Energy Conversion and Heat Engines

8/14/2019 Energy Conversion and Heat Engines

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Energy Conversion and Heat Engines

(With a little bit of Thermodynamics)

Whether it is coal, oil, gas or nuclear power, 80% of the worlds electricity is derived from heat

sources and almost all of the energy conversion processes used convert the thermal energy into

electrical energy involve an intermediate step of converting the heat energy to mechanical energy in

some form of heat engine. To satisfy this need a wide range of energy conversion systems has been

developed to optimise the conversion process to the available heat source.

Despite over 250 years of development sinceJames Watt's steam enginewas first fired up, the best

conversion efficiency achieved today is only around 60% forcombined cyclesteam and gas turbine

systems. Efficiencies in the range of 35% to 45% are more common for steam turbines, 20% to 30%

for piston engines and as low as 3% forOTECocean thermal power plants. This page describes somethermodynamic aspects of a variety of representative heat engines. More detailed descriptions of

these engines can be found on other pages on this site via the links below.

The efficiency of heat engines was first investigated byCarnotin the 1824 and expanded upon

byClapeyronwho provided analytical tools in 1834 andKelvinwho stated the Second Law of

Thermodynamics in 1851 and finally byClausiuswho introduced the concept of entropy in 1865.

The Thermodynamic System

Every thermodynamic system exists in a particular state which is defined by the properties of its

components such as heat, temperature, pressure, volume, density, entropy and phase (liquid, gas

etc) at a given point in time. Thermodynamics concerns the conversions between heat and other

forms of energy in the system and the related energy flows.

In a thermodynamic cycle, energy is applied in one form to change the state of the system and

energy is then extracted in a different form to return the system to its original state. In a heat

engine, the energy is applied in the form of heat to change the state of a working fluid and then

extracted in the form of mechanical work to return the working fluid to its initial state. In other
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words, a heat engine is a system in which energy is interchanged between an energy conversion

system and its surroundings.

It is important to note that though the working fluid in a heat engine may work in a closed cycle, the

"system" and the "state of the system" are defined to include both the physical "engine" as well as

the working environment or surroundings.

Heat Engines

Heat engines employ a range of methods to apply the heat and to convert the pressure and volume

changes into mechanical motion.

From the Gas Laws PV =kN

T

where Pis the pressure, Vthe volume and Tthe temperature of the gas

and kis Boltzmann's constant and Nis the number of molecules in the gas charge.

Putting energy in the form of heat into a gas will increase its temperature, but at the same time the

gas laws mean that the gas pressure or volume or both must increase in proportion. The gas can be

restored to its original state by taking this energy out again but not necessarily in the form of heat.

The pressure and / or volume change can be used to perform work by moving a suitably designedmechanical device such as a piston or a turbine blade.

The greater the temperature change, the more energy which can be extracted from the fluid

The Heat Engine as Part of a System

Heat engines enable heat energy to be converted to

kinetic energy through the medium of a working fluid.

The diagram opposite shows the system heat flow.

Heat is transferred from the source, through working

fluid in the heat engine and into the sink, and in this

process some of the heat is converted into work.

Heat engine theory concerns only the process of

converting heat into mechanical energy, not themethod of providing the heat, the combustion


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process. Combustion is a separate conversion process

and is subject to its own efficiency losses. In some

practical systems such as steam turbines these two

processes are physically separate, but in internal

combustion engines, which account for the majority

of engines, the two processes take place in the same

chamber, at the same time.

Entropy

The concept of entropy is useful for understanding system energy conversions, energy flows and the

workings of heat engines. The word "entropy" comes from the Greek "transformation". Although

entropy was first defined for thermodynamic applications, the concept has been used in other

branches os science, notably electrochemistry and communications. There are thus many definitionsof entropy some of which are contradictory or confusing. The following three examples are

consistent and used in the context of heat engines.

Entropya measure of the disorder of a system. Entropya measure of the amount of energy which is unavailable to do work. EntropySis a state variable for a reversible (loss free) process whose change at any point in

the cycle is defined as:

dS = dQ/T

WhereQ is the heat in Joules entering the system at any point in the cycle

andT is the temperature in K at the point of heat entry

An example is the temperature of an enclosed volume of gas being raised by heat from an energy

source or reservoir.

As the temperature of the gas increases the disorder or kinetic energy of its molecules increaseswhich means that its entropy has increased. This is accompanied by a change of state of the gas

whose volume or pressure to increases depending on the nature of the enclosure.

Second Law of Thermodynamics

The second law concerns changes in entropy. It can be stated in different forms as follows;

The entropy of an isolated system which is not in equilibrium will tend to increase over time,approaching a maximum value when the system is in equilibrium

In any cyclic process the entropy will either increase (or in ideal system remain the same).


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Clausius Inequality

Clausius' theorem is another way of stating the Second Law. Thus:

dQ/T< 0 (Integral around one complete cycle)

The integral represents the net change in the entropy of the working fluid during one complete heat

cycle when in the working fluid in the heat engine returns to its initial state. At first glance it would

appear that this would violate the second law since it shows that the entropy change will always be

zero or negative and we know that entropy can only increase or stay the same.

The explanation is that the equation relates to the energy flow between the heat engine and its

environment during the cycle.

In an ideal (reversible) heat cycle there will be zero entropy change, however for a real (irreversible)

system, the entropy in the working fluid will increase during the energy transformation processes,

but for the working fluid to complete the cycle in the same state as at the start, this surplus entropy

must be passed out of the "engine" into the surroundings (the cold reservoir). The Clausius integral

refers to the ejection of this surplus entropy from the heat engine into the surroundings. This is

consistent with the second law since any real engine cycle will result in more entropy given to the

environment than was taken from it, leading to an overall net increase in the entropy of the overall

system.

One consequence of the entropy loss from the heat engine is that there will be less available energy

to do useful work.

Heat Engine Processes


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The heat cycle involves three or more basic

thermodynamic basic processes, typically four,

to transform the state of the working fluid and

return it to its original state. These are;

compression, heat addition, expansion and

heat rejection and each of these processes can

be carried out under one or more of the

following conditions:

Isothermal - At constant temperature,maintained with heat added or

removed from a heat source or sink

Isobaric- At constant pressure Isometric / Isochoric / Iso-volumetric-

At constant volume

Adiabatic- At constant entropy. Noheat is added or removed from the

system. No work done.

IsentropicAt constant entropy.Reversible adiabatic conditions No

heat added or lost. No work done.

Heat Cycle Analysis

The characteristics of the heat cycle associated with a heat engine are normally described by means

of two state change diagrams, the PV diagram showing the pressure - volume relationship, and the

TS diagram showing the temperature - entropy relationship.

For a constant mass of gas, the operation of a heat engine is a repeating cycle and its PV diagram will

be a closed figure

Examples illustrating the energy conversion processes used in some ideal, closed and open systems

are shown below.

Work Done During One Heat Cycle

The mechanical work taken from the system is given by the equation:

W = - P.dV (Integral around one complete cycle)

From the PV diagram this integral is equivalent to the area enclosed by the curve.


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Heat Engine Efficiency

Carnot showed that the maximum efficiency which can be achieved from a heat engine is given by:

= (Th- Tc)/Th or = 1 - Tc/Th

Efficiency Notes

The efficiency can be improved by maximising the difference between the hot inlet and coldexhaust temperatures of the working fluid during the heat cycle.

The efficiency of all open cycle systems suffers because because of the heat lost in the hightemperature exhaust gases.

The efficiency is also reduced by frictional losses when rotating machinery is involved, by theenergy consumed in the compression stage and by the pumping energy in an I.C.E.

Most energy conversion systems are multi-stage systems so that the overall systemperformance also depends on other factors such as the combustion efficiency of the fuel

used to generate the heat and these efficiency, or loss, factors are independent of, and

additional to, the basic heat (Carnot) cycle of the working fluid.

The Carnot efficiency represents perfection and is not a good measure for comparing theperformance of actual energy conversion systems. Real systems are so diverse that no

simple theoretical standard for comparison exists other than relating the actual energy

output of the system to the calorific content of the fuel used.

Heat Engine Variants

A wide variety of heat engine designs based on a range of different heat cycles has been developed

to optimise the design for different priorities such as the following:

Maximum thermodynamic efficiency per cycle.

Maximum cycle repetition rate (maximises the power)

Maximum capacity (maximises torque) Minimum fuel consumption Ability to use alternative fuels Mechanical simplicity

The following are some examples.


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A summary of the processes used in all of these cycles is given in thetablebelow.

The Carnot Cycle

The Carnot heat engine is a hypothetical, ideal engine that operates on the reversible Carnot cycle. It

is used as a reference cycle although ironically, no real Carnot Engines are known to have been

made. It is a closed cycle using the external application of heat.

The Carnot cyclewhen acting as a heat engine consists of the following steps:

Change

of

State

Carnot Heat Cycle Processes

A to B

Reversible isothermal compression of the cold gas.Isothermal heat rejection.Gas

starts at its "cold" temperature. Heat flows out of the gas to the low temperature

environment.

B to CReversible adiabatic compression of the gas.Compression causes the gas temperature

to rise to its "hot" temperature. No heat gained or lost.

C to D

Reversible isothermal expansion of the hot gas. Isothermal heat addition.Absorption

of heat from the high temperature source. Expanding gas available to do work on the

surroundings (e.g. moving a piston).

D to A

Reversible adiabatic expansion of the gas.The gas continues to expand, doing external

work. The gas expansion causes it to cool to its "cold" temperature. No heat is gained

or lost.
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If the heat cycle is operated clockwise as shown in the above diagram, the engine uses heat to do

net work. If the cycle is operated in reverse (anti-clockwise), it uses work to transfer thermal energy

from a cooler system to a warmer one thereby acting as a refrigerator or a heat pump. Seebelow.

Another apparent violation of the second law?The TS (entropy) diagram shows entropy in a closed

cycle decreasing!

The explanation is that the TS diagram shows entropy flows in a closed cycle, but though the cycle of

working fluid is closed, the heat engine is part of a larger overall closed system which includes the

surroundings. In a reversible system, entropy is exchanged between the heat engine and the

environment and the total system entropy is unchanged. In an irreversible system the same

interchange takes place but the total system entropy actually increases.

The Stirling Cycle

The Stirling cycle is described in detail the section aboutStirling engines.Like the Carnot engine it is

also an external combustion, closed cycle, air engine.

T=0(Constant temperature - Isothermal) V=0(Constant volume - Isometric)

TheStirling Engine uses the following processes

Change

of State

Stirling Engine Heat Cycle Processes

A to BIsothermal Compression. Heat rejection to the cold sink and compression of the cold

air in the cylinder
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B to CIsometric Heat TransferHeat transferred from the regenerator to the the air in the

cylinder increases pressure

C to D Isothermal Expansion. Heat added and the air expands in the cylinder.

D to A Isometric Heat Rejection Heat taken up by the regenerator

The Ericsson Cycle

TheEricsson engine,similar to the Stirling engine but using an open cycle, it is an external

combustion engine with aregeneratorwhich uses a double acting mechanical configuration.

Ericsson also produced closed cycle versions of his engines.

The Rankine Cycle (Vapour Cycle)

The Rankine cycle describes closed cycle systems using external heat sources and two phase working

fluids which are alternately condensed to liquid form and vaporised to gaseous form as they are

expanded and compressed during the heat cycle. The process is described in detail in the section

onSteam Turbineswhich are the major, large scale applications dependent on the Rankine cycle.

Note:Since the work done by the system during one cycle is equal to the area enclosed by the heat

cycle diagram, the information displayed in the diagrams can be used to choose a suitable working

fluid with the optimum characteristics and to set its optimum operating limits and conditions.

The Rankine cycleuses the following processes
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Change

of

State

Rankine Heat Cycle Processes

1 to B The working fluid (water) is heated until it reaches saturation (phase change / boilingpoint) in a constant-pressure process.

B to 2Once saturation is reached, further heat transfer takes place at constant pressure, until

the working fluid is completely vaporised (quality of 100% / dry steam)

2 to 3

The vapour is expanded isentropically (no heat added or lost) through a turbine stage

to produce work rotating the shaft. The vapour (steam) pressure falls as it passes

through the turbine and exits at low pressure.

3 to 4The working fluid is routed through a condenser, where it condenses (phase change)

into liquid (water).

4 to 1 The working fluid is pumped back into the boiler.

Superheating the steam to very high temperatures is used in most installations to maximise

temperature difference between the hot and cold phases of the fluid in order to maximise the

Carnot efficiency.

The Rankine cycle is also used in low temperature applications for which the provision of hightemperature vapour such as steam is not available. Examples areOTECgenerators and generators

depending onsolar heat.

The Stoddard Cycle

TheStoddard engineis an external combustion engine similar to theStirling engineusing single

phase working fluids such as air or other gases. The valve arrangement reduces the working fluid

dead space enabling greater efficiency.

The Lenoir Cycle

Lenoir's enginewas the first internal combustion engine. Internal combustion engines are all open

cycle engines which take in a fresh charge of working fluid with each heat cycle. In these engines the

working fluid is a fuel air mixture which is burned in the engine. The mechanical work output of the

engine comes from the expansion of the hot burning gases.

The Otto Cycle
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The Otto cycle is the standard open cycle used in the four-stroke petrol (gasoline) fuelled internal

combustion engine using spark ignition. It is described in detail in the section onPiston Engines.

S=0(Constant entropy - Adiabatic) V=0(Constant volume - Isometric)

The Otto cycleuses the following processes

Change

of State

Otto Heat Cycle Processes

A to B Compression Stroke. Adiabatic compression of air / fuel mixture in the cylinder

B to CIgnitionof the compressed air / fuel mixture at the top of the compression stroke

while the volume is essentially constant.

C to D Expansion (Power) Stroke. Adiabatic expansion of the hot gases in the cylinder.

D to A

Exhaust Stroke Ejection of the spent, hot gases .

Induction StrokeIntake of the next air charge into the cylinder. The volume of exhaust

gasses is the same as the air charge.

The Atkinson Cycle

TheAtkinson cycleis a variation on the Otto cycle which effectively increased the engine's expansion

ratio compared with the compression ratio by using a complex crankshaft linkage. This enables the

exhaust stroke to be longer than the induction stroke and hence the swept volumes are different.

The greater expansion allows more energy to be extracted from the fuel charge and allows the

engine to run cooler. It provides better efficiency at the expense of power density.
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The Miller Cycle

TheMiller cycleis another variation on the Otto cycle providing asymmetrical compression and

expansion ratios by means of valve timing arrangements. The induction and exhaust strokes are

identical in this engine, but the valve timing effectively reduces the induction fuel / air charge. It has

the same benefits and drawbacks as the Atkinson engine.

The Diesel Cycle

TheDiesel engineis described in detail in the section on piston engines. In the Diesel cycle, heat is

supplied at constant pressure whereas in the Otto cycle heat is supplied at constant volume. Similar

in construction to the Otto engine, the Diesel is also a closed cycle internal combustion engine but

instead of using a spark to ignite the fuel, ignition is achieved by rapid compression of the fuel air

mixture to a higher pressure than in the Otto engine. The higher compression ratio allows greater

efficiencies to be achieved by the Diesel.

S=0(Constant entropy - Adiabatic) V=0(Constant volume - Isometric)

The Diesel cycleuses the following processes

Change

of

State

Dieasel Heat Cycle Processes

A to B Compression Stroke. Adiabatic compression of air in the cylinder. No fuel added yet.

B to CIgnitionIsobaric heat addition. Fuel introduced into the compressed air at the top of

the compression stroke. Fuel mixture ignited while the pressure is essentially constant.

C to D Expansion (Power) Stroke. Adiabatic expansion of the hot gases in the cylinder.
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D to A

Exhaust Stroke Ejection of the spent, hot gases .

Induction StrokeIntake of the next air charge into the cylinder. The volume of exhaust

gasses is the same as the air charge.

The Brayton Cycle also known as the Gas Turbine Cycle

This cycle describes a continuous combustion cycle which was first used in theBrayton piston

engine.Though Brayton engines are no longer made, the Brayton cycle describes the heat cycle used

in modernGas Turbineengines.

S=0(Constant entropy - Adiabatic) S=0(Constant pressure - Isobaric)

The Brayton cycleuses the following processes

Change

of State

Brayton Heat Cycle Processes

A to B Adiabatic Compression. Air drawn into the turbine and compressed in the compressorstage.

B to CIsobaric IgnitionFuel mixed with the high pressure air and burned at constant

pressure.

C to D Adiabatic ExpansionHot gases expand in the turbine stages.

D to AIsobaric ExhaustConstant pressure ejection of the spent, hot gases to the

environment.
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Summary

Heat Engine Processes Summary

Combustion Type Cycle/Process Compression Heat Addition Expansion Heat Rejection

External

Combustion

(Closed Cycle)

Carnot isentropic isothermal isentropic isothermal

Stirling isothermal isometric isothermal isometric

Ericsson isothermal isobaric isothermal isobaric

Rankine (Steam) adiabatic isobaric adiabatic isobaric

Stoddard adiabatic isobaric adiabatic isobaric

Internal

Combustion

(Open Cycle)

Lenoir none isometric isentropic isobaric

Otto (Petrol) adiabatic isometric adiabatic isometric

Atkinson adiabatic isometric adiabatic isometric

Miller adiabatic isometric adiabatic isometric

Diesel adiabatic isobaric adiabatic isometric

Brayton (Jet) adiabatic isobaric adiabatic isobaric

Heat Pumps and Refrigerators - Vapour Compression Systems

Vapour compression heat pumps and refrigerators have much in common with heat engines. The

difference is that the heat cycle is operated in the opposite direction.

The objective of a heat pump is to supply heat to a warm medium The objective of a refrigerator is to remove heat from a cold medium

The two processes are complementary and work on the same principles. They both use an external

energy source to transfer heat "uphill" from a cold medium to a warm medium which are isolated or

insulated from each other. The only difference is whether the priority of the application is is the

heating or cooling effect.

Since the heat pump can provide both heating and cooling, the cost of a heat pump environmental

control system can be spread over both the heating and cooling seasons.
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Vapour compression systems and use theJoule - Thomson effectand a version of the (Rankine)

cycle with a variety of working fluids or refrigerants.

The working fluids used in early compression systems were toxic gases such as ammonia (NH3),

methyl chloride (CH3Cl), and sulphur dioxide (SO2) but after several fatal accidents in the 1920s,

caused by leaking methyl chloride, the search for a less dangerous refrigerant resulted in the

development of Freon a chlorofluorocarbon (CFC). Decades later it was discovered that CFCs were

responsible for depleting the Ozone layer making the planet more prone to climate change. In

response a range of alternative, chlorine free, hydrofluorocarbons (HFCs) refrigerants have been

developed.

History

The diagram below shows the system components and the heat and working fluid flows.

History

Thediagrams below show the corresponding heat cycle diagrams.
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The table below shows the processes involved in vapour compression systems

Change

of

State

Vapour Compression Heat Pump and Refrigerator Systems

1 to 2 The working fluid (refrigerant) in vapour state is compressed, raising its temperature.

2 to 3The super heated vapour is cooled to saturated vapour. Heat is removed from

refrigerant at constant pressure and rejected to the environment.

3 to 4 The vapour condenses at constant temperature to a liquid releasing more heat.

4 to 5

The expansion valve (throttle) creates a sudden reduction of pressure which lowers the

boiling point of the liquid, which flashes to liquid + vapour taking in heat from the

medium surrounding the evaporator.

5 to 1Liquid is evaporated and expands at constant pressure removing heat from the

environment

Gas Absorption Refrigeration Systems

An alternative to vapour compression refrigeration systems is the gas absorption system which, in its

simplest version, has no moving parts. Energy for cycling the working fluid and changing the hot,


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high pressure vapour back to a liquid is provided paradoxically by the application of more heat,

rather than by means of a compressor as used in the compression system.. The working fluid in a

typical system is ammonia but it needs two other auxilliary fluids at different stages in the cycle,

hydrogen gas to control the pressure of the evaporation process and water, used as an absorber, to

separate the ammonia from the hydrogen. The system is ideal for locations which do not have an

electricity supply.

The processes involved in using heat to achieve cooling are described below.

Change

of State

Gas Absorption Refrigeration Systems

1 to 2

The working fluid (anhydrous ammonia) in liquid state is is released into an

evaporator containing an auxilliary gas (hydrogen) at a system pressure which is

normally just high enough to keep the ammonia in liquid state at room temperature.

(Hydrogen does not react with ammonia) (Ammonia boils at -33C)

2 to 3

By mixing the gases, the effective pressure of the indiviual gasses is reduced since the

sum of the partial pressures of the gases must equal the system pressure which

remains unchanged. (Dalton's Law)The reduced partial pressure of the ammonia

reduces its boiling point to below room temperature so that it vapourises removing

heat from the environment. (Joule-Thomson Effect)

3 to 4

The ammonia is then separated from the hydrogen / ammonia gas mixture for

recycling by passing the mixture through a stream or container of water which

absorbs the ammonia from the mixture. (Hydrogen is not soluble in water)

4 to 5

The ammonia in solution with water is directed through a heater (called a generator)

to vaporise the ammonia which bubbles out of the water.

5 to 1A condenser (heat sink) cools the hot ammonia vapour which condenses into

anhydrous liquid ammonia (no water content) ready for the next cycle.
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Documents

Energy Conversion and Heat Engines