July 02, 2007

Thermodynamics of Thermal Cycles

Thermal Machines

A machine is a mechanical device with moving parts that helps to do some useful action, usually work. Machines may be just mechanical (pulley-and-belt), hydraulic (water wheel, the earliest engine), pneumatic (windmill), electrical (electric motor, the most common nowadays), chemical (fuel cell), or thermal.

I am restricting it to devices that converts heat to work (heat engine), and to devices that pump low-temperature energy to high-temperature energy (by using some source of exergy), all working cyclically. The heat-pumping machine may be intended to produce cold (refrigerator), or to produce heat (heat pump), or both at the same time (refrigerator with heat recovery, or heat pump).

Heat Engines

Defining it?
A heat engine is a machine that produces work from heat, like the steam engine. Heat engines provide nearly 90% of the motive power generated in the world, the other 10% provided by hydroelectric power stations. Nearly 60% of all the world energy consumption is devoted to run heat engines, the rest being devoted to industrial and domestic heating.

A heat engine is a device where a working fluid performs four basic processes: heat input, hot expansion, heat rejection, and cold compression. By means of these internal processes, the heat engine gets heat from a hot source, produces some work, and rejects the rest of the energy balance as heat to a colder heat reservoir. All heat engines rely on the compressibility of the working fluid (i.e. a gas or vapor) and the fact that a hot expansion delivers more work than that needed for a cold compression (of a gas, vapor or liquid).

What it is for?
Motive power (engines and motors) is used as stand-alone plants to deliver motion or electricity to other systems, or within vehicles to provide motive power (propulsion) and auxiliary energy (there are nearly a billion, vehicles worldwide, more than 80% of them passenger cars). The steam engine is now only found in the largest power stations, and today the most common heat engine is the internal combustion reciprocating engine (for cars, trucks, ships, small airplanes, and stationary engines), with a third type, the gas turbine engine gaining ground (for most aircraft, the faster types of ship, modern power stations and combined power-and-heat stations).

The largest thermal power plants are vapor turbines, typically limited to 1000 MW per unit in nuclear power stations because of heat transfer limitations from the reactor (fuel-fired power stations are limited to some 400 MW per unit because of combustion intensity limitations). Gas turbines may also reach some 300 MW per unit, and the largest reciprocating engines are marine diesel engines of some 50 MW.

Thermal aspects of heat engines

Carnot cycle
With his 1824 masterpiece Nicolas Leonard Sadi Carnot was the first to provide a thermodynamic model of a heat engine, abstracting from the only available heat engine, the steam engine, to pinpoint the fundamentals: the idea of a generic working fluid, performing a generic cyclic process, interacting with generic heat reservoirs.

In his only publication, Carnot concluded that all heat engines where limited in their energy-conversion efficiency by the operating temperatures, and that the maximum efficiency is obtained when the working fluid is assumed to follow four ideal processes.

  1. An isentropic compression (D to A), to change temperature without heat transfer.

  2. An isothermal heat input (A to B), from the hot source, at the hot-source temperature.

  3. An isentropic expansion (B to C), to change temperature without heat transfer.

  4. An isothermal heat rejection to the cold source (usually the environment), at the cold-source temperature. (C to D).
Carnot reached those conclusions by a set of rational deductions, namely:

  • 'Any engine with friction would have less efficiency than one without',

  • ‘Among all engines exchanging heat at different temperatures, the one with highest efficiency only exchanges heat at the two extreme temperatures (the hottest and the coldest)' and,
  • 'All reversible engines working with the same couple of temperature extremes have the same efficiency'.

However, none of the process is 100% efficient & therefore, Carnot cycle is totally a theoretical one. The efficiency of each thermodynamic step varies & depends on the type of process e.g. step 1 of assumed isentropic compression is having a maximum efficiency of ~80%, Heat input using internal combustion have a maximum of 60% efficiency, Isentropic expansion with maximum 85% and last step may have different figures from 85 to 100% depending on direct or indirect rejection of heat. So mathematically we get 41% in overall which is quite practically achieved efficiency for IC engines and 35% for other cycles where last step is also contributing like in heat pumps etc.

This was the basis for all building blocks for different cycles generated later on in an effort to increase the efficiency of total cycle.

In Practical situations where we can have combustion temperatures limited to ~1200°C and ambient sink of 30°C, the carnot efficiency is only 80%. With a factor of 41% efficiency as explained above practically possible maximum efficiency in carnot is ~32%.


For this series, I am dividing different cycles in the following categories, which I shall discuss later one by one.

Gas Cycles without phase change

  • Carnot Cycle
  • Brayton Cycle
  • Ericsson Cycle
  • Stirling Cycle
  • Stoddard Cycle

Gas Cycles with phase change

  • Rankine
  • Kalina
  • Regenerative

IC Cycles

  • Diesel
  • Otto
  • Atkinson
  • Bourke
  • Lenoir
  • Miller
  • One stroke
  • Two Stroke
  • Wankel

Mixed Cycles

  • Combined
  • Crower
  • Dual

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Anonymous said...

it can be useful if given p-v and t-s diagrams of all cycles stated

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