Efficiency Ideal cycle

The previous section dealt with the concepts of the various cycles. Work output and efficiency of all actual cycles are considerably less than those of the corresponding ideal cycles because of the effect of compressor, combustor, and turbine efficiencies and pressure losses in the system. 

It is also interesting to compare the more detailed calculations performed here with the approximate calculation in Example 24.1. Example 24.1 estimated the power to be 1.4 MW on the basis of the COP for an ideal cycle with an assumed 60% efficiency. 

First, we define an ideal cycle and the material properties from a chemist s point of view that should be met for high performance and economic efficiency. The most important parameters for the evaluation of these processes with respect to efficiency are productivity (Equation [5]) and stability. However, it appears that with respect to materials chemistry and physics these properties represent opposing factors that is, the optimization of productivity is likely to decrease stability and lifetime, and vice versa. 

The effect of increasing the compression ratio, defined as the ratio of the volumes at the beginning and end of the compression stroke, is to increase the efficiency of the engine, i.e., to increase the work produced per unit quantity of fuel. We demonstrate this for an idealized cycle, called the air-standard cycle, shown in Fig. 8.9. It consists of two adiabatic and two constant-volume steps, which comprise a heat-engine cycle for which air is the working fluid. In step DA, sufficient heat is absorbed by the air at constant volume to raise its temperature and pressure to the values resulting from combustion in an actual Otto engine. Then the air is expanded adiabatically and reversibly (step AB), cooled... 

Irreversibilities in the compressor and turbine greatly reduce the thermal, efficiency of the power plant, because the net work is the difference between the work required by the compressor and the work produced by the turbine. The temperature of the air entering the compressor TA and the temperature of the air entering the turbine, the specified maximum for Tc, are the same as for the ideal cycle. However, the temperature after irreversible compression in the compressor Ts is higher than the temperature after isentropic compression T B, and the temperature after i never - ible expansion in the turbine TD is higher than the temperature after isentropic expansion T d. 

This analysis shows that, even with a compressor and turbine of rather high efficiencies, the thermal efficiency (23.5 percent) is considerably reduced from the ideal-cycle value of 40 percent. 

Efl ciency.—The maximum ideal efficiency (Otto cycle) is... 

The current thermodynamic cycle analysis gives an efficiency of 0.46 for a stoichiometric hydrogen-air mixture initially at 298 K and 1 atm. Using the approach given in [16], this translates into a force for unit mass flow rate (Specific Thrust) of 1802 N s/kg and a fuel-based Igp of 6257 s for the ideal cycle. The differences between two estimates using identical analysis are probably due to... 

If co-generation is taken into account, the usefiil energy per kg steam is Wc+Qh= 357.7+2250.5=2608.2 kW (we neglect the power consumption for water recompression). The total heat consumed to bring the steam to the original state is gi=3 517-908.8=2608.2. Thus, for this part of the process the heat efficiency in an ideal cycle is 100% ... 

The ideal cycle efficiency can also be expressed in terms of T and T, . 

Carnot s cycle A hypothetical scheme for an ideal heat machine. Shows that the maximum efficiency for the conversion of heat into work depends only on the two temperatures between which the heat engine works, and not at all on the nature of the substance employed. 

The thermal efficiency of the process (QE) should be compared with a thermodynamically ideal Carnot cycle, which can be done by comparing the respective indicator diagrams. These show the variation of temperamre, volume and pressure in the combustion chamber during the operating cycle. In the Carnot cycle one mole of gas is subjected to alternate isothermal and adiabatic compression or expansion at two temperatures. By die first law of thermodynamics the isothermal work done on (compression) or by the gas (expansion) is accompanied by the absorption or evolution of heat (Figure 2.2). 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

The thermal efficiency of an ideal simple cycle is decreased by the addition of an intercooler. Figure 2-7 shows the schematic of such a cycle. The ideal simple gas turbine cycle is 1-2-3-4-1, and the cycle with the intercooling added is -a-b-c-2- i-A-. Both cycles in their ideal form are reversible and can be simulated by a number of Carnot cycles. Thus, if the simple gas turbine cycle 1-2-3-4-1 is divided into a number of cycles like m-n-o-p-m,... 

In Chapter 1, the gas turbine plant was considered briefly in relation to an ideal plant based on the Carnot cycle. From the simple analysis in Section 1.4, it was explained that the closed cycle gas turbine failed to match the Carnot plant in thermal efficiency because of... 

According to r] = l-Rf the efficiency of the ideal Otto cycle increases indefinitely with increasing compression ratio. Actual engine experiments, which inherently include the real effects of incomplete combustion, heat loss, and finite combustion time neglected in fuel-air cycle analysis, indicate an efficiency that IS less than that given by r =l-R when a = 0.28. Furthermore, measured experimental efficiency reached a maximum at a compression ratio of about 17 in large-displacement automotive cylinders but at a somewhat lower compression ratio in smaller cylinders. 

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