Optimum pressure ratios

To obtain a more accurate relationship between the overall thermal efficiency and the inlet turbine temperatures, overall pressure ratios, and output work, consider the following relationships. For maximum overall thermal cycle efficiency, the following equation gives the optimum pressure ratio for fixed inlet temperatures and efficiencies to the compressor and turbine ... 

The optimum pressure ratio for maximum output work for a turbine taking into aeeount the effieieneies of the eompressor and the turbine expander seetion ean be expressed by the following relationship ... 

Figure 2-3 shows the optimum pressure ratio for maximum effieieney or work per lb (kg) of air. The optimum pressure ratio based on work oeeurs at a lower pressure ratio than the point of maximum effieieney at the same firing Temperature. 

Analysis of this cycle indicates that an increase in inlet temperature to the turbine causes an increase in the cycle efficiency. The optimum pressure ratio for maximum efficiency varies with the turbine inlet temperature from an optimum of about 15.5 1 at a temperature of 1500°F (816°C) to about 43 1 at a temperature of about 2400 °F (1316 °C). The pressure ratio for maximum work, however, varies from about 11.5 1 to about 35 1 for the same respective temperatures. 

The first point to note is that the classic Hawthorne and Davis argument is reinforced— that the optimum pressure ratio for the [CBT]ig plant (r = 45) is very much higher than that for the [CBTX]ig plant (r = 9). (The optimum r for the latter would decrease if the effectiveness (s) of the heat exchanger were increased, but it would increase towards that of the [CBT]ig plant if e fell towards zero.)... 

While the lowest and highest optimum pressure ratios are for these two plants, the addition of reheating and intercooling increases the optimum pressure ratios above that of... 

It has been emphasised in the earlier chapters that the thermal efficiency of the gas turbine increases with its maximum nominal temperature, which was denoted as T. Within limits this statement is true for all gas turbine-based cycles and can be sustained, although not indefinitely, as long as the optimum pressure ratio is selected for any value of Ty, further the specific power increases with T. However, in practice higher maximum temperature requires improved combustion technology, particularly if an increase in harmful emissions such as NO is to be avoided. 

Fig. 4.10 shows more fully calculated overall efficiencies (for turbine cooling only) replotted against isentropic temperature ratio for various selected values of Tj = T,.,. This figure may be compared directly with Fig. 3.9 (the a/s calculations for the corresponding CHT cycle) and Fig. 3.13 (the real gas calculations of efficiency for the uncoooled CBT cycle). The optimum pressure ratio for maximum efficiency again increases with maximum cycle temperature T. ... 

Fig. 5.2 shows that for the single-step cooled CBT plant at a given combustion temperature, the overall efficiency of the cooled gas turbine efficiency increases with pressure ratio initially but, compared with an uncooled cycle, reaches a maximum at a lower optimum pressure ratio. Fig. 5.3 shows that for a given pressure ratio the efficiency generally increases with the combustion temperature even though the required cooling fraction increases. 

Plots of efficiency against pressure ratio for the full injection EGT plant, for a maximum to minimum temperature 5, are shown in Fig. 6.9, compared with lower values of efficiency in the dry CBTX plant. There are. several points to be noted first that an increase in efficiency is worthwhile, up to 10% secondly that the total water injection is up to over 10% of the air mass flow and thirdly that the optimum pressure ratio increases to about 8, from about 5 for that of the dry cycle. 

Similar calculations (Fig. 6.10) were made for intercooled cycles, without and with water injection, i.e. comparing the efficiency of the dry CICBTX cycle with an elementary recuperated water injection plant, now a simple version of the. so-called RWl plant (see Section 6.4.2.1). Again there is an increase in thermal efficiency with water injection, but it is not as great as for the simple EGT plant compared with the dry CBTX plant the optimum pressure ratio, about 8 for the dry intercooled plant, appears to change little with water injection. 

In summary, all these wet cycles may be expected to deliver higher thermal efficiencies than their original dry equivalents, at higher optimum pressure ratios. The specific work quantities will also increase, depending on the amount of water injected. 

Macchi et al. provided a similar comprehensive study of the more complex RWI cycles as illustrated in Fig. 6.19, which shows similar carpet plots of thermal efficiency against specific work for maximum temperatures of 1250 and 1500°C, for surface intercoolers. The division of pressure ratio between LP and HP compressors is again optimised within these calculations, leading to an LP pressure ratio less than that in the HP. For the RWI cycle at 1250°C the optimisation appears to lead to a higher optimum overall pressure ratio (about 20) than that obtained by Horlock [5], who assumed LP and HP pressure ratios to be same in his study of the simplest RWI (EGT) cycle. His estimate of optimum pressure ratio... 

Rufli s calculations (Fig. 7.7a, b), indicated that the optimum pressure ratio for a CCGT plant is relatively low compared with that of a simple gas turbine (CBT) plant. In both cases, the optimum pressure ratio increa.ses with maximum temperature. Davidson and Keeley [6] have given a comparative plot of the efficiencies of the two plants (Fig. 7.9), showing that the optimum pressure ratio for a CCGT plant is about the same as that giving maximum specific work for a CBT plant. 

It can be seen from Fig. 7.10 that the eurve for wcv lies above that for wh. As for the gas turbine eyele the pressure ratio for maximum effieiency in the eombined plant may be obtained by drawing a tangent to the work output curve from a point on the x-axis where x= 1 +7 (.(0— 1), i.e. X = 4.6 in the example. The optimum pressure ratio for the eombined plant (r = 18) is less than that for the gas turbine alone (r = 30) although it is still greater than the pres.sure ratio which gives maximum speeific work in the higher plant (r = 11). However, the efficieney tjcp varies little with r about the optimum point. 

Rice found high CCGT efficiencies with gas turbine reheat at optimum pressure ratios even higher than those discussed above. 

Horlock, J.H. (1995), The optimum pressure ratio for a CCGT plant, Proc. In.stn. Mech. Engrs. 209, 259-264. 

Pressure ratio. As the design pressure ratio across the compressor increases, the power output initially increases to a maximum and then starts to decrease. The optimum pressure ratio increases with increasing expander inlet temperature. Pressure ratios for industrial machines are typically in the range 10 to 15 but can be higher. For aero-derivative machines, pressure ratios are typically 20 to 30. 

Hydrostatic Bearing, Table 1 Optimum pressure ratio (Pr/Ps) for high stiffness design... 

A unique feature of the proposed system will allow the fuel cell and turbine modules to operate at independent pressures. The fuel cell will be operated at ambient pressure. This can increase the fuel cell stack life and save on piping and vessel costs. The turbine can then operate at its optimum pressure ratio. 

For a given firing temperature there is an optimum pressure ratio for achieving maximum thermal efficiency. 

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