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Tungri

The Tungri (or Tongri, or Tungrians) were a tribe, or group of tribes, who lived in the Belgic part of Gaul, during the times of the Roman Empire. Within the Roman Empire, their territory was called the Civitas Tungrorum. They were described by Tacitus as being the same people who were first called "Germani" (Germanic), meaning that all other tribes who were later referred to this way, including those in Germania east of the river Rhine, were named after them. More specifically, Tacitus was thereby equating the Tungri with the "Germani Cisrhenani" described generations earlier by Julius Caesar. Their name is the source of several place names in Belgium, Germany and the Netherlands, including Tongeren, Tongerlo Abbey, and Tongelre.

Origins
In a comment in his book Germania, Tacitus remarks that Germani was the original tribal name of the Tungri with whom the Gauls were in contact; among the Gauls the term Germani came to be widely applied. "The name Germania, on the other hand, they say, is modern and newly introduced, from the fact that the tribes which first crossed the Rhine and drove out the Gauls, and are now called Tungrians, were then called Germani. Thus what was the name of a tribe, and not of a race, gradually prevailed, till all called themselves by this self-invented name of Germani, which the conquerors had first employed to inspire terror."

Some generations earlier, Julius Caesar, on the other hand, did not mention the Tungri but stated that the Condrusi, the Eburones, the Caeroesi and the Paemani, living in the same approximate area as the later Tungri, were "called by the common name of Germani" and had settled in Gaul already before the Cimbrian War, having come from Germany east of the Rhine. Caesar cited them as providing one collective contribution of men to the Belgic revolt against him within which the Eburones were the most important. The Eburones, who apparently lived as far east as Cologne, were led by Ambiorix and Cativolcus. Also neighbouring these tribes where the Aduatuci, whose origin Caesar describes more specifically as having descended from the Cimbri and Teutones, against whom the Germani had been the only tribe in Gaul to successfully defend themselves. Their descendants, if there were any, presumably lived amongst the Tungri.

Already during the campaign of Caesar, the Tencteri and Usipetes crossed the Rhine for cattle raids on the territories of the Menapii, the Eburones and the Condrusi, giving Caesar an excuse for new military intervention in the area. He pursued them back over the Rhine where they were helped by the Sicambri. Later, Caesar himself encouraged the Sicambri to cross the Rhine into the territory of the Eburones, seeking to plunder the lands of the people whose fortress he had just taken. These tribes who crossed the Rhine and became part of Roman Germania Inferior were themselves apparently heavily influenced by Gaulish culture, some using Gaulish personal names or Gaulish tribal names.

Later, as the area became part of the Roman Empire, some of these tribes from over the Rhine, including the Sicambri and the Ubii, were forced by Tiberius to settle in the northeast of Gaul. Romanized provinces with tribal names developed from the merging of incoming groups with people who had lived there before Caesar. This is a likely origin of both the Tungri and the other tribal groups of Germania Inferior. The Roman civitas of the Tungri is smaller than the area which Caesar ascribed to the earlier Germani Cisrhenani, with the areas near the Rhine governed as a military frontier, and populated at least partly with soldiers and immigrants from the other side of the Rhine.

The exact history of each of the populations is not known although the areas nearer to the Rhine appear to have had larger-scale immigration, and the Tungri were suspected, according to Tacitus, of having been less influenced in their makeup by that process. Smaller tribal groups such as the Condrusi (one of the Germani tribes mentioned by Caesar) and the Texuandri (perhaps the same as the Eburones) continued to exist as recognized groups for the administrative purpose of mustering troops. To the north of the Tungri, in the Rhine-Maas delta, were the Batavians, a similarly new formation, apparently made up of incoming Chatti, with a possible contribution from the Eburones. To the northeast of the Tungri, near the Rhine, were the Cugerni, who are thought to be Sicambri, and then, around the area of Cologne and Bonn, the Ubii were settled.

Location
Pliny the Elder is the first writer to mention the Tungri in Gallia Belgica, in his Natural History. He notes that their territory"...has a spring of great renown, which sparkles as it bursts forth with bubbles innumerable, and has a certain ferruginous taste, only to be perceived after it has been drunk. This water is strongly purgative, is curative of tertian fevers, and disperses urinary calculi: upon the application of fire it assumes a turbid appearance, and finally turns red"

It has been suggested that this refers to the well-known waters of Spa in the province of Liège, or else to waters found at Tongeren, which are suitably iron-bearing, and today referred to as the "Plinius bron".

Both Pliny and Ptolemy's Geography are unclear concerning the exact position of the Tungri but are understood as placing them east of the Scheldt, and to the north of the Arduenna Silva (Forest of Ardennes), along the middle and lower valley of the Mosa (Meuse).

The Eburones had a fort called Atuatuca (or Aduatuca). Caesar reported that the word Atuatuca meant a fortress. Under Roman occupation, a new city Aduatuca Tungrorum, modern Tongeren in the Limburg province of Belgium, became the capital city of the region.

Under the Romans, the Tungri civitas was first a part of Gallia Belgica, and later split out to join the territories of the Ubii to the southeast, and the Cugerni, who are generally equated with being descended from the Sicambri, to the northeast, and become part of Germania Inferior, which still later evolved into Germania Secunda. In other directions, their neighbours in Roman times were the Belgic Nervii on the west and the Remi and Treveri to the south, all of which were tribes who had been in those regions since before Caesar's campaign.

Part of the empire
Tacitus in his Histories notes two cohorts of Tungri in the civil war of 69 AD.

The Tungri were mentioned in the Notitia Dignitatum, an early fifth-century document, in which every military and governmental post in the late Roman Empire was transcribed. The document mentions the Tribune of the First Cohort of Tungri stationed at Vercovicium (Housesteads, Northumberland) on Hadrian's Wall where it was located from 205/208.

The 2nd Cohort of Tungrians, also a milliaria equitata (nominally 1000 men strong), was stationed at Birrens fort from 159 to about 184.

Cohors IV Tungrorum was based in Abusina during the second century.

Tausius, the Roman soldier who killed the emperor Pertinax, was a Tungrian.

Religion
The goddess Vihansa (probably meaning 'holy deity') is mentioned on a bronze tablet found near Tongeren and engraved by a centurion dedicating his shield and spear to the deity.

title: Tungri


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User talk:Snowspinner~enwiki/Mess of Xena articles

There are 43 42 37 30 articles on this list in all. The list is at User:Snowspinner/Mess of Xena articles. The articles were all created by User:24.19.6.250, who is a persistant vandal, defacing several mythology articles and replacing their content with stuff about Xena. Some research into these articles has shown that none of the articles are actually about characters on the television show Xena: Warrior Princess. They appear to be characters from an online RPG or from fanfiction. In any case, articles are all stubs, will never become more than stubs, and cause our information about the television show to be heavily corrupted and inaccurate. The whole lot should go. Snowspinner 01:36, 6 May 2004 (UTC) Update: I have just gone through each of these systematically. 13 of the characters were actual Xena characters. The remaining 30 on the list show no signs of being real - some are definitely fanfic characters, some appear entirely figments of the author's imagination. I invite anyone with any doubts on this matter to Google the characters and see what you find - results are either fanfic, non-English, irrelevent, or non-existant in all cases. Snowspinner 03:13, 6 May 2004 (UTC)

 * Keep all, for now. Go through them, correct the facts, then list the ones that *really* need to go on VfD invidually. You've nominated articles on Xena characters that are indeed significant characters in the show itself and should almost certainly stay -- Livia/Eve and Hope (fictional character), at least -- and there are probably others, as well. There's too great a variety here to consider them all at once. - Seth Ilys 01:44, 6 May 2004 (UTC)
 * I'm happy to remove any that are on legitimate characters if you point me towards them. I'm happy to list these all separately if you like for individual discussion, but I think that if you look at the user's edit history, as well as try doing some research on some of these articles, you'll find very little to keep. I'll look into Hope and Livia/Eve though, and pull them if needed. Snowspinner 01:50, 6 May 2004 (UTC)
 * I just checked those two out. Although they are Xena characters, the descriptions given are totally inaccurate. Livia/Eve is not the daughter of Ares, as stated in the article, and Hope's daughter is not an unknown Amazon. There may be content in these articles, and if someone wants to go through and pick out all of the accurate content, that would be one thing. But I'd rather not have this junk lying around when someone who's actually interested in productively editing articles on Xena comes along. Snowspinner 01:57, 6 May 2004 (UTC)
 * Keep, and tag them for Pages_needing_attention. Alcarillo 02:45, 6 May 2004 (UTC)
 * They've been needing attention for some time now. The ideal solution would involve a knowledgeable, dedicated Xena fan, who hasn't shown up yet.  Until then, we're better off with nothing than with all this rubbish.  Delete.   JamesMLane 04:32, 6 May 2004 (UTC)
 * OK, I've gone through the list and deleted some characters that were real. Happy to continue doing work on this as people point out real ones, but the majority of ones I'm checking do appear false. Snowspinner 02:45, 6 May 2004 (UTC)
 * A lot of these pages aren't even significant enough to link from the main Xena: Warrior Princess page. I'd keep the ones linking from there and delete the rest. Alternatively, transfer all the pages into a 'Mythos of Xena' page as subsections. -- EuroTom 02:48, 6 May 2004 (UTC)
 * The problem with merging the content is that you then have to set up the articles as redirects. It would be better to write a completely new page, and delete all those useless stubs. Delete. --Ben Brockert 03:01, May 6, 2004 (UTC)
 * Delete the unverifiable fanfic articles; keep the rest. -Sean 04:18, 6 May 2004 (UTC)
 * Delete all. Wile E. Heresiarch 05:35, 6 May 2004 (UTC)
 * Is there any sort of rule or threshold for inclusion regarding fanfic characters if they develop enough of an independent following? Not that I'm in any way voting to keep these, just wondering if there is a precedent? Rhymeless 07:01, 6 May 2004 (UTC)
 * If there's that much nonsense in this set of articles, just delete any that aren't easilly verifiable. Not worth spending lots of time on.  Even if accurate, this stuff is really fansite material anyway, so no big loss if we accidentally delete something factual.  Wikipedia is under no obligation to spend time verifying any load of rubbish that an anon submits. Isomorphic 04:53, 7 May 2004 (UTC)
 * Delete the fanfic; merge all the sub-minor characters into one article and make the others redirects. I was intending to do this, but was dissuaded by the sheer volume of work. DJ Clayworth 17:12, 7 May 2004 (UTC)
 * Delete all the fanfic articles, and merge the real ones into a single page. There seems to be a monotonous tone to the fanfic articles especially; they're all Amazon queens who become destructive goddesses.  Some of them, like Valeria, occupy namespace and stand in the way of writing (relatively) important articles about, in this case, the Robert E. Howard character, important in the Conan the Barbarian mythos.  Having these out there might mislead someone into thinking they've already been covered.  Smerdis of Tlön 00:46, 8 May 2004 (UTC)

 * This got de-listed from VfD as per time running out, but doesn't seem to have been deleted itself, nor does any action seem to have been taken on the articles. Is this because it's judged that there was no consensus to delete, or just because none of the admins were up to the admittedly daunting task of going and deleting 30 pages?
 * It's been moved to Votes for deletion/Old as part of the usual VfD cleanup. It's essentially in purgatory. An admin will get to it and do something with it sometime soon. --Ben Brockert 13:59, May 15, 2004 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Rankine cycle

The Rankine cycle is an idealized thermodynamic cycle describing the process by which certain heat engines, such as steam turbines or reciprocating steam engines, allow mechanical work to be extracted from a fluid as it moves between a heat source and heat sink. The Rankine cycle is named after William John Macquorn Rankine, a Scottish polymath professor at Glasgow University.

Heat energy is supplied to the system via a boiler where the working fluid (typically water) is converted to a high-pressure gaseous state (steam) in order to turn a turbine. After passing over the turbine the fluid is allowed to condense back into a liquid state as waste heat energy is rejected before being returned to boiler, completing the cycle. Friction losses throughout the system are often neglected for the purpose of simplifying calculations as such losses are usually much less significant than thermodynamic losses, especially in larger systems.

Description
The Rankine cycle closely describes the process by which steam engines commonly found in thermal power generation plants harness the thermal energy of a fuel or other heat source to generate electricity. Possible heat sources include combustion of fossil fuels such as coal, natural gas, and oil, use of mined resources for nuclear fission, renewable fuels like biomass and ethanol, and energy capture of natural sources such as concentrated solar power and geothermal energy. Common heat sinks include ambient air above or around a facility and bodies of water such as rivers, ponds, and oceans.

The ability of a Rankine engine to harness energy depends on the relative temperature difference between the heat source and heat sink. The greater the differential, the more mechanical power can be efficiently extracted out of heat energy, as per Carnot's theorem.

The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid. Unless the pressure and temperature reach supercritical levels in the boiler, the temperature range over which the cycle can operate is quite small. As of 2022, most supercritical power plants adopt a steam inlet pressure of 24.1 MPa and inlet temperature between 538°C and 566°C, which results in plant efficiency of 40%. However, if pressure is further increased to 31 MPa the power plant is referred to as ultra-supercritical, and one can increase the steam inlet temperature to 600°C, thus achieving a thermal efficiency of 42%. This low steam turbine entry temperature (compared to a gas turbine) is why the Rankine (steam) cycle is often used as a bottoming cycle to recover otherwise rejected heat in combined-cycle gas turbine power stations. The idea is that very hot combustion products are first expanded in a gas turbine, and then the exhaust gases, which are still relatively hot, are used as a heat source for the Rankine cycle, thus reducing the temperature difference between the heat source and the working fluid and therefore reducing the amount of entropy generated by irreversibility.

Rankine engines generally operate in a closed loop in which the working fluid is reused. The water vapor with condensed droplets often seen billowing from power stations is created by the cooling systems (not directly from the closed-loop Rankine power cycle). This "exhaust" heat is represented by the "Qout" flowing out of the lower side of the cycle shown in the T–s diagram below. Cooling towers operate as large heat exchangers by absorbing the latent heat of vaporization of the working fluid and simultaneously evaporating cooling water to the atmosphere.

While many substances can be used as the working fluid, water is usually chosen for its simple chemistry, relative abundance, low cost, and thermodynamic properties. By condensing the working steam vapor to a liquid, the pressure at the turbine outlet is lowered, and the energy required by the feed pump consumes only 1% to 3% of the turbine output power. These factors contribute to a higher efficiency for the cycle. The benefit of this is offset by the low temperatures of steam admitted to the turbine(s). Gas turbines, for instance, have turbine entry temperatures approaching 1500 °C. However, the thermal efficiencies of actual large steam power stations and large modern gas turbine stations are similar.

The four processes in the Rankine cycle
There are four processes in the Rankine cycle. The states are identified by numbers (in brown) in the T–s diagram.

In an ideal Rankine cycle the pump and turbine would be isentropic: i.e., the pump and turbine would generate no entropy and would hence maximize the net work output. Processes 1–2 and 3–4 would be represented by vertical lines on the T–s diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the state of the working fluid from ending up in the superheated vapor region after the expansion in the turbine, which reduces the energy removed by the condensers.

The actual vapor power cycle differs from the ideal Rankine cycle because of irreversibilities in the inherent components caused by fluid friction and heat loss to the surroundings; fluid friction causes pressure drops in the boiler, the condenser, and the piping between the components, and as a result the steam leaves the boiler at a lower pressure; heat loss reduces the net work output, thus heat addition to the steam in the boiler is required to maintain the same level of net work output.

Equations
$$\eta_\text{therm}$$ defines the thermodynamic efficiency of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output, it can be simplified:
 * $$ \eta_\text{therm} = \frac{\dot{W}_\text{turb} - \dot{W}_\text{pump}}{\dot{Q}_\text{in}} \approx \frac{\dot{W}_\text{turb}}{\dot{Q}_\text{in}}$$

Each of the next four equations is derived from the energy and mass balance for a control volume.

 * $$\frac{\dot{Q}_\text{in}}{\dot{m}} = h_3 - h_2,$$

 * $$\frac{\dot{Q}_\text{out}}{\dot{m}} = h_4 - h_1,$$

 * $$\frac{\dot{W}_\text{pump}}{\dot{m}} = h_2 - h_1,$$

 * $$\frac{\dot{W}_\text{turbine}}{\dot{m}} = h_3 - h_4.$$

When dealing with the efficiencies of the turbines and pumps, an adjustment to the work terms must be made:

 * $$ \frac{\dot{W}_\text{pump}}{\dot{m}} = h_2 - h_1 \approx \frac{v_1 \Delta p}{\eta_\text{pump}} = \frac{v_1 (p_2 - p_1)}{\eta_\text{pump}},$$

 * $$ \frac{\dot{W}_\text{turbine}}{\dot{m}} = h_3-h_4 \approx (h_3 - h_4) \eta_\text{turbine}.$$

Real Rankine cycle (non-ideal)
In a real power-plant cycle (the name "Rankine" cycle is used only for the ideal cycle), the compression by the pump and the expansion in the turbine are not isentropic. In other words, these processes are non-reversible, and entropy is increased during the two processes. This somewhat increases the power required by the pump and decreases the power generated by the turbine.

In particular, the efficiency of the steam turbine will be limited by water-droplet formation. As the water condenses, water droplets hit the turbine blades at high speed, causing pitting and erosion, gradually decreasing the life of turbine blades and efficiency of the turbine. The easiest way to overcome this problem is by superheating the steam. On the T–s diagram above, state 3 is at a border of the two-phase region of steam and water, so after expansion the steam will be very wet. By superheating, state 3 will move to the right (and up) in the diagram and hence produce a drier steam after expansion.

Variations of the basic Rankine cycle
The overall thermodynamic efficiency can be increased by raising the average heat input temperature
 * $$\bar{T}_\text{in} = \frac{\int_2^3 T\,dQ}{Q_\text{in}}$$

of that cycle. Increasing the temperature of the steam into the superheat region is a simple way of doing this. There are also variations of the basic Rankine cycle designed to raise the thermal efficiency of the cycle in this way; two of these are described below.

Rankine cycle with reheat
The purpose of a reheating cycle is to remove the moisture carried by the steam at the final stages of the expansion process. In this variation, two turbines work in series. The first accepts vapor from the boiler at high pressure. After the vapor has passed through the first turbine, it re-enters the boiler and is reheated before passing through a second, lower-pressure, turbine. The reheat temperatures are very close or equal to the inlet temperatures, whereas the optimal reheat pressure needed is only one fourth of the original boiler pressure. Among other advantages, this prevents the vapor from condensing during its expansion and thereby reducing the damage in the turbine blades, and improves the efficiency of the cycle, because more of the heat flow into the cycle occurs at higher temperature. The reheat cycle was first introduced in the 1920s, but was not operational for long due to technical difficulties. In the 1940s, it was reintroduced with the increasing manufacture of high-pressure boilers, and eventually double reheating was introduced in the 1950s. The idea behind double reheating is to increase the average temperature. It was observed that more than two stages of reheating are generally unnecessary, since the next stage increases the cycle efficiency only half as much as the preceding stage. Today, double reheating is commonly used in power plants that operate under supercritical pressure.

Regenerative Rankine cycle
The regenerative Rankine cycle is so named because after emerging from the condenser (possibly as a subcooled liquid) the working fluid is heated by steam tapped from the hot portion of the cycle. On the diagram shown, the fluid at 2 is mixed with the fluid at 4 (both at the same pressure) to end up with the saturated liquid at 7. This is called "direct-contact heating". The Regenerative Rankine cycle (with minor variants) is commonly used in real power stations.

Another variation sends bleed steam from between turbine stages to feedwater heaters to preheat the water on its way from the condenser to the boiler. These heaters do not mix the input steam and condensate, function as an ordinary tubular heat exchanger, and are named "closed feedwater heaters".

Regeneration increases the cycle heat input temperature by eliminating the addition of heat from the boiler/fuel source at the relatively low feedwater temperatures that would exist without regenerative feedwater heating. This improves the efficiency of the cycle, as more of the heat flow into the cycle occurs at higher temperature.

Organic Rankine cycle
The organic Rankine cycle (ORC) uses an organic fluid such as n-pentane or toluene in place of water and steam. This allows use of lower-temperature heat sources, such as solar ponds, which typically operate at around 70 –90 °C. The efficiency of the cycle is much lower as a result of the lower temperature range, but this can be worthwhile because of the lower cost involved in gathering heat at this lower temperature. Alternatively, fluids can be used that have boiling points above water, and this may have thermodynamic benefits (See, for example, mercury vapour turbine). The properties of the actual working fluid have great influence on the quality of steam (vapour) after the expansion step, influencing the design of the whole cycle.

The Rankine cycle does not restrict the working fluid in its definition, so the name "organic cycle" is simply a marketing concept and the cycle should not be regarded as a separate thermodynamic cycle.

Supercritical Rankine cycle
The Rankine cycle applied using a supercritical fluid combines the concepts of heat regeneration and supercritical Rankine cycle into a unified process called the regenerative supercritical cycle (RGSC). It is optimised for temperature sources 125–450 °C.

title: Rankine cycle


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Talk:Rankine cycle

First thing to show is p-v diagram. Why is the word steam in the intro. — Preceding unsigned comment added by 128.118.7.237 (talk) 22:05, 22 November 2020 (UTC)

Work: W=VdP vs W=-PdV
Could someone explain why in Process 3–4 the work is assumed to be equal to the change of enthalpy, rather than to the change of internal energy? For an adiabatic transformation, the work is equal to the change of internal energy (https://en.wikipedia.org/wiki/Internal_energy) dW=-PdV. For the work to be equal to VdP, the potential PV would have to be conserved ( d(PV)=0 ), which is true, for an ideal gas, only if the transformation is isothermal. Percht (talk) 21:06, 27 January 2021 (UTC)

Untitled
why is there no PV diagram? — Preceding unsigned comment added by 86.26.165.15 (talk) 12:53, 9 March 2015 (UTC)

If anyone can get the image fit more nicely on the page, feel free. I messed with it for quite a while to get it to fit at all.

I think the Equations section could use some more clarification. Varable definitions, dot represents time derivative (I assume?).--Cmprince 21:58, 10 Dec 2004 (UTC)

 * Point taken. Adding variable definitions. --ABQCat 22:01, 10 Dec 2004 (UTC)

 * Cool. I haven't had to do any thermodynamics in years, so I'd have had to dig out a book (horrors!) :) --Cmprince 22:36, 10 Dec 2004 (UTC)
 * Yeah. I noticed that there was no article on the Rankine cycle after I finished with my thermodynamics course last semester, and decided (perhaps as a form of therapy to deal with the horrid subject matter?) to regurgitate what I had managed to learn and what I found useful into this article.  Hopefully it'll help other people who are just as clueless as I was at points.  --ABQCat 22:40, 10 Dec 2004 (UTC)

Test in introduction is wrong
It is stated in the introduction that: "This cycle generates about 90% of all electric power used throughout the world". The reference is from 2000 and is only for USA. Looking at the Key World Energy Statistics 2011 published by the International Energy Agency one sees at page 24 that hydro is 16.2% in 2009. We need to also take into account Brayton cycle and combined cycles. So I am fairly new here in the editing process... do I just delete the statement. Volusteinn (talk) 18:20, 5 March 2012 (UTC)
 * I agree, I looked at some IEA reports on electricity production by fuel and I counted coal, nuclear, biomass and solar thermal. Natural gas and petrol(diesel) would be used in Brayton and Diesel cycles respectively. By my crude figure, I think we can safely say that at least 55% of world wide electricity production in 2009 was by rankine cycle steam, if all fuels above were solely used for it. Unfortunately, I have searched for world electricity production by generation method to no avail and this was the closest I got. It also means it is not a verifiable source.150.203.45.42 (talk) 03:55, 4 April 2012 (UTC)

Diagram doesn't match text
The text (correctly) describes an ideal Rankine cycle as "heated at constant pressure by an external heat source to become a superheated vapor", but the diagram shows the vapor heated to the critical vapor point, not superheated.

Anyone have a better diagram handy? -- Kaszeta 15:30, 9 August 2005 (UTC)
 * As I recall, I picked this image because I had extracted it from a government publication. Not really feeling like creating my own image (which I may spend some time on here if a search is unproductive), I used it.  Not sure if the text describing the superheating was written by me or a later contributor, but you're definitely correct about it not matching the image.
 * As a side note, and in case I'm perhaps being dense (despite having checked a few dusty textbooks), the equations were re-numbered recently such that heat processes were swapped for work processes. I'm quite certain I'm correct, but would value feedback here if I'm not.  --ABQCat 08:17, 19 December 2005 (UTC)
 * Same publication has a somewhat appropriate version of the image showing superheating. I'll take a closer look, but if it seems appropriate I'll upload it and replace the current image.  --ABQCat 01:13, 20 December 2005 (UTC)

The equations do not match the diagram. The subscripts on the enthalpies are incorrect, indicating that Qin and Qout are on the left and right sides of the figure, which is incorrect.

I've changed the equations, and I've also edited the image for clarity. --Dric dolphin 01:52, 5 September 2006 (UTC)

I have been taught by two professors, one at UCLA and one at UC Davis, that the turbine compression cannot occur within the vapor dome, otherwise you will destroy your turbine. Maybe a different diagram should be used? — Preceding unsigned comment added by Clinsoccer (talk • contribs) 06:18, 8 March 2018 (UTC)

This point is discussed under 'Real Rankine cycle (non-ideal)'. But I agree that the first T-s diagram of a typical Rankine cycle operating between pressures of 0.06 bar and 50 bar needs to be modified as it is incorrect in showing the path between 2 and 3 as following the vapor dome (which would be inconsistent with a constant pressure process). One can see this by comparing the path 2-3 for this diagram and the subsequent one, which I think is correct.Bruckner130564 (talk) 09:53, 26 August 2021 (UTC)

Efficiency
Some typical and maximum efficiency levels would be useful. Tobyw 12:14, 8 March 2006 (UTC)
 * "However, the thermal efficiency of actual large steam power stations and large modern gas turbine stations are similar." Large hardcoal fired power stations (new) have an eta_el = 46%, whereas the best gas turbine is around 40% - however CCGT go beyond >60%. So this sentence should be amended or stated more precisely. --Gunnar (talk) 06:55, 26 July 2018 (UTC)

Missing/empty link
There's an empty link,, in the Regenerative Rankine cycle subsection near the bottom. I would have fixed this myself, but I don't know what it's supposed to say.

 * It was empty as a result of vandalism by 213.181.226.27 on 26th October 2005. I fixed it.

New graph.
I've uploaded a new vector version of the graph to the wiki commons. Although I applied to make it almost pixel-perfect, I would like someone more confortable with this page to move on the article. As you're reading this, I will have marked the old image as superceded.

 MaxDZ8 talk  16:04, 24 May 2007 (UTC)

Rewrite (and a question)
I've reworded the processes section with a new diagram, Data was plotted from IAPWS IF-97 in SI units. I'll be changing other parts of the article very soon too, equations need tidying up a little and perhaps some more info about where this cycle is used and why it is used above others. Also super heating among other things needs covering. I've also made another diagram of a schematic that I'll try to include, Ts diagrams don't mean all that much to non-Engineering/Physics students. Andrew.Ainsworth 09:40, 23 August 2007 (UTC)

The section on the reversed cycle is really a red herring. All reversed cycles are refrigeration/heat pump ones. The vapour compression cycle is really derived from the Carnot rather than the Rankine cycle. Should this section just be removed? (Donebythesecondlaw 13:28, 19 September 2007 (UTC))

i have a question,do somebody known which software can make a organic Rankine cycle T-S diagram???

Various changes.
I inflict (lecture?!) thermodynamics to undergraduates,and I have made a couple of changes to this article.

I have put in a few more diagrams for the reheat and regenerative cycles. I have a load more, but I wanted to keep the size down.

I have moved the description to the top, to let people know what they are reading about.

I have also put in a few more technical bits about overall efficiencies and Carnot efficiencies.

I have also clarified the reverse Rankine cycle bit. This is still a bit tenuous and it migh be best to remove it entirely! (Donebythesecondlaw 13:32, 19 September 2007 (UTC))

New image
Replaced layout picture with better quality one, opinions? Andrew.Ainsworth (talk) 16:48, 29 November 2007 (UTC) I've just rewritten the description section, certain statements seemed ambiguous to me ("In general terms the Rankine cycle is similar to a Carnot cycle but with the compression process taking place on a liquid") and the order of material didn't seem to flow either. Perhaps a bit long now though, some of that text may belong in another part of the article really. I thought the picture was also best updated as now people can see where the phase change occurs. Andrew.Ainsworth (talk) 01:50, 30 November 2007 (UTC)

Fixed a mistake in the equations too: $$\frac{\dot{W}_{\mathit{turbine}}} {\dot{m}} = h_3 - h_4 = (h_3 - h_4,s)\times\eta_{turb}$$ where h4,s is the enthalpy after an isentropic expansion. Andrew.Ainsworth (talk) 02:00, 30 November 2007 (UTC)

Description section
What is "heat addition temperature"? --Milkbreath 16:42, 2 December 2007 (UTC)

This whole paragraph is a bit odd, and actually contradicts somewhat the next paragraph. These should be concatenated and the numbers (such as efficiencies, 42% includes boiler efficiency) reconciled. Donebythesecondlaw 16:19, 3 December 2007 (UTC)

I have tried to sort this out. Donebythesecondlaw 11:36, 4 December 2007 (UTC)

The paragraph was a bit odd on reading again. Something about the following is what I was trying to include. Perhaps the section on alternatives to the basic Rankine cycle is where it's needed. What I meant by heat addition temperature was the average temperature of heat addition defined by:

$$\bar{T}_\mathit{in} = \frac{\int_2^3 T\,dQ}{Q_\mathit{in}} $$

In a similar way the rejection temperature is defined by:

$$\bar{T}_\mathit{out} = \frac{\int_4^1 T\,dQ}{Q_\mathit{out}} $$

and the efficiency of the cycle will be given:

$$1 - \frac{\bar{T}_\mathit{in}}{\bar{T}_\mathit{out}} $$

As the exhaust temperature is constant the only factor in increasing efficiency is increasing the inlet temperature, so superheating or feedheating would be ways to go. Andrew.Ainsworth (talk) 21:42, 7 December 2007 (UTC)

I put in the first of these equations along with a description. Can anyone shrink it a bit? Donebythesecondlaw (talk) 09:55, 21 December 2007 (UTC)

Just noticed I made a mistake above, the efficiency would be given by 1 - Tout/Tin. Andrew.Ainsworth (talk) 17:55, 22 December 2007 (UTC)

Processes of the Rankine cycle section
Last sentence: what does it mean for a Rankine cycle to be "exposed"? --Milkbreath 16:54, 2 December 2007 (UTC)

Not a clue; probably best to remove it. On a separate note, how do we get the Wikipedia credibility of this raised? It is beginning to look good. Donebythesecondlaw 16:11, 3 December 2007 (UTC)

 * Don't imagine for one second that I have the first clue about thermodynamics. I don't. I just bounce around copyediting, and I like things to make sense even when I don't understand what that sense is. As for raising the profile, one can submit an article for different reviews. I believe the first step is to submit for peer review. You should probably also bring this up on the talk page for WikiProject Physics. I would do it myself, but whoever does it should be able to respond to criticisms and suggestions by altering the content, and, as I said, that ain't me. --Milkbreath 18:05, 3 December 2007 (UTC)

I have tried to sort out the "exposed" sentence. It now makes sense, but may not say the right thing. Donebythesecondlaw 11:36, 4 December 2007 (UTC)

For large central station power plants in public utility service, it is not uncommon for the boiler / turbine to operate above the critical point. This moves the turbine operation to the left on the Entropy (S) sacle, increasing the delta H (entropy) available for conversion to shaft power & thus increasing ovearll cycle efficiency. Chas in BR (talk) 20:33, 3 August 2009 (UTC) Perhaps this super-critical version could become one of the == Variations of the Rankine cycle section =="  Chas in BR (talk) 20:35, 3 August 2009 (UTC)

How about a P-v diagram?
Could come in handy for someone, you never know.

PV pdiagrams are only of interest for closed systems. As the integral of pdv is the work. — Preceding unsigned comment added by 84.51.137.53 (talk) 18:21, 9 March 2015 (UTC)

Questioning statement about lost heat of vaporization
As an engineer I once worked in a steam plant and as best I can I racall, some condensation was allowed in the turbine, up to a maximum of about 12% moisture, after which erosion of the turbine blade by the water droplets was serious. I believe the statement made at steam turbine stating 10% exit moisture is probably correct. Phmoreno (talk) 14:07, 29 October 2010 (UTC)

Inline citations
This is not my field of expertise but I would like to check the text against citations- could someone devote a little time to providing some! A start class article:= The article has a usable amount of good content but is weak in many areas, usually in referencing. This describes this perfectly- it is not a C class article till this is rectified.--ClemRutter (talk) 12:22, 5 January 2011 (UTC)

Inconsistency
If the entry temperature of steam turbines is allegedly limited to 525 degrees because of the creep limit of stainless steel,    then how do gas turbines have an entry temperature of 1500 degrees ? Why not make the steam turbines out of whatever it is that the gas turbines are made from - presumably not stainless steel. Actually I think the alleged entry temperature limit of steam turbines is spurious.Eregli bob (talk) 15:55, 2 August 2011 (UTC)

Gas turbines use different materials for blades than steam turbines. Gas turbines use Co-Cr superalloys and the blades are cast as single crystals.McNiel (1990) pps 126-8. There are technical difficulties in producing steam at ultra high temperatures: what are you going to use for boiler tubes and steam piping?Phmoreno (talk) 19:07, 2 August 2011 (UTC)

In An Encyclopedia of the History of Technology McNeil (1990), a super-critical turbine is mentioned operating with 621 C steam at the inlet, but it goes on to say that "by 1955 the average steam temperature reached its present plateau of 566 C." This is a ferretic stainless with 11-13% Cr.Phmoreno (talk) 18:56, 2 August 2011 (UTC)

Gas turbine parts exposed to hot gas are protected by various forms of air cooling. 86.181.114.173 (talk) 11:25, 14 September 2011 (UTC)

Energy loss
< This (evaporation) energy is lost to the cycle because the condensation that can take place in the turbine is limited to about 10% in order to minimize blade erosion >

This is not correct. The energy is lost to the cycle because of the second law! The shape of the saturation line (and hence the steam condition at condenser entry) has nothing to do with it. 86.181.114.173 (talk) 11:35, 14 September 2011 (UTC)

Description
'The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid'

Try as I might, I cannot make any sense of that statement. It may have to go.

109.145.108.66 (talk) 21:23, 13 July 2015 (UTC)

Assessment comment
Substituted at 03:55, 30 April 2016 (UTC)

Under the Equations for the Rankine Cycle
I feel some more detailed information should be added like this accordingly to demonstrate the stages of how the Rankine Cycle works and it would as well help when making use of the Equations in calculations on Rankine Cycle to know what equation is next for usage;

=
==========================

The Rankine Cycle works in this order continuously; Pump===>Boiler===>Turbine===>Condenser.

For Pump work

Note: The function of the ```Pump``` is to move fluid(liquid or gas) into the ```Boiler```, so in that process, a work is done, to calculate that work done, we have to use the equation below;

w(pump) = [dot]W(pump) / m(dot) = h2 - h1

For Boiler( heat addition); Note: The function of the ```Boiler``` is to increase the temperature of the fluid(liquid or gas) moved into it(the Boiler) by the Pump, so in that process, there is an added heat, to calculate the heat added, we have to use the equation below;

q(in) = [dot]Q(in) / [dot]m = h3 - h2

For Turbine work; Note: A Turbine is a rotary machine that uses the kinetic energy of a continuous stream of fluid(liquid or gas) to turn a shaft. Therefore, a turbine does a work, to find the work done by the turbine, we have to use the equation below

w(turb) = [dot]W(turb) / m(dot) = h3 - h4

For Condenser( heat rejection); Note: The function of the ```Condenser``` is to cool the temperature of the fluid extracted into it(the Condenser) by the ```Turbine```, so in that process, there is an added heat, to calculate the heat added, we have to use the equation below;

q(out) = [dot]Q(out) / [dot]m = h4 - h1

Note: the fluid(liquid or gas) extracted into the condenser from the turbine is then moved by the pump again [i.e it returns to the beginning and then repeats itself in the same sequence(Cycle)].

=
============================== Thank you. I would have loved to edit it myself, but I'm having difficulties editing the mathematical expressions, so i dont want to mess with. Its saying parse error. Victoriod (talk) 11:55, 17 July 2019 (UTC)

title: Talk:Rankine cycle


text:
Wikipedia talk:MediaWiki interface messages

I moved the page from Template:All messages to MediaWiki interface messages since it does not contain custom messages and is not a message itself. Is this OK or is this auto-generated, which perhaps makes it necessary to keep the old name?--Patrick 10:08, 17 May 2004 (UTC)

 * It was auto-generated. I expect when the MediaWiki default bot comes round again, it will overwrite Template:All messages. However, it won't matter for long as the interface and custom messages will be completely separated in MediaWiki 1.3. Angela. 20:49, May 17, 2004 (UTC)

 * Thanks.--Patrick 22:42, 17 May 2004 (UTC)

authors: Template namespace initialisation script


text:
Remi

The Remi (Gaulish: Rēmi, 'the first, the princes') were a Belgic tribe dwelling in the Aisne, Vesle and Suippe river valleys during the Iron Age and the Roman period. Their territory roughly corresponded the modern Marne and Ardennes and parts of the Aisne and Meuse departments.

Name
They are mentioned as Remi by Caesar (mid-1st c. BC) and Pliny (1st c. AD), Rhē̃moi (Ῥη̃μοι; var. Ῥημοὶ) by Strabo (early 1st c. AD) and Ptolemy (2nd c. AD), Remos by Tacitus (early 2nd c. AD), Rhēmō̃n (Ῥημω̃ν) and Rhēmoĩs (Ῥημοι̃ς) by Cassius Dio (3rd c. AD), and as Nemorum in the Notitia Dignitatum (5th c. AD).

The Gaulish ethnonym Rēmi ( sing. Rēmos) literally means 'the first ones', that is to say 'the princes'. It stems from a Proto-Celtic form reconstructed as *reimos ('first, prince, chief'; cf. Old Irish rem- 'in front of', Welsh rwyf 'prince, chief', Mid. Cornish ruif 'king'), itself from Proto-Indo-European *prei-mos ('first, leader'; cf. Latin prīmus 'furthest in front, foremost').

The city of Reims, attested ca. 400 AD as civitate Remorum (Rems in 1284), is named after the Belgic tribe.

Territory
The Remi dwelled in the Aisne, Vesle and Suippe valleys, with a heavy concentration in the middle Aisne valley. Their territory was located south of the Suessiones. As they were encircled by forests, however, the lands under their control nowhere bordered on neighbouring tribes.

La Tène period
Before the Roman conquest (57 BC), the villages of the Remi were located along natural pathways and terrestrial cross-ways such as at Nizy-le-Comte, Thugny-Trugny, or Acy-Romance, which occupied from the early 2nd century BC up until the 1st century AD. The rural areas of the Aisne valley were densely occupied and structured around trade relations with Mediterranean merchants, with large farms held by local aristocrats and bordered by numerous hamlets.

In the late 2nd–early 1st century BC, a few oppida were erected at Bibrax (Vieux Laon, Saint-Thomas), Nandin (Château-Porcien), Moulin à Vent (Voncq), La Cheppe, and Vieux Reims (Condé-sur-Suippe/Variscourt).

Roman period
At the beginning of the Roman period, the Remi left the villages and oppida that were in unfavourable positions within the emerging economic system of the Empire. For instance, the oppidum of Saint-Thomas (Bibrax) was abandoned in the middle of the 1st century BC, whereas Le Moulin à Vent, which bordered the trade route between Reims and Trier, developed into the town of Voncq, attested as Vongo vicus in the 3rd c. AD.

Durocortorum (modern Reims), a former oppidum probably built in the late 2nd–early 1st century BC and mentioned by Caesar in the mid-1st century BC, was promoted as the capital of their civitas at the end of the 1st century BC. The name of the settlement stems from the Gaulish word duron ('gates' > 'enclosed town, market town').

Secondary agglomerations of the Roman period are also known at Vervins, Chaourse, Nizy-le-Comte, Laon or Coucy-les-Eppes. Nizy-le-Comte, occupied at least until the end of the 4th century AD, probably reached around 80 hectares at its height.

La Tène period
According to archaeologist Jean-Louis Brunaux, large-scale migrations occurred in the northern part of Gaul in the late 4th–early 3rd century BC, which may correspond to the coming of the Belgae. However, those cultural changes emerged later among the Remi: whereas new funerary customs (from burial to cremation) are noticeable from 250 to 200 BC onward on the territories of the Ambi or Bellovaci, incineration did not occur before 200–150 in the Aisne valley. As such, the Remi were probably not regarded as culturally integrated to the Belgae at the time of Caesar's conquest of the region. By the mid-1st century BC, the Remi already possessed a structured economic system with monetary issuance, since they had prospered from their local agricultural production and from trade between northern Gaul and the Mediterranean area. After a period of regression in the 4th–3rd century, trade relations eventually recovered and gained in intensity during the second part of the 2nd century. A local landed nobility founded on agricultural and mining possessions subsequently emerged in the Aisne valley, and the Remi elite came to be influenced by the Latin culture through contacts with Roman merchants. Wine, in particular, was imported in large quantity from southern Europe by the local Remi elite before the Roman conquest.

Gallic Wars
During the Gallic Wars (58–50 BC), under the leadership of Iccius and Andecombogius, the Remi allied themselves with Julius Caesar:

"The Remi, the Belgic tribe nearest to Gaul, sent as deputies to him Iccius and Andecumborius, the first men of the community, to tell him that they surrendered themselves and all their stuff to the protection and power of Rome; that they had neither taken part with the rest of the Belgae, nor conspired against Rome; and that they were ready to give hostages, to do his commands, to receive him in their towns, and to assist him with corn and everything else. All the rest of the Belgae, they said, were under arms, and the Germans dwelling on the hither side of the Rhine had joined with them; and the infatuation of them all was so great that the Remi had not been able to dissuade even the Suessiones from taking part with them, though these were their own brethren and kinsfolk, observing the same law and ordinances, and sharing one government, one ruler with themselves."

They maintained their loyalty to Rome throughout the entire war, and were one of the few Gallic polities not to join in the rebellion of Vercingetorix.

When the Belgae besieged the oppidum of Bibrax (Saint-Thomas), defended by the Remi and their leader Iccius at the Battle of the Axona (57 BC), Caesar sent Numidian, Cretan and Balearic soldiers to avoid the seizure of the stronghold.

Roman period
A founding myth preserved or invented by Flodoard of Reims (d. 966) makes Remus, brother of Romulus, the eponymous founder of the Remi, having escaped their fraternal rivalry instead of dying in Latium.

Political organization
Until the Gallic Wars (58–50 BC), the Remi shared a common cultural identity with the neighbouring Suessiones, with whom with they were linked by the same law, the same magistrates and a unified commander-in-chief. In reality, this virtual state of union between the two tribes probably leaned in favour of the Suessiones. When Caesar entered Gallia Belgica in 57 BC, the Remi asked the protection of the Romans, thus gaining independence from a possibly asymmetrical relationship.

Economy
In the second part of the 2nd century BC, as the result of early trade contacts with the Mediterranean world, and encouraged by a political will to build economic relations with Rome, the Remi were the first people to issue coins in Gallia Belgica. Their oppida were responsible for the minting of coins in the late 2nd and early 1st centuries BC.

Religion
Two pre-Roman sanctuaries located at La Soragne (Bâalons-Bouvellemont) and Flavier (Mouzon) attest the religious offering of miniature weapons. In another sanctuary (Nepellier, in Nanteuil-sur-Aisne) were found Celtic sun crosses, along with destroyed weapons, coins, and human remains. Nepellier dates back to 250–200 BC and continued to be used during the Roman period until its destruction in Late Antiquity.

During the Roman period, Mars Camulus was probably the principal god of the Remi. Gallo-Roman sanctuaries are attested at Nizy-le-Comte, Versigny, and Sissonne. A statuette of Jupiter with a wheel was found in Landouzy-la-Ville. Although it features distinct Gallic characteristics, the inscription honours the Roman god Jupiter and the Imperial numen. Another inscription from Nizy-le-Comte was dedicated to Apollo.

title: Remi