1. The Heat Engine, the Prime Movers, and the Modern Closed Energy Conversion Systems

Thomas Savery, 1650–1715. On 2 July 1698 Savery patented an early steam engine “for raising water by force of fire” [2].

Thomas Newcomen, 1664–1729. An English ironmonger who, assisted by John Calley, a plumber, realised the “atmospheric engine.” Ultimately, Newcomen’s machine was capable of working with steam at low pressure, using atmospheric pressure to lower a piston in a cylinder, inside which, the mixing of water with the steam caused the latter to condense.

James Watt, 1736–1819 Scottish.

William John Macquom Rankine, 1820–1872. Scottish engineer and physicist.

The modern steam turbine was invented by Charles Algernon Parsons, 1854–1931, an Anglo-Irish engineer.

The results in this and in the following sections can also be obtained by the rigorous application of the energy and entropy balances, as presented and discussed in Appendix B.

A thermal reservoir is an ideal system which constantly maintains a stable state of equilibrium. A thermal reservoir is such in as much that any exchange of heat energy will not affect the temperature, which remains constant [3, p. 106].

Nicolas Leonard Sadi Carnot, 1796–1832. French physicist and engineer. Author of fundamental studies on the performance of thermal machines and considered one of the founders of the science of thermodynamics.

By first principle we mean the First Principle of Thermodynamics.

The work \(T_{0}\dot{S}_{\mathrm{G},j}\) irredeemably lost, relative to the jth transformation, can also be calculated as the change in exergy between the start and finishing states of the process. (For the exergy calculation, see Appendix B.1).

The application of entropic analysis to various typical thermodynamic cycles is discussed in Appendix C.

For example, the length of the LP last-stage blade of the largest nuclear turbine is today 1.75  m, with a corresponding annular exhaust area of 25.83  m². At a speed of 3,000 rpm, the resulting peripheral velocity is about 640  m/ s. A small radial compressor (see [8]) at 250,000 rpm with a maximum diameter of 37  c m has a peripheral maximum velocity of about 480  m/ s.

That is, the heat exergy once the temperature at which the heat is made available has been fixed. For the definition and the use of exergy balances, see Appendix B.

An exception being the fuel cells, which convert the chemical energy of the fuels, usually hydrogen or methane, directly into electricity.

John Ericsson (1803–1889) was a Swedish-American inventor and a mechanical engineer. Ericsson invented a regenerative engine in the 1820s which uses hot air. A similar engine had been patented in 1816 by the Reverend Robert Stirling, whose technical priority of invention provides the usual term “Stirling Engine” for the device.

In gas cycles (Joule–Brayton, but also, e.g. Otto and Diesel); the differences between the compression and the expansion works are just a consequence of the average temperature of the working fluid during the two transformations (see Sect. 1.7). As a result, in the Joule–Brayton cycles, the compression and expansion operations only differ by a factor of 2–3, with the risk that the cycle will perform very badly. In the worst cases, the difference in the two works may be zero, unless the turbomachines are really very efficient. In the reciprocating internal combustion engines, since it is relatively easy to cool the engine and by virtue of its periodic operation, it is possible to reach very high maximum temperatures. So it is always possible to obtain a significant output.

Inside the cylinders of a reciprocating engine, for example, the residential time interval of the gas is very short and, often, the combustion is not complete. The reciprocating engines, generally speaking, are more polluting than the external combustion ones.

Gas turbines, for example, are internal combustion engines requiring combustion gases not chemically and physically aggressive to the turbine and to the combustion chamber. In other words, the gases must not be corrosive and erosive, and they should not soil the surfaces or clog up the circuits beyond well-defined and accepted limits. These constraints place restrictions on the choice of fuels.

If the cycle has no superheating phase, it is called saturated steam cycle. In this case \(T_{5} = T_{4} =\ T_{\mathrm{E}}\).

The water, which constitutes the working fluid for the power stations, must be not only demineralised but also non-aerated. In fact, at high temperatures, the oxygen from the air which has dissolved in the water becomes corrosive for iron materials. This degassing process is carried out with a special device, the deareator, consisting of a mixture heat exchanger in which the liquid, shaped as thin sheets and free-falling, exposes to the gas-phase large surfaces for heat and mass exchange. The dissolved gas, in first approximation, even within the liquid, obeys the law of perfect gases and, in the absence of atmospheric air, expands (abandoning the liquid) and tends to assume a specific volume that corresponds to the partial residual pressure of the air in the exchanger. This pressure is kept low, driving away the air as it is gradually separated. Although, in principle, the degassing is possible at any temperature, experience teaches that it is most efficient at 100–150 ^∘ C.

The Korneuburg A power station (Austria) was, in 1961, the first true combined gas-steam cycle to enter service. The power station used two gas turbines of 25  M W each and a steam turbine of 25  M W, too. The overall efficiency was around 32 %. Modern combined cycles using natural gas as fuel can reach plant efficiencies of nearly 60 % and typical power levels of 400  M W.

It was named after the inventors Jakob Ackeret (1898–1981), a Swiss aeronautical engineer and a pupil of A. Stodola, and Curt Keller.

The specific adiabatic work is equal to the difference in enthalpy: \(W = \Delta H\) (see Appendix A.2). Then, \(\left (\partial H/\partial P\right )_{S} = 1/\rho\).

In principle, both solar and nuclear sources are suitable for closed-cycle gas turbines intended for applications in space (e.g. space missions).

However, it should be noted that even in open gas cycles, in a combined cycle layout, the exchanger for waste heat release is, in fact, present: the recovery boiler.

In reality, by “recuperative” heat exchanger, we mean an exchanger in which the two fluids (the hot one and the colder one) are physically separated by solid walls and their flow is continuous. By the term “regenerative” heat exchanger, we mean a heat exchanger made with a porous matrix, through which two fluids flow alternatively (namely, the hot one and the cold one).

In fact, there is very limited surface space available inside them for heat exchange to take place, and the fluid touches them at such high speed. For this reason, in the case of compressors, when seeking to reduce the average temperatures of the transformation, the compression is interrupted once the fluid has undergone a significant reheating; the gas is sent to a heat exchanger, where its temperature is brought back to values similar to the start; the compression is then completed at a second stage (intercooled compression). Naturally, there may be more than one intercooling stage.

The parameters that define the adimensional numbers in question are \(4r_{\mathrm{h}} = 4A_{\mathrm{c}}L/A\), \(G =\dot{ m}/A_{\mathrm{c}}\), with r _h being the hydraulic radius, A _c the minimum total free-flow cross-sectional area, L the length of tubes and A the total surface area. G is the mass velocity. The coefficient h is the heat transfer coefficient, μ is the viscosity and k is the thermal conductivity of the gas considered.

Robert Stirling (1790–1878), a Minister in the Church of Scotland at Galston, Ayrshire.

James Stirling (1800–1876), a Scottish engineer.

Another peculiarity of these engines is their self-starting capacity. By heating the expansion space and cooling the compression volume, the engine starts up automatically.

From John Ericsson (1803–1889), an engineer born in Sweden. He emigrated to America and created numerous technically different engines.

Ossian Ringbom, Finnish, “subject of the Czar of Russia, residing at Borga” patented in the United States (Patent no. 856102, 4 June 1907. Application filed 17 July 1905) and in the UK (Patent no. 10675, 22 May 1906. Date of Application, 22 May 1905) his own hot-air engine.

The dead spaces reduce the compression ratio and the specific useful power.

The engine efficiency calculated by applying Schmidt’s analysis (the ideal isothermal analysis), for example, coincides with that of the ideal thermodynamic cycle (the efficiency of Carnot’s machine), whilst the hypothesis of adiabaticity (the ideal adiabatic analysis) leads to lower efficiency, around 20–30 % lower than that of the ideal isothermal model. However, this is still significantly higher than that of a real engine.

The engine GPU-3 (Ground Power Unit) is a rhombic drive Stirling engine generator, developed by General Motors in 1965 for the US Army. The values of the volumes in the engine are as follows: V _CL,C = 28.68  c m³, V _CL,E = 30.52  c m³, V _SW,C = 114.13  c m³, V _SW,E = 120.82  c m³, V _K = 13.18  c m³, V _H = 70.28  c m³ and V _R = 50.55  c m³. For the examples considered here, the movement of the pistons is assumed to be pure sinusoidal, in accordance with (1.43a) and (1.43b) with ϕ = 90 ​​^∘.