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Binary liquid metal–organic Rankine cycle for small power distributed high efficiency systems

Identifieur interne : 000B70 ( Istex/Corpus ); précédent : 000B69; suivant : 000B71

Binary liquid metal–organic Rankine cycle for small power distributed high efficiency systems

Auteurs : Paola Bombarda ; Costante Invernizzi

Source :

RBID : ISTEX:F8928B070E8387E892808F5BFC6FFFDE2A75645A

Abstract

There is a common interest in the distributed power generation: generally for the combined production of electrical and thermal energy and often, although not necessarily, in association with renewable energies as heat sources for the prime mover. For example, in the field of distributed concentrated solar power generation of small size, the gas engine technology now seems to be prevailing (Stirling engines operating at maximum temperatures of 600–800 ℃, with peak net efficiencies at 20–30% and power up to several kilowatts are commonly considered). Organic Rankine engines, fed by biomass, in the power range of about 1 MW are actually a standard. From a strictly thermodynamic point of view, the binary cycle technology, accomplished by alkaline metal Rankine cycle as the topping cycle and a Rankine cycle with organic fluid as the bottoming cycle, could be an advantageous alternative. By their very nature, Rankine cycles have good thermodynamic qualities and, potentially, their thermodynamic performance, for the same maximum and minimum temperatures, could be better than that of a gas cycles. This paper discusses the possibility of adopting binary cycles with a power level in the order of tens of kilowatts. Following an overview of the characteristics of alkaline metals and a look at the possible organic fluids that can be employed in Rankine engines at high temperature (400 ℃), assuming a limit condensation pressure of 0.05 bar, the thermodynamic efficiency of binary cycles was evaluated and the preliminary sizing of turbines was discussed. The results (e.g. a net cycle efficiency of around 0.46, with maximum temperature of 800–850 ℃) appear encouraging, even though setting up the systems may be far from easy. For instance, there are difficulties due to the extremely high volumetric expansion ratios of bottoming cycles (400–600, an order of magnitude larger than those of the topping cycles with alkaline metals that we considered), which are moreover associated with a very low minimum pressure and elevated number of revolutions of the turbomachinery (50,000–200,000 r/min). Without doubt, the design tends to be easier as the power levels increase and the minimum condensation pressure for the bottoming cycle rises. Although the authors know of no activity in progress on binary cycles at present, the interesting prospects suggest the topic deserves further study and research.

Url:
DOI: 10.1177/0957650914562094

Links to Exploration step

ISTEX:F8928B070E8387E892808F5BFC6FFFDE2A75645A

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</permissions>
<abstract>
<p>There is a common interest in the distributed power generation: generally for the combined production of electrical and thermal energy and often, although not necessarily, in association with renewable energies as heat sources for the prime mover. For example, in the field of distributed concentrated solar power generation of small size, the gas engine technology now seems to be prevailing (Stirling engines operating at maximum temperatures of 600–800 ℃, with peak net efficiencies at 20–30% and power up to several kilowatts are commonly considered). Organic Rankine engines, fed by biomass, in the power range of about 1 MW are actually a standard. From a strictly thermodynamic point of view, the binary cycle technology, accomplished by alkaline metal Rankine cycle as the topping cycle and a Rankine cycle with organic fluid as the bottoming cycle, could be an advantageous alternative. By their very nature, Rankine cycles have good thermodynamic qualities and, potentially, their thermodynamic performance, for the same maximum and minimum temperatures, could be better than that of a gas cycles. This paper discusses the possibility of adopting binary cycles with a power level in the order of tens of kilowatts. Following an overview of the characteristics of alkaline metals and a look at the possible organic fluids that can be employed in Rankine engines at high temperature (400 ℃), assuming a limit condensation pressure of 0.05 bar, the thermodynamic efficiency of binary cycles was evaluated and the preliminary sizing of turbines was discussed. The results (e.g. a net cycle efficiency of around 0.46, with maximum temperature of 800–850 ℃) appear encouraging, even though setting up the systems may be far from easy. For instance, there are difficulties due to the extremely high volumetric expansion ratios of bottoming cycles (400–600, an order of magnitude larger than those of the topping cycles with alkaline metals that we considered), which are moreover associated with a very low minimum pressure and elevated number of revolutions of the turbomachinery (50,000–200,000 r/min). Without doubt, the design tends to be easier as the power levels increase and the minimum condensation pressure for the bottoming cycle rises. Although the authors know of no activity in progress on binary cycles at present, the interesting prospects suggest the topic deserves further study and research.</p>
</abstract>
<kwd-group>
<kwd>Distributed generation</kwd>
<kwd>binary cycles</kwd>
<kwd>Rankine cycles</kwd>
<kwd>liquid alkali metal cycles</kwd>
<kwd>organic Rankine cycle</kwd>
<kwd>high temperature organic Rankine cycle</kwd>
<kwd>solar energy</kwd>
<kwd>thermodynamic conversion</kwd>
<kwd>heat engines</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="sec1-0957650914562094" sec-type="intro">
<title>Introduction</title>
<p>The efficiency of the distributed thermodynamic energy conversion systems is, owing to their high system costs, a key and discriminatory parameter. Even more so, considering the exploitation of renewable energies in association with the distributed generation.</p>
<p>In fact, the distributed energy generation well associate with the use of renewable energies, as well as, obviously, with the use of natural gas, where a distribution network is available. In any case, given the high costs of the engine a high conversion efficiency is essential and can be often convenient resort to the cogeneration too.</p>
<p>Among all renewable energies, the solar energy has, at least in principle, the potential of satisfying all mankind energy needs: in fact, the exploitation of this fundamental source of energy is continuously growing. Concentrating solar power technologies represent a possible key technology for electric power generation, and are at present not far from reaching cost competitiveness, at least for favorable sites and power plants with electric power in the range of some tens of megawatts. At present, in the field of distributed thermodynamic solar power generation resorting to concentration, the solar dish system combined to a Stirling cycle seems to be the preferred option for small power systems, in which case the cycle maximum temperatures are usually between 600 ℃ and 800 ℃ (with resulting peak net efficiencies in the order of 20–30%, depending on the engine and the power size).
<sup>
<xref ref-type="bibr" rid="bibr1-0957650914562094">1</xref>
,
<xref ref-type="bibr" rid="bibr2-0957650914562094">2</xref>
</sup>
</p>
<p>As a further example of engines using renewable energies, biomass plants based on the conventional organic Rankine cycles, have efficiencies of about 20% (with net power of about 1 MW) even though with maximum temperatures of the hot combustion gases of 1000 ℃.
<sup>
<xref ref-type="bibr" rid="bibr3-0957650914562094">3</xref>
</sup>
</p>
<p>Binary cycles based on Rankine cycles can be adopted and, in principle, easily adapted to any power level, provided that suitable working fluids are selected. In this paper, we concentrate on the lowest power levels: the most critical from a technology point of view for the design of the turbines.</p>
<p>The adoption of a binary alkali metal/steam cycle as the power cycle for a solar plant of tens of megawatts was suggested in Angelino and Invernizzi;
<sup>
<xref ref-type="bibr" rid="bibr4-0957650914562094">4</xref>
</sup>
with this configuration, the cycle could reach efficiencies of 55–60%, similar or even greater than that of a combined gas–steam cycle, but at lower maximum temperature (800–900 ℃).</p>
<p>However, the alkali metal and steam binary cycles are appropriate only in a convenient power range: in the very high power range their suitability is limited by the extreme low condensation pressure typical of the alkali metals (e.g. 0.017 bar at 450 ℃ for potassium) with huge volumetric flow rates per unit power, while in the small power range their suitability is limited by the intrinsic thermodynamic characteristics of the steam (high enthalpy drops, high maximum pressures).</p>
<p>With reference to this last point, the aim of this paper is to evaluate the potential arising from the possible use of binary alkali metal and organic fluid Rankine cycles, for small power plants (some tens of kilowatts). When designing a small power plant, a crucial point is the design of the expander: as a general rule, turbines perform better than volumetric expanders when, as in Rankine cycles, volumetric expansion ratios are large.</p>
<p>Experience and familiarity with small and micro-turbines exist since a long time.
<sup>
<xref ref-type="bibr" rid="bibr5-0957650914562094">5</xref>
<xref ref-type="bibr" rid="bibr6-0957650914562094"></xref>
<xref ref-type="bibr" rid="bibr7-0957650914562094">7</xref>
</sup>
The design of small turbines is nevertheless generally very demanding: the already mentioned high volumetric expansion ratio, typical of the Rankine cycles, above all when operating with thermal sources and sinks featured by a large temperature span, makes it very difficult to obtain a good design for small power turbines, with a simple layout of the individual stages; moreover, the very high rotational speed required and the potentially high fluid-dynamic losses, make as well the design very challenging. This is especially true when the working fluid has a low molecular mass, like in the case of steam, which has a very high enthalpy drop across the turbine, and low mass and volume flow rates at turbine inlet: in this case the adoption of a different fluid, an organic working fluid for example, could facilitate the turbine design.</p>
<p>Several small organic Rankine engines were already manufactured in the past. For example, a survey of various successful hermetically sealed engines with power sizes between 0.1 and 3 kW is presented in Bronicki.
<sup>
<xref ref-type="bibr" rid="bibr8-0957650914562094">8</xref>
</sup>
</p>
<p>In the present paper, attention is focused on the binary cycles appropriate for a possible small plant, imagined as an alternative of, for instance, but not necessarily, the usual solar dishes plant or small biomass or gas units. In the paper, after a review of liquid metals as working fluids and a broad survey of organic working fluids for high temperature applications, a preliminary design of the turbines is discussed, with some significant examples. Given the small level of power considered, the turbines may indeed be the more critical components.</p>
<p>Cost considerations and safety problems due to the interaction between liquid metals and organic working fluids, even if very important, are here not considered.</p>
</sec>
<sec id="sec2-0957650914562094">
<title>Basic assumptions and binary cycle working fluids</title>
<p>As already outlined in the previous section, a binary alkali metal and organic fluid Rankine cycle is selected. The assumed main parameters are reported in
<xref ref-type="table" rid="table1-0957650914562094">Table 1</xref>
. For the bottoming cycle a minimum condensation pressure (instead of a minimum condensation temperature) is assumed, because a too low condensation pressure (easily attainable with the selected organic fluids) could make the plant construction unfeasible.
<table-wrap id="table1-0957650914562094" position="float">
<label>Table 1.</label>
<caption>
<p>Basic assumptions: temperatures and pressures for the considered binary cycles.</p>
</caption>
<graphic alternate-form-of="table1-0957650914562094" xlink:href="10.1177_0957650914562094-table1.tif"></graphic>
<table frame="hsides">
<tbody align="left" valign="top">
<tr>
<td>Topping cycle: maximum temperature</td>
<td>850 ℃</td>
</tr>
<tr>
<td>Topping cycle: condensation temperature</td>
<td>450 ℃</td>
</tr>
<tr>
<td>Bottoming cycle: maximum temperature</td>
<td>400 ℃</td>
</tr>
<tr>
<td>Bottoming cycle: minimum condensation pressure</td>
<td>0.05 bar</td>
</tr>
</tbody>
</table>
</table-wrap>
</p>
<p>As far as the internal heat transfer between the topping and the bottoming cycle is concerned, recalling that organic fluids are hardly ever thermo-chemically stable, at temperatures above 400 ℃, the condensation temperature of the topping cycle is assumed such that the evaporation temperature of the bottoming cycle is compatible with organic fluid thermal stability.</p>
<p>Finally, the choice of the cycle working fluid must be conducted recalling that the plant power is small and on the basis of the temperature span selected: alkali metals were investigated for the topping cycle and organic fluids were considered for the bottoming cycle.</p>
<p>The topping cycle maximum temperature was then fixed at 850 ℃, as a reasonable technological limit, according to the survey results in the following section.</p>
<sec id="sec3-0957650914562094">
<title>Topping cycle working fluids: The alkali liquid metals</title>
<p>The interest in Rankine cycles operating with metals grew in the 1960s in view of possible applications for space missions.
<sup>
<xref ref-type="bibr" rid="bibr9-0957650914562094">9</xref>
</sup>
Actually, between 1920s and 1950s, some power systems (with maximum powers of about 50 MW) with binary mercury and steam cycles were realized in the United States.
<sup>
<xref ref-type="bibr" rid="bibr10-0957650914562094">10</xref>
</sup>
</p>
<p>In this paper, due the high toxicity of mercury, the attention is focused on alkali metals (see
<xref ref-type="table" rid="table2-0957650914562094">Table 2</xref>
). By their nature, alkali metals seem suitable for the design of small power engine. In fact, owing to the low condensation pressures, the volume flows at turbine outlet of alkali metal cycles are actually very large and this fact limits the maximum power obtainable, making it very difficult to build large power plants.
<table-wrap id="table2-0957650914562094" position="float">
<label>Table 2.</label>
<caption>
<p>Thermodynamic properties of the working fluids considered in this work: the alkali metals.</p>
</caption>
<graphic alternate-form-of="table2-0957650914562094" xlink:href="10.1177_0957650914562094-table2.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th>Fluid</th>
<th>
<italic>T
<sub>cr</sub>
</italic>
(℃)</th>
<th>
<italic>P
<sub>cr</sub>
</italic>
(bar)</th>
<th>
<italic>P
<sub>C</sub>
</italic>
at 450 ℃ (bar)</th>
<th>Molecular weight</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Caesium</td>
<td>1775</td>
<td>117</td>
<td>0.0646</td>
<td>132.9</td>
</tr>
<tr>
<td>Rubidium</td>
<td>1833</td>
<td>134</td>
<td>0.0527</td>
<td>85.48</td>
</tr>
<tr>
<td>Potassium</td>
<td>1900</td>
<td>167</td>
<td>0.0169</td>
<td>39.10</td>
</tr>
<tr>
<td>Sodium</td>
<td>2300</td>
<td>341</td>
<td>0.0018</td>
<td>22.99</td>
</tr>
</tbody>
</table>
</table-wrap>
</p>
<p>Sodium (largely used as refrigerant in some types of fast nuclear reactors) with a boiling temperature of 883 ℃ has, however, a too low condensation pressure (about 0.002 bar at 450 ℃, see
<xref ref-type="table" rid="table2-0957650914562094">Table 2</xref>
) and cannot be proposed for a Rankine cycle. Potassium and caesium gained serious attentions and were exhaustively studied in the past.
<sup>
<xref ref-type="bibr" rid="bibr11-0957650914562094">11</xref>
<xref ref-type="bibr" rid="bibr12-0957650914562094"></xref>
<xref ref-type="bibr" rid="bibr13-0957650914562094">13</xref>
</sup>
</p>
<p>In Gruntz,
<sup>
<xref ref-type="bibr" rid="bibr14-0957650914562094">14</xref>
</sup>
a detailed study of a binary potassium-steam Rankine power system of 5000 kW for remote power stations, small ships, or submarines was presented. According to that study, potassium is compatible with conventional stainless steels (316 and 321 types) up to 870 ℃, and with cobalt alloys (like Haynes 25) up to 1090 ℃. For temperatures between 1000 ℃ and 1090 ℃, potassium seems compatible with refractory alloys based on niobium, molybdenum, and tantalum. Several experimental tests with boilers, condensers, radiators, and turbines were carried out at the Garret AiResearch, as reported in Gruntz.
<sup>
<xref ref-type="bibr" rid="bibr14-0957650914562094">14</xref>
</sup>
</p>
<p>In Morozov et al.,
<sup>
<xref ref-type="bibr" rid="bibr15-0957650914562094">15</xref>
</sup>
an exhaustive study regarding the adoption of potassium in a small solar power plant (about 5 kW) is conducted, whereby chromium–nickel stainless steels resulted compatible with liquid and vapor potassium up to 920 ℃. Results came from an intense experimental activity carried out with evaporators, condensers, pumps, valves, pipelines, and turbines, reaching 10,000 operating hours. It can be finally stated that there is a good base knowledge regarding potassium small power systems. Many technical problems were addressed and resolved. Potassium has a wide availability and is of low cost. Nevertheless, its vapor pressure at a temperature of 450 ℃ is quite low (0.017 bar, see
<xref ref-type="table" rid="table2-0957650914562094">Table 2</xref>
).</p>
<p>Caesium and rubidium have a similar vapor pressure curve (see
<xref ref-type="table" rid="table2-0957650914562094">Table 2</xref>
), but rubidium is more abundant in the lithosphere and in the sea water than caesium. The high molecular mass of caesium and rubidium substantially reduces the number of expansion stages required for the turbine with respect to potassium. In principle, designing turbines with metal vapors is not much complicated than designing large steam turbines, even though the vapor quality during expansion may reach critical values in connexion to the blade erosion. A similar situation happens during steam expansion in conventional nuclear plants: the problem can be just resolved by resorting to adequate fluid dynamics design and to extraction devices, similar to those adopted in steam cycles (see, e.g. Manson,
<sup>
<xref ref-type="bibr" rid="bibr16-0957650914562094">16</xref>
</sup>
Yoder et al.,
<sup>
<xref ref-type="bibr" rid="bibr17-0957650914562094">17</xref>
</sup>
Stanisa et al.;
<sup>
<xref ref-type="bibr" rid="bibr18-0957650914562094">18</xref>
</sup>
see also El-Wakil
<sup>
<xref ref-type="bibr" rid="bibr19-0957650914562094">19</xref>
</sup>
(Section 13-9)).</p>
</sec>
<sec id="sec4-0957650914562094">
<title>Bottoming cycle working fluids: Organic fluids</title>
<p>Some industrial high temperature heat transfer fluids are based on organic fluids and the majority of these fluids are aromatic compounds; regardless of the particular fluid type, they all exhibit high boiling temperatures. In the following, some working fluids potentially usable at maximum temperatures of about 400 ℃ will be presented and discussed; some of them were already investigated in the past, though their use was disregarded later. Mixtures of polyphenyls (then marked with the old trade names of Santowax R and Santowax O-M) were, for example, proposed and used in late 1950s as organic coolants in peculiar nuclear reactors (Chapter 17).
<sup>
<xref ref-type="bibr" rid="bibr19-0957650914562094">19</xref>
</sup>
</p>
<sec id="sec5-0957650914562094">
<title>Aromatic hydrocarbons</title>
<sec id="sec6-0957650914562094">
<title>The eutectic mixture of diphenyl and diphenyl oxide</title>
<p>The eutectic mixture of diphenyl ((C
<sub>6</sub>
H
<sub>5</sub>
)
<sub>2</sub>
), 26.5% in mass) and diphenyl oxide (C
<sub>6</sub>
H
<sub>5</sub>
)
<sub>2</sub>
O, 73.5%), see
<xref ref-type="table" rid="table3-0957650914562094">Table 3</xref>
, is a well-known synthetic heat transfer fluid, also known by the commercial names of Therminol VP1, Downtherm A, or Diphyl.
<sup>
<xref ref-type="bibr" rid="bibr20-0957650914562094">20</xref>
,
<xref ref-type="bibr" rid="bibr21-0957650914562094">21</xref>
</sup>
The mixture, according to the manufacturers, is utilizable up to 400 ℃. Its pour point is 12 ℃, its critical temperature and critical pressure are respectively 498.89 ℃ and 33.09 bar.
<table-wrap id="table3-0957650914562094" position="float">
<label>Table 3.</label>
<caption>
<p>Thermodynamic properties of the working fluids considered in this work: aromatic hydrocarbons.</p>
</caption>
<graphic alternate-form-of="table3-0957650914562094" xlink:href="10.1177_0957650914562094-table3.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th>Fluid</th>
<th>
<italic>T
<sub>cr</sub>
</italic>
(℃)</th>
<th>
<italic>P
<sub>cr</sub>
</italic>
(bar)</th>
<th>
<italic>σ</italic>
<sup>f</sup>
</th>
<th>
<italic>T
<sub>C</sub>
</italic>
at 5 kPa
<sup>e</sup>
</th>
<th>Molecular weight</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Diphenyl (DIPHE01)</td>
<td>499.85</td>
<td>33.8</td>
<td></td>
<td>150.66</td>
<td>154.21</td>
</tr>
<tr>
<td>Diphenyl oxyde (DIPHE02)</td>
<td>493.65</td>
<td>30.8</td>
<td></td>
<td>149.585</td>
<td>170.21</td>
</tr>
<tr>
<td>DIPHE01 + DIPHE02
<sup>a</sup>
</td>
<td>498.89</td>
<td>33.09</td>
<td>34.8</td>
<td>149.83</td>
<td></td>
</tr>
<tr>
<td>Toluene</td>
<td>318.6</td>
<td>41.01</td>
<td>9.63</td>
<td>30.488</td>
<td>92.14</td>
</tr>
<tr>
<td>m-Xylene
<sup>b</sup>
</td>
<td>343.85</td>
<td>35.41</td>
<td>14.6</td>
<td>53.726</td>
<td>106.17</td>
</tr>
<tr>
<td>Trimethylbenzene
<sup>c</sup>
</td>
<td>375.95</td>
<td>32.32</td>
<td>20.9</td>
<td>79.321</td>
<td>120.19</td>
</tr>
<tr>
<td>Tetramethylbenzene
<sup>d</sup>
</td>
<td>405.85</td>
<td>29.7</td>
<td>27.96</td>
<td>103.18</td>
<td>134.22</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn1-0957650914562094">
<label>a</label>
<p>Eutectic mixture. Mass composition: 0.265 DIPHE01 + 0.735 DIPHE02.</p>
</fn>
<fn id="table-fn2-0957650914562094">
<label>b</label>
<p>1,3-dimethylbenzene.</p>
</fn>
<fn id="table-fn3-0957650914562094">
<label>c</label>
<p>1,2,4-trimethylbenzene.</p>
</fn>
<fn id="table-fn4-0957650914562094">
<label>d</label>
<p>1,2,3,5-tetramethylbenzene.</p>
</fn>
<fn id="table-fn5-0957650914562094">
<label>e</label>
<p>
<italic>T
<sub>C</sub>
</italic>
, condensation temperature in ℃.</p>
</fn>
<fn id="table-fn6-0957650914562094">
<label>f</label>
<p>
<italic>σ</italic>
, parameter of molecular complexity, see equation (1).</p>
</fn>
</table-wrap-foot>
</table-wrap>
</p>
<p>In this work, the thermodynamic properties of the eutectic mixture are evaluated by the UNIFAC method,
<sup>
<xref ref-type="bibr" rid="bibr23-0957650914562094">23</xref>
,
<xref ref-type="bibr" rid="bibr24-0957650914562094">24</xref>
</sup>
and the predictive Readlich–Kwong–Soave equation of state (PRKS).
<sup>
<xref ref-type="bibr" rid="bibr25-0957650914562094">25</xref>
</sup>
A comparison among some obtained results and data from Solutia
<sup>
<xref ref-type="bibr" rid="bibr20-0957650914562094">20</xref>
</sup>
and Down
<sup>
<xref ref-type="bibr" rid="bibr21-0957650914562094">21</xref>
</sup>
is shown in
<xref ref-type="fig" rid="fig1-0957650914562094">Figure 1</xref>
. The agreement between the saturated vapor enthalpies is not always perfect, but, for the purposes of this study, acceptable.
<fig id="fig1-0957650914562094" position="float">
<label>Figure 1.</label>
<caption>
<p>Saturation dome for the eutectic mixture of diphenyl and diphenyl oxide in the PH plane. Comparison among calculated values and some reference values.
<sup>
<xref ref-type="bibr" rid="bibr20-0957650914562094">20</xref>
,
<xref ref-type="bibr" rid="bibr21-0957650914562094">21</xref>
</sup>
</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig1.tif"></graphic>
</fig>
</p>
<p>The thermal stability and material compatibility of these fluids was investigated in the past. In Dow,
<sup>
<xref ref-type="bibr" rid="bibr22-0957650914562094">22</xref>
</sup>
a Rankine cycle with diphenyl oxide superimposed on a steam cycle is discussed. According to the paper’s author, at a maximum temperature of 400 ℃, with a boiler in normal carbon steel, the organic working fluid did not show degradation effects due to the high operating temperature. In Killeffer,
<sup>
<xref ref-type="bibr" rid="bibr26-0957650914562094">26</xref>
</sup>
a steam boiler using the eutectic mixture of diphenyl and diphenyl oxide as an intermediate heat transfer fluid (at 382 ℃ and 7 bar) is described. The boiler operated successfully all over 1 year. In Dean,
<sup>
<xref ref-type="bibr" rid="bibr27-0957650914562094">27</xref>
</sup>
some old (1939) industrial applications of the mixture in heating systems and boilers were discussed.</p>
<p>A radioisotope unit utilizing a binary cycle (monochlorobenzene as working fluid for the bottoming cycle and the eutectic mixture diphenyl–diphenyl oxide for the topping cycle) was described in Bronicki.
<sup>
<xref ref-type="bibr" rid="bibr8-0957650914562094">8</xref>
</sup>
The system, started in 1971 and successfully operated, had for the diphenyl–diphenyl oxide unit a boiler temperature of 195 ℃ and a condensation temperature of 112 ℃ (corresponding to a vapor pressure of about 0.011 bar).</p>
<p>Nowadays,
<sup>
<xref ref-type="bibr" rid="bibr28-0957650914562094">28</xref>
<xref ref-type="bibr" rid="bibr29-0957650914562094"></xref>
<xref ref-type="bibr" rid="bibr30-0957650914562094">30</xref>
</sup>
the eutectic mixture of diphenyl and diphenyl oxide is among the considered heat transfer fluids and thermal storage media used in the parabolic trough solar thermal power plants up to 400 ℃, also because of its low pour temperature.</p>
<p>After a comprehensive study,
<sup>
<xref ref-type="bibr" rid="bibr31-0957650914562094">31</xref>
</sup>
dedicated to the research of possible fluids for heat pipes, diphenyl and the eutectic mixture of diphenyl and diphenyl oxide proved to be thermo-chemically stable at 400 ℃ in 304 stainless steel for 1200 h; however, after 1500 h, the eutectic mixture produced noncondensable gases in a fair quantity (a clear sign of thermal decomposition). The same mixture did not show signs of decomposition after 5520 h in 316 stainless steel with repeated heating cycles (one every 24 h) between 325 ℃ and 380 ℃. It must be noted, however, that the operating conditions of the fluid in a heat pipe are particularly severe.</p>
<p>In Niggemann,
<sup>
<xref ref-type="bibr" rid="bibr32-0957650914562094">32</xref>
</sup>
the results of a test on the eutectic mixture of biphenyl and biphenyl-ether in a closed boiler loop with an outlet temperature of 370 ℃ are presented: during 6367 h, (before an accidental overheating) the eutectic mixture showed an excellent stability, without any evident variation in the physical properties analyzed (viscosity, refractive index, specific gravity, and freezing point).</p>
</sec>
<sec id="sec7-0957650914562094">
<title>Others aromatic hydrocarbons</title>
<p>Among the aromatic hydrocarbons (see
<xref ref-type="table" rid="table3-0957650914562094">Table 3</xref>
), toluene,
<sup>
<xref ref-type="bibr" rid="bibr33-0957650914562094">33</xref>
,
<xref ref-type="bibr" rid="bibr34-0957650914562094">34</xref>
</sup>
meta-xylene, trimethylbenzene, and tetramethyl-benzene
<sup>
<xref ref-type="bibr" rid="bibr36-0957650914562094">36</xref>
</sup>
were considered as possible working fluids in Rankine cycles thanks to their good thermochemical stability. The fluid thermodynamic properties are here evaluated by means of the Peng–Robinson equation of state,
<sup>
<xref ref-type="bibr" rid="bibr35-0957650914562094">35</xref>
</sup>
and by the data available in the database of Aspen Plus.</p>
<p>According to Cole et al.,
<sup>
<xref ref-type="bibr" rid="bibr47-0957650914562094">47</xref>
</sup>
in a perfectly sealed closed system, in which no air is present, toluene results in a very thermally stable working fluid at least up to a temperature of 370 ℃ in 304 and 316 stainless steels components.</p>
</sec>
<sec id="sec8-0957650914562094">
<title>Heterocyclic organic compound</title>
<p>Pyridine and 2-methylpyridine (see
<xref ref-type="table" rid="table6-0957650914562094">Table 6</xref>
) are well-known heterocyclic organic compounds. In Somekh,
<sup>
<xref ref-type="bibr" rid="bibr49-0957650914562094">49</xref>
</sup>
the water–pyridine azeotrope is stated as thermo-chemically stable in stainless steel containers at 400 ℃ while the 6061 aluminium alloy (Alloy 61 S) is considered compatible and suitable for the condenser. </p>
<p>A mixture of water and 2-methylpyridine (with molar composition of 65% water and 35% 2-methylpyridine) is proposed in Millet et al.,
<sup>
<xref ref-type="bibr" rid="bibr48-0957650914562094">48</xref>
</sup>
after an extensive investigation, as working fluid for Rankine cycles with a maximum temperature of about 380 ℃. Nevertheless, in Cole et al.,
<sup>
<xref ref-type="bibr" rid="bibr46-0957650914562094">46</xref>
</sup>
the same mixture of 2-methylpyridine/water is recommended only for operating temperatures up to 330 ℃ and, preferably, no higher than 300 ℃. The toxicity of pyridine and 2-methylpyridine is higher than that of toluene and this fact may limit their use.</p>
</sec>
</sec>
<sec id="sec9-0957650914562094">
<title>Linear polysiloxanes</title>
<p>Dimethyl poly-siloxanes (see
<xref ref-type="table" rid="table4-0957650914562094">Table 4</xref>
) are the basic components of Syltherm 800, a heat transfer fluid with estimated
<italic>T
<sub>cr</sub>
</italic>
and
<italic>P
<sub>cr</sub>
</italic>
respectively equal to 367 ℃ and 10.9 bar and operational temperature ranging from −40 ℃ to 400 ℃.
<sup>
<xref ref-type="bibr" rid="bibr37-0957650914562094">37</xref>
</sup>
<table-wrap id="table4-0957650914562094" position="float">
<label>Table 4.</label>
<caption>
<p>Thermodynamic parameters of the working fluids considered in this work: linear polysiloxanes.</p>
</caption>
<graphic alternate-form-of="table4-0957650914562094" xlink:href="10.1177_0957650914562094-table4.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th>Fluid</th>
<th>
<italic>T
<sub>cr</sub>
</italic>
(℃)</th>
<th>
<italic>P
<sub>cr</sub>
</italic>
(bar)</th>
<th>
<italic>σ</italic>
<sup>h</sup>
</th>
<th>
<italic>T
<sub>C</sub>
</italic>
at 5 kPa
<sup>g</sup>
(℃)</th>
<th>Molecular weight</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>MM
<sup>a</sup>
</td>
<td>245.55</td>
<td>19.14</td>
<td>28.7</td>
<td>22.278</td>
<td>162.38</td>
</tr>
<tr>
<td>MDM
<sup>b</sup>
</td>
<td>291.25</td>
<td>14.4</td>
<td>43.4</td>
<td>66.043</td>
<td>236.53</td>
</tr>
<tr>
<td>MD
<sub>2</sub>
M
<sup>c</sup>
</td>
<td>326.25</td>
<td>12.27</td>
<td>63.1</td>
<td>102.09</td>
<td>310.69</td>
</tr>
<tr>
<td>MD
<sub>3</sub>
M
<sup>d</sup>
</td>
<td>355.25</td>
<td>9.45</td>
<td>84.3</td>
<td>131.68</td>
<td>384.84</td>
</tr>
<tr>
<td>MD
<sub>4</sub>
M
<sup>e</sup>
</td>
<td>380.05</td>
<td>8.04</td>
<td>106.0</td>
<td>156.88</td>
<td>459.00</td>
</tr>
<tr>
<td>MD
<sub>5</sub>
M
<sup>e</sup>
</td>
<td>398.65</td>
<td>6.77</td>
<td>128.1</td>
<td>180.99</td>
<td>533.15</td>
</tr>
<tr>
<td>MD
<sub>6</sub>
M
<sup>e</sup>
</td>
<td>415.75</td>
<td>6.24</td>
<td>149.7</td>
<td>201.34</td>
<td>607.31</td>
</tr>
<tr>
<td>MD
<sub>7</sub>
M
<sup>f</sup>
</td>
<td>430.35</td>
<td>5.406</td>
<td>171.9</td>
<td>222.47</td>
<td>681.46</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn7-0957650914562094">
<label>a</label>
<p>Hexamethyl-disiloxane.</p>
</fn>
<fn id="table-fn8-0957650914562094">
<label>b</label>
<p>Octamethyl-trisiloxane.</p>
</fn>
<fn id="table-fn9-0957650914562094">
<label>c</label>
<p>Decamethyl-tetrasiloxane.</p>
</fn>
<fn id="table-fn10-0957650914562094">
<label>d</label>
<p>Dodecamethyl-pentasiloxane.</p>
</fn>
<fn id="table-fn11-0957650914562094">
<label>e</label>
<p>Tetradecamethyl-hexasiloxane.</p>
</fn>
<fn id="table-fn12-0957650914562094">
<label>f</label>
<p>Eicosamethyl-nonasiloxane.</p>
</fn>
<fn id="table-fn13-0957650914562094">
<label>g</label>
<p>
<italic>T
<sub>C</sub>
</italic>
, condensation temperature in ℃.</p>
</fn>
<fn id="table-fn14-0957650914562094">
<label>h</label>
<p>σ, parameter of molecular complexity, see equation (1).</p>
</fn>
</table-wrap-foot>
</table-wrap>
</p>
<p>In
<xref ref-type="fig" rid="fig2-0957650914562094">Figure 2</xref>
are reported the calculated vapor pressures of some linear dimethyl poly-siloxanes and, for a comparison, the vapor pressure of Syltherm 800. In this work, the thermodynamic properties of pure linear dimethyl poly-siloxanes are computed by means of the Peng–Robinson equation of state,
<sup>
<xref ref-type="bibr" rid="bibr35-0957650914562094">35</xref>
</sup>
and by the data available in the database of Aspen Plus.
<fig id="fig2-0957650914562094" position="float">
<label>Figure 2.</label>
<caption>
<p>Vapor pressure curves of some poly-siloxanes and of the heat transfer fluid Syltherm 800, from Dow.
<sup>
<xref ref-type="bibr" rid="bibr37-0957650914562094">37</xref>
</sup>
</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig2.tif"></graphic>
</fig>
</p>
<p>Polysiloxanes were proposed in Angelino and Invernizzi
<sup>
<xref ref-type="bibr" rid="bibr38-0957650914562094">38</xref>
</sup>
as working fluids for space power systems, and linear polysiloxanes are now extensively used in organic Rankine cycles for biomass plants.</p>
</sec>
<sec id="sec10-0957650914562094">
<title>Perfluorocarbons</title>
<p>Perfluorocarbons (see
<xref ref-type="table" rid="table5-0957650914562094">Table 5</xref>
) are fluids considered thermo-chemically very stable.
<sup>
<xref ref-type="bibr" rid="bibr5-0957650914562094">5</xref>
</sup>
Their chemical inertness and nonflammability are well known and perfluorocarbons (as pure fluids or in mixtures) are commonly available as heat transfer fluids. In
<xref ref-type="fig" rid="fig3-0957650914562094">Figure 3</xref>
, there is a comparison in the P-H thermodynamic plane among the properties calculated in this work by means of Aspen Plus, utilizing the UNIFAC method and the predictive Readlich–Kwong–Soave equation of state (PRKS),
<sup>
<xref ref-type="bibr" rid="bibr23-0957650914562094">23</xref>
,
<xref ref-type="bibr" rid="bibr25-0957650914562094">25</xref>
</sup>
with reference data from Imperial Smelting.
<sup>
<xref ref-type="bibr" rid="bibr41-0957650914562094">41</xref>
,
<xref ref-type="bibr" rid="bibr42-0957650914562094">42</xref>
</sup>
The results are, for our aims, quite acceptable.
<fig id="fig3-0957650914562094" position="float">
<label>Figure 3.</label>
<caption>
<p>Saturation dome for two perfluorocarbon fluids in the PH plane. Comparison of calculated values and some reference values.
<sup>
<xref ref-type="bibr" rid="bibr41-0957650914562094">41</xref>
,
<xref ref-type="bibr" rid="bibr42-0957650914562094">42</xref>
</sup>
</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig3.tif"></graphic>
</fig>
<table-wrap id="table5-0957650914562094" position="float">
<label>Table 5.</label>
<caption>
<p>Thermodynamic parameters of the working fluids considered in this work: perfluorocarbons.</p>
</caption>
<graphic alternate-form-of="table5-0957650914562094" xlink:href="10.1177_0957650914562094-table5.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th>Fluid</th>
<th>
<italic>T
<sub>cr</sub>
</italic>
(℃)</th>
<th>
<italic>P
<sub>cr</sub>
</italic>
(bar)</th>
<th>
<italic>σ</italic>
<sup>c</sup>
</th>
<th>
<italic>T
<sub>C</sub>
</italic>
at 5 kPa
<sup>d</sup>
(℃)</th>
<th>Molecular weight</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Perfluoro-n-pentane</td>
<td>149.95</td>
<td>20.466</td>
<td>20.9</td>
<td></td>
<td>288.04</td>
</tr>
<tr>
<td>Perfluoro-n-hexane</td>
<td>176.4</td>
<td>18.02</td>
<td>27.95</td>
<td></td>
<td>338.04</td>
</tr>
<tr>
<td>Perfluoro-n-heptane</td>
<td>202.5</td>
<td>16.1</td>
<td>35.9</td>
<td>11.430</td>
<td>388.05</td>
</tr>
<tr>
<td>Perfluoro-n-octane</td>
<td>229.05</td>
<td>14.78</td>
<td>45.7</td>
<td>26.241</td>
<td>438.06</td>
</tr>
<tr>
<td>Perfluoro-n-nonane</td>
<td>250.75</td>
<td>12.96</td>
<td>54.8</td>
<td>43.239</td>
<td>488.07</td>
</tr>
<tr>
<td>Perfluoro-n-decane</td>
<td>269.2</td>
<td>11.72</td>
<td>65.0</td>
<td>55.472</td>
<td>538.07</td>
</tr>
<tr>
<td>Perfluoro-n-dodecane</td>
<td>297.35</td>
<td>9.723</td>
<td>81.7</td>
<td>85.863</td>
<td>638.09</td>
</tr>
<tr>
<td>Hexafluoro-benzene</td>
<td>243.58</td>
<td>32.728</td>
<td>12.6</td>
<td></td>
<td>186.06</td>
</tr>
<tr>
<td>FLUTEC PP9
<sup>a</sup>
</td>
<td>313.4</td>
<td>16.5948</td>
<td>69.3</td>
<td>74.423</td>
<td>512.09</td>
</tr>
<tr>
<td>FLUTEC PP2
<sup>b</sup>
</td>
<td>213.65</td>
<td>23.3048</td>
<td>27.0</td>
<td>6.7307</td>
<td>350.05</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn17-0957650914562094">
<label>a</label>
<p>Perfluoro-1-methyldecalin.</p>
</fn>
<fn id="table-fn18-0957650914562094">
<label>b</label>
<p>Perfluoro-methylcyclohexane.</p>
</fn>
<fn id="table-fn19-0957650914562094">
<label>c</label>
<p>
<italic>σ</italic>
, parameter of molecular complexity, see equation (1).</p>
</fn>
<fn id="table-fn20-0957650914562094">
<label>d</label>
<p>
<italic>T
<sub>C</sub>
</italic>
, condensation temperature in ℃.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="table6-0957650914562094" position="float">
<label>Table 6.</label>
<caption>
<p>Thermodynamic parameters of the working fluids considered in this work: a miscellany of some organic and inorganic fluids.</p>
</caption>
<graphic alternate-form-of="table6-0957650914562094" xlink:href="10.1177_0957650914562094-table6.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th>Fluid</th>
<th>
<italic>T
<sub>cr</sub>
</italic>
(℃)</th>
<th>
<italic>P
<sub>cr</sub>
</italic>
(bar)</th>
<th>
<italic>σ</italic>
<sup>a</sup>
</th>
<th>
<italic>T
<sub>C</sub>
</italic>
at 5 kPa
<sup>b</sup>
(℃)</th>
<th>Molecular weight</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Water</td>
<td>373.946</td>
<td>220.64</td>
<td>−10.2</td>
<td>32.863</td>
<td>18.01</td>
</tr>
<tr>
<td>Pyridine</td>
<td>346.8</td>
<td>56.3</td>
<td>4.50</td>
<td>36.205</td>
<td>79.10</td>
</tr>
<tr>
<td>2-Methylpyridine</td>
<td>347.85</td>
<td>46.0</td>
<td></td>
<td>47.7</td>
<td>93.129</td>
</tr>
<tr>
<td>Titanium tetrachloride</td>
<td>364.85</td>
<td>46.6095</td>
<td>1.991</td>
<td>53.180</td>
<td>189.69</td>
</tr>
<tr>
<td>Titanium tetrabromide</td>
<td>522.55</td>
<td>62.72</td>
<td>1.2793</td>
<td>127.8943</td>
<td>367.50</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn15-0957650914562094">
<label>a</label>
<p>
<italic>σ</italic>
, parameter of molecular complexity, see equation (1).</p>
</fn>
<fn id="table-fn16-0957650914562094">
<label>b</label>
<p>
<italic>T
<sub>C</sub>
</italic>
, condensation temperature in ℃.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</p>
<p>As an example, Fluorinert and Flutec are trademarked brand names for perfluorocarbons fluids proposed for various applications (electronics, cosmetics, etc.). Fluorinert fluids
<sup>
<xref ref-type="bibr" rid="bibr39-0957650914562094">39</xref>
</sup>
are available with boiling points ranging from 30 ℃ to 215 ℃, and pour points from −110 ℃ to −25 ℃; Flutec vapors, in absence of air, are declared utilizable
<sup>
<xref ref-type="bibr" rid="bibr40-0957650914562094">40</xref>
</sup>
(in inert or passivated containers) until 400–450 ℃, depending on the fluid type.</p>
<p>In Miller et al.,
<sup>
<xref ref-type="bibr" rid="bibr48-0957650914562094">48</xref>
</sup>
the authors, after a comprehensive survey, suggest a mixture of 60% mol pentafluorobenzene and 40% mol hexafluorobenzene as a first choice for applications in Rankine cycles satisfying constraints as: melting point less than −40 ℃, no health and environmental hazards, no flammability and high thermochemical stability in mild steel boilers at least up to 380 ℃.</p>
<p>In Angelino et al.
<sup>
<xref ref-type="bibr" rid="bibr43-0957650914562094">43</xref>
</sup>
are described the results of a test program on an solar engine using the perfluoro-dimethyl-cycle-hexane (commercial name Flutec PP3) as working fluid at a 250 ℃ and designed for a superheating temperature of 280 ℃.</p>
</sec>
<sec id="sec11-0957650914562094">
<title>Halides</title>
<p>Halides, already proposed as potentially good working fluids in heat pipes in the “intermediate” temperature range, from 200 ℃ up to 400 ℃,
<sup>
<xref ref-type="bibr" rid="bibr31-0957650914562094">31</xref>
,
<xref ref-type="bibr" rid="bibr44-0957650914562094">44</xref>
,
<xref ref-type="bibr" rid="bibr45-0957650914562094">45</xref>
</sup>
could also be of interest as working fluids for power cycles.</p>
<p>In the present paper, titanium tetrachloride and titanium tetrabromide will be considered. Titanium tetrachloride,
<inline-formula id="ilm1-0957650914562094">
<mml:math display="inline" id="mml-math1-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>TiCl</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
(see
<xref ref-type="table" rid="table6-0957650914562094">Table 6</xref>
) with a melting point at −24 ℃ is a metal halide liquid at room temperature; titanium tetrabromide,
<inline-formula id="ilm2-0957650914562094">
<mml:math display="inline" id="mml-math2-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>TiBr</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, on the other hand, has a melting temperature of 39 ℃. The required thermodynamic properties are evaluated by Aspen Plus and the equation of state of Peng and Robinson.
<sup>
<xref ref-type="bibr" rid="bibr35-0957650914562094">35</xref>
</sup>
The critical point of
<inline-formula id="ilm3-0957650914562094">
<mml:math display="inline" id="mml-math3-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>TiBr</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and its heat capacity in the ideal gas conditions were taken from Zamfirescu et al.
<sup>
<xref ref-type="bibr" rid="bibr50-0957650914562094">50</xref>
</sup>
In
<xref ref-type="fig" rid="fig4-0957650914562094">Figure 4</xref>
are shown the vapor pressure curves of
<inline-formula id="ilm4-0957650914562094">
<mml:math display="inline" id="mml-math4-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>TiCl</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
<sup>
<xref ref-type="bibr" rid="bibr51-0957650914562094">51</xref>
,
<xref ref-type="bibr" rid="bibr52-0957650914562094">52</xref>
</sup>
and of
<inline-formula id="ilm5-0957650914562094">
<mml:math display="inline" id="mml-math5-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>TiBr</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
.
<sup>
<xref ref-type="bibr" rid="bibr53-0957650914562094">53</xref>
</sup>
The calculated values agree well with the assumed experimental references.
<fig id="fig4-0957650914562094" position="float">
<label>Figure 4.</label>
<caption>
<p>Vapor pressure of titanium tetrachloride and titanium tetrabromide. Comparison of calculated and some reference values.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig4.tif"></graphic>
</fig>
</p>
<p>According to the NFPA standard, the two halides are not flammable but nevertheless hazardous: a short exposure to them could cause serious temporary or moderate residual injury. Titanium tetrabromide is normally stable, but can become unstable at elevated temperatures and pressures and titanium tetrachloride reacts dangerously with water (like cesium, potassium and sodium, for example). The reaction of the two compounds with water releases respectively hydrogen chloride (toxic and corrosive) and hydrogen bromide (corrosive). According to Anderson,
<sup>
<xref ref-type="bibr" rid="bibr31-0957650914562094">31</xref>
</sup>
<inline-formula id="ilm6-0957650914562094">
<mml:math display="inline" id="mml-math6-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>TiBr</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
proved to be thermo-chemically stable during 3000 h at 380 ℃, in contact with commercially pure titanium (CP-Ti). Titanium tetracholoride resulted thermo-chemically stable during 3 years of operation in heat pipes manufactured with mild steel and stainless steel, at a temperature of 159 ℃, and for 3000 h at 300 ℃ in case of Hastelloy (special high temperature alloy) heat pipe.
<sup>
<xref ref-type="bibr" rid="bibr31-0957650914562094">31</xref>
</sup>
</p>
<p>The previous, albeit partial, review shows that (a) aromatic hydrocarbons, (b) perfluorocarbons and (c) some heterocyclic compounds, seem, among the organic working fluids, thermochemically stable at operating temperatures of about 400 ℃, although with contradictory results.</p>
<p>Halides, and, in particular, for its thermophysical properties (melting point, critical temperature, molar mass, and molecular complexity), titanium tetrachloride, are very stable fluids and potentially good working fluids. Unfortunately, titanium tetrachloride reacts violently with water.</p>
<p>As a matter of fact, all organic working fluids degrade at rates proportional to the operating temperature and to the time exposure. This fact must be taken into serious consideration, especially in hermetic engines, with small power levels and with very low condensing pressures.</p>
</sec>
</sec>
</sec>
<sec id="sec12-0957650914562094">
<title>The performances of the alkali metals topping cycles</title>
<p>In
<xref ref-type="fig" rid="fig5-0957650914562094">Figure 5</xref>
are represented three topping cycles with potassium, rubidium, and caesium in the thermodynamic plane T-S. The high values of
<italic>T
<sub>cr</sub>
</italic>
with respect to the maximum assumed temperature
<italic>T</italic>
<sub>max</sub>
(850 ℃) and the small specific heat capacity of the alkali metals have, as a consequence, an high ratio of evaporation to sensible heat (6.8 for the potassium cycle and 5.4 for the caesium one). A high value of evaporation heat respect to the pre-heating heat makes pointless an internal regeneration, simplifying considerably the cycle layout.
<fig id="fig5-0957650914562094" position="float">
<label>Figure 5.</label>
<caption>
<p>Thermodynamic cycles with potassium, rubidium and caesium in the TS plane.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig5.tif"></graphic>
</fig>
</p>
<p>In fact, let
<italic>η</italic>
<sub>1</sub>
be the topping alkali metal cycle efficiency, the cycle second law efficiency
<inline-formula id="ilm7-0957650914562094">
<mml:math display="inline" id="mml-math7-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, with respect to a Carnot cycle efficiency
<inline-formula id="ilm8-0957650914562094">
<mml:math display="inline" id="mml-math8-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
operating between
<inline-formula id="ilm9-0957650914562094">
<mml:math display="inline" id="mml-math9-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula id="ilm10-0957650914562094">
<mml:math display="inline" id="mml-math10-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>cond</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, results high in all cases (about 0.58), with no need of a regeneration.</p>
<p>The increase of the molecular weight of the working fluid (39.1 for potassium, 85.48 for rubidium and 132.9 for caesium) reduces the cycle area (see
<xref ref-type="fig" rid="fig5-0957650914562094">Figure 5</xref>
) and consequently the useful power per unit mass of working fluid.</p>
<p>Results of cycle calculations for potassium and caesium are given in
<xref ref-type="table" rid="table7-0957650914562094">Table 7</xref>
. The thermodynamic properties of the considered alkali metals were calculated according the relations reported in Reynolds.
<sup>
<xref ref-type="bibr" rid="bibr54-0957650914562094">54</xref>
</sup>
<table-wrap id="table7-0957650914562094" position="float">
<label>Table 7.</label>
<caption>
<p>Cycle efficiencies, volume flow ratio, and turbine isentropic work for potassium and caesium cycles.</p>
</caption>
<graphic alternate-form-of="table7-0957650914562094" xlink:href="10.1177_0957650914562094-table7.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th>Fluid</th>
<th>
<inline-formula id="ilm11-0957650914562094">
<mml:math display="inline" id="mml-math11-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>max</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
(bar)</th>
<th>
<italic>η</italic>
<sub>1</sub>
</th>
<th>
<inline-formula id="ilm12-0957650914562094">
<mml:math display="inline" id="mml-math12-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>VFR</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>a</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th>
<inline-formula id="ilm13-0957650914562094">
<mml:math display="inline" id="mml-math13-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
(kJ/kg)</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Caesium</td>
<td>3.039</td>
<td>0.2059</td>
<td>24.346978</td>
<td>173.27047</td>
</tr>
<tr>
<td>Potassium</td>
<td>1.490</td>
<td>0.2086</td>
<td>44.335506</td>
<td>691.43646</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn21-0957650914562094">
<label>a</label>
<p>
<inline-formula id="ilm14-0957650914562094">
<mml:math display="inline" id="mml-math14-0957650914562094">
<mml:mrow>
<mml:mi>VFR</mml:mi>
<mml:mo>=</mml:mo>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>out</mml:mtext>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
<mml:mi></mml:mi>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>in</mml:mtext>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
<mml:mi></mml:mi>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</p>
</fn>
</table-wrap-foot>
</table-wrap>
</p>
<p>The parameters assumed for the calculations are the following (according to
<xref ref-type="table" rid="table1-0957650914562094">Table 1</xref>
):
<inline-formula id="ilm15-0957650914562094">
<mml:math display="inline" id="mml-math15-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 450 ℃,
<inline-formula id="ilm16-0957650914562094">
<mml:math display="inline" id="mml-math16-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 800 ℃,
<italic>T</italic>
<sub>max,1</sub>
 = 850 ℃. The turbine and the pump efficiencies were respectively assumed to be equal to 0.75 and 0.50. The product between the mechanical
<italic>η
<sub>M</sub>
</italic>
and the electrical
<italic>η
<sub>G</sub>
</italic>
efficiencies was assumed to be equal to 0.9.</p>
<p>The isentropic enthalpy drop in turbine for potassium is about four times greater than the corresponding value for caesium (see
<xref ref-type="table" rid="table7-0957650914562094">Table 7</xref>
). The isentropic volume flow ratio across the turbine in the potassium cycle is about twice that of caesium one.</p>
</sec>
<sec id="sec13-0957650914562094">
<title>The performances of the ORCs bottoming cycles</title>
<p>Similarly to all Rankine cycles, even the performances of the cycles using organic working fluids are substantially affected by the critical temperature and by the parameter of molecular complexity
<italic>σ</italic>
of the working fluid. The parameter of molecular complexity is correlated to the structure and to the number of atoms of the molecule and it can be defined as (Chapter 2, Section 2.5, pp.109–111)
<sup>
<xref ref-type="bibr" rid="bibr55-0957650914562094">55</xref>
</sup>
<disp-formula id="disp-formula1-0957650914562094">
<label>(1)</label>
<mml:math display="inline" id="math1-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>[</mml:mo>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>SV</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo></mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>[</mml:mo>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>vp</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>dP</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>vp</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mtext>d</mml:mtext>
<mml:mrow>
<mml:mi>T </mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo></mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>ln</mml:mi>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>49</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo>×</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>7</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mi>ω</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula1-0957650914562094" xlink:href="10.1177_0957650914562094-eq1.tif"></graphic>
</disp-formula>
where
<inline-formula id="ilm17-0957650914562094">
<mml:math display="inline" id="mml-math17-0957650914562094">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
is the molar ideal heat capacity at constant pressure evaluated at a reduced temperature of
<inline-formula id="ilm18-0957650914562094">
<mml:math display="inline" id="mml-math18-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
and
<italic>ω</italic>
is the acentric factor.
<sup>
<xref ref-type="bibr" rid="bibr56-0957650914562094">56</xref>
</sup>
The parameter
<italic>σ</italic>
is reported for the considered fluids in
<xref ref-type="table" rid="table3-0957650914562094">Tables 3</xref>
<xref ref-type="table" rid="table4-0957650914562094"></xref>
<xref ref-type="table" rid="table5-0957650914562094"></xref>
to
<xref ref-type="table" rid="table6-0957650914562094">6</xref>
. The ideal molar heat capacity and the acentric factor, increase basically with the number of atoms in the molecule.</p>
<p>The acentric factor
<italic>ω</italic>
is strictly correlated with the relative variation of the vapor pressure
<inline-formula id="ilm19-0957650914562094">
<mml:math display="inline" id="mml-math19-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>[</mml:mo>
</mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mtext>d</mml:mtext>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>vp</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mtext>d</mml:mtext>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>vp</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
at
<inline-formula id="ilm20-0957650914562094">
<mml:math display="inline" id="mml-math20-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
. An increase in
<italic>ω</italic>
(or, in general, of the
<italic>N</italic>
number of atoms in the molecule) produces an increase in the relative variation of the reduced vapor pressure and a decrease in the slope of the saturated vapor entropy (or a decrease of
<italic>σ</italic>
). However, the effect of
<italic>ω</italic>
is overwhelmed by the rapid increase of the molar specific heat with
<italic>N</italic>
and the entropy slope increases rapidly with the number of atoms.</p>
<p>For the considered organic fluids, using the data reported in
<xref ref-type="table" rid="table3-0957650914562094">Tables 3</xref>
<xref ref-type="table" rid="table4-0957650914562094"></xref>
<xref ref-type="table" rid="table5-0957650914562094"></xref>
to
<xref ref-type="table" rid="table6-0957650914562094">6</xref>
and the values of
<inline-formula id="ilm21-0957650914562094">
<mml:math display="inline" id="mml-math21-0957650914562094">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
from literature, the parameter of molecular complexity may be calculated according to equation (1). The resulting parameters
<italic>σ</italic>
are reported in
<xref ref-type="table" rid="table3-0957650914562094">Tables 3</xref>
<xref ref-type="table" rid="table4-0957650914562094"></xref>
<xref ref-type="table" rid="table5-0957650914562094"></xref>
to
<xref ref-type="table" rid="table6-0957650914562094">6</xref>
and in
<xref ref-type="fig" rid="fig6-0957650914562094">Figure 6</xref>
the critical temperature
<italic>T
<sub>cr</sub>
</italic>
is correlated as a function of the parameter of molecular complexity.
<fig id="fig6-0957650914562094" position="float">
<label>Figure 6.</label>
<caption>
<p>Parameter of molecular complexity as a function of the critical temperature for some fluid families.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig6.tif"></graphic>
</fig>
</p>
<p>For the same critical temperature, siloxanes and perfluorocarbons have a molecular complexity greater than aromatic hydrocarbons. For the application here considered, i.e. a bottoming cycle, the ideal working fluid should have a critical temperature as high as possible, a low molecular complexity, and a high molecular mass. From this point of view, the eutectic mixture of diphenyl and diphenyl oxide, titanium tetrachloride, and titanium tetrabromide seem favored.</p>
<p>Once fixed, the minimum condensation pressure (
<italic>P
<sub>C</sub>
</italic>
<sub>,2,min</sub>
 =  0.05 bar,
<xref ref-type="table" rid="table1-0957650914562094">Table 1</xref>
) and the reduced condensation temperature of the bottoming cycle
<inline-formula id="ilm22-0957650914562094">
<mml:math display="inline" id="mml-math22-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, can be correlated as a function of the molecular complexity, and it basically increases with
<italic>σ</italic>
(see
<xref ref-type="fig" rid="fig7-0957650914562094">Figure 7</xref>
).
<fig id="fig7-0957650914562094" position="float">
<label>Figure 7.</label>
<caption>
<p>Reduced condensation temperature (
<inline-formula id="ilm23-0957650914562094">
<mml:math display="inline" id="mml-math23-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) at
<inline-formula id="ilm24-0957650914562094">
<mml:math display="inline" id="mml-math24-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 0.05 bar as a function of the molecular complexity parameter for some fluids. Key: 1 – toluene, 3 – pyridine, 6 – perfluoro-nonane, 7 – 1,3-dimethylbenzene (m-xylene), 8 – titanium tetrachloride, 9 – perfluoro-decane, 10 –
<inline-formula id="ilm25-0957650914562094">
<mml:math display="inline" id="mml-math25-0957650914562094">
<mml:mrow>
<mml:mtext>MDM</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 11 – 1,2,4-trimethylbenzene, 12 – Flutec PP9, 13 – perfluoro-dodecane, 14 – 1,2,3,5-tetramethylbenzene, 15 –
<inline-formula id="ilm26-0957650914562094">
<mml:math display="inline" id="mml-math26-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 16 – titanium tetrabromide, 17 –
<inline-formula id="ilm27-0957650914562094">
<mml:math display="inline" id="mml-math27-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 18 – Therminol VP1, 19 –
<inline-formula id="ilm28-0957650914562094">
<mml:math display="inline" id="mml-math28-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 20 –
<inline-formula id="ilm29-0957650914562094">
<mml:math display="inline" id="mml-math29-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 21 –
<inline-formula id="ilm30-0957650914562094">
<mml:math display="inline" id="mml-math30-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>7</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 22 – Flutec PP2, 23 –
<inline-formula id="ilm31-0957650914562094">
<mml:math display="inline" id="mml-math31-0957650914562094">
<mml:mrow>
<mml:mtext>MM</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 24 perfluoro-heptane, 25 – perfluoro-octane, 26 –
<inline-formula id="ilm32-0957650914562094">
<mml:math display="inline" id="mml-math32-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig7.tif"></graphic>
</fig>
</p>
<p>As a consequence, thermodynamic cycles using working fluids with higher
<italic>T
<sub>cr</sub>
</italic>
and high
<italic>σ</italic>
will have higher
<inline-formula id="ilm33-0957650914562094">
<mml:math display="inline" id="mml-math33-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
. A few examples will clarify this statement:
<list id="list1-0957650914562094" list-type="bullet">
<list-item>
<p>With reference to working fluids with medium values of
<italic>σ</italic>
,
<inline-formula id="ilm34-0957650914562094">
<mml:math display="inline" id="mml-math34-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 149.8 ℃ for the eutectic mixture of diphenyl and diphenyl oxide (
<italic>σ</italic>
 = 34.77,
<italic>T
<sub>cr</sub>
</italic>
 =  498.89 ℃) and
<inline-formula id="ilm35-0957650914562094">
<mml:math display="inline" id="mml-math35-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 103.2 ℃ for tetramethylbenzene (
<inline-formula id="ilm36-0957650914562094">
<mml:math display="inline" id="mml-math36-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>27</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>96</mml:mn>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 405.85 ℃) and
<inline-formula id="ilm37-0957650914562094">
<mml:math display="inline" id="mml-math37-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 22.28 ℃ for MM (
<inline-formula id="ilm38-0957650914562094">
<mml:math display="inline" id="mml-math38-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>28</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>72</mml:mn>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 245.55 ℃).</p>
</list-item>
<list-item>
<p>With reference to working fluids with a low
<italic>σ</italic>
,
<inline-formula id="ilm39-0957650914562094">
<mml:math display="inline" id="mml-math39-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 127.89 ℃ for titanium tetrabromide (
<inline-formula id="ilm40-0957650914562094">
<mml:math display="inline" id="mml-math40-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>28</mml:mn>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 522.55 ℃) and
<inline-formula id="ilm41-0957650914562094">
<mml:math display="inline" id="mml-math41-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 53.18 ℃ for titanium tetrachloride (
<inline-formula id="ilm42-0957650914562094">
<mml:math display="inline" id="mml-math42-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>99</mml:mn>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 364.85 ℃).</p>
</list-item>
<list-item>
<p>As further examples, at about the same critical temperature, MD
<sub>5</sub>
M (
<inline-formula id="ilm43-0957650914562094">
<mml:math display="inline" id="mml-math43-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>128</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
) and tetramethylbenzene have respectively
<inline-formula id="ilm44-0957650914562094">
<mml:math display="inline" id="mml-math44-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 180.99 ℃ and
<inline-formula id="ilm45-0957650914562094">
<mml:math display="inline" id="mml-math45-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 103.18 ℃ and titanium tetrabromide and the eutectic mixture of diphenyl and diphenyl oxyde have respectively condensation temperatures of 127.89 ℃ and 149.8 ℃.</p>
</list-item>
</list>
</p>
<p>The bottoming cycle efficiency
<italic>η</italic>
<sub>2</sub>
, at the optimum evaporation pressure being the maximum temperature
<inline-formula id="ilm46-0957650914562094">
<mml:math display="inline" id="mml-math46-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
fixed (
<inline-formula id="ilm47-0957650914562094">
<mml:math display="inline" id="mml-math47-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
equal to 400 ℃,
<xref ref-type="table" rid="table1-0957650914562094">Table 1</xref>
), increases with decreasing
<inline-formula id="ilm48-0957650914562094">
<mml:math display="inline" id="mml-math48-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
(see
<xref ref-type="fig" rid="fig8-0957650914562094">Figure 8</xref>
).
<fig id="fig8-0957650914562094" position="float">
<label>Figure 8.</label>
<caption>
<p>Cycle efficiency
<italic>η</italic>
<sub>2</sub>
at optimum maximum pressure, for some fluids as a function of the condensation temperature
<inline-formula id="ilm49-0957650914562094">
<mml:math display="inline" id="mml-math49-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
. Key: 1 – toluene, 2 – water, 3 – pyridine, 4 – eutectic water/pyridine mixture, 6 – perfluoro-nonane, 7 – 1.3-dimethylbenzene (m-xylene), 8 – titanium tetrachloride, 9 – perfluoro-decane, 10 –
<inline-formula id="ilm50-0957650914562094">
<mml:math display="inline" id="mml-math50-0957650914562094">
<mml:mrow>
<mml:mtext>MDM</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 11 1,2,4-trimethylbenzene, 12 – Flutec PP9, 13 – perfluoro-dodecane, 14 – 1,2,3,5-tetramethylbenzene, 15 –
<inline-formula id="ilm51-0957650914562094">
<mml:math display="inline" id="mml-math51-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 16 – titanium tetrabromide, 17 –
<inline-formula id="ilm52-0957650914562094">
<mml:math display="inline" id="mml-math52-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
,18 – Therminol VP1, 19 –
<inline-formula id="ilm53-0957650914562094">
<mml:math display="inline" id="mml-math53-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 20 –
<inline-formula id="ilm54-0957650914562094">
<mml:math display="inline" id="mml-math54-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 21 –
<inline-formula id="ilm55-0957650914562094">
<mml:math display="inline" id="mml-math55-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>7</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 22 – Flutec PP2, 23 –
<inline-formula id="ilm56-0957650914562094">
<mml:math display="inline" id="mml-math56-0957650914562094">
<mml:mrow>
<mml:mtext>MM</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
, 24 – perfluoro-heptane, 25 – perfluoro-octane, 26 –
<inline-formula id="ilm57-0957650914562094">
<mml:math display="inline" id="mml-math57-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>5</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig8.tif"></graphic>
</fig>
</p>
<p>
<xref ref-type="fig" rid="fig6-0957650914562094">Figures 6</xref>
<xref ref-type="fig" rid="fig7-0957650914562094"></xref>
to
<xref ref-type="fig" rid="fig8-0957650914562094">8</xref>
can be used to estimate the performance of ORC cycles. For fixed
<italic>σ</italic>
,
<xref ref-type="fig" rid="fig7-0957650914562094">Figure 7</xref>
gives the reduced condensation temperature
<inline-formula id="ilm58-0957650914562094">
<mml:math display="inline" id="mml-math58-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<xref ref-type="fig" rid="fig8-0957650914562094">Figure 8</xref>
gives the net cycle efficiency
<italic>η</italic>
<sub>2</sub>
. From
<xref ref-type="fig" rid="fig6-0957650914562094">Figures 6</xref>
one may choose the critical temperature
<italic>T
<sub>cr</sub>
</italic>
, the fluid family and, as a consequence, the condensation temperature
<inline-formula id="ilm59-0957650914562094">
<mml:math display="inline" id="mml-math59-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
.</p>
<p>The influence of the molecular complexity on the cycle performance can be appreciated by observing
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(a)</xref>
to (
<xref ref-type="fig" rid="fig9-0957650914562094">c</xref>
): in all cases,
<italic>T
<sub>cr</sub>
</italic>
is lower than
<inline-formula id="ilm60-0957650914562094">
<mml:math display="inline" id="mml-math60-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and all the cycles exhibit a similar condensation temperature (about 50 ℃).
<fig id="fig9-0957650914562094" position="float">
<label>Figure 9.</label>
<caption>
<p>Some bottoming cycles with
<inline-formula id="ilm61-0957650914562094">
<mml:math display="inline" id="mml-math61-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 50 ℃ in the TS plane: (a) thermodynamic cycle with titanium tetrachloride; (b) thermodynamic cycle with 1,3-dimethylbenzene (m-xylene); (c) thermodynamic cycle with perfluoro-n-decane.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig9.tif"></graphic>
</fig>
</p>
<p>Adopting a recuperative cycle in all the cases, the cycle efficiencies
<italic>η</italic>
<sub>2</sub>
become equal to 0.285 for titanium tetrachloride (
<inline-formula id="ilm62-0957650914562094">
<mml:math display="inline" id="mml-math62-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>99</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
), 0.316 for m-xylene (1,3-dimethylbenzene,
<inline-formula id="ilm63-0957650914562094">
<mml:math display="inline" id="mml-math63-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>14</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>59</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
), and 0.298 for perfluoro-n-decane (
<inline-formula id="ilm64-0957650914562094">
<mml:math display="inline" id="mml-math64-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>65</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>01</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
).</p>
<p>The efficiency
<inline-formula id="ilm65-0957650914562094">
<mml:math display="inline" id="mml-math65-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, with respect to a Carnot cycle operating between
<inline-formula id="ilm66-0957650914562094">
<mml:math display="inline" id="mml-math66-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula id="ilm67-0957650914562094">
<mml:math display="inline" id="mml-math67-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, which is roughly the same in the three cases (about 0.515), becomes higher for the cycle in
<xref ref-type="fig" rid="fig9-0957650914562094">Figura 9(b)</xref>
using m-xylene. This results is a consequence of the different
<italic>σ</italic>
and of the different distributions of the associated thermodynamic losses
<inline-formula id="ilm68-0957650914562094">
<mml:math display="inline" id="mml-math68-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
. In fact (Chapter 1, Section 1.2, p. 11)
<sup>
<xref ref-type="bibr" rid="bibr55-0957650914562094">55</xref>
</sup>
<disp-formula id="disp-formula2-0957650914562094">
<label>(2)</label>
<mml:math display="inline" id="math2-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>Σ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>in</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>Σ</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula2-0957650914562094" xlink:href="10.1177_0957650914562094-eq2.tif"></graphic>
</disp-formula>
where, in this case,
<italic>T</italic>
<sub>0</sub>
may be assumed to be equal to
<inline-formula id="ilm69-0957650914562094">
<mml:math display="inline" id="mml-math69-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>in</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the thermal power introduced in the bottoming cycle, and
<inline-formula id="ilm70-0957650914562094">
<mml:math display="inline" id="mml-math70-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the entropy production due to the
<italic>j</italic>
th thermodynamic irreversibility in the bottoming cycle.</p>
<p>The cycle with titanium tetrachloride (
<inline-formula id="ilm71-0957650914562094">
<mml:math display="inline" id="mml-math71-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>99</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
, in
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(a)</xref>
) has a loss of
<inline-formula id="ilm72-0957650914562094">
<mml:math display="inline" id="mml-math72-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
in the heater that is 1.66 times greater than the corresponding loss for the cycle in
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(b)</xref>
. The cycle in
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(c)</xref>
(with perfluoro-n-decane,
<inline-formula id="ilm73-0957650914562094">
<mml:math display="inline" id="mml-math73-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>65</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>01</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
) has a loss of
<inline-formula id="ilm74-0957650914562094">
<mml:math display="inline" id="mml-math74-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
in the recuperator that is about three times grater than that of the cycle in
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(b)</xref>
. The final result is just the greater cycle efficiency
<italic>η</italic>
<sub>2</sub>
for m-xylene.</p>
<p>The discussed results for the considered cases can be extended to a general rule: whatever the temperature
<inline-formula id="ilm75-0957650914562094">
<mml:math display="inline" id="mml-math75-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
, working fluids with medium values of
<italic>σ</italic>
allow the highest efficiencies
<italic>η</italic>
<sub>2</sub>
.</p>
<p>In
<xref ref-type="fig" rid="fig10-0957650914562094">Figure 10(a)</xref>
and (
<xref ref-type="fig" rid="fig10-0957650914562094">b</xref>
), as a further example, are reported two cycles with
<inline-formula id="ilm76-0957650914562094">
<mml:math display="inline" id="mml-math76-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
equals about at 100 ℃, with tetramethyl benzene (
<inline-formula id="ilm77-0957650914562094">
<mml:math display="inline" id="mml-math77-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>27</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>96</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
) and with
<inline-formula id="ilm78-0957650914562094">
<mml:math display="inline" id="mml-math78-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
(dodecamethyl-tetrasiloxane,
<inline-formula id="ilm79-0957650914562094">
<mml:math display="inline" id="mml-math79-0957650914562094">
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>63</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
).
<fig id="fig10-0957650914562094" position="float">
<label>Figure 10.</label>
<caption>
<p>Two bottoming cycles with
<inline-formula id="ilm80-0957650914562094">
<mml:math display="inline" id="mml-math80-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
 100 ℃ in the TS plane: (a) thermodynamic cycle with 1,2,3,5-tetramethylbenzene; (b) thermodynamic cycle with
<inline-formula id="ilm81-0957650914562094">
<mml:math display="inline" id="mml-math81-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>MD</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mtext>M</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig10.tif"></graphic>
</fig>
</p>
<p>The case of working fluids with
<italic>T
<sub>cr</sub>
</italic>
higher than
<inline-formula id="ilm82-0957650914562094">
<mml:math display="inline" id="mml-math82-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is investigated in
<xref ref-type="fig" rid="fig11-0957650914562094">Figure 11(a)</xref>
and (
<xref ref-type="fig" rid="fig11-0957650914562094">b</xref>
). The cycle with titanium tetrabromide (without recuperator) has a particularly simple layout and a good thermodynamic performance (
<inline-formula id="ilm83-0957650914562094">
<mml:math display="inline" id="mml-math83-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>555</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
is the same as that of the cycle in
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(a)</xref>
). The cycle with the eutectic mixture of biphenyl oxide and biphenyl (of very good thermodynamic quality,
<inline-formula id="ilm84-0957650914562094">
<mml:math display="inline" id="mml-math84-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>637</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
) has yet a
<inline-formula id="ilm85-0957650914562094">
<mml:math display="inline" id="mml-math85-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
rather high (about 150 ℃).
<fig id="fig11-0957650914562094" position="float">
<label>Figure 11.</label>
<caption>
<p>Two organic Rankine cycles in the TS plane: (a) titanium tetrabromide; (b) eutectic mixture of diphenyl and diphenyl oxyde.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig11.tif"></graphic>
</fig>
</p>
</sec>
<sec id="sec14-0957650914562094">
<title>The binary cycles</title>
<p>The thermodynamic efficiency of a binary cycle, in case all the thermal power at the condenser of the topping cycle (identified by the index 1) is recovered by the bottoming one (identified by the index 2), can be calculated as
<disp-formula id="disp-formula3-0957650914562094">
<label>(3)</label>
<mml:math display="inline" id="math3-0957650914562094">
<mml:mrow>
<mml:mi>η</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula3-0957650914562094" xlink:href="10.1177_0957650914562094-eq3.tif"></graphic>
</disp-formula>
where, as already seen, the efficiency
<italic>η</italic>
<sub>2</sub>
is chiefly a function of the condensation temperature
<inline-formula id="ilm86-0957650914562094">
<mml:math display="inline" id="mml-math86-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
(according to
<xref ref-type="fig" rid="fig8-0957650914562094">Figure 8</xref>
).</p>
<p>As
<italic>η</italic>
<sub>2</sub>
increases linearly when
<inline-formula id="ilm87-0957650914562094">
<mml:math display="inline" id="mml-math87-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
decreases, also the binary efficiency
<italic>η</italic>
, according to equation (3), increases linearly when
<inline-formula id="ilm88-0957650914562094">
<mml:math display="inline" id="mml-math88-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
decreases. For example,
<italic>η</italic>
is approximately equal to about 0.44 for
<inline-formula id="ilm89-0957650914562094">
<mml:math display="inline" id="mml-math89-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
50 ℃ and about 0.40 for
<inline-formula id="ilm90-0957650914562094">
<mml:math display="inline" id="mml-math90-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
equal to 100 ℃.</p>
<p>The potassium and caesium cycles have actually the same efficiency
<italic>η</italic>
<sub>1</sub>
but the volumetric expansion flow ratios and the isentropic enthalpy drop across the turbine are very different (see
<xref ref-type="table" rid="table7-0957650914562094">Table 7</xref>
). Consequently, the turbine configuration is very different in the two cases.</p>
<p>For the cycle calculations discussed in the previous sections, we assumed values of turbine efficiencies equal to 0.75 and 0.80, respectively for alkali metal cycles and for the organic Rankine cycles.</p>
<p>The values of turbine efficiencies strongly affect the cycle performance and moreover, due to the low power levels here considered and, particularly, to the large
<inline-formula id="ilm91-0957650914562094">
<mml:math display="inline" id="mml-math91-0957650914562094">
<mml:mrow>
<mml:mtext>VFR</mml:mtext>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>out</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>in</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
for the bottoming cycles operating with organic fluids, actual values of turbomachinery efficiencies may be quite different from the supposed values. No matter how, the effect of
<inline-formula id="ilm92-0957650914562094">
<mml:math display="inline" id="mml-math92-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and of
<inline-formula id="ilm93-0957650914562094">
<mml:math display="inline" id="mml-math93-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
on the binary cycle efficiency
<italic>η</italic>
can be appraised by
<disp-formula id="disp-formula4-0957650914562094">
<label>(4a)</label>
<mml:math display="inline" id="math4-0957650914562094">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>δ</mml:mi>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo></mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>×</mml:mo>
<mml:mi>δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula4-0957650914562094" xlink:href="10.1177_0957650914562094-eq4.tif"></graphic>
</disp-formula>
<disp-formula id="disp-formula5-0957650914562094">
<label>(4b)</label>
<mml:math display="inline" id="math5-0957650914562094">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>δ</mml:mi>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo></mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>×</mml:mo>
<mml:mi>δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula5-0957650914562094" xlink:href="10.1177_0957650914562094-eq5.tif"></graphic>
</disp-formula>
<disp-formula id="disp-formula6-0957650914562094">
<label>(4c)</label>
<mml:math display="inline" id="math6-0957650914562094">
<mml:mrow>
<mml:mi>δ</mml:mi>
<mml:mi>η</mml:mi>
<mml:mo></mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>×</mml:mo>
<mml:mi>δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>×</mml:mo>
<mml:mi>δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula6-0957650914562094" xlink:href="10.1177_0957650914562094-eq6.tif"></graphic>
</disp-formula>
</p>
<p>For example, if
<inline-formula id="ilm94-0957650914562094">
<mml:math display="inline" id="mml-math94-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>316</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
(1,3-dimethylbenzene cycle) and
<inline-formula id="ilm95-0957650914562094">
<mml:math display="inline" id="mml-math95-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>206</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
(caesium cycle), the efficiency
<italic>η</italic>
results 0.457. Assuming
<inline-formula id="ilm96-0957650914562094">
<mml:math display="inline" id="mml-math96-0957650914562094">
<mml:mrow>
<mml:mi>δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mo>-</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
the reduction
<inline-formula id="ilm97-0957650914562094">
<mml:math display="inline" id="mml-math97-0957650914562094">
<mml:mrow>
<mml:mi>δ</mml:mi>
<mml:mi>η</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
is approximately 0.0502 and
<italic>η</italic>
is about 0.407. The effect of the decrease in the adiabatic efficiency of the turbines on the overall performance results so considerably mitigated by the terms
<inline-formula id="ilm98-0957650914562094">
<mml:math display="inline" id="mml-math98-0957650914562094">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula id="ilm99-0957650914562094">
<mml:math display="inline" id="mml-math99-0957650914562094">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
, according to equation (4c). In fact, assuming the turbines efficiencies are not correlated among them, a reduction in the turbine efficiency
<inline-formula id="ilm100-0957650914562094">
<mml:math display="inline" id="mml-math100-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
increases the thermal power available in the bottoming cycle that is able to recover in part the losses. On the other hand, a reduction in the turbine efficiency
<inline-formula id="ilm101-0957650914562094">
<mml:math display="inline" id="mml-math101-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
results in a decrease in the cycle efficiency
<italic>η</italic>
<sub>2</sub>
, but this reduction is, in part, balanced by the efficiency
<italic>η</italic>
<sub>1</sub>
of the topping cycle.</p>
</sec>
<sec id="sec15-0957650914562094">
<title>The preliminary design of the turbines</title>
<p>As it is well known, turbine design can be handled by means of similarity rules. The similarity parameters usually introduced are, for each
<italic>j</italic>
th turbine stage, the specific speed
<inline-formula id="ilm102-0957650914562094">
<mml:math display="inline" id="mml-math102-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>ω</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
<disp-formula id="disp-formula7-0957650914562094">
<label>(5)</label>
<mml:math display="inline" id="math7-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>ω</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
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</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
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<mml:mi>π</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>60</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mfrac>
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</mml:mrow>
<mml:mi>·</mml:mi>
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</mml:mrow>
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:msubsup>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
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</mml:mrow>
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<mml:mn>4</mml:mn>
</mml:mrow>
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</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula7-0957650914562094" xlink:href="10.1177_0957650914562094-eq7.tif"></graphic>
</disp-formula>
and the specific diameter
<inline-formula id="ilm103-0957650914562094">
<mml:math display="inline" id="mml-math103-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
<disp-formula id="disp-formula8-0957650914562094">
<label>(6)</label>
<mml:math display="inline" id="math8-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
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<mml:mrow>
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<mml:mi>Δ</mml:mi>
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</mml:mrow>
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<mml:mo>,</mml:mo>
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</mml:mrow>
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</mml:mrow>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<graphic alternate-form-of="disp-formula8-0957650914562094" xlink:href="10.1177_0957650914562094-eq8.tif"></graphic>
</disp-formula>
where
<inline-formula id="ilm104-0957650914562094">
<mml:math display="inline" id="mml-math104-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>out</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mi>S</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the stage isentropic outlet volume flow rate and
<inline-formula id="ilm105-0957650914562094">
<mml:math display="inline" id="mml-math105-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the static isentropic enthalpy drop of the stage.
<italic>N</italic>
represents the rotational speed and
<italic>D</italic>
the mean rotor diameter.
<sup>
<xref ref-type="bibr" rid="bibr59-0957650914562094">59</xref>
</sup>
</p>
<p>Assuming that the stage is axial, the selected rotational speed should optimize, for each
<italic>j</italic>
th stage, the values of
<inline-formula id="ilm106-0957650914562094">
<mml:math display="inline" id="mml-math106-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>ω</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula id="ilm107-0957650914562094">
<mml:math display="inline" id="mml-math107-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
.</p>
<p>Many generalized diagrams available in open literature provide
<inline-formula id="ilm108-0957650914562094">
<mml:math display="inline" id="mml-math108-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>ω</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula id="ilm109-0957650914562094">
<mml:math display="inline" id="mml-math109-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
near approximate optimal conditions. In this work, we referred to those reported in Nichols.
<sup>
<xref ref-type="bibr" rid="bibr59-0957650914562094">59</xref>
</sup>
</p>
<p>Large variations of volume flow rate and large
<inline-formula id="ilm110-0957650914562094">
<mml:math display="inline" id="mml-math110-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
imply several turbine stage. Then, the large variations in the volume flow ratio
<inline-formula id="ilm111-0957650914562094">
<mml:math display="inline" id="mml-math111-0957650914562094">
<mml:mrow>
<mml:mtext>VFR</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>
involve correspondingly large variations of the specific speed (and in
<inline-formula id="ilm112-0957650914562094">
<mml:math display="inline" id="mml-math112-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
), from one stage to the next one during the expansion. This fact may introduce some difficulties in the turbine design optimization process.</p>
<p>In the following, the preliminary sizing of the turbines were developed according to a simplified and approximate procedure, assuming ideal turbines stages (without considering the traditional fluid-dynamic losses: profile losses, secondary and tip-clearing losses, effects of the trailing-edge thickness, rotor frictional losses, losses associated with the leakages of the expanding vapors, effects of the Mach and Reynolds numbers, effects of quality, etc.), resorting to the free-vortex theory and only considering total admission cases. The rotational speed
<italic>N</italic>
and the number of stages were selected assuring: (i) as much as possible,
<inline-formula id="ilm113-0957650914562094">
<mml:math display="inline" id="mml-math113-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>ω</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula id="ilm114-0957650914562094">
<mml:math display="inline" id="mml-math114-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>s</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
near optimal values, according to Nichols;
<sup>
<xref ref-type="bibr" rid="bibr59-0957650914562094">59</xref>
</sup>
(ii) the ratio
<inline-formula id="ilm115-0957650914562094">
<mml:math display="inline" id="mml-math115-0957650914562094">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>h</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>D</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mi></mml:mi>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
(the mean blade height to the mean diameter ratio for each stage) in a reasonable range (
<inline-formula id="ilm116-0957650914562094">
<mml:math display="inline" id="mml-math116-0957650914562094">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>025</mml:mn>
<mml:mo><</mml:mo>
<mml:mo stretchy="false">(</mml:mo>
<mml:mi>h</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>D</mml:mi>
<mml:mo stretchy="false">)</mml:mo>
<mml:mi></mml:mi>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mo><</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
); and (iii) a discharge kinetic energy small enough (less than 10%), consistently with the small number of stages.</p>
<p>Calculations were performed for potassium and caesium turbine and for selected organic fluids; results (reported in
<xref ref-type="table" rid="table8-0957650914562094">Tables 8</xref>
<xref ref-type="fig" rid="fig9-0957650914562094"></xref>
to
<xref ref-type="table" rid="table10-0957650914562094">10</xref>
) are to be considered only as approximate and above all significant in relative terms, as an indication of general results and trends.
<table-wrap id="table10-0957650914562094" position="float">
<label>Table 10.</label>
<caption>
<p>Preliminary estimated characteristics of axial turbines with the eutectic mixture of diphenyl and diphenyl oxide (DIPHE) and titanium tetrachloride (TiCl
<sub>4</sub>
).</p>
</caption>
<graphic alternate-form-of="table10-0957650914562094" xlink:href="10.1177_0957650914562094-table10.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th></th>
<th>DIPHE</th>
<th>TiCl4a</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Number of stages</td>
<td>2</td>
<td>1</td>
</tr>
<tr>
<td>Number of revolution (r/min)</td>
<td>100,000</td>
<td>110,000</td>
</tr>
<tr>
<td>Overall volume expansion ratio</td>
<td>239.16</td>
<td>64.732</td>
</tr>
<tr>
<td>Overall isentropic work (kJ/kg)</td>
<td>169.67</td>
<td>103.87</td>
</tr>
<tr>
<td>Isentropic power per stage (kW)</td>
<td>3.9743</td>
<td>7.9265</td>
</tr>
<tr>
<td colspan="3">First stage</td>
</tr>
<tr>
<td> Tip diameter (cm)</td>
<td>4.500</td>
<td>4.408</td>
</tr>
<tr>
<td> Mean diameter (cm)</td>
<td>4.301</td>
<td>4.166</td>
</tr>
<tr>
<td>
<italic>h/D</italic>
<sup>b</sup>
</td>
<td>0.046329</td>
<td>0.057976</td>
</tr>
<tr>
<td> Reaction degree at  mean radius</td>
<td>0.2</td>
<td>0.15</td>
</tr>
<tr>
<td> Volume flow ratio</td>
<td>17.541</td>
<td>64.732</td>
</tr>
<tr>
<td> Exhaust volume flow (m
<sup>3</sup>
/s)</td>
<td>21.453 × 10
<sup>−3</sup>
</td>
<td>45.705 × 10
<sup>−3</sup>
</td>
</tr>
<tr>
<td colspan="3">Last stage</td>
</tr>
<tr>
<td> Tip diameter (cm)</td>
<td>6.4869</td>
<td></td>
</tr>
<tr>
<td> Mean diameter (cm)</td>
<td>5.4402</td>
<td></td>
</tr>
<tr>
<td>
<italic>h/D</italic>
<sup>b</sup>
</td>
<td>0.19239</td>
<td></td>
</tr>
<tr>
<td> Reaction degree at  mean radius</td>
<td>0.5</td>
<td></td>
</tr>
<tr>
<td> Volume flow ratio</td>
<td>13.634</td>
<td></td>
</tr>
<tr>
<td> Exhaust volume  flow (m
<sup>3</sup>
/s)</td>
<td>0.2925</td>
<td></td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn23-0957650914562094">
<label>a</label>
<p>Condensation pressure
<italic>P
<sub>C</sub>
</italic>
<sup></sup>
=  0.35 bar (
<italic>T
<sub>C</sub>
</italic>
<sup></sup>
=  100 ℃).</p>
</fn>
<fn id="table-fn24-0957650914562094">
<label>b</label>
<p>Mean rotor blade height to mean diameter ratio.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="table8-0957650914562094" position="float">
<label>Table 8.</label>
<caption>
<p>Preliminary estimated characteristics of 10 kW (isentropic) axial turbines with potassium and caesium.</p>
</caption>
<graphic alternate-form-of="table8-0957650914562094" xlink:href="10.1177_0957650914562094-table8.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th></th>
<th>Potassium</th>
<th>Caesium</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Number of stages</td>
<td>10</td>
<td>3</td>
</tr>
<tr>
<td>Number of revolution (r/min)</td>
<td>60,000</td>
<td>60,000</td>
</tr>
<tr>
<td>Overall volume expansion ratio</td>
<td>44.335</td>
<td>24.347</td>
</tr>
<tr>
<td>Overall isentropic work (kJ/kg)</td>
<td>691.43</td>
<td>173.27</td>
</tr>
<tr>
<td>Isentropic power per stage (kW)</td>
<td>1.0</td>
<td>3.333</td>
</tr>
<tr>
<td colspan="3">First stage</td>
</tr>
<tr>
<td> Tip diameter (cm)</td>
<td>6.387</td>
<td>7.17</td>
</tr>
<tr>
<td> Mean diameter (cm)</td>
<td>6.204</td>
<td>6.983</td>
</tr>
<tr>
<td>
<italic>h/D</italic>
<sup>a</sup>
</td>
<td>0.029421</td>
<td>0.026739</td>
</tr>
<tr>
<td> Reaction degree at mean radius</td>
<td>0.09</td>
<td>0.4</td>
</tr>
<tr>
<td> Volume flow ratio</td>
<td>1.259</td>
<td>2.2298</td>
</tr>
<tr>
<td> Exhaust volume flow (m
<sup>3</sup>
/s)</td>
<td>0.0272</td>
<td>0.027008</td>
</tr>
<tr>
<td colspan="3">Last stage</td>
</tr>
<tr>
<td> Tip diameter (cm)</td>
<td>11.15</td>
<td>8.472</td>
</tr>
<tr>
<td> Mean diameter (cm)</td>
<td>8.543</td>
<td>6.983</td>
</tr>
<tr>
<td>
<italic>h/D</italic>
<sup>a</sup>
</td>
<td>0.30528</td>
<td>0.21324</td>
</tr>
<tr>
<td> Reaction degree at mean radius</td>
<td>0.52</td>
<td>0.4</td>
</tr>
<tr>
<td> Volume flow ratio</td>
<td>1.687</td>
<td>3.804</td>
</tr>
<tr>
<td> Exhaust volume flow (m
<sup>3</sup>
/s)</td>
<td>0.95666</td>
<td>0.29489</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn22-0957650914562094">
<label>a</label>
<p>Mean rotor blade height to mean diameter ratio.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</p>
<sec id="sec16-0957650914562094">
<title>The turbines for the alkali metal topping cycles</title>
<p>In the case of alkali metal turbines, due to the low vapor qualities (0.8–0.9), the peripheral velocities need to be low in order to reduce the erosion due to impingement of liquid droplets against the surfaces of the stage buckets. In the preliminary design, the centrifugal stresses were not considered because they are strictly correlated to the used material (e.g. refractory materials or iron alloys).</p>
<p>Results for potassium and caesium axial turbines are shown in
<xref ref-type="table" rid="table8-0957650914562094">Table 8</xref>
. The isentropic turbine power is assumed to be equal to 10 kW in both the cases.</p>
<p>For the potassium turbine the number of stages was fixed to 10, so that the maximum peripheral velocities are in the range of about 300–350 m/s. The selected rotational speed
<italic>N</italic>
 = 60,000 r/min is a compromise so that, at constant isentropic power per stage, most of the stages have an acceptable
<italic>h</italic>
/
<italic>D</italic>
ratio, even if the last stage is close to the maximum allowed value. On the other hand, increasing the rotational speed might oblige to resort to the partial admission (the ratio
<inline-formula id="ilm117-0957650914562094">
<mml:math display="inline" id="mml-math117-0957650914562094">
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>D</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>03</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
is already near to the minimum value).</p>
<p>Assuming approximately the same load for stage as for potassium, three stages are obtained for the caesium turbine each one with a mean diameter of about 7 cm. The mean diameter for the potassium turbines is 6.4 cm (see
<xref ref-type="table" rid="table8-0957650914562094">Table 8</xref>
).</p>
</sec>
<sec id="sec17-0957650914562094">
<title>The turbines for the bottoming ORC cycles</title>
<p>Regarding the power of the topping alkali metal cycle to be fixed, the mass flow of the bottoming organic working fluid and, therefore, the power of the bottoming thermodynamic cycle is obtained from the thermal power balance at the primary heat exchanger of the bottoming cycle.</p>
<p>Roughly, an isentropic power of 9 kW is available in the organic Rankine cycles of
<xref ref-type="fig" rid="fig9-0957650914562094">Figures 9</xref>
<xref ref-type="fig" rid="fig10-0957650914562094"></xref>
to
<xref ref-type="fig" rid="fig11-0957650914562094">11</xref>
, considering both the potassium and caesium as working fluids for the upper cycle.</p>
<p>The organic Rankine cycles, with the assumed condensation pressure
<inline-formula id="ilm118-0957650914562094">
<mml:math display="inline" id="mml-math118-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
equal to 0.05 bar, is featured in all cases by VFRs rather large: at least an order of magnitude greater than those of potassium and caesium cyles. This fact makes the design of very efficient turbines difficult.</p>
<p>Because of the small level of power considered here, the high volumetric expansion ratios (about 1000 for 1,2,3,5-tetramethylbenzene, about 230 for the eutectic mixture of diphenyl and diphenyl oxide) and the high molecular mass of the working fluids (i.e. low speed of sound, high Mach numbers, nozzles of convergent/divergent type, supersonic relative inlet flow in the rotor) it is very difficult to obtain high turbine efficiencies. Anyway, turboexpanders and cyogenic turboexpanders with revolutions over 100,000 r/min are usual in the industry.
<sup>
<xref ref-type="bibr" rid="bibr57-0957650914562094">57</xref>
,
<xref ref-type="bibr" rid="bibr58-0957650914562094">58</xref>
</sup>
</p>
<p>In
<xref ref-type="table" rid="table9-0957650914562094">Table 9</xref>
are reported some results relative to turbines for 1,2,3,5-trimethylbenzene and 1,3-dimethylbenzene (m-xylene). Owing to the large volumetric expansion ratio, it ensues difficult to assure the same medium diameter in all stages.
<table-wrap id="table9-0957650914562094" position="float">
<label>Table 9.</label>
<caption>
<p>Preliminary estimated characteristics of axial turbines with 1,2,3,5-tetramethylbenzene (
<inline-formula id="ilm119-0957650914562094">
<mml:math display="inline" id="mml-math119-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mtext>CH</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) and 1,3-dimethylbenzene (
<inline-formula id="ilm120-0957650914562094">
<mml:math display="inline" id="mml-math120-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mtext>CH</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
).</p>
</caption>
<graphic alternate-form-of="table9-0957650914562094" xlink:href="10.1177_0957650914562094-table9.tif"></graphic>
<table frame="hsides">
<thead align="left" valign="top">
<tr>
<th></th>
<th>
<inline-formula id="ilm121-0957650914562094">
<mml:math display="inline" id="mml-math121-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mtext>CH</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
<th>
<inline-formula id="ilm122-0957650914562094">
<mml:math display="inline" id="mml-math122-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mtext>C</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>6</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mtext>H</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>4</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>(</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mtext>CH</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mo> </mml:mo>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</th>
</tr>
</thead>
<tbody align="left" valign="top">
<tr>
<td>Number of stages</td>
<td>3</td>
<td>4</td>
</tr>
<tr>
<td>Number of revolution (r/min)</td>
<td>150,000</td>
<td>180,000</td>
</tr>
<tr>
<td>Overall volume expansion ratio</td>
<td>1052.3</td>
<td>623.59</td>
</tr>
<tr>
<td>Overall isentropic work (kJ/kg)</td>
<td>221.61</td>
<td>300.71</td>
</tr>
<tr>
<td>Isentropic power per stage (kW)</td>
<td>2.9723</td>
<td>2.5979</td>
</tr>
<tr>
<td colspan="3">First stage</td>
</tr>
<tr>
<td> Tip diameter (cm)</td>
<td>2.6193</td>
<td>2.1586</td>
</tr>
<tr>
<td> Mean diameter (cm)</td>
<td>2.5226</td>
<td>2.0946</td>
</tr>
<tr>
<td>
<italic>h/D</italic>
<sup>a</sup>
</td>
<td>0.03832</td>
<td>0.030711</td>
</tr>
<tr>
<td> Reaction degree at mean radius</td>
<td>0.1</td>
<td>0.1</td>
</tr>
<tr>
<td> Volume flow ratio</td>
<td>19.777</td>
<td>5.9150</td>
</tr>
<tr>
<td> Exhaust volume flow (m
<sup>3</sup>
/s)</td>
<td>5.31 10
<sup>−3</sup>
</td>
<td>2.8598 10
<sup>−3</sup>
</td>
</tr>
<tr>
<td colspan="3">Last stage</td>
</tr>
<tr>
<td> Tip diameter (cm)</td>
<td>5.7032</td>
<td>5.1037</td>
</tr>
<tr>
<td> Mean diameter (cm)</td>
<td>4.3693</td>
<td>3.6279</td>
</tr>
<tr>
<td>
<italic>h/D</italic>
<sup>a</sup>
</td>
<td>0.30527</td>
<td>0.40682</td>
</tr>
<tr>
<td> Reaction degree at mean radius</td>
<td>0.70</td>
<td>0.7</td>
</tr>
<tr>
<td> Volume flow ratio</td>
<td>7.3964</td>
<td>4.9877</td>
</tr>
<tr>
<td> Exhaust volume flow (m
<sup>3</sup>
/s)</td>
<td>0.28254</td>
<td>0.3015</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="table-fn25-0957650914562094">
<label>a</label>
<p>Mean rotor blade height to mean diameter ratio.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</p>
<p>In the case of m-xylene (molar mass 106.167) the turbine has four stages and a ratio
<italic>d</italic>
/
<italic>D</italic>
equal to 0.4 for the last stage. The tip peripheral velocity of the last stage results are rather high: about 480 m/s at 180,000 r/min.</p>
<p>In
<xref ref-type="table" rid="table10-0957650914562094">Table 10</xref>
there are some data for the turbine with the eutectic mixture of diphenyl and diphenyl oxide (molar mass 165.66): two stages at 100,000 r/min.</p>
<p>If the condensation pressure becomes higher than 0.05 bar, there will be better improvement in the turbine design. For example (see
<xref ref-type="table" rid="table10-0957650914562094">Table 10</xref>
), a cycle operating with titanium tetrachloride (molar mass 189.6908) condensing at
<italic>T
<sub>C</sub>
</italic>
<sub>,2</sub>
 =  100 ℃ (
<italic>P
<sub>C</sub>
</italic>
<sub>,2</sub>
 =  0.35 bar, isentropic turbine power of about 8 kW) could have a single stage turbine with about 4 cm of rotor mean diameter at 110,000 r/min, a ratio
<inline-formula id="ilm123-0957650914562094">
<mml:math display="inline" id="mml-math123-0957650914562094">
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>D</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>06</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
, with a supersonic flow at the rotor inlet. The specific speed ω
<italic>
<sub>s</sub>
</italic>
and the specific diameter
<italic>D
<sub>s</sub>
</italic>
result in this case will be equal to 0.43 and 3.5, respectively.</p>
<p>In
<xref ref-type="fig" rid="fig12-0957650914562094">Figure 12</xref>
are reported, as an example, the vapor pressure curves for some organic fluids with low and intermediate parameters of molecular complexity (
<inline-formula id="ilm124-0957650914562094">
<mml:math display="inline" id="mml-math124-0957650914562094">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo><</mml:mo>
<mml:mi>σ</mml:mi>
<mml:mo><</mml:mo>
<mml:mn>30</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
). Among them, tetramethylbenzene has a vapor pressure just equal to 0.05 bar at 100 ℃ (see the cycle in
<xref ref-type="fig" rid="fig9-0957650914562094">Figure 9(a)</xref>
) and hexafluorobenzene at 80 ℃ has a vapor pressure of 1.0 bar. Titanium tetrachloride and 1,3-dimethylbenzene have the same vapor pressure curve, but very different molecular complexity (
<italic>σ</italic>
respectively equal to about 2 and about 15) and molecular mass (respectively 190 and 106).
<fig id="fig12-0957650914562094" position="float">
<label>Figure 12.</label>
<caption>
<p>Vapor pressure curves of some organic working fluids between 50 ℃ and 100 ℃.</p>
</caption>
<graphic xlink:href="10.1177_0957650914562094-fig12.tif"></graphic>
</fig>
</p>
<p>In conclusion, as usual, the working fluid and the condensation pressure must always be chosen from time to time according to the power level and to the cooling medium.</p>
</sec>
</sec>
<sec id="sec18-0957650914562094" sec-type="conclusions">
<title>Conclusions</title>
<p>The calculations and results presented and discussed in the previous sections would suggest that, for this case study, the turbines are among the most critical components to design and build, especially for the bottoming cycle. This is due to the large volumetric expansion ratios combined with the low power levels involved. In any case, the turbomachinery for the power levels and thermodynamic conditions we have assumed, would seem to be technologically feasible, even though the design conditions could certainly be improved. For instance, partial admission could be adopted. In fact, if the first stage has a partial admission, the rotational speed could be significantly reduced, thus enabling a better power regulation, acting upon the admission arc and modifying the mass flow, according to the changed working conditions at constant input conditions into the turbine.</p>
<p>With the mimimum condensation pressure
<inline-formula id="ilm125-0957650914562094">
<mml:math display="inline" id="mml-math125-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
that we considered (0.05 bar), the dimension of the final stages of the turbine for the thermodynamic bottoming cycle is made awkward by the elevated VFRs that result. Condensation at higher pressures is definitely better for the design phase.</p>
<p>Perhaps, a multi-stage outflow radial turbines could be, in the considered cases, a useful alternative to the axial turbines to manage elevated VFRs, avoiding to resort to expensive multi-flow axial turbines. An outflow radial turbine was really proposed by Charles Algernon Parson in the late 1800s for the ship “Turbinia” (p. 338),
<sup>
<xref ref-type="bibr" rid="bibr60-0957650914562094">60</xref>
</sup>
and many times investigated, see, for example, Martin and Kolenc.
<sup>
<xref ref-type="bibr" rid="bibr61-0957650914562094">61</xref>
</sup>
</p>
<p>The use of the binary cycle at the temperatures we considered gives good efficiency in all cases and, although the effects of a reduction on the turbine efficiency is always negative for overall performance, this is partly compensated by the presence of two thermodynamic cycles placed in series, according to equation (4c). For example, net cycle efficiencies between 41 and 46 percent (according to the turbines efficiencies) could be achieved resorting to binary cycles with caesium and 1,3-dimethylbenzene, with a condensation temperature of about 53 ℃ (condensation pressure of 0.05 bar).</p>
<p>This analysis, which is largely centered on the thermodynamic characteristics, does certainly not exhaust all the aspects that need to be considered when choosing the working fluid for the bottoming cycle. For example, if the whole engine with organic fluid was completely hermetic, then the working fluid would also require good lubricating characteristics. Furthermore, even the slightest thermodynamic decomposition of the organic working fluid, which always would lead to the formation of light compounds (e.g. methane), would have extremely harmful effects in a hermetic system with condensation at 0.05 bar, bringing about a significant rise in condensation pressure, even for modest levels of decomposition.</p>
<p>In conclusion, using binary cycles for systems of distributed solar power generation, with power levels between tens of kilowatts and a few megawatts, adopting organic fluid Rankine cycles for the bottoming engine, seems to be promising. In any case, as usual, the choice of working fluid and condensation pressure at the minimum temperature is crucial.</p>
<p>The condensation pressures
<inline-formula id="ilm126-0957650914562094">
<mml:math display="inline" id="mml-math126-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
considered here, with elevated VFRs in the case studies analyzed, are at the limit of feasibility, though. It would be better, according to the application in question, to fix the condensation pressure and the working fluid according to power level.</p>
</sec>
</body>
<back>
<sec id="sec20-0957650914562094">
<title>Funding</title>
<p>This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="bibr1-0957650914562094">
<label>1</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Pitz-Paal</surname>
<given-names>R</given-names>
</name>
</person-group>
<article-title>High temperature solar concentrators</article-title>
. In:
<person-group person-group-type="editor">
<name>
<surname>Galvez</surname>
<given-names>JB</given-names>
</name>
<name>
<surname>Rodriguez</surname>
<given-names>SM</given-names>
</name>
</person-group>
(eds).
<source>Solar energy conversion and photoenergy systems - Encyclopedia of life support systems (EOLSS).
<italic>Developed under the Auspices of the UNESCO</italic>
</source>
,
<publisher-loc>Oxford, UK</publisher-loc>
:
<publisher-name>Eolss Publishers</publisher-name>
,
<year>2007</year>
.</citation>
</ref>
<ref id="bibr2-0957650914562094">
<label>2</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Granados</surname>
<given-names>FJG</given-names>
</name>
<name>
<surname>Silva Pérez</surname>
<given-names>MA</given-names>
</name>
<name>
<surname>Ruiz-Hernández</surname>
<given-names>V</given-names>
</name>
</person-group>
.
<article-title>Thermal model of the EuroDish solar stirling engine</article-title>
.
<source>J Solar Energy Eng</source>
<year>2008</year>
;
<volume>130</volume>
:
<fpage>011014-1</fpage>
<lpage>011014-8</lpage>
.</citation>
</ref>
<ref id="bibr3-0957650914562094">
<label>3</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Invernizzi</surname>
<given-names>CM</given-names>
</name>
<name>
<surname>Iora</surname>
<given-names>P</given-names>
</name>
<name>
<surname>Sandrini</surname>
<given-names>R</given-names>
</name>
</person-group>
.
<article-title>Biomass combined cycles based on externally fired gas turbines and organic Rankine expanders</article-title>
.
<source>Proc IMechE, Part A: J Power and Energy</source>
<year>2011</year>
;
<volume>225</volume>
:
<fpage>1066</fpage>
<lpage>1075</lpage>
.</citation>
</ref>
<ref id="bibr4-0957650914562094">
<label>4</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Angelino</surname>
<given-names>G</given-names>
</name>
<name>
<surname>Invernizzi</surname>
<given-names>C</given-names>
</name>
</person-group>
.
<article-title>Binary conversion cycles for concentrating solar power technology</article-title>
.
<source>Sol Energy</source>
<year>2008</year>
;
<volume>82</volume>
:
<fpage>637</fpage>
<lpage>647</lpage>
.</citation>
</ref>
<ref id="bibr5-0957650914562094">
<label>5</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ray</surname>
<given-names>SK</given-names>
</name>
<name>
<surname>Moss</surname>
<given-names>G</given-names>
</name>
</person-group>
.
<article-title>Fluorochemicals as working fluids for small Rankine cycle power units</article-title>
.
<source>Adv Energy Convers</source>
<year>1966</year>
;
<volume>6</volume>
:
<fpage>89</fpage>
<lpage>102</lpage>
.</citation>
</ref>
<ref id="bibr6-0957650914562094">
<label>6</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Bammert</surname>
<given-names>K</given-names>
</name>
<name>
<surname>Heikal</surname>
<given-names>H</given-names>
</name>
<name>
<surname>Mobarak</surname>
<given-names>A</given-names>
</name>
</person-group>
.
<article-title>Turbomachinery for small solar power plants</article-title>
.
<source>Forschung im Ingenieurwesen</source>
<year>1981</year>
;
<volume>47</volume>
(
<issue>6</issue>
):
<fpage>169</fpage>
<lpage>178</lpage>
.</citation>
</ref>
<ref id="bibr7-0957650914562094">
<label>7</label>
<citation citation-type="other">
<comment>Various Authors.
<italic>Small high pressure ratio turbines. Lecture Series 1987-07</italic>
. Rhode saint Geneve, Belgium: von Karman Institute for Fluid Dynamics, 15–18 June 1987</comment>
.</citation>
</ref>
<ref id="bibr8-0957650914562094">
<label>8</label>
<citation citation-type="other">
<comment>Bronicki LY. The Ormat Rankine power unit. In:
<italic>7th Intersociety energy conversion engineering conference</italic>
, San Diego, USA, 1972, pp.327–334</comment>
.</citation>
</ref>
<ref id="bibr9-0957650914562094">
<label>9</label>
<citation citation-type="other">
<comment>Janicke MJ. Vapor cycle coolant requirements for nuclear space-power plants. Report, Argonne National Laboratory, ANL-6857, March 1964</comment>
.</citation>
</ref>
<ref id="bibr10-0957650914562094">
<label>10</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Gaffert</surname>
<given-names>GA</given-names>
</name>
</person-group>
.
<source>Steam power stations</source>
,
<publisher-loc>New York</publisher-loc>
:
<publisher-name>McGraw Hill</publisher-name>
,
<year>1952</year>
, pp.
<fpage>563</fpage>
<lpage>578</lpage>
.</citation>
</ref>
<ref id="bibr11-0957650914562094">
<label>11</label>
<citation citation-type="other">
<comment>Fraas AP, Burton DW, LaVerne ME, et al. Design comparison of cesium and potassium vapor turbine-generator units for space power plants. Report, Oak Ridge National Laboratory, ORNL-TM-2024, February 1969</comment>
.</citation>
</ref>
<ref id="bibr12-0957650914562094">
<label>12</label>
<citation citation-type="other">
<comment>Rossbach RJ. Potassium topping cycles for stationary power. Report, NASA CR-2518, March 1975</comment>
.</citation>
</ref>
<ref id="bibr13-0957650914562094">
<label>13</label>
<citation citation-type="other">
<comment>Fraas AP. A cesium vapor cycle for an advanced LMFBR. In:
<italic>The ASME winter annual meeting</italic>
, Houston, TX, USA, 30 November to 5 December 1975</comment>
.</citation>
</ref>
<ref id="bibr14-0957650914562094">
<label>14</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Gruntz</surname>
<given-names>RD</given-names>
</name>
</person-group>
.
<article-title>A liquid metal Rankine topping cycle for a steam power plant</article-title>
.
<source>J Spacecraft</source>
<year>1967</year>
;
<volume>4</volume>
(
<issue>7</issue>
):
<fpage>839</fpage>
<lpage>864</lpage>
.</citation>
</ref>
<ref id="bibr15-0957650914562094">
<label>15</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Morozov Yu</surname>
<given-names>D</given-names>
</name>
<name>
<surname>Prisniakov</surname>
<given-names>VF</given-names>
</name>
<name>
<surname>Privalov</surname>
<given-names>AN</given-names>
</name>
<etal></etal>
</person-group>
.
<article-title>Solar dynamic Rankine space power plant using vapour-liquid metallic techniques</article-title>
.
<source>Space Technol</source>
<year>1966</year>
;
<volume>16</volume>
(
<issue>4</issue>
):
<fpage>169</fpage>
<lpage>176</lpage>
.</citation>
</ref>
<ref id="bibr16-0957650914562094">
<label>16</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Manson</surname>
<given-names>SV</given-names>
</name>
</person-group>
.
<article-title>A review of the alkali metal Rankine technology program</article-title>
.
<source>J Spacecraft Rockets</source>
<year>1968</year>
;
<volume>5</volume>
(
<issue>11</issue>
):
<fpage>1249</fpage>
<lpage>1259</lpage>
.</citation>
</ref>
<ref id="bibr17-0957650914562094">
<label>17</label>
<citation citation-type="other">
<comment>Yoder GL, Carbajo JJ, Murphy RW, et al. Technology development program for an advanced potassium Rankine power conversion system compatible with several space reactor design. Report, ORNL/TM-2004/214, September 2005</comment>
.</citation>
</ref>
<ref id="bibr18-0957650914562094">
<label>18</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Stanisa</surname>
<given-names>B</given-names>
</name>
<name>
<surname>Schauperl</surname>
<given-names>Z</given-names>
</name>
<name>
<surname>Grilec</surname>
<given-names>K</given-names>
</name>
</person-group>
.
<article-title>Erosion behaviour of turbine rotor blades installed in the Krsko nuclear power plant</article-title>
.
<source>Wear</source>
<year>2003</year>
;
<volume>254</volume>
:
<fpage>735</fpage>
<lpage>741</lpage>
.</citation>
</ref>
<ref id="bibr19-0957650914562094">
<label>19</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>El-Wakil</surname>
<given-names>MM</given-names>
</name>
</person-group>
.
<source>Nuclear power engineering</source>
,
<publisher-loc>New York</publisher-loc>
:
<publisher-name>McGraw-Hill</publisher-name>
,
<year>1962</year>
.</citation>
</ref>
<ref id="bibr20-0957650914562094">
<label>20</label>
<citation citation-type="other">
<comment>Solutia. Therminol VP-1. Vapor phase/liquid phase heat transfer fluid 12–400 ℃, Product Bulletin, Solutia Inc., St. Louis, Missouri. Date unknown</comment>
.</citation>
</ref>
<ref id="bibr21-0957650914562094">
<label>21</label>
<citation citation-type="other">
<comment>Down. Downtherm A. Synthetic organic heat transfer fluid - liquid and vapor phase data, Product Information, The Dow Chemical Company. Date unknown</comment>
.</citation>
</ref>
<ref id="bibr22-0957650914562094">
<label>22</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dow</surname>
<given-names>HH</given-names>
</name>
</person-group>
.
<article-title>Diphenyl oxide bi-fluid power plants</article-title>
.
<source>J Am Soc Naval Engrs</source>
<year>1926</year>
;
<volume>38</volume>
(
<issue>4</issue>
):
<fpage>940</fpage>
<lpage>950</lpage>
.</citation>
</ref>
<ref id="bibr23-0957650914562094">
<label>23</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Poling</surname>
<given-names>BE</given-names>
</name>
<name>
<surname>Prausnitz</surname>
<given-names>JM</given-names>
</name>
<name>
<surname>O’Connell</surname>
<given-names>JP</given-names>
</name>
</person-group>
.
<source>The properties of gases and liquids</source>
,
<publisher-loc>5th ed. New York</publisher-loc>
:
<publisher-name>McGraw-Hill</publisher-name>
,
<year>2001</year>
.</citation>
</ref>
<ref id="bibr24-0957650914562094">
<label>24</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kuramochi</surname>
<given-names>H</given-names>
</name>
<name>
<surname>Ohsako</surname>
<given-names>M</given-names>
</name>
<name>
<surname>Maeda</surname>
<given-names>K</given-names>
</name>
<etal></etal>
</person-group>
.
<article-title>Prediction of physico-chemical properties for PCDDs/DFs using the UNIFAC model with an alternative approximation for group assignment</article-title>
.
<source>Chemosphere</source>
<year>2002</year>
;
<volume>49</volume>
:
<fpage>135</fpage>
<lpage>142</lpage>
.</citation>
</ref>
<ref id="bibr25-0957650914562094">
<label>25</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Holderbaum</surname>
<given-names>T</given-names>
</name>
<name>
<surname>Gmehling</surname>
<given-names>J</given-names>
</name>
</person-group>
.
<article-title>PSRK: A group-contribution equation of state based on UNIFAC</article-title>
.
<source>Fluid Phase Equilibria</source>
<year>1991</year>
;
<volume>70</volume>
:
<fpage>251</fpage>
<lpage>265</lpage>
.</citation>
</ref>
<ref id="bibr26-0957650914562094">
<label>26</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Killeffer</surname>
<given-names>DH</given-names>
</name>
</person-group>
.
<article-title>Stable organic compounds in power generation. Diphenyl-Diphenyl oxide mixtures in an efficient boiler plant of unique design</article-title>
.
<source>Ind Eng Chem</source>
<year>1935</year>
;
<volume>27</volume>
(
<issue>1</issue>
):
<fpage>10</fpage>
<lpage>15</lpage>
.</citation>
</ref>
<ref id="bibr27-0957650914562094">
<label>27</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dean</surname>
<given-names>DK</given-names>
</name>
</person-group>
.
<article-title>Applications of Downtherm vapor heating</article-title>
.
<source>Ind Eng Chem</source>
<year>1939</year>
;
<volume>31</volume>
(
<issue>7</issue>
):
<fpage>797</fpage>
<lpage>804</lpage>
.</citation>
</ref>
<ref id="bibr28-0957650914562094">
<label>28</label>
<citation citation-type="other">
<comment>Blake DM, Moens L, Hale MJ, et al. New heat transfer and storage fluids for parabolic trough solar thermal electric plants. In:
<italic>Proceedings of the 11th SolarPACES international symposium on concentrating solar power and chemical energy technologies</italic>
, Zurich, Switzerland, 4–6 September 2002</comment>
.</citation>
</ref>
<ref id="bibr29-0957650914562094">
<label>29</label>
<citation citation-type="other">
<comment>Gomez JC, Glatzmaier GC and Mehos M. Heat capacity uncertainty calculation for the eutectic mixture of biphenyl/diphenyl ether used as heat transfer fluid. In:
<italic>SolarPACES 2012</italic>
, Marrakech, Morocco, 11–14 September 2012, paper NREL/CP-5500-56446</comment>
.</citation>
</ref>
<ref id="bibr30-0957650914562094">
<label>30</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cabaleiro</surname>
<given-names>D</given-names>
</name>
<name>
<surname>Pastoriza-Gallego</surname>
<given-names>MJ</given-names>
</name>
<name>
<surname>Piñeiro</surname>
<given-names>MM</given-names>
</name>
<etal></etal>
</person-group>
.
<article-title>Thermophysical properties of (diphenyl ether + biphenyl) mixtures for their use as heat transfer fluids</article-title>
.
<source>J Chem Thermodyn</source>
<year>2012</year>
;
<volume>50</volume>
:
<fpage>80</fpage>
<lpage>88</lpage>
.</citation>
</ref>
<ref id="bibr31-0957650914562094">
<label>31</label>
<citation citation-type="other">
<comment>Anderson WG. Intermediate temperature fluids for heat pipes and loop heat pipes. In:
<italic>15th International heat pipe conference</italic>
, Clemson, USA, 25–30 April 2010</comment>
.</citation>
</ref>
<ref id="bibr32-0957650914562094">
<label>32</label>
<citation citation-type="other">
<comment>Niggemann RE. Quarterly Progress Report No. 12 - Organic Rankine cycle technology program. Report, Sundstrand Corporation. Report No. SAN-651-96 Prepared under contract AT(04-3)-651 for the San Francisco Operations Office U.S. Atomic Energy Commission, 15 April 1965</comment>
.</citation>
</ref>
<ref id="bibr33-0957650914562094">
<label>33</label>
<citation citation-type="other">
<comment>Prasad A. Power generation from waste heat using Organic Rankine cycles systems. In:
<italic>Proceedings from the second industrial energy technology conference</italic>
, Houston, TX, USA, 13–16 April 1980, ESL-IE-80-04-116, pp.637–642</comment>
.</citation>
</ref>
<ref id="bibr34-0957650914562094">
<label>34</label>
<citation citation-type="other">
<comment>van Buijtenen JP. The Tri-O-Gen organic Rankine cycle: Development and perspectives. Technical Paper.
<italic>Power Engineer</italic>
, March 2009, pp.4–12</comment>
.</citation>
</ref>
<ref id="bibr35-0957650914562094">
<label>35</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>D-Y</given-names>
</name>
<name>
<surname>Robinson</surname>
<given-names>DB</given-names>
</name>
</person-group>
.
<article-title>A new two-constant equation of state</article-title>
.
<source>Ind Eng Chem Fundam</source>
<year>1976</year>
;
<volume>15</volume>
(
<issue>1</issue>
):
<fpage>59</fpage>
<lpage>64</lpage>
.</citation>
</ref>
<ref id="bibr36-0957650914562094">
<label>36</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Angelino</surname>
<given-names>G</given-names>
</name>
<name>
<surname>Invernizzi</surname>
<given-names>C</given-names>
</name>
<name>
<surname>Macchi</surname>
<given-names>E</given-names>
</name>
</person-group>
<article-title>Organic working fluid optimization for space power cycles</article-title>
. In:
<person-group person-group-type="editor">
<name>
<surname>Angelino</surname>
<given-names>G</given-names>
</name>
<name>
<surname>De Luca</surname>
<given-names>L</given-names>
</name>
<name>
<surname>Sirignano</surname>
<given-names>WA</given-names>
</name>
</person-group>
(eds).
<source>Modern research topics in aerospace propulsion</source>
,
<publisher-loc>New York</publisher-loc>
:
<publisher-name>Springer-Verlag</publisher-name>
,
<year>1991</year>
, pp.
<fpage>297</fpage>
<lpage>326</lpage>
.</citation>
</ref>
<ref id="bibr37-0957650914562094">
<label>37</label>
<citation citation-type="other">
<comment>Dow. Syltherm 800 heat transfer fluid. Product Technical Data, The Dow Chemical Company. Date unknown</comment>
.</citation>
</ref>
<ref id="bibr38-0957650914562094">
<label>38</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Angelino</surname>
<given-names>G</given-names>
</name>
<name>
<surname>Invernizzi</surname>
<given-names>C</given-names>
</name>
</person-group>
.
<article-title>Cyclic methylsiloxanes as working fluids for space power cycles</article-title>
.
<source>Trans ASME J Solar Energy Eng</source>
<year>1993</year>
;
<volume>115</volume>
:
<fpage>130</fpage>
<lpage>137</lpage>
.</citation>
</ref>
<ref id="bibr39-0957650914562094">
<label>39</label>
<citation citation-type="other">
<comment>3M Electronics. Thermal management fluids and services - Real world solutions for electronics industry - 3M Innovation, 3M Electronics Markets Materials Division, 2003</comment>
.</citation>
</ref>
<ref id="bibr40-0957650914562094">
<label>40</label>
<citation citation-type="other">
<comment>F2 Chemicals. Stability and compatibility of the flutec perfluorocarbons. Technical Article, F2 Chemicals Ltd, 2012</comment>
.</citation>
</ref>
<ref id="bibr41-0957650914562094">
<label>41</label>
<citation citation-type="other">
<comment>Imperial Smelting. Thermodynamic properties of Flutec PP9 in metric units. Imperial Smelting Corporation (NSC) Ltd., Avonmouth, Bristol, England. Date unknown</comment>
.</citation>
</ref>
<ref id="bibr42-0957650914562094">
<label>42</label>
<citation citation-type="other">
<comment>Imperial Smelting. Thermodynamic properties of Flutec PP2 in metric units. Imperial Smelting Corporation (NSC) Ltd., Avonmouth, Bristol, England. Date unknown</comment>
.</citation>
</ref>
<ref id="bibr43-0957650914562094">
<label>43</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Angelino</surname>
<given-names>G</given-names>
</name>
<name>
<surname>Gaia</surname>
<given-names>M</given-names>
</name>
<name>
<surname>Macchi</surname>
<given-names>E</given-names>
</name>
<etal></etal>
</person-group>
.
<article-title>Test results of a medium temperature solar engine</article-title>
.
<source>Int J Ambient Energy</source>
<year>1982</year>
;
<volume>3</volume>
:
<fpage>115</fpage>
<lpage>126</lpage>
.</citation>
</ref>
<ref id="bibr44-0957650914562094">
<label>44</label>
<citation citation-type="other">
<comment>Anderson WG, Rosenfeld JH, Agirasa D, et al. Evaluation of heat pipe working fluids in the temperature range 450 to 700 K. In:
<italic>Space technology and applications international forum – STAIF 2004</italic>
, 2004, paper CP699</comment>
.</citation>
</ref>
<ref id="bibr45-0957650914562094">
<label>45</label>
<citation citation-type="other">
<comment>Devarakonda A and Anderson WG. Thermo-physical properties of intermediate temperature heat pipe fluids. Report, NASA/CR–2005-213582, March 2005</comment>
.</citation>
</ref>
<ref id="bibr46-0957650914562094">
<label>46</label>
<citation citation-type="other">
<comment>Cole RL, Demirgian JC and Allen JW. Organic Rankine - Cycle power systems working fluids study. Report, Topical Report No. 3 – 2-Methylpyridine/Water. ANL/CNSV-TM–202 Argonne National Laboratory. September 1987</comment>
.</citation>
</ref>
<ref id="bibr47-0957650914562094">
<label>47</label>
<citation citation-type="other">
<comment>Cole RL, Demirgian JC and Allen JW. Predicting toluene degradation in Organic Rankine-Cycle engines. In:
<italic>Intersociety energy conversion engineering conference</italic>
, Philadelphia, PA, USA, 10–14 August 1987, paper no. 879075</comment>
.</citation>
</ref>
<ref id="bibr48-0957650914562094">
<label>48</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Miller</surname>
<given-names>DR</given-names>
</name>
<name>
<surname>Null</surname>
<given-names>HR</given-names>
</name>
<name>
<surname>Thompson</surname>
<given-names>QE</given-names>
</name>
</person-group>
.
<source>Optimum working fluids for automotive Rankine engines - 
<italic>Volume II - Technical section</italic>
</source>
,
<publisher-loc>St. Louis, MI</publisher-loc>
:
<publisher-name>Monsanto Research Corporation</publisher-name>
,
<year>1973</year>
.</citation>
</ref>
<ref id="bibr49-0957650914562094">
<label>49</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Somekh</surname>
<given-names>GS</given-names>
</name>
</person-group>
.
<article-title>Water-pyridine is an excellent Rankine cycle fluid</article-title>
.
<source>J Eng Power</source>
<year>1975</year>
;
<volume>97</volume>
(
<issue>4</issue>
):
<fpage>583</fpage>
<lpage>588</lpage>
.</citation>
</ref>
<ref id="bibr50-0957650914562094">
<label>50</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zamfirescu</surname>
<given-names>C</given-names>
</name>
<name>
<surname>Dincer</surname>
<given-names>I</given-names>
</name>
<name>
<surname>Naterer</surname>
<given-names>G</given-names>
</name>
</person-group>
.
<article-title>Performance evaluation of organic and titanium based working fluids for high-temperature heat pumps</article-title>
.
<source>Thermochim Acta</source>
<year>2009</year>
;
<volume>496</volume>
:
<fpage>18</fpage>
<lpage>25</lpage>
.</citation>
</ref>
<ref id="bibr51-0957650914562094">
<label>51</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Philips Pike</surname>
<given-names>F</given-names>
</name>
<name>
<surname>Foster</surname>
<given-names>C</given-names>
<suffix>Jr</suffix>
</name>
</person-group>
.
<article-title>Vapor pressure and boiling point of titanium tetrachloride</article-title>
.
<source>J Chem Eng Data</source>
<year>1959</year>
;
<volume>4</volume>
(
<issue>4</issue>
):
<fpage>305</fpage>
<lpage>306</lpage>
.</citation>
</ref>
<ref id="bibr52-0957650914562094">
<label>52</label>
<citation citation-type="other">
<comment>NIST Chemical WebBook: Standard reference database. National Institute of Standards and Technology (NIST), Gaithersburg, MD, USA. “
<ext-link ext-link-type="uri" xlink:href="http://webbook.nist.gov/">http://webbook.nist.gov/</ext-link>
” (2003, accessed 17 April 2013)</comment>
.</citation>
</ref>
<ref id="bibr53-0957650914562094">
<label>53</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hall</surname>
<given-names>EH</given-names>
</name>
<name>
<surname>Blocher</surname>
<given-names>JM</given-names>
</name>
<name>
<surname>Campbell</surname>
<given-names>IE</given-names>
</name>
</person-group>
.
<article-title>Vapor pressure of titanium tetrabromide</article-title>
.
<source>J Electrochem Soc</source>
<year>1958</year>
;
<volume>105</volume>
(
<issue>5</issue>
):
<fpage>271</fpage>
<lpage>275</lpage>
.</citation>
</ref>
<ref id="bibr54-0957650914562094">
<label>54</label>
<citation citation-type="other">
<comment>Reynolds WC.
<italic>Thermodynamic properties in SI. Graphs, tables and computational equations for 40 substances</italic>
. Stanford University, Stanford, CA, USA, 1979</comment>
.</citation>
</ref>
<ref id="bibr55-0957650914562094">
<label>55</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Invernizzi</surname>
<given-names>CM</given-names>
</name>
</person-group>
.
<source>Closed power cycles. Thermodynamic fundamentals and applications</source>
,
<publisher-loc>London</publisher-loc>
:
<publisher-name>Springer-Verlag</publisher-name>
,
<year>2013</year>
.</citation>
</ref>
<ref id="bibr56-0957650914562094">
<label>56</label>
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Pitzer</surname>
<given-names>KS</given-names>
</name>
<name>
<surname>Lippmann</surname>
<given-names>DZ</given-names>
</name>
<name>
<surname>Curl</surname>
<given-names>RF</given-names>
</name>
<etal></etal>
</person-group>
.
<article-title>The volumetric and thermodynamic properties of fluids II. Compressibility factor, vapour pressure and entropy of vaporization</article-title>
.
<source>J Am Chem Soc</source>
<year>1955</year>
;
<volume>77</volume>
(
<issue>13</issue>
):
<fpage>3433</fpage>
<lpage>3440</lpage>
.</citation>
</ref>
<ref id="bibr57-0957650914562094">
<label>57</label>
<citation citation-type="other">
<comment>Kardine WA, Agahi R, Ershaghi B, et al. Application of high speed and high efficiency hydrogen turboexpanders in refinery service. In:
<italic>Proceedings of the twenty-fifth turbomachinery symposium</italic>
, Texas A and M University, 1996, pp.95–101</comment>
.</citation>
</ref>
<ref id="bibr58-0957650914562094">
<label>58</label>
<citation citation-type="other">
<comment>General Electric. Rotoflow turbo-expanders for hydrocarbon applications. GE Power Systems, Oil & Gas, 2001</comment>
.</citation>
</ref>
<ref id="bibr59-0957650914562094">
<label>59</label>
<citation citation-type="other">
<comment>Nichols KE. How to select turbomachinery for your application. Barber-Nichols Engineering Company, Arvada, CO, USA</comment>
.</citation>
</ref>
<ref id="bibr60-0957650914562094">
<label>60</label>
<citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname>Derry</surname>
<given-names>TK</given-names>
</name>
<name>
<surname>Williams</surname>
<given-names>TI</given-names>
</name>
</person-group>
.
<source>A short history of technology - From the earliest times to AD 1900</source>
,
<publisher-loc>Oxford</publisher-loc>
:
<publisher-name>Oxford University Press</publisher-name>
,
<year>1960</year>
.</citation>
</ref>
<ref id="bibr61-0957650914562094">
<label>61</label>
<citation citation-type="other">
<comment>Martin C and Kolenc T. Study of advanced radial outflow turbine for solar steam Rankine engines. NASA Report DOE/NASA/0086-79/1, December 1979</comment>
.</citation>
</ref>
</ref-list>
<app-group>
<app id="app1-0957650914562094">
<title>Appendix</title>
<sec id="sec21-0957650914562094">
<title>Notation</title>
<p>
<def-list id="list2-0957650914562094">
<def-item>
<term>
<italic>D</italic>
</term>
<def>
<p>mean rotor turbine diameter (m)</p>
</def>
</def-item>
<def-item>
<term>
<italic>D
<sub>s</sub>
</italic>
</term>
<def>
<p>specific diameter (see equation (6))</p>
</def>
</def-item>
<def-item>
<term>LMTD
<sub>R</sub>
</term>
<def>
<p>logarithmic mean temperature difference in the recuperator (℃)</p>
</def>
</def-item>
<def-item>
<term>
<italic>N</italic>
</term>
<def>
<p>rotational speed (rpm), see equation 5</p>
</def>
</def-item>
<def-item>
<term>
<italic>P</italic>
</term>
<def>
<p>pressure (bar)</p>
</def>
</def-item>
<def-item>
<term>
<italic>P
<sub>C</sub>
</italic>
</term>
<def>
<p>condensation pressure (bar)</p>
</def>
</def-item>
<def-item>
<term>
<italic>P
<sub>cr</sub>
</italic>
</term>
<def>
<p>pressure at the critical point (bar)</p>
</def>
</def-item>
<def-item>
<term>
<italic>P</italic>
<sub>max</sub>
</term>
<def>
<p>maximum cycle pressure (bar)</p>
</def>
</def-item>
<def-item>
<term>
<italic>P
<sub>r</sub>
</italic>
</term>
<def>
<p>reduced pressure (
<inline-formula id="ilm127-0957650914562094">
<mml:math display="inline" id="mml-math127-0957650914562094">
<mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>P</mml:mi>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
)</p>
</def>
</def-item>
<def-item>
<term>
<italic>P
<sub>vp</sub>
</italic>
</term>
<def>
<p>vapor pressure (bar)</p>
</def>
</def-item>
<def-item>
<term>
<inline-formula id="ilm128-0957650914562094">
<mml:math display="inline" id="mml-math128-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>in</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>input thermal power (W)</p>
</def>
</def-item>
<def-item>
<term>
<italic>T</italic>
</term>
<def>
<p>temperature (℃)</p>
</def>
</def-item>
<def-item>
<term>
<italic>T
<sub>C</sub>
</italic>
</term>
<def>
<p>condensation temperature (℃)</p>
</def>
</def-item>
<def-item>
<term>
<italic>T
<sub>cr</sub>
</italic>
</term>
<def>
<p>temperature at the critical point (℃)</p>
</def>
</def-item>
<def-item>
<term>
<italic>T</italic>
<sub>max</sub>
</term>
<def>
<p>maximum temperature (℃)</p>
</def>
</def-item>
<def-item>
<term>
<italic>T
<sub>r</sub>
</italic>
</term>
<def>
<p>reduced temperature (
<inline-formula id="ilm129-0957650914562094">
<mml:math display="inline" id="mml-math129-0957650914562094">
<mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>T</mml:mi>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
)</p>
</def>
</def-item>
<def-item>
<term>
<inline-formula id="ilm130-0957650914562094">
<mml:math display="inline" id="mml-math130-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>out</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>isentropic turbine outlet volumetric flow rate (m
<sup>3</sup>
/s)</p>
</def>
</def-item>
<def-item>
<term>
<inline-formula id="ilm131-0957650914562094">
<mml:math display="inline" id="mml-math131-0957650914562094">
<mml:mrow>
<mml:mrow>
<mml:mover>
<mml:mrow>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>in</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>turbine inlet volumetric flow rate (m
<sup>3</sup>
/s)</p>
</def>
</def-item>
<def-item>
<term>
<inline-formula id="ilm132-0957650914562094">
<mml:math display="inline" id="mml-math132-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>specific isentropic enthalpy drop (J/kg)</p>
</def>
</def-item>
<def-item>
<term>
<italic>σ</italic>
</term>
<def>
<p>parameter of molecular complexity (see equation (1))</p>
</def>
</def-item>
<def-item>
<term>
<italic>η</italic>
</term>
<def>
<p>net cycle efficiency (
<inline-formula id="ilm133-0957650914562094">
<mml:math display="inline" id="mml-math133-0957650914562094">
<mml:mrow>
<mml:mo>=</mml:mo>
<mml:mover>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
<mml:mo>/</mml:mo>
<mml:mover>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mi>·</mml:mi>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula>
)</p>
</def>
</def-item>
<def-item>
<term>
<italic>η</italic>
<sub>max</sub>
</term>
<def>
<p>maximum cycle efficiency (
<inline-formula id="ilm134-0957650914562094">
<mml:math display="inline" id="mml-math134-0957650914562094">
<mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>-</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
)</p>
</def>
</def-item>
<def-item>
<term>
<italic>η
<sub>II</sub>
</italic>
</term>
<def>
<p>second law efficiency (
<inline-formula id="ilm135-0957650914562094">
<mml:math display="inline" id="mml-math135-0957650914562094">
<mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>η</mml:mi>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>max</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
)</p>
</def>
</def-item>
<def-item>
<term>
<inline-formula id="ilm136-0957650914562094">
<mml:math display="inline" id="mml-math136-0957650914562094">
<mml:mrow>
<mml:mi>Δ</mml:mi>
<mml:mrow>
<mml:mi>η</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>II</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</term>
<def>
<p>second law efficiency loss due to the
<italic>j</italic>
th thermodynamic irreversibility(see equation (2))</p>
</def>
</def-item>
<def-item>
<term>
<italic>ω</italic>
</term>
<def>
<p>acentric factor (
<inline-formula id="ilm137-0957650914562094">
<mml:math display="inline" id="mml-math137-0957650914562094">
<mml:mrow>
<mml:mo>=</mml:mo>
<mml:mo>-</mml:mo>
<mml:mi>log</mml:mi>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>vp</mml:mi>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>cr</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
<mml:mi></mml:mi>
<mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
<mml:mo>-</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>.</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
)</p>
</def>
</def-item>
<def-item>
<term>
<italic>ω
<sub>s</sub>
</italic>
</term>
<def>
<p>specific speed (see equation (5))</p>
</def>
</def-item>
<def-item>
<term>1, 2</term>
<def>
<p>indicate, respectively, the topping and to the bottoming thermodynamic cycle</p>
</def>
</def-item>
</def-list>
</p>
</sec>
</app>
</app-group>
</back>
</article>
</istex:document>
</istex:metadataXml>
<mods version="3.6">
<titleInfo lang="en">
<title>Binary liquid metal–organic Rankine cycle for small power distributed high efficiency systems</title>
</titleInfo>
<titleInfo type="alternative" lang="en" contentType="CDATA">
<title>Binary liquid metal–organic Rankine cycle for small power distributed high efficiency systems</title>
</titleInfo>
<name type="personal">
<namePart type="given">Paola</namePart>
<namePart type="family">Bombarda</namePart>
<affiliation></affiliation>
<affiliation></affiliation>
<affiliation>1Department of Energy, Polytechnic of Milan, Milano, Italy</affiliation>
<affiliation>2Department of Mechanical and Industrial Engineering, University of Brescia, Brescia, Italy</affiliation>
<role>
<roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Costante</namePart>
<namePart type="family">Invernizzi</namePart>
<affiliation></affiliation>
<affiliation></affiliation>
<affiliation>1Department of Energy, Polytechnic of Milan, Milano, Italy</affiliation>
<affiliation>2Department of Mechanical and Industrial Engineering, University of Brescia, Brescia, Italy</affiliation>
<role>
<roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="research-article" displayLabel="research-article"></genre>
<originInfo>
<publisher>SAGE Publications</publisher>
<place>
<placeTerm type="text">Sage UK: London, England</placeTerm>
</place>
<dateIssued encoding="w3cdtf">2015</dateIssued>
<copyrightDate encoding="w3cdtf">2015</copyrightDate>
</originInfo>
<language>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
<languageTerm type="code" authority="rfc3066">en</languageTerm>
</language>
<physicalDescription>
<internetMediaType>text/html</internetMediaType>
</physicalDescription>
<abstract lang="en">There is a common interest in the distributed power generation: generally for the combined production of electrical and thermal energy and often, although not necessarily, in association with renewable energies as heat sources for the prime mover. For example, in the field of distributed concentrated solar power generation of small size, the gas engine technology now seems to be prevailing (Stirling engines operating at maximum temperatures of 600–800 ℃, with peak net efficiencies at 20–30% and power up to several kilowatts are commonly considered). Organic Rankine engines, fed by biomass, in the power range of about 1 MW are actually a standard. From a strictly thermodynamic point of view, the binary cycle technology, accomplished by alkaline metal Rankine cycle as the topping cycle and a Rankine cycle with organic fluid as the bottoming cycle, could be an advantageous alternative. By their very nature, Rankine cycles have good thermodynamic qualities and, potentially, their thermodynamic performance, for the same maximum and minimum temperatures, could be better than that of a gas cycles. This paper discusses the possibility of adopting binary cycles with a power level in the order of tens of kilowatts. Following an overview of the characteristics of alkaline metals and a look at the possible organic fluids that can be employed in Rankine engines at high temperature (400 ℃), assuming a limit condensation pressure of 0.05 bar, the thermodynamic efficiency of binary cycles was evaluated and the preliminary sizing of turbines was discussed. The results (e.g. a net cycle efficiency of around 0.46, with maximum temperature of 800–850 ℃) appear encouraging, even though setting up the systems may be far from easy. For instance, there are difficulties due to the extremely high volumetric expansion ratios of bottoming cycles (400–600, an order of magnitude larger than those of the topping cycles with alkaline metals that we considered), which are moreover associated with a very low minimum pressure and elevated number of revolutions of the turbomachinery (50,000–200,000 r/min). Without doubt, the design tends to be easier as the power levels increase and the minimum condensation pressure for the bottoming cycle rises. Although the authors know of no activity in progress on binary cycles at present, the interesting prospects suggest the topic deserves further study and research.</abstract>
<subject>
<genre>keywords</genre>
<topic>Distributed generation</topic>
<topic>binary cycles</topic>
<topic>Rankine cycles</topic>
<topic>liquid alkali metal cycles</topic>
<topic>organic Rankine cycle</topic>
<topic>high temperature organic Rankine cycle</topic>
<topic>solar energy</topic>
<topic>thermodynamic conversion</topic>
<topic>heat engines</topic>
</subject>
<relatedItem type="host">
<titleInfo>
<title>Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy</title>
</titleInfo>
<genre type="journal">journal</genre>
<identifier type="ISSN">0957-6509</identifier>
<identifier type="eISSN">2041-2967</identifier>
<identifier type="PublisherID">PIA</identifier>
<identifier type="PublisherID-hwp">sppia</identifier>
<part>
<date>2015</date>
<detail type="volume">
<caption>vol.</caption>
<number>229</number>
</detail>
<detail type="issue">
<caption>no.</caption>
<number>2</number>
</detail>
<extent unit="pages">
<start>192</start>
<end>209</end>
</extent>
</part>
</relatedItem>
<identifier type="istex">F8928B070E8387E892808F5BFC6FFFDE2A75645A</identifier>
<identifier type="DOI">10.1177/0957650914562094</identifier>
<identifier type="ArticleID">10.1177_0957650914562094</identifier>
<accessCondition type="use and reproduction" contentType="copyright">© IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav</accessCondition>
<recordInfo>
<recordContentSource>SAGE</recordContentSource>
<recordOrigin>Institution of Mechanical Engineers</recordOrigin>
</recordInfo>
</mods>
</metadata>
<serie></serie>
</istex>
</record>

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