Classification of Thermodynamic Cycles!
Thermodynamic Cycle # I. Carnot Cycle:
It consists of two isothermal processes and two isentropic processes. This cycle is represented on temperature-entropy and pressure-volume diagrams as shown in fig. 2-34.
Consider one kg of air at temperature T1 as the working fluid in the engine cylinder.
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Let point 1 (fig. 2-34) represent the state of the working fluid as regards pressure P and volume V at absolute temperature T1.
(1) Isothermal Expansion:
At point ‘a’ the hot body at temperature T1 is brought in contact with the cylinder head at AB and heat is supplied at temperature T1 to the working fluid (air). This causes the air to expand isothermally along the curve ‘a-b’ from volume V2 to V3 until point ‘b’ is reached. This point is the end of isothermal expansion. The temperature through this process ‘ab’ has been maintained constant at T1. As the air expands, it forces the piston outward thus doing work on the piston.
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(2) Isentropic Expansion:
At point ‘b’ the hot body is removed and replaced by the non-conductor cover. Since all the elements of the engine which are now in contact with the working fluid (air) are non-conductors, no heat can be added or abstracted from the air. The air now expands isentropically along curve 3-4 doing work on the piston at the expense of its internal energy. Consequently the temperature falls from T1 to T2 and the volume increases from V3 to V4. At point ‘c’ the piston is at the end of the outward stroke.
(3) Isothermal Compression:
At point ‘c’ the non-conducting cover is removed and the cold body at temperature T2 is brought in contact with the conducting cylinder head at AB. The piston now moves inward compressing the air isothermally along the curve ‘ c-d’ from volume V4 to V1, until point 1 is reached. During this compression, the heat which is rejected by the air goes into the cold body. This makes the isothermal compression at constant temperature T2 possible.
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(4) Isentropic Compression:
At point 1 the cold body is removed and the non-conducting cover again takes the position at AB. The air is now isentropically compressed along the curve 1-2 until it reaches the starting point 1 of the cycle, where it resumes its initial conditions of temperature, pressure and volume, and the piston is returned to the end of the stroke.
Since no transfer of heat occurs during both isentropic operations, by the law of conservation of energy, the difference between the heat received and heat rejected must be equal to the net work done. The process is considered to be a non-flow process.
The corresponding heat and work of each process are shown in the following table 2-9.
We assume that the unit mass takes part in various processes of the cycle.
The Carnot cycle efficiency depends on temperature of heat source and heat sink. This cycle is an ideal cycle and cannot be implemented because isentropic compression and expansion cannot be obtained in actual system. The isothermal heat addition and rejection is difficult to obtain.
Thermodynamic Cycle # II. Otto Cycle:
The cycle in which heat is added at constant volume is the prototype of the actual cycle used in engines with spark ignition (automobiles, aircraft, etc.).
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Such engines are distinguished by compression of the fuel mixture (mixture of fuel vapour with air). The constant volume cycle or Otto cycle is sketched on temperature-entropy and pressure-volume diagram as shown in fig. 2-35.
This cycle consists of two isentropic processes and two constant volume processes. The isentropic line 1-2 corresponds to compression of the combustible mixture, constant volume line 2-3 to combustion of mixture (addition of heat), resulting in a rise in pressure to P3. After this the products of combustion expand isentropically (process 3-4), and during constant volume (process 4-1) heat is removed from the gas.
Fig. 2-36 shows hypothetical indicator diagram for constant volume cycle (Otto cycle). The corresponding heat and work of each process are shown in table 2-10:
The efficiency expression indicates that the efficiency of the ideal engine depends only on the cylinder dimensions. Variations in heat input alter the output of the engine but not the efficiency. The power output of the engine will depend upon the quantity of fuel supplied.
In order to compare the efficiency of a cycle it is necessary to eliminate the effect of the calorific value of the fuel. To do so this, pure air is assumed to be the working fluid inside the engine cylinder. The thermal efficiency thus determined is known as the Air Standard Efficiency (A.S.E.) of the cycle or the efficiency of the standard engine of comparison. It is sometimes called the ideal or theoretical efficiency.
It should be noted that the constant volume cycle or Otto cycle has the highest efficiency of the practical internal combustion engine cycles. For this reason, it has been suggested that the performance of all types of internal combustion engines be referred to the Air Standard Efficiency of the constant volume cycle.
The ratio between the actual thermal efficiency and the air standard efficiency of an engine is called the relative efficiency. It is sometimes referred to as the efficiency ratio.
The following table 2-11 shows the value of air standard efficiency for various ratio of compression and the curve is plotted from these values in fig. 2-37.
Fig. 2-37 shows the effect of compression ratio on the efficiency. As the compression ratio is increased, the thermal efficiency increases. The return for the given theoretical increase of compression ratio diminishes as the ratio of compression increases.
Thus from the efficiency expression we may conclude that, in order to increase the efficiency of the engine, we may employ higher compression ratios. However, there are practical difficulties in using higher compression ratios because of the problems of detonation and knocking in the engine due to fuel quality restrictions.
There are many other criteria besides thermal efficiency that are used to evaluate the performance and suitability of an engine. For instance a high specific power based on engine weight would be desirable in transportation application, but this index of performance is really not too satisfactory since it is a function of engine speed.
Increasing the engine speed to increase the power has the detrimental effect of increasing mechanical friction and inertia loads. A more meaningful index of performance which is frequently used to compare engine outputs is the mean effective pressure (m.e.p) which is defined as the work performed during the cycle divided by the piston displacement volume.
When the gas changes its state from P1, V1 to P2, V2, the work done is represented on P-V diagram, as shown in fig. 2-38(a), by the area bounded by the curve, volume axis and ordinates at the initial and final state points.
This area may have any shape depending upon the operation. If the above area is to be represented by a rectangle as shown in fig. 2-38(b) whose one Side (base) represents the change in volume and as the area represents the work done, the other side (the height of the rectangle) has the units of pressure in N/m2. The height of the rectangle multiplied by its unit will represent what is known as the Mean Effective Pressure during the process.
Thermodynamic Cycle # III. Diesel Cycle:
The cycle in which heat is added at constant pressure is known as Diesel cycle. It consists of two isentropic, one constant pressure and one constant volume (fig. 2-39).
This cycle is typical of heavy fuel engines referred to as Diesel. Air is compressed along isentropic lines 1-2, resulting in a rise of temperature to that required for self-ignition of fuels. The fuel is injected into the compressed air and combustion takes place during constant pressure process 2-3 (addition of heat). Next are the processes of isentropic expansion 3-4 and constant-volume exhaust 4-1 (removal of heat).
Fig. 2-40 shows the hypothetical indicator diagram for constant pressure cycle (Diesel cycle). The process 5-1 is constant pressure suction and 1-5 constant pressure exhaust process.
The following table 2-12 shows the heat and work relations for the cycle.
But in the engine working on the Diesel cycle, only air is taken in during the suction stroke, therefore the compression ratio is made higher than that in an engine working on the Otto cycle because there is no danger of pre-ignition. Thus there is no limit imposed by pre-ignition and so by increasing the compression ratio say 11 to 22, a higher efficiency is obtainable in the Diesel cycle than is possible with Otto cycle.
When the cut-off ratio is 2.5 and the compression ratio is 15, then ɸ = 1.24, and the efficiency of the cycle is-
It will not be out of place here to mention some of the essential features of Diesel engines.
(i) Due to higher compression ratio, the temperature at the end of compression is sufficient to ignite the fuel oil which is injected into the cylinder at the end of compression stroke. Such engines are known as Compression Ignition Engines.
(ii) The fuel injection is either by means of a compressed air or by mechanical means.
(iii) The combustion is regulated so that there is no appreciable rise in pressure during injection.
(iv) There is no danger of pre-ignition.
The Diesel engine has the advantage of being able to burn the comparatively low cost fuel oils which are extracted from crude oil after the lower boiling range petrol and kerosene have been removed. At the same time some large modern engines can achieve brake thermal efficiency as high as 42%. The Diesel engine has, therefore, one of the highest thermal efficiencies of all power cycles that are commercially available.
This is an equation of indicated mean effective pressure for Diesel cycle. Although the actual engines have m.e.p. less than indicated mean effective pressure. The actual mean effective pressure is called to be brake mean effective pressure.
The brake mean effective pressure of Diesel engines are currently running from 4.8 to 18.6 bar and have exceeded 27.6 bar experimentally. The Diesel engine is used in a broad range of heavy duty applications because of its high efficiency and reliability.
These range from 30 MW versions for power generation and marine application to 3 MW Diesel electric locomotives which dramatically increased the thermal efficiency of locomotives from 10% to 35% when the conversion from steam was made.
Diesels are also used in a few low weight applications including some automobiles. The smaller engines generally use the Otto cycle because it results in a lighter and less expensive engine than the Diesel cycle.
Thermodynamic Cycle # IV. Dual Combustion Cycle:
In this cycle the combustion of fuel takes place partly at constant volume and partly at constant pressure. This kind of cycle is experienced in high speed Diesel engines. This cycle consists of two isentropic, one constant volume cooling process and one heating process, first at constant volume, and then at constant pressure. Fig. 2-41 shows Dual cycle on temperature-entropy diagram and pressure volume diagram.
Fig. 2-42 shows the hypothetical P-V diagram of Dual cycle in which suction and exhaust process of working medium occurs at constant pressure 1-6. Fig. 2-43 shows the actual Dual cycle in a working engine where work is required for pumping of working medium.
The following table 2-13 shows the heat and work relations for the cycle:
Thermodynamic Cycle # V. Stirling Cycle:
In 1927 Dr. Robert Stirling and his brother James Stirling patented an engine to work on a perfect reversible cycle. This was achieved by means of a device called the regenerator which alternatively stores and rejects heat in a manner which theoretically is thermodynamically reversible. This regenerator was also invented by Stirling.
This cycle consists of two constant volume and two isothermal processes as shown in fig. 2-44.
The following table 2-15 shows the heat and work relations involved in various processes:
The regeneration can be done by using the heat rejected in the process 3-4 to heat the working medium in the process 1-2. The regenerator is said to be 100% effective when the heat added in process 1-2 is entirely furnished by the heat rejected in the process 3-4.
We assume that the regenerator is 100% efficient.
where r= the volume ratio.
The cycle efficiency is equal to Carnot efficiency. This must be so, because the Stirling cycle is thermodynamically reversible owing to the action of the regenerator and all reversible cycles have the same efficiency for the same temperature limits.
In 1845 Dr. Stirling constructed hot air engine working on this cycle and was installed in a Dundee foundry. This engine worked for three years and after which the heater was burnt. It worked between temperature limits of 343°C and 65°. It developed 33.6 brake kW at 28 r.p.m. The overall efficiency of this engine was 0.3%.
Thermodynamic Cycle # VI. Ericsson Cycle:
This cycle was invented in 1850. This cycle consists of two isothermals and two constant pressure processes as shown in fig. 2-45. This cycle is made thermodynamically reversible by the use of the regenerator.
The following table 2-16 gives the heat and work relations for various processes of the cycle:
Regeneration can be done by using the heat rejected in the process 3-4 to heat the working medium in the process 1-2. We assume that the effectiveness of the regeneration is 100%.
Thermodynamic Cycle # VII. Brayton Cycle:
This type of cycle is very important in engineering. This cycle is employed in gas turbines. Unlike Otto and Diesel Cycles which are employed in reciprocating engines, the various processes take place in separate steady flow machines such as compressor, turbine, heater and cooler.
The Brayton cycle consists of two isentropic processes and two constant pressure processes.
The working medium may be air or some other gas and if air is used, then heater can be a combustion chamber in which fuel is burnt directly in the air. In open type of cycle the air is supplied directly from the atmosphere to the compressor and the turbine exhausts directly to the atmosphere and the cooler is not used.
The isentropic compression of air is carried out in a compressor which is of the centrifugal type or axial type, which is connected directly or geared to the turbine shaft. The isentropic expansion of heated air is carried out in a turbine. The constant pressure processes are carried out in heater and cooler. The Brayton cycle is sketched on temperature-entropy and pressure-volume diagrams as shown in fig. 2-47.
Thus the efficiency of the Brayton cycle has got the similar expression as the efficiency of the Otto cycle.
In actual gas turbine installation the efficiency of the plant will be lower due to following reasons:
(1) The processes in compressor and in turbine are not without friction.
(2) There is pressure drop in pipings and heater.
(3) The heat losses occur in machines and in piping.
(4) The combustion may not be complete in the combustor.
(5) The variation in specific heats and temperatures lowers the efficiencies.
(6) There is a variation in composition of the working medium.
In order to improve the basic gas turbine cycle the following means are employed:
(i) Regeneration
(ii) Reheat, and
(iii) Multi-stage compression.
Regenerative heating is carried out by heating the air leaving compressor by means of exhaust gases leaving the turbine. Due to multi-Staging the power Consumption of compressor will be lower. However, with inter-cooling, the discharged air is at a lower temperature than if compression is single-stage consequently more heat must be supplied.
Thus two effects tend to neutralize each other. In some cases the efficiency may be lowered. If multi-staging in combined with regeneration, the marked increase in thermal efficiency of the cycle is noticed. This is due to the heating of the relatively cool air from multi-stage compressor by the exhaust gases from the turbine.
At present two trends are evident in modern gas turbine installation. In mobile plants such as in locomotives, aeroplanes, etc., single-stage compression without inter-cooling is the rule and regeneration is employed in very few cases. For stationary power generation plant highly efficient but complex plants are suggested which may work on open or closed cycle.
The comparison of efficiencies of the theoretical cycles can be made by comparing their work output and heat input in the corresponding P-V and T-ɸ diagrams.
There are three practical considerations for the comparison of the various cycles:
(1) Temperature range
(2) Pressure range
(3) Volume range.
The minimum temperature of the cycle is limited by the surroundings and the maximum temperature by the materials of construction. The economy of turbo-machineries requires that there should be maximum output for a given pressure ratio, while the economy of reciprocating machines requires the maximum output for a given volume.
The following table 2-18 gives the order of decreasing efficiency for various practical considerations:
Thermodynamic Cycle # VIII. Reversed Brayton Cycle (Bell Coleman Cycle):
The reversed Brayton cycle is used in refrigeration cycles. In these cycles work is supplied and heat is carried out from products to provide cooling effect.
Coefficient of Performance (COP):
The coefficient of performance is just reverse to the efficiency used in the above cycle. It can be defined as the ratio of heat added or rejected to the work supplied.
This COP is a very useful term when it is applied to reversed engine such as a refrigeration system. Consider a refrigeration system in which the product is cooled by extraction of heat means the flowing medium. The system receives heat from the product and to operate the system work is supplied to the system.
The COP is an assessment of the heat extracted to the amount of work supplied. In Other words, it is a coefficient of the performance of the system. The reversed Brayton cycle is applicable to heat pump or refrigeration system.
The reversed Brayton cycle consists of two isentropic processes and two constant pressure processes.
The isentropic compression of air is carried out in a compressor which is of the centrifugal type or axial type, which is connected to motor shaft. The electric motor is rotated by electrical supply. The constant pressure cooling process of air is carried out in cooler.
The Cooled air at high pressure is passed on to the air motor in which isentropic expansion of air occurs. This results in a low temperature air. The low temperature air is further passed to a heater where cooling of product is carried out by low temperature air. The reversed Brayton cycle is sketched on temperature-entropy and pressure-volume diagrams as shown in fig. 2-49.
The following table 2-19 shows heat and work on each process of the cycle:
Thermodynamic Cycle # IX. Air Standard Cycles:
Air standard cycles are the thermodynamic cycles based on air as standard medium. The air undergoes a series of thermodynamic processes wherein the heat is added and rejected to surrounding. The air reaches to its original state point after completing a series of thermodynamic processes.
The air standard cycles are used for heat engines, gas turbine, air motors, I. C. engine, etc. These are the cycles in which the working fluid as air passes through a series of thermodynamic processes and on completion the fluid returns to its original conditions.
During the thermodynamic cycle the properties of fluid change and energy transfer takes place. The basic objective of these cycles is to convert maximum heat energy into useful work.