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To be continued . . .
Airship Propulsion, Part Three, Steaming Along
Written by Iver P. Cooper
In Part Two, I set forth the criteria for an airship engine, briefly discussed some of the options, and explained the advantages and disadvantages of the internal combustion engine. Now we'll examine the principal alternative, steam propulsion.
Small steam engines are built in the 1632 universe as early as January 1632. (Bergstralh, "Tool or Die," Grantville Gazette 9). As far as I can tell, the first steam locomotive is in operation in late 1632. (Flint and Zeek, "The Suhl Incident," 1634: The Ram Rebellion). Steam propulsion never caught on for aircraft, because the powerplants had a low power-to-weight ratio. Nonetheless, the Danish Royal Anne is reportedly equipped with "mono-tube steam generators, condensers, and uniflow steam engines. " (Evans, "No Ship for Tranquebar, Part Two," Grantville Gazette 28).
There is no doubt that airships can employ steam propulsion; the 1852 Giffard airship stands as proof. Rather, the question is whether steam engines will be competitive with internal combustion engines. A large airship is likely to cost considerably more than even a naval fleet flagship. Consequently, investors (private or public) will need to be persuaded that the proposed propulsion system will provide the desired performance.
In the competition for funds, steam proponents will be at a disadvantage. While steam locomotives enjoyed more than a century of success, the same cannot be said of steam airplanes or airships. Hence, one cannot make the argument, "it made lots of money in the old time line."
The three great potential weaknesses of steam propulsion for airships are low thermal efficiency, low power-weight ratio (relative to gasoline but not diesel engines), and high maintenance costs. (I assume that steam engines for airships will be of the condensing type, i.e., will recycle their water, and thus water supply will not be an issue except as the condenser affects weight and maintenance). In this article, we will explore just how serious these weaknesses are, and whether they can be alleviated.
Steam propulsion also has its strengths, notably low initial costs, an ability to use a greater variety of fuels (including coal, wood, and heavy oil), and insensitivity of power delivered to altitude. (Odom). However, the fuel diversity advantage comes with the caveat that use of fuel of low energy density means that to maintain range one must carry a greater weight of fuel (and thus less payload).
There are railfans and steamheads in Grantville, and their personal libraries may well provide useful technical information about twentieth-century steam locomotive and car designs. However, this is something of a double-edged sword, as it will reveal that the steam locomotive was eclipsed by diesel-electric and straight electric locomotives because of higher fuel, watering and maintenance costs, and that steam cars were likewise defeated in the marketplace by gas-powered cars. (The steamheads may argue that advanced steam technology would have overcome these problems, but the financiers could still reject their proposals as too speculative.)
Thermal Efficiency of Steam Propulsion
Stationary steam powerplants can achieve very high efficiencies, perhaps 50% (Semmings 162), but they also use much higher pressures and boiler temperatures than any vehicular plant, and are equipped with subatmospheric condensers and other refinements that add weight and cost.
The steam locomotive evolved in a period in which fuel (wood, coal or oil) was cheap and therefore little concern was given to thermal efficiency. As Ennis (354) aptly states, "the aim in locomotive design is not the greatest economy of steam, but the installation of the greatest possible power-producing capacity in a definitely limited space."
In The American Diesel Locomotive, Solomon explained, "During the nineteenth century, the best steam engines operated at about 6 percent thermal efficiency, a figure that climbed to 10 to 12 percent by the end of the steam era." (13). Even that figure was tarnished by his The American Steam Locomotive, which said, "At optimum performance, the modern steam locomotive can theoretically produce a maximum of 12 percent thermal efficiency, but 6 to 8 percent is the maximum achievable in actual operation." (120).
We need to be very precise as to what these numbers mean. Usually, steam locomotive efficiency is quoted as overall drawbar efficiency. That's the product of (1)–(6) below.
Efficiency may also be quoted as the overall wheel rim efficiency, which is the product of just (1)–(5). I have overall wheel rim efficiencies for the South African Railway steam locomotives 19D (4.0%), 24 (3.9%), 25NC (3.2%), GMA/M (2.4%) and 26 (4.8%). In contrast, the SAR diesel locomotives scored much higher: 31 (23.1%), 32-000 (22.2%), 35-000 (23.0%). (Wardale 44, 290).
Since we would be hooking the steam powerplant up to a propeller shaft, we need to find the overall cylinder efficiency, the product of (1)–(4).
In the mid-twentieth century, a typical steam locomotive had an overall boiler efficiency of 72%, a cylinder efficiency of 14%, and transmission efficiency of 90%; that would imply an overall cylinder efficiency of at best 9%. (Cox 178).
It is interesting to see efficiency breakdowns for some real (standard and second generation) and hypothetical (second and third generation) locomotives (Table S2). Steam proponents are quick to urge that the actual locomotive numbers can be bettered. Porta envisioned "second generation steam" (SGS) as featuring 290–362 psi pressure, 450oC steam, double expansion, a gas producer combustion system, feedwater treatment to minimize scaling, corrosion, etc., feedwater and combustion air preheating, and an advanced (Lempor) exhaust system; Porta prophesied that this could achieve 14% efficiency. His concept of third generation steam (TGS) added higher pressure (870 psi) and temperature (550oC), triple expansion, and multistage feedwater and combustion air heating, hopefully achieving 21% efficiency, or even 27% if a condenser were provided. (Rhodes). But this author is not inclined to put much faith in efficiency figures for hypothetical engines, and Wardale's claims for his own hypothetical SGS modifications (grey columns in table S2) were more conservative.
The numbers above present only part of the picture, as we have no idea of the circumstances under which efficiency was measured. It can vary depending on the feedwater temperature, the fuel, the firing rate, the actual (vs. design) boiler pressure, and the moment in the piston stroke at which the inlet valve is closed (cutoff). (Hudson).
Cylinder Efficiency
The lowest efficiency in table S2 is the cylinder efficiency. Let's look at what theory tells us is the highest possible value, to put this in better perspective.
Steam engines are true heat engines; their working fluid (water) cyclically receives heat from a high temperature source (boiler), converts some of the heat energy to work (steam-driven piston movement), and reject the remaining waste heat to a heat sink (condenser or outside air). The theoretical (Carnot cyle) maximum efficiency is expressed by the equation
ECarnot=1-(Tsink/Tsource)
with temperatures in oK.
All reversible heat engines have the same thermal efficiency when operating between the same two temperatures; all real-life heat engines have lower efficiencies than the corresponding reversible heat engines.
For a variety of reasons, real-life heat engines don't even come close to approximating a Carnot cycle. The Rankine cycle is less efficient, but provides a better model of what happens in a real steam engine. A hidden limitation on the efficiency of the water-steam Rankine cycle is that some heat must be used to change water into steam (unless boiler pressure is supercritical) and this heat doesn't do any useful work.
Calculating the efficiency of a Rankine cycle is much more complicated than doing so for a Carnot cycle, as you must consider the enthalpy and entropy of the steam at various temperatures and pressures, and steam under the typical conditions does not behave like an "ideal gas." I have no doubt that the Grantville power plant (coal-fired steam turbine) engineers can make the admittedly complex thermodynamic efficiency calculations. All you need are steam tables (these exist in CRC and Marks'
Handbook) and knowledge of the thermodynamic relationships. I wrote my own spreadsheet and tested it against multiple thermodynamic textbook examples, so I know it can be done.
As shown in table S3, for a non-condensing locomotive with a mere 50 psi boiler pressure, even the theoretical efficiency is only a little over 6%. The theoretical efficiency of the Rankine cycle may be increased by a variety of means.
Three expedients—increasing boiler pressure, superheating the steam, and heating the feedwater to the boiler—were used reasonably frequently as the steam locomotive evolved.
Boiler pressure. To safely increase the boiler pressure, you need a higher tensile strength structural metal (steel is superior to wrought iron), a greater thickness of metal (thus, a heavier boiler), or a smaller diameter boiler. Looking at locomotive data available in Grantville, I see pressures of 50 psi (1830), 130 (1860), 180 (1880), 190 (1900). (Alexander). EB11 Table XII lists locomotives up to 235 psi, and Halberstadt, Working Steam, up to 300. "In practice, for locomotives there is an optimum in the range 200–300 psig." (Semmens 152ff).
Steam locomotives were occasionally constructed with pressures above 350 psi, but none were particularly successful. Scale and corrosion problems increased, and distilled water had to be used in a closed circuit as in the Schmidt system. The increased acquisition and maintenance costs were found not to be justified by the efficiency gain. (HPSLT). However, historical steam car engines ran at higher pressures, typically 400–1200 psi. (Crank).
Superheating. This is heating the water beyond its boiling point, which not only increases efficiency, but also decreases moisture content, rendering the steam less corrosive. However, higher temperatures can weaken or even melt the steam containment structure. For carbon steel, the highest allowable temperature is 950oF. (Ganapathy). Superheating may also dictate use of high-temperature lubricants.
Using exhaust steam or combustion gases in the flue, you can increase temperatures perhaps 24–40oF, which is sufficient to dry the steam. For a greater effect, the superheater must be exposed to hotter temperatures. In an integral superheater, the superheater is inside the firebox, preferably in a zone with temperatures of at least 1000oF (the higher the temperature and the greater the superheater surface, the greater the heating effect). Or the superheater may be separately fired; it was found that the superheater could use a cheaper grade of coal. In early twentieth-century stationary plants, integral superheaters could achieve up to 300oF and separately fired ones at least 500oF (but the efficiency of the separate superheater was only 25%). (Ennis 428, Jude 252).
According to Marks, Mechanical Engineers' Handbook 1216 (1922), typically up to 250oF (139oC) superheat was used on locomotives.
Feedwater heating. Exhaust steam may be used to preheat the feedwater for the boiler. Preheating to 150oF theoretically increases cycle efficiency by 0.7% in a 105 psi boiler and 1% in a 285 psi boiler. (Lamb 38). Exhaust steam at best increases the feedwater temperature to the atmospheric boiling point (212oF) (Ennis 429); that is, it causes a non-condensing engine (open cycle) to have the efficiency of an atmospheric condensing (closed cycle) one.
A second option, used in the "economizer," employs the waste gas from the furnace. This can achieve a feedwater temperature of 300oF or more. (Ennis).
Steam may be deliberately bled off at an intermediate expansion state to heat the feedwater (regenerative heating) instead of being used to do work. While less work is done, the heat is used more efficiently. Stationary powerplants may have a series of feedwater heaters at different bleed points.
In an open feedwater heater, the steam is mixed directly with the feedwater (or condenser water), and in a closed one, heat transfer is permitted without physical mixing. For the former, the feedwater temperature achievable is limited by the saturation temperature corresponding to the pressure of the hot water pump, whereas the latter requires scaling up the heat exchanger tubes. (Wardale 157). Also, the former captures lubrication oil from the cylinder and mixes it into the boiler feedwater, whereas the additional piping of the latter is prone to leaks.
Both types were used on locomotives; the "Worthington" was open and the Elesco and Coffin were closed. (Barris). The weight of a feedwater heater was perhaps one ton for a 200 ton locomotive, and it increased sustained boiler capacity by 15% (closed) or 17% (open). (Wardale 156). While the feedwater heater was invented earlier, only three units were sold in the USA before 1919. "By 1936 heaters were in use on perhaps a fourth of all steam locomotives in services, and were built into all new steam locomotives." (Hultgren 224).
Table S3NC shows the effect of different boiler pressures and degrees of superheat, and in one instance feedwater heating, on theoretical cycle (cylinder) efficiency and steam quality for several actual locomotives (the first two are in Grantville Literature), as well as some hypothetical variations.
(Exhaust is at 170.3 kPa, 10 psig. (Lamb 36). QJ locomotive had a feedwater heater but the extraction pressure is not reported and so efficiency calculation ignores it; the other locomotives didn't have one.)
Several other expedients were rarely or never used in locomotive practice, but could be applied to an airship engine (with varying degrees of practicality).
Condenser pressure. Generally speaking, locomotive steam engines weren't equipped with condensers and thus operated on an open Rankine cycle. The few exceptions were those operating in arid regions or close to a front line (where the concern was that the exhaust plumes could be spotted by enemy aircraft).
The 1917 Stanley Steamer had a primitive condenser (closed Rankine cycle) that operated at normal pressure thus the heat sink temperature was 212oF.
Reducing condenser pressure further (by cooling) lowers the "rejection" temperature and thus improves efficiency. It unfortunately increases moisture content and thus both drag force (Vosough) and corrosion. The condenser pressure cannot be lower than "the saturation pressure corresponding to the saturation temperature of the cooling medium" and because of heat flow considerations will need to be higher. For example, a stationary plant using water cooling might condense to a pressure for which the saturation temperature is 10oC higher than water temperature. (Cengel 522). Ennis (332) says that "condensing water is generally not available at temperatures below 60o or 70oF."
Bear in mind that the lower the pressure, the more susceptible the system is to leakage; in the early 1900s, the minimum condenser pressure was perhaps 1 psia (Ennis 318) and that's still a practical limit (Vosough). The initial cost also increases nonlinearly; in 1906 a 27" vacuum (0.147 psia) costs 20% more, and a 28" (0.98), 57% more, than a 26" (1.96) (Jude 246).
While condensers are common in stationary plants, "it is much harder to accommodate an adequate condenser on a locomotive which has to be mobile and whose size is constrained by the loading-gauge." (Semmens 155). Also note that "there is an element of danger involved in returning condensed steam from reciprocating engines to the boilers, on account of the cylinder oil it contains." (Ennis 431).
Unlike condensers for stationary or marine plants, which dump heat into rivers or the ocean, those for land or air vehicles cannot rely on water as the ultimate cooling medium; the water remains on board, and would get hotter and hotter, eventually turning to steam itself. Rather, the water is used just as a heat exchange medium, transporting the heat to a radiator which dumps it into the atmosphere. The airship condenser and radiator, in combination, must—in sustained operation—continue to remove enough heat so as to restore steam to its liquid state, whereas a car radiator only must get rid of enough heat so that the engine doesn't overheat.
But air, at sea level temperature and pressure, has only about 1/4 the heat capacity per unit weight and 1/3,500th the heat capacity per unit volume. And the heat conductivity of air is less that 1/10th that of water, which reduces the efficiency of heat exchange. (Valentine). The faster the engine is running, the greater the steam flow rate and therefore the greater the cooling rate needed.
Normally, a locomotive will use the e
xhaust steam, funneled into blast pipes, to create a strong draft and thereby achieve a high rate of combustion. With a condensing plant, you need an alternative source of forced draft, such as (on the SAR 25C) a turbine driven by the exhaust steam before it was condensed. (Smith).
Reheating. At an intermediate stage of expansion, the steam can be reheated by passing it in fire tubes back through the boiler, thus restoring it to the inlet temperature. This dries out the steam, improving its quality, and also increases efficiency slightly. Reheat was first used in a stationary power plant in the 1920s. Reheat was used in the SNCF 160 A-1 (1940) compound expansion locomotive; the reheater was essentially a Schmidt superheater.
For a single reheat, the optimum extraction pressure from an efficiency standpoint is usually at about 20–25% of the boiler pressure. (Srinivas). Ideally, the steam is extracted when it is no longer superheated but still of high quality (low moisture). Consequently, a second reheat stage is typically used only in plants operated at very high (supercritical) pressures (3500 psia). The efficiency improvement from a second stage is likely to be something like half that of the first stage. (Logan, 443).
Table S3C shows the effect of condenser pressure, reheating, and/or feedwater heating on locomotives modified for condensing operation, on the Stanley Steamer, and on the Besler Steam Plane, the last being the most efficient.
(If reheat, to boiler temp.)
Remember, cylinder (cycle) efficiency is only part of the picture; boiler efficiency is very important.
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Of course, a real life steam powerplant doesn't achieve the theoretical cycle efficiency because of various "irreversibilities," such as fluid friction, incomplete absorption of heat from the combustion gases, and heat losses from the steam to the surroundings (Ennis 301ff, Cengel 519ff). For stationary plants, the actual efficiency is typically 40–80% (usually 50–70%) of the theoretical one (Ennis 398); figure 60–70% if high superheat is used. (399). In table S3, in the case of the locomotives for which we have both actual and theoretical cylinder efficiencies, the former was 68–85% of the latter. I am inclined to assume an actual/theoretical efficiency ratio of 70% for back-of-the-envelope calculations.