

In this case, the atmospheric temperature is 303K and the temperature of the solid mass Tk is fixed

at the average of suction and discharge reservoir, which is 303K too. The main factors affecting the

exergy destruction rate due to heat transfer are the heat flow rate and temperature of the bulk fluid

in each of the control volume, Tj.

Exergy destruction rate due to heat transfer in the suction control volume is significantly higher than

that of the discharge control volume across the whole range of rotor angle. This is because the

temperature difference between the suction control volume and the solid mass is significantly

larger, resulting in higher heat flow rate throughout.

0 1 2 3 4 5 6

0

50

100

150

Exergy destruction rates due to fluid mixing

Rotor angle (rad)

Exerg

y d

estr

uction r

ate

s (

W)

Suction

Leakage

Discharge

53

Figure 30: Exergy destruction rates due to heat transfer

5.4.4 Exergy destruction rates due to friction

Figure 31 shows the breakdown of exergy destruction rates due to heat transfer. As discussed in

Chapter 4, exergy destruction due to friction is expressed as:

(4.21)

As the atmospheric temperature To and temperature of the solid mass Tk are fixed, the friction

power loss is directly related to the exergy destruction rate. Exergy destruction due to vane friction

is dominant, while the rest are of comparable values.

0 1 2 3 4 5 60

20

40

60

80

100

120

140

160

180

Rotor angle (rad)

Exerg

y d

estr

uction r

ate

s (

W)

Exergy destruction rates due to heat transfer



54

Figure 31: Exergy destruction rates due to friction

5.4.5 Overall exergy destruction

Figure 32 shows the overall breakdown of the exergy destruction that occurs for the different

components during the operation of the expander. Friction accounts for almost half of the exergy

destruction within the expander, followed closing by throttling, and then heat transfer, and finally

fluid mixing is almost negligible.

In the simulation study, the discharge reservoir has same conditions as that of atmosphere. Using

the exergy of the high-pressure fluid in the suction reservoir as the exergy supplied and the overall

exergy destroyed, the second-law efficiency can be computed:

(3.22)

The exergy rate supplied by the high-pressure fluid is 661.59 W and the exergy rate destroyed is

465.6 W. It is found that the second-law efficiency is 29.6%. This shows that in order to improve the

exergy efficiency of the expander, it is important to work on the friction and throttling components

especially. Further discussion will be done for the parametric study in Chapter 6 to identify the

optimum operating conditions of the expander.

0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

Exerg

y d

estr

uction r

ate

s (

W)

Rotor angle (rad)

Exergy destruction rates due to friction

Endface

Cylinder bearing

Rotor bearing

Vane

55

Figure 32: Breakdown of exergy destruction

Components (average) Average exergy destruction rates (W)

Throttling 179.0

Fluid mixing 5.1

Heat transfer 55.3

Friction 226.2

Total 465.6

Table 2: Summary of average exergy destruction rates

Total Heat transfer

12%

Total Throttling 38%

Total Fluid mixing

1%

Total Friction 49%

56

Chapter 6: Parametric study

6.1 Introduction

In order to have a fuller understanding of the RV expander under different operating conditions, a

parametric study of the exergy analysis is undertaken. The aim of the parametric study is to

determine the optimum operating conditions for each parameter chosen. The bases of comparison

are the exergy destruction rates for each process and the overall second-law efficiency.

The parameters to be examined are:

Suction reservoir pressure

Rotational speed of rotor

Rotational inertia of cylinder

These parameters are selected because they are known to affect the power generation capacity and

working processes of the expander significantly. Also, one of these parameters can be changed

independently without affecting the other parameters during the study.

6.1.1 Suction reservoir pressure

The suction reservoir pressure determines the power generation capacity of the expander to a huge

extent. Variations in suction reservoir pressure will affect the mass inflow rate through the suction

port into the suction chamber and the maximum operating pressure in the suction chamber. The

selected pressures are:

4 bar

6 bar

8 bar (benchmark)

10 bar

12 bar

57

6.1.2 Rotational speed of rotor

In the Revolving Vane Expander model, the rotor is assumed to rotate at a constant velocity. The

benchmark speed is 3000 rpm or 50 Hz. By changing the input rotational speed of the rotor, it is

likely to affect the rate of power generation and frictional losses between the moving components

within the expander. The selected rotational speeds are defined to be as such:

2400 rpm of 40 Hz

3000 rpm or 50 Hz (benchmark)

3600 rpm or 60 Hz

6.1.3 Inertia of cylinder

The rotational inertia (subsequently referred to as just inertia) of the cylinder can be changed by

using a different material. For example, by using aluminium with a density of 2700 kg/m3, instead of

steel with a density of 7200 kg/m3, the inertia will be reduced to about 1/3 of the original inertia.

The effect of cylinder inertia will likely cause a change in the friction of the moving components and

affect the exergy destruction involved.

Using normalised cylinder inertia, with the benchmark inertia as the value of 1, the selected cylinder

inertias are:

1/3 of cylinder inertia


1 time of cylinder inertia (original)

6.2 Effects of variation of suction reservoir pressure

For this parametric study, the suction reservoir pressure is varied while keeping the inertia of

cylinder constant and rotor speed at 3000 rpm. According to Subiantoro[4], in order to allow the

suction fluid to be expanded in an adiabatic manner and as close as possible to the discharge

58

reservoir pressure at 1 bar absolute, the suction valve opening angle is varied according to the

values in Table 3. The summary of the average exergy destruction due to variation of suction

pressure is shown in Table 4.

Operating conditions 4 bar 6 bar 8 bar 10 bar 12 bar

Suction valve opening angle

(degree)

116 94 84 67 58

Table 3: Suction valve opening angle according to suction pressure [4]


Heat transfer loss (W) 22.38 39.05 55.25 66.86 78.40

Throttling loss (W) 99.67 118.75 179.09 206.43 249.22

Mixing loss (W) 1.91 2.82 5.09 4.99 6.12

Frictional loss (W) 224.06 224.85 226.17 226.02 226.50

Total exergy destruction (W) 348.01 385.47 465.61 504.31 560.25

Table 4: Exergy destruction with variation of suction pressure

6.2.1 Heat transfer with variation of suction pressure

From Table 4, exergy destruction due to heat transfer increases steadily from 22.38 W to 78.40 W as

suction pressure increases from 4 bar to 12 bar correspondingly. The main reason is the increase in

heat transfer rates due to the higher heat transfer coefficient, h. From equation 4.8, it is shown that

the heat transfer rate is proportional to the heat transfer coefficient.

(4.8)

(4.9)

(4.10)

59

The maximum pressure in the suction control volume is limited by the suction reservoir pressure. As

the suction control volume pressure increases, the density of the fluid in the control volume

increases too, due to a closer packing of the molecules. As a result, the Reynolds number increases

as it is directly proportional to the density of fluid. A higher Reynolds number leads to higher Nusselt

number and heat transfer coefficient correspondingly. Figure 33 shows the maximum density of fluid

increases from about 7 kg/m3 to 11 kg/m3 as the pressure of suction control volume increases from 6

bar to 10 bar correspondingly.

Figure 33: Densities of fluid in suction control volume

6.2.2 Throttling with variation of suction reservoir pressure

Exergy destruction due to throttling increases from 99.67 W to 249.22 W as the suction pressure

increases from 4 bar to 12 bar correspondingly. From equation 4.19, it can be seen that exergy

destruction due to throttling is dependent on the mass flow rates and entropy difference between

the throttled fluid and bulk fluid in the suction control reservoir.

(4.19)

The pressure difference between the suction reservoir and suction control volume is the main

driving force for fluid inflow. As the pressure difference increases, the mass flow rates increases too.

0 1 2 3 4 5 60

2

4

6

8

10

12

Rotor angle (rad)

Density (

kg/m

3)

Densities of fluid in suction control volume

6 bar

8 bar

10 bar

60

Table 5 shows the increase in average suction flow rate and leakages as the suction reservoir

pressure increases.

The entropy difference is proportional to the pressure difference too. Figure 34 shows the increase

in entropy difference as the suction reservoir pressure increases from 6 bar to 10 bar. Hence, a

higher suction pressure causes both mass flow rate and entropy difference to increase, which results

in higher throttling exergy destruction.


Average suction flow

rate (g/s)

2.99

3.56

3.68

3.70

3.74

Average leakages

(g/s)

0.244

0.353

0.449

0.477

0.523

Table 5: Mass flow rate with variation of suction pressure

Figure 34: Entropy difference for variation of suction reservoir pressure

0 1 2 3 4 5 60

100

200

300

400

500

600

700

Rotor angle (rad)

Entr

opy d

iffe

rence (

J/k

g.K

)

Entropy difference of suction fluid

6 bar

8 bar

10 bar

61

6.2.3 Fluid mixing with variation of suction reservoir pressure

Fluid mixing exergy destruction increases from 1.91 W to 6.12 W as the suction reservoir pressure

increases from 4 bar to 12 bar correspondingly. From equation 4.20, fluid mixing exergy destruction

is dependent on mass flow rate, entropy difference and enthalpy difference. The magnitude of

contribution of fluid mixing exergy destruction is negligible to the overall exergy destruction (about

1%), hence it is not an important parameter for consideration.

(4.20)

6.2.4 Friction with variation of suction reservoir pressure

From Table 4 it can be observed that frictional exergy destruction is almost constant for different

suction reservoir pressure. The main contribution to friction is the vane friction. At such operating

conditions which are considered as low-pressure conditions, the dominant effect of vane friction is

due to the inertia of the cylinder, which is kept constant for this parametric study. Hence, variation

in suction reservoir pressure has negligible effect on the frictional exergy destruction of the

expander.

6.2.5 Overall analysis of exergy destruction due to variation in suction reservoir

pressure

Generally, a higher suction reservoir pressure results in higher exergy destruction of the expander.

The biggest contribution to the increase in exergy destruction as suction pressure increases is

throttling, followed by heat transfer. Changes in fluid mixing and frictional exergy destruction are

negligible.

However, it is important to consider the second-order efficiency of the system too. From equation

3.10, the exergy supplied changes as the pressure of the suction fluid changes too. A higher suction

62

pressure results in higher exergy supplied, as the fluid have a higher potential to do useful work. The

increase in suction mass flow rate also increases the rate of exergy supplied.

(3.10)

(3.22)

Table 6 shows the resulting second-law efficiency. It is observed that second-law efficiency climbs

rapidly as suction pressure increases from 4 bar to 6 bar from 3% to 30%, but efficiency stays almost

constant at about 30% from 6 bar to 12 bar. Figure 35 shows that the second-law efficiency stabilizes

at suction pressures above 6 bar.


Exergy destoyed (W) 348.01 385.47 465.61 504.31 560.25

Exergy supplied (W) 358.76 550.68 661.59 737.18 803.15

Second-law efficiency 3.00% 30.0% 29.6% 31.6% 30.2%

Table 6: Second-law efficiency with variation of suction pressure

Figure 35: Second-law efficiency for variation of suction reservoir pressure

4 5 6 7 8 9 10 11 120

5

10

15

20

25

30

35

Second-law efficiency for variation of suction reservoir pressure

Suction reservoir pressure (bar)

Second-law

eff

icie

ncy (

%)

63

In conclusion, the optimum suction reservoir pressure is 6 bar and above for the expander from this

preliminary parametric study as the second-law efficiency peaks and stabilizes. From exergy analysis

viewpoint, the expander is not suitable to be operating at low suction pressure as second-law

efficiency deteriorates rapidly at low suction pressure. It is important to note that this is a specific

behaviour of this particular expander as the prototype was designed for such applications. When an

expander is needed for 4 bar operation, some of the design parameters, such as the bearing sized,

etc. need to be modified.

6.3 Effects of variation of rotational speed

For this parametric study, the rotational speed is varied while keeping the inertia of cylinder

constant and suction reservoir pressure at 8 bar. The summary of the average exergy destruction

due to variation of suction pressure is shown in Table 7.

Operating conditions 40 Hz 50 Hz 60 Hz

Heat transfer loss (W) 44.51 55.25 65.54

Throttling loss (W) 149.13 179.09 208.43

Mixing loss (W) 4.61 5.09 5.82

Frictional loss (W) 122.93 226.17 373.80

Total exergy destruction (W) 321.18 465.61 653.60

Table 7: Exergy destruction with variation of rotational speed

6.3.1 Heat transfer with variation of rotational speed

Exergy destruction due to heat transfer increases from 44.51 W to 65.54 W as the rotational speed

increases from 40 Hz to 60 Hz correspondingly. The main reason is the increase in heat transfer

coefficient, h. As the rotational speed increases, the fluid is modelled to have a higher velocity, U, as

shown in equation 4.9. Figure 36 shows that the maximum fluid velocity increases from about 8.5

64

m/s to 13 m/s as rotational speed increases from 40 Hz to 60 Hz. This causes a higher Reynolds

number and correspondingly higher heat transfer coefficient.

(4.8)

(4.9)

(4.10)

Figure 36: Fluid velocities for variation of rotational speed

6.3.2 Throttling with variation of rotational speed

Exergy destruction due to throttling increases 149.13 W to 208.43 W as the rotational speed

increases from 40 Hz to 60 Hz correspondingly. From equation 4.19, the throttling loss is dependent

on the mass flow rate and entropy difference. In this case, the dominant factor contributing to the

increase is the higher mass flow rate. Table 8 shows that the average suction mass flow rate

increases from 2.98 g/s to 4.22 g/s as rotational speed increases from 40 Hz to 60 Hz.

(4.19)

0 1 2 3 4 5 67

8

9

10

11

12

13

14

Rotar angle (rad)

Flu

id v

elo

city,

U (

m/s

)

Fluid velocity for variation of rotational speed

40 Hz

50 Hz

60 Hz

65


Average suction mass flow rate (g/s) 2.98 3.68 4.22

Table 8: Mass flow rate with variation of rotational speed

6.3.3 Fluid mixing with variation of rotational speed

Exergy destruction due to fluid mixing increases from 4.61 W to 5.82 W as the rotational speed

increases from 40 Hz to 60 Hz correspondingly. The main reason is the increase in mass flow rate,

which is the same as the previous section for the throttling. However, the increase in exergy

destruction is negligible for fluid mixing as compared to that of heat transfer and throttling.

6.3.4 Friction with variation of rotational speed

Exergy destruction due to friction increases significantly from 122.93 W to 373.80 W as the

rotational speed increases from 40 Hz to 60 Hz. As the rotational speed increases, the relative

velocities of the moving components increase, which causes the frictional loss to increase. The vane

friction increase has the dominant contribution.

From equation 4.12, the normal force of the vane acting on the cylinder is proportional to the

angular acceleration of the cylinder. Figure 37 shows that the peak angular acceleration increases

from about 1.0 X 104 rad/s2 to 2.5 X 104 rad/s2 as rotational speed increases from 40 Hz to 60 Hz

correspondingly.

(4.12)

66

Figure 37: Cylinder angular acceleration for variation of rotational speed

6.3.5 Overall analysis of exergy destruction due to variation in rotational speed

Generally, exergy destruction increases as the rotational speed increases. The main contribution is

the increase in frictional losses, followed by throttling, then heat transfer. Fluid mixing loss is

negligible in this case.

As the rotational speed increases from 40 Hz to 60 Hz, the exergy supplied increases from 522.65 W

to 839.36 W due to higher mass flow rate. Table 9 shows the summary of the second-law efficiencies

for various rotational speeds. The second-law efficiency is highest at 40 Hz with 38.55% and lowest

at 60 Hz with 22.13%.

In conclusion, the optimum rotational speed of this particular expander is 40 Hz. A low operating

speed is favourable to maximise the work potential of the high-pressure fluid. However, a low

operating speed will limit the output power of the expander, hence a compromise is needed

between the required power output and second-law efficiency.

0 1 2 3 4 5 6-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

4

Rotor angle (rad)

Cylin

der

angula

r accele

ration (

rad/s

2)

Cylinder angular acceleration for variation of rotational speed

40 Hz

50 Hz

60 Hz

67


Exergy destroyed (W) 321.18 465.61 653.60

Exergy supplied (W) 522.65 661.59 839.36

Second-law efficiency 38.55% 29.62% 22.13%

Table 9: Second-law efficiency with variation of rotational speed

Figure 38: Second-law efficiency for variation of rotational speed

6.4 Effects of inertia of cylinder

For this parametric study, the inertia of cylinder is varied while the suction pressure is fixed at 8 bars

and rotational speed of rotor is fixed at 3000 rpm. The summary of the average exergy destruction is

shown in Table 10 below.

Operating conditions 1/3 of cylinder inertia


1 time of cylinder inertia

Heat transfer loss (W) 54.98 55.13 55.25

Throttling loss (W) 163.04 175.35 179.09

Mixing loss (W) 5.15 5.16 5.09

Frictional loss (W) 109.24 166.88 226.17

Total exergy destruction (W) 332.41 402.53 465.61

Table 10: Exergy destruction wtih variation of inertia of cylinder

40 42 44 46 48 50 52 54 56 58 6022

24

26

28

30

32

34

36

38

40

Rotational speed (Hz)

Second-law

eff

icie

ncy (

%)

Second-law efficiency for variation of rotational speed

68

6.4.1 Heat transfer with variation of inertia of cylinder

The heat transfers rates are almost constant at about 55 W as the inertia of cylinder is varied. This is

because the modelling of the heat transfer is dependent on the properties of the fluid only, which

are kept the same for the 3 simulations. Also, the temperature of the solid mass is assumed to be

constant throughout the operation due to a significantly higher heat resistance as compared to the

fluid. Therefore, variation of inertia cylinder has negligible effect on the heat transfer exergy

destruction.

A more realistic representation will be factoring temperature change within the solid mass of the

expander during operation. Due to different densities and heat conduction properties of the

materials used, it is likely that heat transfer rates will vary. However, this is outside the scope of our

simulations for now.

6.4.2 Throttling with variation of inertia of cylinder

Throttling exergy destruction increases slightly as cylinder inertia increases, but is considered to be

negligible as compared to changes in frictional exergy destruction. This is because throttling is

mainly dependent on pressure difference between the suction reservoir pressure and suction

control volume, which is kept the same for this parametric study. The variation in the throttling

exergy destruction is due to the small fluctuations of mass flow rates and entropy difference for the

different operating conditions, hence can be ignored for this case.

6.4.3 Fluid mixing with variation of inertia of cylinder

Fluid mixing exergy destruction is almost constant at about 5 W for the different cylinder inertia. The

reason is similar to that as mentioned in the previous section of throttling losses. Hence, fluid mixing

is not an important consideration for variation of cylinder inertia.

69

6.4.4 Friction with variation of inertia of cylinder

Frictional exergy destruction is the most dominant factor when inertia of cylinder is varied. The main

contributing component is the vane friction losses. This is because the normal force between the

vane and cylinder is directly proportional to the inertia of cylinder as shown in equation 4.12.

(4.12)

The average frictional loss due to the vane is summarised in table 11. The average exergy

destruction due to vane friction is almost proportional to the cylinder inertia.

Average exergy

destruction (W)

1/3 time of cylinder

inertia

2/3 time of cylinder

inertia

1 time of cylinder

inertia

Vane friction loss (W) 57.63 115.61 172.96

Table 11: Vane friction loss due to different cylinder inertia

6.4.5 Overall analysis of exergy destruction due to variation in cylinder inertia

Generally, the exergy destruction increases as the normalized cylinder inertia increases. The main

reason is the increase in frictional exergy destruction, as the other components of exergy

destruction stay fairly constant.

The exergy supplied by the fluid is maintained at a constant rate in this case as the suction reservoir

pressure and rotational speed are kept the same, i.e. the fluid supplied has the same potential to do

useful work. Hence, the second-law efficiency is the highest when cylinder inertia is at 1/3 of the

normalized cylinder inertia. Table 12 shows the summary of second-law efficiency when the cylinder

inertia is varied. Figure 39 shows that the exergy destruction rises steadily while the exergy supplied

is constant. Figure 40 shows that the second-law efficiency decreases steadily as the inertia of

cylinder increases from 1/3 to 1 time of original inertia.

70

In conclusion, the optimum normalized cylinder inertia is 1/3 of the benchmark inertia. Lower

cylinder inertia helps to improve the second-law efficiency significantly. In order to achieve that, the

material used for the expander should have a low density and some parts of the cylinder can be

made hollow.

Operating conditions 1/3 of cylinder inertia 2/3 of cylinder inertia 1 time of cylinder

inertia

Exergy destroyed (W) 332.41 402.53 465.61

Exergy supplied (W) 661.59 661.59 661.59

Second-law efficiency 49.85% 39.16% 29.62%

Table 12: Second-law efficiency with variation of cylinder inertia

Figure 39: Overall exergy analysis for variation of inertia of cylinder

0.4 0.5 0.6 0.7 0.8 0.9 1300

350

400

450

500

550

600

650

700

Normalized inertia of cylinder

Exerg

y (

W)

Overall exergy analysis for variation of inertia of cylinder

Exergy destruction

Exergy supplied

71

Figure 40: Second-law efficiency for variation of inertia of cylinder

0.4 0.5 0.6 0.7 0.8 0.9 125

30

35

40

45

50

Normalized inertia of cylinder

Second-law

eff

icie

ncy (

%)

Second-law efficiency for variation of inertia of cylinder

72

Chapter 7: Conclusion and further studies

An exergy analysis has been applied on the Revolving Vane Expander in this report. Using the

mathematical modelling of the expander, a computer simulation using Matlab has been carried out

to investigate the thermodynamic properties of the expander during operation. By identifying the

sources of exergy destruction within the expander and exergy supplied by the high-pressure fluid,

the second-law efficiency of the expander is quantified as 29.6% under the benchmark operating

conditions of suction reservoir pressure at 8 bar absolute and rotational speed of 50 Hz.

A parametric study is carried out with the aims of identifying the optimum operating conditions of

the expander. The parameters which are varied are the suction reservoir pressure, rotational speed

and inertia of cylinder. The parameter with the highest second-law efficiency is selected to be the

optimum operating condition.

For the parametric study of suction reservoir pressure, the suction pressure is increased from 4 bar

to 12 bar while keeping the rotational speed and inertia of cylinder constant. The result shows that

second-law efficiency increases rapidly from 3.0% to 30.0% as suction pressure increases from 4 bar

to 6 bar, but remains relatively constant at 30.0% as suction pressure increases further from 6 bar to

12 bar. From the view-point of exergy analysis, the expander is suitable to operate at suction

reservoir pressure from 6 bar to 12 bar. In general, a higher suction pressure is favourable as it

allows higher power output from the expander.

For the parametric study of rotational speed, the speed is increased from 40 Hz to 60 Hz while

keeping the suction reservoir pressure and inertia of cylinder constant. The result shows that

second-law efficiency decreases from 38.55% at 40 Hz to 22.13% at 60 Hz. Hence, from the exergy

analysis viewpoint, the optimum rotational speed of the expander in study is 40 Hz. In general, a low

rotational speed is favourable for operating the expander, but will result in lower power output.

73

For the parametric study of inertia of cylinder, the normalized inertia is increased from 1/3 of

original inertia to 1 time of original inertia while keeping the suction reservoir pressure and

rotational speed constant. The result shows that the second-law efficiency decreases from 49.85% at

1/3 of inertia to 29.62% at 1 time of original inertia. From the viewpoint of exergy analysis, the

optimum inertia of cylinder is 1/3 of original inertia. In general, a low inertia of cylinder is desirable

to maximise the second-law efficiency, however it is limited by the types of material available which

have low densities and able to withstand the operating conditions of the expander.

In conclusion, in order to improve on the second-law efficiency of the expander, the suction

reservoir pressure should be high, the rotational speed should be kept low and the inertia of cylinder

should be kept low as well.

The application of exergy analysis is beneficial to the study of thermodynamic devices as it

incorporates the first and second law of thermodynamics, which makes the analysis of efficiency

fuller and more comprehensive. Moreover, the sources of inefficiencies can be identified and

quantified to allow improvements to be made to the devices. The main limitation of exergy analysis

is that detailed information is required about the devices and considerable amount of time has to be

invested to prepare an accurate analysis.

7.1 Further studies For the Revolving Vane Expander, further studies can be done to investigate the exergy destruction

sites and second-law efficiencies when different fluids are used as the refrigerant. The expander in

this study is suited for air as the fluid; however it may not function optimally when different fluids

are used.

Also, the dimensions of the rotor and cylinder can be varied to determine the optimum dimensions.

The RV expander in this study has a rotor radius of 29 mm, a cylinder radius of 35 mm and an

expander length of 25 mm. This results in an expander with a capacity of about 30 cm3. To keep the

RV expander at the same capacity, there are many possible variations of the rotor radius, cylinder

74

radius and expander length. Hence, further work can be done to determine the effect of differing

dimensions on the exergy destruction and second-law efficiency of the expander.

75

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