This paper describes a design-based effort to build an effective closed-system air standard gas power cycle

Principles and theory

An isentropic process is one in which the entropy of the fluid remains constant. This will be true if the process the system goes through is reversible and adiabatic. An isentropic process can also be called a constant entropy process.

Isentropic process: or

When the constant-specific heat assumption is valid, the isentropic relations for ideal gases are obtained by setting the following:

Ideal gas (1)

Equation 1 is the first isentropic relation for ideal gases under the constant-specific-heat relationship assumption. The second isentropic relation is obtained in a similar manner from the following:

Ideal gas (2)

The third isentropic relation is the following equation:

Ideal gas (3)

The specific heat ratio k, in general, varies with temperature, and this an average k value for the given temperature range should be used.

We are going to use a compressor, a combustor, and a turbine. According to the principle of the isentropic cycle, air is compressed in the compressor. The air is then mixed with fuel, and burned under constant pressure conditions in the combustor. The resulting hot gas is allowed to expand through a turbine to perform work. Most of the work produced in the turbine is used to run the compressor and the rest is available to run auxiliary equipment and produce power. The gas turbine is used in a wide range of applications.

The thermal efficiency is important because it gives the fraction of the heat input that is converted to net work output that measures the performance of the heat engine.

Therefore, heat engines are built for the purpose of converting heat to work, and engineers are constantly trying to improve the efficiencies of these devices since increased efficiency means less fuel consumption.

Air-Standard Assumptions

In gas power cycles, the working fluid remains a gas throughout the entire cycle. Spark-ignition engines, diesel engines, and conventional gas turbines are familiar examples of devices that operate on gas cycles. In all these engines, energy is provided by burning a fuel within the system boundaries. That is, they are internal combustion engines. Because of this combustion process, the composition of the working fluid changes from air and fuel to combustion products during the course of the cycle. However, considering that air is predominantly nitrogen that undergoes hardly any chemical reactions in the combustion chamber, the working fluid closely resembles air at all times.

Even though internal combustion engines operate on a mechanical cycle (the piston returns to its starting position at the end of each revolution), the working fluid does not undergo a complete thermodynamic cycle. It is thrown out of the engine at some point in the cycle (as exhaust gases) instead of being returned to the initial state. Working on an open cycle is the characteristic of all internal combustion engines.

The actual gas power cycles are rather complex. To reduce the analysis to a manageable level, we utilize the following approximations, commonly known as the air-standard assumptions:

. The working fluid is air, which continuously circulates in a closed loop and always behaves as an ideal gas.

2. All the processes that make up the cycle are internally reversible.

3. The combustion process is replaced by a heat-addition process from an external source.

4. The exhaust process is replaced by a heat-rejection process that restores the working fluid to its initial state.

Another assumption that is often utilized to simplify the analysis even more is that air has constant specific heats whose values are determined at room temperature (25°C, or 77°F). When this assumption is utilized, the air-standard assumptions are called the cold-air-standard assumptions. A cycle for which the air-standard assumptions are applicable is frequently referred to as an air-standard cycle.

The air-standard assumptions previously stated provide considerable simplification in the analysis without significantly deviating from the actual cycles. This simplified model enables us to study qualitatively the influence of major parameters on the performance of the actual engines.

Analysis

An air standard cycle with variable specific heats is executed in a closed system with 0.003 kg of air and consists of the following three processes:

The cycle is to be shown on P-v and T-s diagrams, and the net work per cycle and the thermal efficiency are to be determined.

Assumptions: 1. The air-standard assumptions are applicable.

2. Kinetic and potential energy changes are negligible.

3. Air is an ideal gas with variable specific heats.

Analysis: (b) The properties of air at various states are:

-2 v constant heat addition from 95 kPa and 17°C to 280 kPa.

2-3 Isentropic expansion to 95 kPa.

3-1 P= constant heat rejection to initial state.

P-v Diagram T-s Diagram

Properties: The properties of air are given in Table A-17.

Calculations

Conclusion

A cycle during which a net amount of work is produced is called a power cycle, and power cycle during which are working fluid remains gas throughout is called a gas power cycle. The actual gas cycle are rather complex. The approximations used to simplify the analysis are known as the air-standard assumptions. Under these assumptions, all the processes are assumed to be internally reversible; the working fluid is assumed to be air, which behaves as an ideal gas; and the combustion and exhaust process are replaced by heat-addition and heat-rejection processes, respectively.