The potential efficiency of the Stirling engine is higher than other comparable engines, but much more effort has been put into improving open-cycle engines. The results of comparing different engines in terms of their efficiency do not have widespread, because, as noted earlier, car manufacturers and those who operate stationary installations, as a rule, prefer to compare engines by specific effective fuel consumption. Although this parameter is directly related to efficiency,
I - limiting efficiency of the Stirling engine; 2-ultimate strength of the material; 3 - limiting efficiency of the engine with forced ignition; 4- potentially achievable efficiency of the Stirling Engine; 5 - internal combustion engines; 6 - steam engine; 7- Stirling engine.
Nevertheless, it is useful to consider the results of measuring the efficiency directly. An excellent illustration of the current performance of engines and their potential values of efficiency is the graph compiled in the work and presented in Fig. 1.110 in a slightly modified form.
The efficiency values achieved so far for the experimental Stirling engines are shown in fig. 1.111.
Efficiency of CYCLE Carnot, %
Rice. 1.111. Real efficiencies of experimental Stirling engines according to NASA, Rpt CR-I59 63I, rebuilt by the authors.
1 - data from General Motors; 2 - data from United Stirling (Sweden); 3 - data of firms "Ford" and "Philips".
B. Specific effective fuel consumption
Before comparing specific engines in terms of specific effective fuel consumption, it would be desirable to collect and summarize more information about the difference in performance between compared engines, using a combination of results from a range of typical engines each type. It should be noted that a large number of results related to Stirling engines are obtained on dynamometers, and not in vehicle tests, and some data are obtained on the basis of computer calculations of models with a sufficient degree of reliability. The results of car tests until 1980 did not coincide with the calculated data with a sufficient degree of accuracy, but they outlined ways to realize the potential of the engine. Specific effective fuel consumption of various energy power plants, intended for use as automotive energy sources, are compared in fig. 1.112.
This graph clearly shows the advantages of the Stirling engine over the entire range of operating conditions. Since the specific effective fuel consumption is considered both as a function of speed and as a function of load, in Fig. 1.113 and 1.114 show the corresponding curves for the full range of operating speeds at 50% and 20% of full load, respectively.
The advantages of the Stirling engine are very clear in this case too. Input data for these summary graphs
1-diesel with normal system intake; 2 - diesel turbocharged; 3-petrol engine with forced ignition and homogeneous charge; 4-single-shaft gas turbine; 5-double-shaft gas turbine; 6 - Stirling engine.
x*^c
■e-b in -0.2
J____ I___ I___ L
Speed/Maximum speed
Rice. 1.113. Comparison of specific effective fuel consumption of various power plants at 50% load.
1-single-shaft gas turbine; 2-shaft gas turbine; 3 - diesel turbocharged; 4-petrol engine with forced ignition and homogeneous charge; 5 Stirling engine.
They were taken from work. As fuel prices continue to rise, specific effective consumption is becoming more of a defining characteristic, and while there is continued active exploration and research into other energy sources, there is no doubt that hydrocarbon fuels will remain the main source of energy for the foreseeable future. Moreover,
Even with astronomical price increases, the reduction in fuel consumption will be negligible. Western experience shows that since the beginning of the oil crisis in the 1970s, oil prices have had little effect on fuel consumption. A study published in 1980 by the US Department of Energy showed that even a 100% increase in fuel prices would reduce fuel consumption by only
II%. If fuel consumption is not too strongly influenced by economic factors, it is unlikely that it will fall, giving in to political pressure. The impact of official regulations aimed at fuel economy is also problematic.
Obviously, the decrease in the specific effective consumption fuel consumption can help reduce fuel consumption, since a 10% reduction in fuel consumption would save, for example, over 305 million liters of imported crude oil per day for the United States, which corresponds to a saving of over $5 billion per year. Overall, however, this is a very small savings. Therefore, while reducing specific fuel efficiency is important, it does not provide a solution to the energy problem for most countries. Energy sources replacing liquid hydrocarbons may have a more tangible effect in the foreseeable future, and the problems associated with this issue will be considered later. In addition, it should be noted that the availability of energy is as significant as its cost.
B. Developed power
A valid comparison in this regard can only be made on the basis of the ratio of mass to developed power, and the compared engines must be designed for the same application. Next, it is necessary to compare the ratio of the mass of the entire power plant to the developed power. The power plant, intended for use on a car, will include transmission units, rechargeable batteries, cooling system, etc. For engines selected for comparison, these data are presented in fig. 1.115 and 1.116.
In both cases, as can be seen from the graphs, the Stirling engine does not have clear benefits, however, it must be taken into account that in the development of Stirling engines, little attention has not yet been paid to optimizing the power-to-weight ratio, which was reflected in the presented results. One cannot count on the fact that for such an optimization there are great opportunities, on the other hand, it would be wrong to say that the results achieved are the limit. In the US engine development program, which was scheduled to reach the start of production by 1984, great efforts are being made to reduce the weight of the engine. It should be borne in mind that, as shown in Table. 1.7, due to their inherent performance characteristics, Stirling engines (like single-shaft gas turbines) do not need to have the same power ratings as other engines, and therefore may be lighter than existing automotive engines.
Another factor to take into account is the size of the engine for a given power. This factor is important not only from the point of view of compactness, but, for example, when installed on a ship from the point of view of the loss of useful volume of holds. It has been established that the Stirling engine takes
Rice. 1.115. The ratio between the mass of the engine and the power it develops for power plants various types.
1- diesel with a normal intake system;
2- Stirling engine; 3-diesel turbocharged; 4 - gasoline engine with forced ignition and layered charge; 5 - gasoline engine with forced ignition and homogeneous charge; 6 - two-shaft gas turbine; 7- single-shaft gas turbine.
Rice. 1.116. The ratio between the mass of the installation and the power developed by it for power plants of various types.
1 - diesel with a normal intake system; 2 - Stirling engine; 3 - turbocharged diesel; 4 - gasoline engine with forced ignition and layered charge; G "- gasoline engine with forced ignition and homogeneous charge; 6-rotor engine with forced ignition; 7-two-shaft gas turbine; 8 - one - ial gas turbine.
Approximately the same space as an equivalent diesel. More recent data allows you to compile a summary table of the ratio of power to volume occupied for different engines power 78-126 kW (Table 1.8).
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Table 1.8. Engine power ratio R to volume V, Occupied by the power plant |
It follows from the table that positive ignition engines with a homogeneous charge still outperform all other engines in this indicator, however, promising engines with a layered charge will not have such an undeniable advantage as engines with a homogeneous charge. If ceramic components are used in Stirling engines and gas turbines, then the situation may change dramatically. At modern level technical progress the Stirling engine is generally superior diesel engines.
Stirling engine torque variations as a function of speed and pressure have already been considered in comparison with other power plants. When using this engine in a car, the features of its torque-speed characteristics are especially favorable from the point of view of the effective acceleration of the car and contribute to the simplification and cheapening of transmission units. However, to complete the picture, it is necessary to say a few words about the cyclic torque fluctuations. The literature reports that the Stirling engine has smoother torque changes compared to other reciprocating engines. "Smooth" seems to mean that the change in torque with a change in the angle of rotation of the crank of this engine is relatively small. We deliberately used the word "apparently" because
ku, when asked what exactly the term "smooth" means, we are not able to give an unambiguous definition. This issue is discussed in detail in Chap. 2. Here it will suffice to note that the changes in torque depending on the angle of rotation of the crank y multi-cylinder engine Stirling is less than, for example, an engine with forced ignition (Fig. 1.117).
Smaller torque fluctuations also mean that fluctuations angular velocity the Stirling engine is also significantly less than other engines. This statement applies, of course, to engines without flywheels. In practice, this means that Stirling engines can be equipped with a less massive flywheel and that starting a Stirling engine requires less mechanical effort. Further, due to the small cyclical fluctuations in torque and rotational speed, Stirling engines may be more suitable for stand-alone electric generators.
These claims, however, need to be verified because although the peak torque ratio e< его среднему значению у четырехцилиндрового двигателя Стирлинга без маховика близко к 1,1, для одноцилиндрового двигателя Стирлинга это значение увеличивается до 3,5, что выглядит не так уж многообещающе. Тем не менее у четырехцилиндрового двигателя Стирлинга это отношение такое же, как у восьмицилиндрового two-stroke diesel, and half that of a four-cylinder four-stroke diesel.
Estimating the cost is always difficult, and its forecast, taking into account future developments, is very inaccurate. However, there is no doubt that such an assessment is necessary to compare alternative engines, while taking into account the most expensive components. The cost of a Stirling engine is approximately 1.5 to 15 times higher than an equivalent diesel. This assessment is made on the basis of technical literature; it was presented at technical conferences and meetings. At first glance, this assessment seems unfounded, but most likely.
It is true, and this will become clear from what follows. Unsubstantiated claims about perceived value tend to make no sense, but unfortunately such claims are made in many publications. However, more detailed research in this area is now available through programs commissioned by the US Department of Energy.
The cost can be determined by various factors, of which the main ones are:
1) labor costs;
2) materials;
3) capital equipment;
4) production equipment;
5) operation and maintenance;
6) design development.
This list is by no means exhaustive. Many components of the cost directly depend on the mass production. Although this is obvious, it does not hurt to repeat this statement again, since this aspect of valuation is neglected in many publications. The dependence of the economy on the scale of output can mean that one type of engine is more expensive than another in small batches, but cheaper as production increases. It is necessary to take into account the scope of the engine. For example, the cost of a car engine is only a small fraction of the total cost of a car, so when comparing the cost various engines it must be taken into account that a significant difference in the cost of engines may not noticeably affect the cost of the car when installing these engines. This feature can be illustrated by a simple calculation. If we assume for example that the cost of an engine is 10% of the total cost of a car, then if the car costs $6,000, the engine will cost $600. Suppose another engine costs twice as much, that is, costs $1,200; Then total cost the car will be $6,600, only 10% higher, and the buyer may be willing to pay a slightly higher price for a more suitable vehicle.
Before looking at cost and costs under industrial production conditions, we would like to consider, based on our own experience, the evolution of cost when building or purchasing a prototype Stirling engine or an engine of this type intended for research purposes. The power of such engines will be considered limited to 100 kW. The purchase price of such an engine, taking into account the price level of 1981, will be about $6,700/kW. One is Io, if the engine is built by the same organization that will use it, or manufactured by a third party with detailed documentation and machine design, its cost will be in the range of 100-3500 USD/kW. As the Stirling engine becomes more mainstream and less "research", its cost will plummet. One of the manufacturers small engines Stirling (less than 1 kW) believes that with the production of 1000 such engines per year, the cost of one engine compared to its cost for individual production can decrease by 30 times.
This dependence of cost on the scale of production is confirmed by recent studies of a number of engines powered by solar energy performed by the Laboratory jet engines(USA) . A comparison was made between the Stirling engine and gas turbine in modifications designed for the use of solar energy. The gas turbine was specially designed by Garrett, and the Stirling engine was taken from a series manufactured by United Sterling. Table 1.9.
Table 1.9. Dependence of cost on output volume (comparison of Stirling engine and gas turbine)
Total unit cost, USD/kWh
The total unit cost includes the costs of paying work force, cost of materials, costs^ for capital equipment and tools. The impact of production volume on value can be clearly seen from the data presented. The total unit cost of a gas turbine with an increase in output decreases by 3 times, while the same index of the Stirling engine decreases by more than 6 times. With a small production volume, the Stirling engine is more than 50% more expensive than a gas turbine, and with an annual production of 400,000 engines, it is 30% cheaper. For our purposes, 400,000 engines per year seems a bit high, but for automotive engines, this can be considered normal.
Potential manufacturers of Stirling engines will be more interested in the estimated cost of these engines for use in automobiles. The cost of production, given in table. 1.10, take into account
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Table 1.10. Manufacturing cost automotive engines with a production volume of 400,000 pieces / year (in 1981 prices) |
It accounts for labor costs, the cost of materials, capital equipment, and tools, and is largely similar in its cost structure to that calculated for solar engines. However, in automotive version the engines have a more advanced design than in the solar engine variant. Stirling engines and gas turbines require different special materials than conventional engines. Of course, this is largely a matter of supply and market conditions, so if the Stirling engine or gas turbine were "conventional" engines, then the materials for them could have a lower cost, since the mining industry and the steel industry would be focused on the production of these materials. , and materials for the production of positive ignition engines and diesels would become "special". Moreover, special materials often require corresponding special production equipment, which contributes to the additional cost increase. Given the materials and production equipment currently used in the automotive industry, it is to be expected that, in terms of cost, conventional engines will be preferred. To clarify this aspect of the formation of manufacturing costs, in Table. 1.10 shows the cost of engines of two power ratings (75 and 112 kW) and also shows the percentage of the total cost attributable to material and production equipment.
Engine consumers are interested in sales prices, not manufacturing costs, which is not surprising. Therefore, in Table. 1.11 shows the selling prices of automobile engines with an annual output of 400,000 units. There is also a difference in price compared to the usual gasoline engine with forced ignition and homogeneous charge (GZB).
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Motor power 75 kW Motor power 112 kW Table 1.11. Selling price of automobile engines with a production volume of 400,000 units / year (in 1981 prices)
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In terms of manufacturing cost and selling price, Stirling engines are more expensive than other engines, although with a favorable production volume and application, they can become more cost-effective than their competitors. However, it is quite clear that with the increase in the power of Stirling engines and the volume of their production, they will become more and more competitive from an economic point of view. The relationship between the cost components discussed in this section is shown in fig. 1.118.
The distribution of the total cost of the Stirling engine with an oblique washer of the Ford company according to the structural elements that make up the power plant is given in Table. 1.12 for an annual output of 400,000 pcs. .
Heat exchangers have the highest relative cost, and the firm was looking to reduce this to about 17% through improved design and manufacturing technology until its Stirling engine improvement program ceased to exist.
Even if less expensive materials are used for the Stirling engine and an appropriate production volume is achieved, then even in this case the Stirling engine is unlikely to be cheaper than, say, an engine with positive ignition and a homogeneous charge. However, as discussed above, the consumer may be willing to go for additional expenses for the benefits that will be associated with this engine. If it is possible to realize the potential of the engine to save fuel and lubricating oil and an increase in the installed durability, then a decrease in the cost of operating a Stirling engine can lead to savings in the total cost of acquiring and operating
engine attack, which should impress the consumer more than environmental and energy conversion considerations. Particular attention to such savings should be paid in Western Europe, where "economical" cars with low flow fuels are becoming more popular, although the initial cost of such cars is not much less than more luxurious, but less economical
New cars. Interestingly, in the used car market, an "economy" car is often resold at a higher price than its "brothers" more high class. The calculation of the overall profitability that can be expected from the Stirling engine was performed by United Sterling for the case of installing the engine on a truck. The published data refer to the 1973 price level, but the ensuing catastrophic rise in inflation and the exponential rise in fuel and lubricant prices make it difficult to translate the results to the 1981 price level, while at the same time publishing cost estimates at the 1973 level here. hardly useful.
The economic profitability ratio (ER) was calculated using the following formula:
( Difference in cost ____ / Difference of initial H
__ Operation / V ___________________ cost _______)
In this case, the differences are determined between the corresponding indicators of the Stirling engine and the equivalent diesel engine.
From the results obtained by United Stirling and corrected by the authors (Fig. 1.119), it follows that with an operating mileage of 16,000 km per year, CER \u003d 0 after 4.1 years of operation; in other words, over this period, the lower operating costs of the Stirling engine compared to a diesel engine will balance its large initial cost, and after 5.7 years, the CEP will reach a value of 0.5, i.e., a savings equal to half the difference in the initial capital will be obtained.
Attachments. With an annual mileage of 100,000 km - the average for Europe with international road transport- the initial additional investment will pay off after 2-3 months of operation. These results are obtained for a single car. A similar calculation carried out for the motorcade would have given even more favorable results. Even this short review issues related to the cost of Stirling engines, allows us to draw a reasonable conclusion that this engine, although it has a high manufacturing cost, is potentially less expensive to operate. With a further increase in the cost of petroleum products and difficulties in acquiring them, the advantages of the Stirling engine may become even more tangible.
Although the Stirling engine can run on a variety of energy sources, it is certain that even at the beginning of the next century, hydrocarbon fuels will remain the main source of energy for land transport. This does not mean that hydrocarbon fuels will continue to be obtained from existing sources and that they will retain their modern look. This issue remains to be explored, as there may be additional economic benefits due to the ability of the Stirling engine to run on various types of fuel. Therefore, following the discussion of the manufacturability of the Stirling engine, we will consider the possibility of using alternative hydrocarbon fuels.
Although this issue is considered separately from cost, in fact, the cost of manufacture is directly related to manufacturability. However, for greater clarity of presentation, it is more convenient to consider issues related to manufacturability separately. As can be seen from Table. 1.10, the Stirling engine is more expensive than other automotive engine options; components of this cost are given in table. 1.12. The main reason for such a relative high cost of the Stirling engine is the use of high-alloy alloys for the manufacture of heat exchangers. The design of the heat exchangers involves the use of a very expensive soldering technology and expensive materials for soldering, while the length of the brazed seams is very significant. The tolerances on machined surfaces of Stirling engine parts tend to be tighter, which is a consequence of the closed working cycle. For free-piston Stirling engines, the quality of the machining is probably the most important requirement for proper engine operation.
The assembly of the main mechanical components of the Stirling engine must be done with great care, especially the assembly of the sealing devices. Any inaccuracy in the assembly will lead to engine failure. Roll-stocking seals are particularly susceptible to assembly tampering, and the installation of such a thin and fragile seal requires the utmost cleanliness of the assembly site.
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Table 1.13. Time spent on the manufacture of the engine (distribution by type of work)
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Stirling engines take approximately the same time to manufacture as other engines, but the qualifications of the personnel must be higher for the reasons mentioned above. Although assembly time may be the same as for other engines, the distribution of this time to individual operations will be different, and, of course, this may affect the overall cost. The considerations expressed in this brief discussion are confirmed by the data given in Table. 1.13 and 1.14. The total time spent on the manufacture of one engine is assumed to be 10 hours, regardless of the type of engine.
The tables show that although it takes the same amount of time to cast Stirling engine parts as it does to cast positive ignition engine parts, the cost of casting equipment for the first engine is twice as high. On this basis, the high initial investment required to build Stirling engine factories should be expected, and this probably explains the reticence of engine manufacturers when deciding on a large production program: they are waiting for the moment when all doubts that this engine will be able to realize their potential benefits. The reasons why the cost of 1 kW developed by an experimental custom-made Stirling engine is very high are also quite understandable.
G. Alternative Energy Sources
The energy crisis that occurred concerned only one source of energy - crude oil and liquid hydrocarbon fuels derived from it. Over the past decade (1971-1981), the result of the crisis has been an exponential increase in fuel prices, as well as the difficulty of maintaining secure fuel supplies. However, it must be remembered that our planet does not have unlimited reserves of crude oil, although it will be many years before the available reserves are exhausted enough to have a noticeable global impact. The crisis was exacerbated by the uneven distribution of oil across regions, so that at present there are very few countries that provide for their own oil needs, and very few countries that have such an amount of oil that they have large surpluses. Most countries are forced to import some or even all of what they need hydrocarbon fuel, which takes a significant amount of foreign currency. By 1980, 44.6% of the world's energy consumption will be met by crude oil, and this number shows the monstrous difficulty of the problem to be solved.
The structure of energy consumption varies from country to country, but we took the US consumption pattern as an example, as the US consumes more energy than any other country. The structure of consumption for 1977 is given in Table. 1.15.
The consumption of liquid hydrocarbons in the USA is similar to the global one and accounts for 48.8% of the total energy consumption, which corresponds to 795 million tons/year; 54.5% of this fuel is spent on transport needs. The US has to import 50% of the amount of oil it needs, which is about 375 million tons per year and costs many billions of dollars. Naturally, such costs encourage the search for an alternative
Tivny fuels. However, replacing liquid hydrocarbons as energy sources is a formidable task and will require many years of intensive research and development. The solution of the problem can be helped by the use of solar and geothermal energy, wind energy, but the development of these sources currently shows that in general they will not be of great importance, at least until the beginning of the next century. Nuclear power plants and hydroelectric power plants are predicted to satisfy about 15% of energy consumption by 1990. This means that about 40% of world energy consumption will remain on the share of oil. However, all these alternative sources will have little or no effect on transport oil consumption unless rail freight is increased and railroads are fully electrified. Even so, the problem of supplying railless passenger and freight transport with fuel remains. Obviously, there are three possibilities:
1) the use of fossil fuel resources other than oil;
2) the use of hydrocarbons with a lower degree of purification;
3) the use of synthetic liquid hydrocarbons.
Option 1 is associated with numerous difficulties, among which are not last place it takes to provide the energy equivalent of 795 million tons of oil, which is 4-1018 J. To ensure this equivalent, unrealistically fast rates of development of the industry of solid and gaseous fossil fuels are required. In the near future, it is possible to increase the production of these fuels at existing plants, and although this will help solve the problem, another problem will arise - how to use these fuels in modern engines.
For power plants with external heat input, such as Stirling engines and steam engines, this would not be a problem. The problem can be basically solved for a powerful stationary gas turbine. Other considered engines are not so easy to adapt to alternative fuels, as can be seen from Table. 1.16, where the sign X indicates the possibility of using this fuel, the sign OX indicates a problematic possibility of such use, and a dash means that the fuel cannot be used.
Table 1.16. Adaptability of engines to different types of fuel
Aviation
Type of fuel GZB SZB gas Diesel
Based on coal
TOC o "1-3" h z Mixture of coal dust and residue - - - - OH
Kow oil distillation
Mixture of coal dust and methanol - - - OH
Liquid fuel based on coal
Gasoline XX - -
Mixture of diesel fuel and - X - X
Jet fuels
Heavy fuel oil (fuel oil) - - X
Liquid fuels from shale
Gasoline XX-X
Mixture of diesel fuel and - X - X jet fuel
Fuel based on organo-petroleum - - X XX waste
Methanol XX XX
Hydrogen XX XX
Methane XX XX
Table data. Figure 1.16 shows that the situation is not very encouraging, and there does not seem to be much time for improvement in the case of Option 1.
Option 2 received some support in the popular press, but the octane and cetane number such hydrocarbons are insufficient for the reliable operation of existing engines. Even if these engines can be adapted to run on these fuels, the energy savings will not be as significant as it seems at first glance. It is estimated that when using less refined hydrocarbons, the savings
energy will be no more than 3.8%, and since the use of such fuels will adversely affect unit costs fuel and on the content of emissions into the atmosphere, this option is also not a solution to the problem.
Thus, the only option what remains is the production of synthetic liquid hydrocarbons, i.e. hydrocarbons obtained not from fossil oil, but, for example, from coal, oil shale, tar sands. The disadvantages of this option include high energy costs for the process of obtaining synthetic fuels. For example, liquid fuels derived from coal, especially those intended for positive ignition engines, lose up to 40% of the energy contained in the source from which they are obtained during their production. However, the production of fuel from coal, intended for the Stirling engine, does not require sophisticated technology, and much less energy would be spent on obtaining such fuel. It follows from the foregoing that in order to calculate the overall thermal efficiency of an installation operating on synthetic fuel, it is also necessary to take into account the efficiency of converting the original type of energy into its form suitable for use in this installation. The results of such calculations are presented in Table. 1.17.
Table 1.17. Thermal efficiency characterizing the conversion of energy contained in the fuel source into useful work at the engine outlet
synthetic fuel
efficiency General engine, efficiency,
Shale oil
Gas turbine SZB
Sterling engine
Based on these results, Option 3 appears to be more attractive, except that all of the promising engines for which satisfactory results have been obtained - stratified-charge positive ignition engines, turbocharged diesel engines, Stirling engines and gas turbines - require significant capital investments for production in volumes to ensure their profitability. Modified option 3 considers the possibility of using combustible mixtures composed of synthetic fuels and gasoline derived from petroleum. One such mixture that has been field tested is gasohol (10% granulated ethanol and 90% unleaded gasoline). The test results showed that this mixture has properties almost identical to those of the gasoline that forms its basis, and provides almost the same engine performance as gasoline, and the somewhat lower energy potential per unit volume of the mixture is covered by its higher octane rating. You can also use mixtures of gasoline with methanol.
The use of blends, however, will only slightly reduce the problem of oil imports, namely in proportion to the percentage of synthetic fuel in the blend. At the same time, the capital investment required to build plants for the production of relatively small quantities of such mixtures would exceed the capabilities of small countries and even many multinational companies. For example, according to estimates, it would take at least $10 billion to produce 17.2 million tons/year of gasohol by 1990 (in other words, only 2% of the total demand for liquid hydrocarbons). This calculation is made for a mixture of ethanol with gasoline in a ratio of 5: 95, so that the total amount of oil consumed will decrease by an amount equal to 5% of 2%, i.e. by 0.1%. Taking into account modern prices for oil products, such construction will cost 20 times more than the purchase of the corresponding amount of oil.
It follows from the foregoing that, although necessity forces the search for alternative sources of fuel, huge investments will be required for these sources to be able to have any influence on the pattern of fuel consumption until the end of the first quarter of the next century, especially synthetic fuels. Heavy petroleum fuels and coal can have some influence on the fuel consumption pattern of both small and large stationary power plants. For transport power plants, the only way out is to reduce fuel consumption, and this applies not only to cars, but also to marine vessels, where 72% of onboard power plants are diesel engines. Reducing fuel consumption rates, as already mentioned, only partially solves the problem: engines with significantly lower fuel consumption will have a greater impact on the energy savings problem, especially if they are able to run on different types of fuel. The Stirling engine has shown that even at the present stage of its development it can provide significant fuel savings. However, given the current intensity of research and development, these savings could be even greater. At the end of its Stirling engine program, Ford predicted a 38% reduction in fuel consumption with a 73% confidence level and an 81% reduction in fuel consumption with a 52% confidence level.
Coefficient useful action(efficiency) - a term that can be applied, perhaps, to every system and device. Even a person has an efficiency, though, probably, there is no objective formula for finding it yet. In this article, we will explain in detail what efficiency is and how it can be calculated for various systems.
efficiency definition
Efficiency is an indicator that characterizes the efficiency of a particular system in relation to the return or conversion of energy. Efficiency is a measureless value and is represented either as a numerical value in the range from 0 to 1, or as a percentage.
General formula
Efficiency is indicated by the symbol Ƞ.
The general mathematical formula for finding the efficiency is written as follows:
Ƞ=A/Q, where A is the useful energy/work done by the system, and Q is the energy consumed by this system to organize the process of obtaining a useful output.
The efficiency factor, unfortunately, is always less than one or equal to it, since, according to the law of conservation of energy, we cannot get more work than the energy spent. In addition, the efficiency, in fact, is extremely rarely equal to unity, since useful work is always accompanied by the presence of losses, for example, for heating the mechanism.
Heat engine efficiency
A heat engine is a device that converts thermal energy into mechanical energy. In a heat engine, work is determined by the difference between the amount of heat received from the heater and the amount of heat given to the cooler, and therefore the efficiency is determined by the formula:
- Ƞ=Qн-Qх/Qн, where Qн is the amount of heat received from the heater, and Qх is the amount of heat given to the cooler.
It is believed that the highest efficiency is provided by engines operating on the Carnot cycle. IN this case The efficiency is determined by the formula:
- Ƞ=T1-T2/T1, where T1 is the temperature of the hot source, T2 is the temperature of the cold source.
Electric motor efficiency
An electric motor is a device that converts electrical energy into mechanical energy, so the efficiency in this case is the efficiency ratio of the device in relation to the conversion of electrical energy into mechanical energy. The formula for finding the efficiency of an electric motor looks like this:
- Ƞ=P2/P1, where P1 - failed electric power, P2 - useful mechanical power generated by the engine.
Electrical power is found as the product of system current and voltage (P=UI), and mechanical power is found as the ratio of work to unit time (P=A/t)
transformer efficiency
A transformer is a device that converts alternating current one voltage into an alternating current of another voltage, keeping the frequency. In addition, transformers can also convert AC to DC.
The efficiency of the transformer is found by the formula:
- Ƞ=1/1+(P0+PL*n2)/(P2*n), where P0 - mode loss idle move, PL - load losses, P2 - active power delivered to the load, n - relative degree of loading.
Efficiency or not efficiency?
It is worth noting that in addition to efficiency, there are a number of indicators that characterize the efficiency of energy processes, and sometimes we can find descriptions of the type - efficiency of the order of 130%, however, in this case, you need to understand that the term is not used quite correctly, and, most likely, the author or the manufacturer understands a slightly different characteristic by this abbreviation.
For example, heat pumps are distinguished by the fact that they can give off more heat than they consume. Thus, the refrigerating machine can remove more heat from the cooled object than is spent in energy equivalent for the organization of the removal. The efficiency indicator of a refrigerating machine is called the coefficient of performance, denoted by the letter Ɛ and is determined by the formula: Ɛ=Qx/A, where Qx is the heat removed from the cold end, A is the work expended on the removal process. However, sometimes the coefficient of performance is also called the efficiency of the refrigeration machine.
It is also interesting that the efficiency of boilers operating on organic fuel, is usually calculated according to the lower calorific value, while it can turn out to be more than one. However, it is still traditionally referred to as efficiency. It is possible to determine the efficiency of the boiler by the gross calorific value, and then it will always be less than one, but in this case it will be inconvenient to compare the performance of the boilers with the data of other installations.
The work done by the engine is:
This process was first considered by the French engineer and scientist N. L. S. Carnot in 1824 in the book Reflections on the driving force of fire and on machines capable of developing this force.
The purpose of Carnot's research was to find out the reasons for the imperfection of heat engines of that time (they had an efficiency of ≤ 5%) and to find ways to improve them.
The Carnot cycle is the most efficient of all. Its efficiency is maximum.
The figure shows the thermodynamic processes of the cycle. In the process of isothermal expansion (1-2) at a temperature T 1 , the work is done by changing the internal energy of the heater, i.e., by supplying the amount of heat to the gas Q:
A 12 = Q 1 ,
Cooling of the gas before compression (3-4) occurs during adiabatic expansion (2-3). Change in internal energy ΔU 23 in an adiabatic process ( Q=0) is completely converted into mechanical work:
A 23 = -ΔU 23 ,
The temperature of the gas as a result of adiabatic expansion (2-3) decreases to the temperature of the refrigerator T 2 < T 1 . In the process (3-4), the gas is isothermally compressed, transferring the amount of heat to the refrigerator Q2:
A 34 = Q 2,
The cycle is completed by the process of adiabatic compression (4-1), in which the gas is heated to a temperature T 1.
The maximum value of the efficiency of heat engines operating on ideal gas, according to the Carnot cycle:
.
The essence of the formula is expressed in the proven WITH. Carnot's theorem that the efficiency of any heat engine cannot exceed cycle efficiency Carnot carried out at the same temperature of the heater and refrigerator.
Definition [ | ]
Efficiency
Mathematically definition of efficiency can be written as:
η = A Q , (\displaystyle \eta =(\frac (A)(Q)),)Where A- useful work (energy), and Q- wasted energy.
If the efficiency is expressed as a percentage, then it is calculated by the formula:
η = A Q × 100 % (\displaystyle \eta =(\frac (A)(Q))\times 100\%) ε X = Q X / A (\displaystyle \varepsilon _(\mathrm (X) )=Q_(\mathrm (X) )/A),Where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (refrigeration capacity in refrigeration machines); A (\displaystyle A)
For heat pumps use the term transformation ratio
ε Γ = Q Γ / A (\displaystyle \varepsilon _(\Gamma )=Q_(\Gamma )/A),Where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.
IN perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), hence for the ideal machine ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)
Modern realities involve the widespread operation of heat engines. Numerous attempts to replace them with electric motors have so far failed. Problems associated with the accumulation of electricity in autonomous systems are solved with great difficulty.
Still relevant are the problems of technology for the manufacture of electric power accumulators, taking into account their long-term use. Speed characteristics electric vehicles are far from those of cars on internal combustion engines.
The first steps towards the creation of hybrid engines can significantly reduce harmful emissions in megacities, solving environmental problems.
A bit of history
The possibility of converting steam energy into motion energy was known in antiquity. 130 BC: Philosopher Heron of Alexandria presented to the audience a steam toy - aeolipil. A sphere filled with steam began to rotate under the action of jets emanating from it. This prototype of modern steam turbines did not find application at that time.
For many years and centuries, the development of the philosopher was considered only a fun toy. In 1629, the Italian D. Branchi created an active turbine. Steam set in motion a disk equipped with blades.
From that moment began the rapid development steam engines.
heat engine
The conversion of fuel into energy for the movement of parts of machines and mechanisms is used in heat engines.
The main parts of machines: a heater (a system for obtaining energy from outside), a working fluid (performs a useful action), a refrigerator.
The heater is designed to ensure that the working fluid has accumulated a sufficient supply of internal energy to perform useful work. The refrigerator removes excess energy.
The main characteristic of efficiency is called the efficiency of heat engines. This value shows what part of the energy spent on heating is spent on doing useful work. The higher the efficiency, the more profitable job machine, but this value cannot exceed 100%.
Efficiency calculation
Let the heater acquire from outside the energy equal to Q 1 . The working fluid did work A, while the energy given to the refrigerator was Q 2 .
Based on the definition, we calculate the efficiency:
η= A / Q 1 . We take into account that A \u003d Q 1 - Q 2.
From here, the efficiency of the heat engine, the formula of which has the form η = (Q 1 - Q 2) / Q 1 = 1 - Q 2 / Q 1, allows us to draw the following conclusions:
- Efficiency cannot exceed 1 (or 100%);
- to maximize this value, either an increase in the energy received from the heater or a decrease in the energy given to the refrigerator is necessary;
- an increase in the energy of the heater is achieved by changing the quality of the fuel;
- reducing the energy given to the refrigerator, allow you to achieve design features engines.
Ideal heat engine
Is it possible to create such an engine, the efficiency of which would be maximum (ideally, equal to 100%)? The French theoretical physicist and talented engineer Sadi Carnot tried to find the answer to this question. In 1824, his theoretical calculations about the processes occurring in gases were made public.
The main idea embedded in an ideal machine can be considered to be the carrying out of reversible processes with ideal gas. We start with the expansion of the gas isothermally at a temperature T 1 . The amount of heat required for this is Q 1. After the gas expands without heat exchange. Having reached the temperature T 2, the gas is compressed isothermally, transferring the energy Q 2 to the refrigerator. The return of the gas to its original state is adiabatic.
The efficiency of an ideal Carnot heat engine, when accurately calculated, is equal to the ratio of the temperature difference between the heating and cooling devices to the temperature that the heater has. It looks like this: η=(T 1 - T 2)/ T 1.
The possible efficiency of a heat engine, the formula of which is: η= 1 - T 2 / T 1 , depends only on the temperature of the heater and cooler and cannot be more than 100%.
Moreover, this ratio allows us to prove that the efficiency of heat engines can be equal to unity only when the refrigerator reaches temperatures. As you know, this value is unattainable.
Carnot's theoretical calculations make it possible to determine the maximum efficiency of a heat engine of any design.
Proven Carnot theorem sounds like this. An arbitrary heat engine under no circumstances is capable of having a coefficient of efficiency greater than the similar value of the efficiency of an ideal heat engine.
Example of problem solving
Example 1 What is the efficiency of an ideal heat engine if the heater temperature is 800°C and the refrigerator temperature is 500°C lower?
T 1 \u003d 800 o C \u003d 1073 K, ∆T \u003d 500 o C \u003d 500 K, η -?
By definition: η=(T 1 - T 2)/ T 1.
We are not given the temperature of the refrigerator, but ∆T = (T 1 - T 2), from here:
η \u003d ∆T / T 1 \u003d 500 K / 1073 K \u003d 0.46.
Answer: efficiency = 46%.
Example 2 Determine the efficiency of an ideal heat engine if 650 J of useful work is performed due to the acquired one kilojoule of heater energy. What is the temperature of the heat engine heater if the coolant temperature is 400 K?
Q 1 \u003d 1 kJ \u003d 1000 J, A \u003d 650 J, T 2 \u003d 400 K, η -?, T 1 \u003d?
In this problem, we are talking about a thermal installation, the efficiency of which can be calculated by the formula:
To determine the temperature of the heater, we use the formula for the efficiency of an ideal heat engine:
η \u003d (T 1 - T 2) / T 1 \u003d 1 - T 2 / T 1.
After performing mathematical transformations, we get:
T 1 \u003d T 2 / (1- η).
T 1 \u003d T 2 / (1- A / Q 1).
Let's calculate:
η= 650 J / 1000 J = 0.65.
T 1 \u003d 400 K / (1- 650 J / 1000 J) \u003d 1142.8 K.
Answer: η \u003d 65%, T 1 \u003d 1142.8 K.
Real conditions
The ideal heat engine is designed with ideal processes in mind. Work is done only in isothermal processes, its value is defined as the area bounded by the Carnot cycle graph.
In fact, it is impossible to create conditions for the process of changing the state of a gas without accompanying changes in temperature. There are no materials that would exclude heat exchange with surrounding objects. The adiabatic process is no longer possible. In the case of heat transfer, the temperature of the gas must necessarily change.
The efficiency of heat engines created in real conditions differ significantly from the efficiency of ideal engines. Note that the processes in real engines occurs so rapidly that the variation in the internal thermal energy of the working substance in the process of changing its volume cannot be compensated by the influx of heat from the heater and return to the cooler.
Other heat engines
Real engines operate on different cycles:
- Otto cycle: the process at a constant volume changes adiabatically, creating a closed cycle;
- Diesel cycle: isobar, adiabat, isochor, adiabat;
- the process occurring at constant pressure is replaced by an adiabatic one, closing the cycle.
Create equilibrium processes in real engines (to bring them closer to ideal ones) under conditions modern technology does not seem possible. The efficiency of heat engines is much lower, even taking into account the same temperature conditions, as in an ideal thermal installation.
But do not reduce the role of the calculated efficiency formulas because it becomes the starting point in the process of working on increasing the efficiency of real engines.
Ways to change efficiency
When comparing ideal and real heat engines, it is worth noting that the temperature of the refrigerator of the latter cannot be any. Usually the atmosphere is considered to be a refrigerator. The temperature of the atmosphere can be taken only in approximate calculations. Experience shows that the temperature of the coolant is equal to the temperature of the exhaust gases in the engines, as is the case in internal combustion engines (abbreviated internal combustion engines).
ICE is the most common heat engine in our world. The efficiency of a heat engine in this case depends on the temperature created by the burning fuel. A significant difference between an internal combustion engine and steam engines is the merging of the functions of the heater and the working fluid of the device into air-fuel mixture. Burning, the mixture creates pressure on the moving parts of the engine.
An increase in the temperature of the working gases is achieved by significantly changing the properties of the fuel. Unfortunately, it is not possible to do this indefinitely. Any material from which the combustion chamber of an engine is made has its own melting point. The heat resistance of such materials is the main characteristic of the engine, as well as the ability to significantly affect the efficiency.
Motor efficiency values
If we consider the temperature of the working steam at the inlet of which is 800 K, and the exhaust gas is 300 K, then the efficiency of this machine is 62%. In reality, this value does not exceed 40%. Such a decrease occurs due to heat losses during heating of the turbine housing.
The highest value of internal combustion does not exceed 44%. Increasing this value is a matter of the near future. Changing the properties of materials, fuels is a problem that is being worked on the best minds humanity.
