Compressor efficiency example

For actual Brayton cycles, many irreversibilities in various eomponents are present. The T s diagram of an aetual Brayton cycle is shown in Fig. 4.6. The major irreversibilities occur within the turbine and compressor. To account for these irreversibility effects, turbine efficiency and compressor efficiency must be used in computing the actual work produced or consumed. The effect of irreversibilities on the thermal efficiency of a Brayton cycle is illustrated in the following example. 

Example 7.8 Saturated-vapor steam at 100 kPa (t = 99.63°C) is compressed adiab cally to 300 kPa. If the compressor efficiency is 75 percent, what is the work requi and what are the properties of the discharge stream ... 

Example 73) If methane (assumed to be an ideal gas) is compressed adiabaticall from 20°C and 140 kPa to 560 kPa, estimate the work requirement and the discharge temperature of the methane. The compressor efficiency is 75 percent. 

Solution Saturated steam at 100 kPa is compressed adiabatically to 300 kPa with a compressor efficiency of 0.75. From the results of Example 7.8, we have ... 

Improvements in compressor efficiency have also had a significant effect. In an interesting example of technology cross-fertilization, much of the improvement in compressor efficiency has been driven by advances in computational fluid dynamic modeling. 

Whether or not the air can be used without being cooled will depend to a large extent on the properties of the material to be conveyed. The most efficient form of compression is to carry out the process isothermally, and so cylinders of reciprocating compressors, for example, would be water-cooled, and if staging was employed for achieving high pressures, inter-cooUng would be employed here as well. 

If the compressor in Example 8.12 is adiabatic but irreversible with an efficiency of 0.75, what will the final temperature be What would the anticipated accuracy be in this case ... 

To keep from complicating the example with real world consid a-tions, a few simplifying assumptions will be made. In all cases, the mm-pressor will be considered to be 100% efficient. Intercooling will be perfect, that is, no pressure drop will be considered and the cooler return gas will be the same temperature to the first stage of the compressor. 

The example demonstrates that operating the compressor off the built-in pressure ratio means operating at a lower efficiency. This could be anticipated from Figure 4-3. The optimum port configuration for the various types of screw compressors was determined from a series of prototype tests. The change in volumetric efficiency is not a result of the built-in volume ratio, but is due to the increased slip (internal leak " n... 

For the a/s example quoted earlier, with this form of two stage cooling (with a = 2.79, Ah = 1.22, i//h = 0.1, i/ l = 0.05), the thermal efficiency is reduced from 0.4442 (uncooled) to 0.4257, i.e. by 0.0185, still not a significant reduction. If the second step of cooling uses compressor delivery air rather than air taken at the appropriate pressure along the compressor, then the analysis proceeds as before, except that the expansion work for the processes 7, 11 in Fig. 4.7a is replaced by that corresponding to 7, 11 in Fig. 4.7b. It may be shown [5] that the efficiency may then be written as... 

For the numerical example the cooled efficiency becomes 0.4205, a reduction of 0.0237 from (tj)ru = 0.4442. The extra loss in efficiency for throttling the cooling air from compressor discharge to the appropriate pressure at the LP turbine entry is thus 0.0052 for the numerical example, which is again quite small. 

Compressor Intercooling Whether a compressor should be intercooled or not depends on the trade-off between the increased efficiency of the intercooled compressor and its increased capital cost. In general, intercooling is required for large compressors with pressure ratios that exceed approximately 5 1 (44). The designer also should consider whether the heat is advantageous to the process. For example, when near the 5 1 pressure ratio, it may not be appropriate to intercool if the compressed stream will subsequently require preheating as it would with the process air stream of an MCFC or SOFC system. 

Optimal compressor- types for the various power ranges are plotted in Fig. 4.1-29, which was calculated on the bases of 1 bar intake pressure and an isothermal efficiency of 64% [24]. It can give only approximate reference points for the most favourable area of application, which varies depending on the manufacturer. If the intake pressure is greater than 1 bar, as is the rule, it is necessary to recalculate. For example the compression of ethylene at a flow-rate of 64000 kg/h 51 130 Nm3/h (Standard cubic metre per hour) from 231 to 2151 bar, corresponds to a real intake volume flow-rate at 231 bar of 161 m3/h, and a power consumption of 8200 kW. 

Figure 7.21. Operating ranges of single-stage pumps and compressors [Balje, Trans. ASME, J. Eng. Power. 84, 103 (1962)]. Example atmospheric air at the rate of 100,000 SCFM is compressed to 80,000 ft lbf/ft (41.7psig) at 12,000 rpm calculated Ns = 103 in the radial flow region with about 80% efficiency, Ds = 1.2-1.6, so that D = 2.9-3.9 ft.

Polytropic efficiencies are obtained from measurements of power consumption of test equipment. They are essentially independent of the nature of the gas. As the data of Figure 7.27 indicate, however, they are somewhat dependent on the suction volumetric rate, particularly at low values, and on the compression ratio. Polytropic efficiencies of some large centrifugal compressors are listed in Table 7.6. These data are used in Example 7.9 in the selection of a machine for a specified duty. 

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