AIR STANDARD CYCLES

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Theoretical Analysis

The accurate analysis of the various processes taking place in an internal combustion engine is a very complex problem. If these processes were to be analyzed experimentally, the analysis would be very realistic no doubt. It would also be quite accurate if the tests are carried out correctly and systematically, but it would be time consuming. If a detailed analysis has to be carried out involving changes in operating parameters, the cost of such an analysis would be quite high, even prohibitive. An obvious solution would be to look for a quicker and less expensive way of studying the engine performance characteristics. A theoretical analysis is the obvious answer.

A theoretical analysis, as the name suggests, involves analyzing the engine performance without actually building and physically testing an engine. It involves simulating an engine operation with the help of thermodynamics so as to formulate mathematical expressions which can then be solved in order to obtain the relevant information. The method of solution will depend upon the complexity of the formulation of the mathematical expressions which in turn will depend upon the assumptions that have been introduced in order to analyze the processes in the engine. The more the assumptions, the simpler will be the mathematical expressions and the easier the calculations, but the lesser will be the accuracy of the final results.

The simplest theoretical analysis involves the use of the air standard cycle, which has the largest number of simplifying assumptions.

A Thermodynamic Cycle

In some practical applications, notably steam power and refrigeration, a thermodynamic cycle can be identified.

A thermodynamic cycle occurs when the working fluid of a system experiences a number of processes that eventually return the fluid to its initial state.

In steam power plants, water is pumped (for which work WP is required) into a boiler and evaporated into steam while heat QA is supplied at a high temperature. The steam flows through a turbine doing work WT and then passes into a condenser where it is condensed into water with consequent rejection of heat QR to the atmosphere. Since the water is returned to its initial state, the net change in energy is zero, assuming no loss of water through leakage or evaporation.

An energy equation pertaining only to the system can be derived. Considering a system with one entering and one leaving flow stream for the time period t1 to t2



ΔQ is the heat transfer across the boundary, +ve for heat added to the system and –ve for heat taken from the system.

ΔW is the work transfer across the boundary, +ve for work done by the system and-ve for work added to the system

is the energy of all forms carried by the fluid across the boundary into the system

is the energy of all forms carried by the fluid across the boundary out of system

ΔEsystem is the energy of all forms stored within the system, +ve for energy increase decrease -ve energy


In the case of the steam power system described above

All thermodynamic cycles have a heat rejection process as an invariable characteristic and the net work done is always less than the heat supplied, although, as shown in Eq. 2, it is equal to the sum of heat added and the heat rejected (QR is a negative number).

The thermal efficiency of a cycle, ηth, is defined as the fraction of heat supplied to a thermodynamic cycle that is converted to work, that is

This efficiency is sometimes confused with the enthalpy efficiency, ηe, or the fuel conversion efficiency, ηf

This definition applies to combustion engines which have as a source of energy the chemical energy residing in a fuel used in the engine.

Any device that operated in a thermodynamic cycle, absorbs thermal energy from a source, rejects a part of it to a sink and presents the difference between the energy absorbed and energy rejected as work to the surroundings is called a heat engine.
A heat engine is, thus, a device that produces work. In order to achieve this purpose, the heat engine uses a certain working medium which undergoes the following processes:

1. A compression process where the working medium absorbs energy as work.
2. A heat addition process where the working medium absorbs energy as heat from a
source.
3 An expansion process where the working medium transfers energy as work to the surroundings.
4. A heat rejection process where the working medium rejects energy as heat to a sink.

If the working medium does not undergo any change of phase during its passage through the cycle, the heat engine is said to operate in a non-phase change cycle. A phase change cycle is one in which the working medium undergoes changes of phase. The air standard cycles, using air as the working medium are examples of non-phase change cycles while the steam and vapor compression refrigeration cycles are examples of phase change cycles.