List of 7 Air Standard Cycles | Thermodynamics

Here is a list of seven major air standard cycles.

1. Otto – Cycle (Constant Volume Cycle):

To avoid high values of pressures and compression ratios, a practical cycle was introduced by a German Scientist Dr. A .N. Otto in 1876 and it was successfully applied for the working of petrol and gas engines. This cycle consists of two isentropic processes and two constant volume processes as shown in Fig. 23.1.

The sequences of operations is as follows — air as the working substance in the cylinder is at a pressure P₁, volume V₁ and temperature T₁ and is shown by a point 1 on both P-V and T-S diagram in Fig. 23.1 (a) and (b).

Process 1-2:

Air is compressed isentropically to 2. Ratio V₁ to V₂ is called compression ratio donated by r_k. Cover is adiabatic. At the end of compression, diabatic cover replaces adiabatic cover.

Process 2-3:

At the end of compression, heat is added at constant volume by bringing a hot body near the cylinder diabatic cover. Heat is added at constant volume and hence pressure and temperature increase. Because the heat is added at constant volume, the cycle is called as Constant Volume Cycle.

Process 3-4:

After heat is added, air expands isentropically to state 4. Here the expansion ratio is given by r_e = V₄/V₃. For Ottao cycle r_k = r_e. Adiabatic cover is kept during expansion.

Process 4-1:

At the end of isentropic expansion, adiabatic cover is replaced by diabatic cover and the cold body is brought near the cover. Heat is rejected at constant volume thus decreasing the pressure and temperature to initial values.

Thus the cycle is completed.

(a) Thermal Analysis of Cycle:

We note from these equations that the air-standard efficiency of Otto-Cycle depends upon the compression ratio only and it increases with the increase in compression ratio. The variation of ASE with compression ratio r_k is shown in Fig. 23.2. For r_k =1, efficiency is zero.

The compression ratio used in actual engine working on this cycle lies between 5 and 9 and depends upon the type of the fuel used.

(b) Mean Effective Pressure-MEP:

Mean effective pressure is defined as that constant pressure, acting on the piston throughout the stroke, which will produce the work equal to that of the cycle.

If d and L are the diameter and stroke of the piston, then the work produced by the mean effective pressure is given by –

The unit for pressure scale is bar/mm

So that unit of p_m is bar.

If the scale is N/m²/mm, then p_m-N/m² and so on.

2. Diesel Cycle – (Constant Pressure Cycle):

This cycle was introduced by Rudolph Diesel in 1893 and it is successfully used in all Diesel engines or oil engines.

This cycle consists of two isentropics, one constant pressure and one constant volume processes.

The sequence of operations is as follows:

As before, air as the working substance in the cylinder is at pressure P₁, volume V₁ and temperature T₁.

i. 1-2:

Air is compressed isentropically to 2. Ratio V₁ to V₂ is called compression ratio denoted by r_k. Cylinder cover is adiabatic.

ii. 2- 3:

At the end of compression, diabetic cover is placed and heat is added at constant pressure by bringing a hot body near the cylinder cover. Heat is added for a part of the stroke. At the point 3, the heat addition is stopped or cut-off. The ratio of the volume of cut-off point to the initial volume before heat addition is called the cut-off ratio and is donated by r_c. Therefore, r_c = V₃/V₂. Because the heat is added at constant pressure, the cycle is also called as constant pressure cycle.

iii. 3-4:

After the heat is added, air expands isentropically to state 4. Here the expansion ratio is given by r_e = V₄/V₃ = V₁/V₃.

Here the cover is adiabatic.

iv. 4-1:

Adiabatic cover is replaced by diabatic cover at the end of isentropic expansion, the cold body is brought near the cover. Heat is rejected at constant volume thus decreasing the pressure and temperature to initial values. Thus the cycle is completed.

From this equation we see that the efficiency decreases as cut-off ratio increases.

Again as the compression ratio is equal to that for Otto-cycle, ASE of Otto-cycle is more than ASE of Diesel cycle.

In practice, the compression ratio of Diesel engines ranges from 12 to 22.

3. Dual Combustion or Semi-Diesel Cycle:

From the expression for the air standard efficiency of the Diesel cycle, it is seen that the efficiency decreases as the value of cut-off ratio (r_c) increase and therefore, it is desirable to keep the value of r_c small as possible to increase the efficiency.

This can be done by supplying the heat partly at constant pressure. This type of the cycle is called Dual Combus­tion cycle or semi-Diesel cycle.  

As before the sequential operations for this cycle are:

1-2 Isentropic compression

2-3 Constant volume heat addition

3-4 Constant pressure heat addition

4-5 Isentropic expansion

5-1 Constant volume heat rejection

As before, all the temperatures in the above equation are to be expressed in terms of T₁. Students are to derive the expression of Air Standard Efficiency ASE terms of compression ratio r_k cut-off ratio r_c explosion ratio α and the specific heat ratio γ and get,

It is obvious from this equation that the efficiency of the dual-combustion cycle can be increased by increasing the value of explosion ratio (i.e. more heat is added at constant volume) and decreasing the value of r_c (less heat is added during constant pressure process) keeping the total heat added constant.

The Otto and Diesel cycles are special cases of Dual cycle. If r_c = 1, then V₃ = V₄ and the cycle becomes Otto- cycle. Again if α = 1, then P₂ = P₁ and the cycle becomes Diesel cycle.

Again applying the same procedures used in Otto-cycle and Diesel cycles, the mean effective pressure of the dual combustion can be calculated (students have to derive this relation as an exercise).

4. The Ericsson Cycle:

This cycle consists of two isothermal processes and two constant pressure processes, as shown in Fig. 23.7. It is made to be thermodynamically reversible by the action of a regenerator, during the two constant pressures. A hot-air engine working on this cycle was fitted into a ship named The Ericsson in the year 1853; the cycle has been termed the Ericsson Cycle after its inventor.

Referring to the p-v diagram of Fig. 23.7, hot air at a temperature of T₁ is forced in engine cylinder and expanded isothermally, the heat being supplied by the furnace; this represented by 1-2. The air is then cooled at constant pressure to T₂ by passing it through a regenerator. The process is thus made thermodynamically reversible by this graduated method of cooling.

By this method the air is brought to the condition 3. It is now compressed isothermally by a separate pump, the heat being rejected to a cold water supply; this operation is represented by 3—4. The air is next heated at constant pressure to T₁ by being passed through the regenerator, in the reversed direction, whilst the pressure is maintained constant; this is represented by 4—1. The cycle is thus completed.

It should be noticed that the whole of the heat given to regenerator during the constant pressure operation 2-3 is abstracted from it during the constant pressure operation 4-1. Hence there is no interchange of heat from an external source during these two operations.

which is the same as the Carnot efficiency.

The hot air engine of the Ericsson had four cylinders each of 4.2 m diameter (14 ft); the stroke was 1.8 m (6 ft). This engine developed 300 IP (indicated power) and its speed was 9 rpm, the temperature range being from 212°C (414°F) to 50°C (122°F). Its mean effective pressure MEP was 0.1406 x 10⁵ N/m² (2 psi) and each cylinder was fitted with compression pump. The heating surfaced consisted of the bottom of the cylinders, and although the total heating surface occupied an area of 65 m² (700 sq. ft.) it was found to be insufficient.

5. The Atkinson Cycle:

This cycle was used in the Atkinson gas engine and is show, in its ideal form. It consists of two adiabatics, a constant volume process and a constant pressure process. The heat is supplied during the constant volume process 4-1 and rejected during constant pressure process 2-3. There is no interchange of heat during the adiabatics.

The air standard efficiency for this cycle is obtained by imagining the cylinder to contain 1 kg of air at point 3. The air is then compressed isentropically to 4 at which condition the hot body is placed in contact with the cylinder cover. Heat is now taken in at constant volume and the pressure rises; this operation is represented by 4-1.

The hot body is then removed and the air allowed to expand adiabatically to point 2. During this process work is done on the piston. At point 2 the cold body is placed at the cylinder cover; the air now contracts at constant pressure to point 3 rejecting heating to the cold body during the process. The cold body is then removed and the cycle is thus completed.

Concept:

The cylinder cover is replacable. When heat addition and rejection process take place, the cover is diabatic and during compression and expansion the cover will be adiabatic.

There are two methods for calculating efficiency of Atkinson Cycle. One method is to find efficiency in terms of pressure ratios and the other method is to find efficiency in terms of volume ratio.

Efficiency in Terms of Pressure Ratios:

Efficiency of Atkinson Cycle in Terms of Volume Ratios:

The Atkinson cycle was used in the Atkinson gas engine, but it was slightly modified in practice by the cutting off the toe of the p-v diagram; this was due to the opening of the exhaust valve before the end of the expansion or working stroke.

The Atkinson gas engine proved more efficient than the ordinary gas engine working on the Otto = cycle, but it was not a commercial success on account of the excessive wear of the mechanism due to the toggle joint drive required for a constant pressure process.

The Atkinson cycle is now used by Gas-turbines of the explosive type.

6. Stirling Cycle (Regenerative Cycle):

Stirling constructed a hot air engine in 1845 which works on Stirling cycle. Theoretically, the efficiency of the Stirling cycle is equal to Carnot cycle.

The construction of the generator and its function is explained below:

i. Regenerator:

The construction of the regenerator is shown in Fig. 23.10 which alternately stores and rejects heat in a manner which theoretically, is thermodynamically reversible.

The air near the lower end of the filling (important part of the generator) is maintained at a higher temperature T₂ by supplying the heat from external heat source. The air near the upper end of the wire mesh is maintained at a lower temperature T₁ with the help of external heat sink. The wire mesh filling is used to store the heat. The temperature of the wire gauge varies uniformly from T₁, to T₂ as shown. The heat storing capacity of the wire mesh should be large.

ii. Stirling Cycle:

The Stirling cycle is represented on P-V and T-S diagrams as shown.

The sequence of operations is given below:

(1) The air is compressed isothermally from 1-2.

(2) The air state 2 is passed into the regenerators from the top at a temperature T₁. The air passing through the matrix gets heated from T₁ to T₂ at constant volume. This heat transfer from the matrix to air is considered thermodynamically reversible because in each element of the matrix heat is transfer due to infinitesimal difference in temperature.

(3) Then the air at ‘2’ expands isothermally into the cylinder until it reaches to the state ‘4’.

(4) The air coming out of the engine at temperature T₂ (at 4) enters the generator from the bottom and gets cooled while passing through the generator at constant volume and it comes out at a temperatures T₁ and the cycle is repeated. This heat transfer during 4-1 processes is also considered thermodynamically reversible.

The work done by the cycle per kg air and air standard efficiency of the cycle can be calculated as follows:

Thus the efficiency of the Stiriling cycle is equal to that of Carnot cycle when both are working within same temperature limits.

Heat transferred during 2-3 and 4-1 are equal.

In practice, 10-20% heat losses occur in the generator and the efficiency of the generator lies between 90% and 80%.

If the generator efficiency (ƞ_r) is considered then –

The cycle has not become very successful even though its ideal efficiency is sufficiently high because the regenerator volume has to be very large compared with the engine size.

7. Air-Fuel Cycle:

The air cycle approximation or air standard theory has highly simplified approximations. The air standard theory gives an estimate of engine performance which is much greater than the actual performance. This large divergence is partly due to non-instantaneous burning and valve operation, incomplete combustion etc. But the main reason of divergence is the over simplification in using the values of the properties of the working fluid for cycle analysis.

In the air cycle approximations it was assumed that the working fluid is nothing but air and that this air was a perfect gas and had a constant specific heats. In actual engine the working fluid is not air but a mixture of air, fuel and residual gases. Furthermore, the specific heats of the working substance are not constant but increase as tempera­ture rises and finally, the products of combustion are subjected to dissociation at high temperatures.

If the actual physical properties of the cylinder gases before and after burning are taken into account a much closer approach to actual performance figures is achieved.

The theoretical cycle based on the actual properties of the cylinder gases on the actual properties of the cylinder gases is called the fuel-air cycle and represents a nearly attainable ideal for comparison with actual performance.

The fuel-air cycle calculations take into consideration the following:

1. The actual composition of the cylinder gases i.e. fuel + air + combustion gases. The fuel air ratio is changed during the operation of the engine which changes the relative amounts of CO₂, CO, water vapour etc.

2. The variation in the specific heat of these gases with temperature. Specific heat increases with temperature except the monoatomic gases.

3. The fact that the fuel and air do not completely combine chemically at high temperatures (above 1600 K), CO, H₂, H and O₂ may be present at equilibrium conditions.

4. The variation in the number of molecules present in the cylinder as the pressure and temperature change. The number of molecules present after combustion depends on the fuel-air ratio and the pressure and temperature after the combustion.

The following assumptions are commonly made for fuel-air cycle analysis:

1. There is no chemical change in either fuel or ah prior to combustion.

2. Subsequent to combustion, the charge is always in chemical equilibrium.

3. There is no heat exchange between the gases and the cylinder walls in any process i.e., they are adiabatic. Also expansion and compression processes are frictionless.

4. In reciprocation engines the velocities are negligibly small.

Variable Specific Heats:

All gases, except monoatomic gases, show an increase in specific heat at temperatures. The increase in specific heat does not follow any particular law. However, over the temperature range in general use for gases in heat engines (300 K to 1300 K) the specific heat curve is nearly a straight line which may be approximately expressed in the form,

The physical explanation of increases in specific heat is that as the temperature is raised, larger and larger fractions of the heat input go to produce motion of the atoms within the molecules. Since temperature is the result of motion of the molecules as a whole the energy which goes into moving the atoms does not contribute to the temperature rise. Hence more heat is required to raise the temperature of unit mass through one degree. This heat — by definition — is specific heat.

For air C_p = 1.005 at 0°C and 1.2645 at 2000°C.