Heat Engines

[10.1] What is a heat engine ???

In thermodynamics and engineering, a heat engine is a system that converts heat or thermal energy to mechanical energy, which can then be used to do mechanical work It does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag .

Aeolipile, steam turbine invented in the 1st century AD by Heron of Alexandria and described in his Pneumatica. The aeolipile was a hollow sphere mounted so that it could turn on a pair of hollow tubes that provided steam to the sphere from a cauldron. The steam escaped from the sphere from one or more bent tubes projecting from its equator, causing the sphere to revolve. The aeolipile is the first known device to transform steam into rotary motion. Like many other machines of the time that demonstrated basic mechanical principles, it was simply regarded as a curiosity or a toy and was not used for any practical purpose.

[10.1.1] Thomas Newcomen's Engine

The atmospheric engine was invented by Thomas Newcomen in 1712, and is often referred to simply as a Newcomen engine. The engine was operated by condensing steam drawn into the cylinder, thereby creating a partial vacuum which allowed the atmospheric pressure to push the piston into the cylinder. It was the first practical device to harness steam to produce mechanical work.Newcomen engines were used throughout Britain and Europe, principally to pump water out of mines. Hundreds were constructed through the 18th century.

James Watt's later engine design was an improved version of the Newcomen engine that roughly doubled fuel efficiency. Many atmospheric engines were converted to the Watt design, for a price which was based on a fraction of the fuel-savings. As a result, Watt is today better known than Newcomen in relation to the origin of the steam engine.

[10.1.2] James Watt's Steam Engine

The Watt steam engine, alternatively known as the Boulton and Watt steam engine, was an early steam engine and was one of the driving forces of the Industrial Revolution. James Watt developed the design sporadically from 1763 to 1775 with support from Matthew Boulton. Watt's design saved so much more fuel compared with earlier designs that they were licensed based on the amount of fuel they would save. Watt never ceased developing the steam engine, introducing double-acting designs (with two cylinders) and various systems for taking off rotary power. Watt's design became synonymous with steam engines, and it was many years before significantly new designs began to replace the basic Watt design.

Unfortunately, the first steam engines, invented by Thomas Savery and Thomas Newcomen, needed to burn a lot of coal to run, which made them expensive. James Watt came up with a better way to capture steam. So how did James Watt improve the steam engine? It all began in 1764 when James was given a Newcomen steam engine to repair. James thought the engine wasted a terrible amount of heat. The biggest problem was that only one chamber, or tank, was used. This tank had to be heated as steam came into it, and then cooled.

James came up with the idea of having two separate chambers. One chamber would always be hot so it could receive steam. The second chamber would remain cool so that the steam traveling from the first tank could be converted back into water. This model of steam engine could continue working day and night and prevented a lot of steam from being wasted.In 1769, James Watt received a patent for his improved version of the steam engine.

[10.1.3] Designing Machinery around the Engine

Engines use pistons and cylinders, so the power they produce is a continual back-and-forth, push-and-pull, or reciprocating motion. Trouble is, many machines (and virtually all vehicles) rely on wheels that turn round and round—in other words, rotational motion. There are various different ways of turning reciprocating motion into rotational motion (or vice-versa). If you've ever watched a steam engine chuffing along, you'll have noticed how the wheels are driven by a crank and connecting rod: a simple lever-linkage that connects one side of a wheel to a piston so the wheel turns around as the piston pumps back and forth.

An alternative way to convert reciprocating into rotational motion is to use gears. This is what brilliant Scottish engineer James Watt (1736–1819) decided to do in 1781 when he discovered the crank mechanism he needed to use in his improved design of steam engine was, in fact, already protected by a patent. Watt's design is known as a sun and planet gear) and consists of two or more gear wheels, one of which (the planet) is pushed up and down by the piston rod, moving around the other gear (the Sun), and causing it to rotate.

There are two main types of heat engines: external combustion and internal combustion:

In an external combustion engine, the fuel burns outside and away from the main bit of the engine where the force and motion are produced. A steam engine is a good example: there's a coal fire at one end that heats water to make steam. The steam is piped into a strong metal cylinder where it moves a tight-fitting plunger called a piston back and forth. The moving piston powers whatever the engine is attached to (maybe a factory machine or the wheels of a locomotive). This is an external combustion engine because the coal is burning outside and some distance from the cylinder and piston.
In an internal combustion engine, the fuel burns inside the cylinder. In a typical car engine, for example, there are something like four to six separate cylinders inside which gasoline is constantly burning with oxygen to release heat energy. The cylinders "fire" alternately to ensure the engine produces a steady supply of power that drives the car's wheels.

[10.1.4] External Combustion Engines and Internal Combustion Engines

In an external combustion engine, the fuel isn't burned inside the engine.External engines have a working fluid that is heated by the fuel. Internal combustion engines rely on the explosive power of the fuel within the engine to produce work.

There are two main families of external combustion engines; steam engines which rely on expanding steam (or occasionally some other vapour) to drive a mechanism; or Stirling engines which use hot air (or some other hot gas). The use of both technologies reached their zeniths around 1900 and have declined almost to extinction since. However a brief description is worthwhile, since:

i. they were successfully and widely used in the past for pumping water;

ii. they both have the merit of being well suited to the use of low cost fuels such as coal, peat and biomass;

iii. attempts to update and revive them are taking place. and therefore they may re-appear as viable options in the longer term future.

The primary disadvantage of external combustion engines is that a large area of heat exchanger is necessary to transmit heat into the working cylinder(s) and also to reject heat at the end of the cycle. As a result, external combustion engines are generally bulky and expensive to construct compared with internal combustion engines. Also, since they are no longer generally manufactured they do not enjoy the economies of mass-production available to internal combustion engines. They also will not start so quickly or conveniently as an internal combustion engine; because it takes time to light the fire and heat the machine to its working temperature.

[10.2] Thermodynamic Modeling of Engines

When people constructed different types of engines for different purposes, a need arose to develop a theoretical model that provides information about the limits and improvements of the engine. Therefore, the concept of heat engine established to treat all types of engines that convert heat produced by burning a fuel into useful mechanical work

[10.2.1] Efficiency of a Heat Engine

[10.2.2] Heat Engines and Thermodynamic Cyclic Processes

The design of an engine aims to achieve a regular supply of mechanical work (force) to drive a machine. If the engine is designed to drive a piston, the piston will follow same type of movements at equal intervals. Therefore it is reasonable to consider a heat engine as performing repeated cycles.

[10.2.3] The Working Fluid of a Heat Engine

The working fluid of a heat engine or heat pump is a gas or liquid, usually called a refrigerant, coolant, or working gas, that primarily converts thermal energy (temperature change) into mechanical energy (or vice versa) by phase change and/or heat of compression and expansion.

[10.2.4] Heat reservoirs

A thermal reservoir, also thermal energy reservoir or thermal bath, is a thermodynamic system with a heat capacity so large that the temperature of the reservoir does not change when a reasonable amount of heat is added or extracted. ^[1] It is an effectively infinite pool of thermal energy at a given, constant temperature. Since it can act as a source and sink of heat, it is often also referred to as a heat reservoir or heat bath.

Lakes, oceans and rivers often serve as thermal reservoirs in geophysical processes, such as the weather. In atmospheric science, large air masses in the atmosphere often function as thermal reservoirs.

[10.2.5] Schematic Representation of a Heat Engine

The schematic representation that symbolizes all the basic properties of a heat engine is shown below. The working uid that undergoes a cyclic thermodynamic process is indicated by the circle in the middle. The engine operates acquiring a Q1 amount of heat from a heat source at a high temperature T1, and it exhausts a Q2 amount of heat to a heat sink at a lower temperature, T2. In each cycle, the engine outputs a Wout amount of work.

[10.3] Otto Cycle

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, addition of heat, and removal of heat. The mass of gas that is subjected to those changes is called the system. The system, in this case, is defined to be the fluid (gas) within the cylinder. By describing the changes that take place within the system, it will also describe in inverse, the system's effect on the environment. In the case of the Otto cycle, the effect will be to produce enough net work from the system so as to propel an automobile and its occupants in the environment.

In the Otto cycle an ideal gas is taken a long a cyclic process that consists of 5 individual processes: i. Isobaric expansion (5→1): Gas air mixture enters the cylinder. (intake stroke) ii. Adiabatic compression (1→2): Gas air mixture is compressed from V1 to V2 causing a temperature rise from T1 to T2. (compression stroke) iii. Isochoric heating (2→3): The spark ignites the gas fuel mixture and heat is absorbed at constant volume causing the temperature to rise from T2 to T3. (combustion stroke) iv. Adiabatic expansion (3→4): Gas air mixture expands from V2 to V1 adiabatically pushing the piston and causing temperature to drop from T3 to T4 (power stroke) v. Isochoric cooling (4→1): gas cools down at constant volume and heat is released causing the temperature to drop from T4 to T1 vi. Isobaric compression (1→5) Gas escapes from the cylinder (exhaust stroke)

[10.4] Heat Pumps

A heat pump is a device that transfers heat energy from a source of heat to what is called a thermal reservoir.Heat pumps move thermal energy in the opposite direction of spontaneous heat transfer, by absorbing heat from a cold space and releasing it to a warmer one.

[10.4.1] Coefficient of Performance (C.O.P) of a Heat Pump

A heat pump such as the interior heater in the winter time extract heat from the cold environment from the outside and release heat to the warmer environment in the room. The ratio of useful heat released to the hot temperature environment Qh and the amount of external work input W is defined as the Coefficient of Performance (C.O.P) of a heat pump.

C.O.P = Qh/W

[10.4.2] Coefficient of Performance (C.O.P) of a Refrigerator

A refrigerator is designed to extract heat from the food kept in the cold interior of the refrigerator. The refregerator will release heat to the room at a higher temperature. To perform this task external work must be added to the system. This process can thermodynamically model with a working uid undergoing a cyclic process between the high temperature and the lower temperature. The ratio of useful heat extracted from the cold source Qc and the amount of external work input W is dened as the Coecient of Performance (C.O.P) of a heat pump.

C.O.P = Qc/W

Summary

[10.5] Summarizing the Engines

The efficiency ε of a heat engine that is extracting QH amount of heat from a hot source at temperature TH and performing W amount of work is given by

ε = (W /Qh) = 1 − (Qc/Qh)

where Qc is the amount of heat the engine would exhaust to a heat source at a cold temperature Tc.

[10.5.2] A Refrigerator

The coefficient of performance (C.O.P.) of a refrigerator that extracts Qc amount of heat from a heat source at a cold temperature Tc and requires W amount of work input would be given by,

C.O.P = Qc/W = Qc/(Qh − Qc)

where Qh is the amount of heat the refrigerator would exhaust to a heat sink at a higher temperature Th

[10.5.3] A Heat Pump

The coefficient of performance (C.O.P.) of a heat pump that extracts Qc amount of heat from a heat source at a cold temperature Tc and conveys Qh amount of heat to a heat source at a higher temperature This given by,

C.O.P = Qh /W = Qh/(Qh − Qc)

where W is the work input to the heat pump.

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