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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.

 

Heat Energy Conversion

 

Despite over 250 years of development since James Watt's steam engine was first fired up, the best conversion efficiency achieved today is only around 60% for combined cycle steam 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% for OTEC ocean thermal power plants. This page describes some thermodynamic 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 by Carnot in the 1824 and expanded upon by Clapeyron who provided analytical tools in 1834 and Kelvin who stated the Second Law of Thermodynamics in 1851 and finally by Clausius who 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 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 = kNT

where P is the pressure, V the volume and T the temperature of the gas

and k is Boltzmann's constant and N is 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 designed mechanical 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 the method of providing the heat, the combustion 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.

Heat Engine

 

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 definitions of entropy some of which are contradictory or confusing. The following three examples are consistent and used in the context of heat engines.

  • Entropy a measure of the disorder of a system.
  • Entropy a measure of the amount of energy which is unavailable to do work.
  • Entropy S is a state variable for a reversible (loss free) process whose change at any point in the cycle is defined as:
  • dS = dQ/T

    Where Q is the heat in Joules entering the system at any point in the cycle

    and T 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 increases which 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).

 

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

 

Heat Engine - Heat Cycle

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. No heat is added or removed from the system. No work done.
  • Isentropic At 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.

 

Heat Engine Efficiency

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

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

Efficiency Notes

  • The efficiency can be improved by maximising the difference between the hot inlet and cold exhaust 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 high temperature exhaust gases.
  • The efficiency is also reduced by frictional losses when rotating machinery is involved, by the energy 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 system performance 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 the performance 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.

 

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

 

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.

Carnot Heat Cycle PV Diagram Carnot Heat Cycle Entropy Diagram

The Carnot cycle when 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 C

Reversible 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.

 

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. See below.

 

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 about Stirling engines. Like the Carnot engine it is also an external combustion, closed cycle, air engine.

Stirling Engine PV Diagram

ΔT=0 (Constant temperature - Isothermal)

Stirling Engine Entropy Diagram

ΔV=0 (Constant volume - Isometric)

TheStirling Engine uses the following processes

 

Change

of State

Stirling Engine Heat Cycle Processes

A to B

Isothermal Compression. Heat rejection to the cold sink and compression of the cold air in the cylinder

B to C

Isometric Heat Transfer Heat 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

The Ericsson engine, similar to the Stirling engine but using an open cycle, it is an external combustion engine with a regenerator which 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 on Steam Turbines which are the major, large scale applications dependent on the Rankine cycle.

Rankine Cycle PV Diagram Rankine Cycle Entropy Diagram

 

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 cycle uses the following processes

 

Change

of State

Rankine Heat Cycle Processes

1 to B

The working fluid (water) is heated until it reaches saturation (phase change / boiling point) in a constant-pressure process.

B to 2

Once 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 4

The 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 high temperature vapour such as steam is not available. Examples are OTEC generators and generators depending on solar heat.

 

The Stoddard Cycle

The Stoddard engine is an external combustion engine similar to the Stirling engine using 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 engine was 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

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 on Piston Engines.

Otto Cycle PV Diagram

ΔS=0 (Constant entropy - Adiabatic)

Otto Cycle Entropy Diagram

ΔV=0 (Constant volume - Isometric)

The Otto cycle uses 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 C

Ignition of 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 Stroke Intake of the next air charge into the cylinder. The volume of exhaust gasses is the same as the air charge.

 

The Atkinson Cycle

The Atkinson cycle is 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.

 

The Miller Cycle

The Miller cycle is 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

The Diesel engine is 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.

Diesel Heat Cycle PV Diagram

ΔS=0 (Constant entropy - Adiabatic)

Diesel Heat Cycle Entropy Diagram

ΔV=0 (Constant volume - Isometric)

The Diesel cycle uses 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 C

Ignition Isobaric 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.

D to A

Exhaust Stroke Ejection of the spent, hot gases .

Induction Stroke Intake 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 the Brayton piston engine. Though Brayton engines are no longer made, the Brayton cycle describes the heat cycle used in modern Gas Turbine engines.

Brayton Heat Cycle PV Diagram

ΔS=0 (Constant entropy - Adiabatic)

Brayton Heat Cycle Entropy Diagram

ΔS=0 (Constant pressure - Isobaric)

The Brayton cycle uses the following processes

 

Change

of State

Brayton Heat Cycle Processes

A to B

Adiabatic Compression. Air drawn into the turbine and compressed in the compressor stage.

B to C

Isobaric Ignition Fuel mixed with the high pressure air and burned at constant pressure.

C to D

Adiabatic Expansion Hot gases expand in the turbine stages.

D to A

Isobaric Exhaust Constant pressure ejection of the spent, hot gases to the environment.

 

Summary

Corner

Heat Engine Processes Summary

Corner

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.

 

Vapour compression systems and use the Joule - Thomson effect and 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.

 

Refrigerator and Heat Pump Cycle

 

History

 

The diagrams below show the corresponding heat cycle diagrams.

 

Heat Pump PV Diagram Heat Pump Entropy Diagram

 

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 3

The 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 1

Liquid 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, 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 -33°C)

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 1

A condenser (heat sink) cools the hot ammonia vapour which condenses into anhydrous liquid ammonia (no water content) ready for the next cycle.

 

See also the AMTEC Direct Energy Conversion System

 

 

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