Vapor Cycle Exergy Analysis—Turbine and Pump
Reconsider the turbine and pump of Example 8.2. Determine for each of these components the rate at which exergy is destroyed, in MW. Express each result, and the net power output of the plant, as a percentage of the exergy entering the plant with the fuel. Let T_{0}=22^{\circ} C , p_{0}=1 atm.
Known A vapor power cycle operates with steam as the working fluid. The turbine and pump each have an isentropic efficiency of 85%.
Find For the turbine and the pump individually, determine the rate at which exergy is destroyed, in MW. Express each result, and the net power output, as a percentage of the exergy entering the plant with the fuel.
Schematic and Given Data:
Engineering Model
1. The turbine and the pump can each be analyzed as a control volume at steady state.
2. The turbine and pump operate adiabatically and each has an isentropic efficiency of 85%.
3. Kinetic and potential energy effects are negligible.
4. Only 69% of the exergy entering the plant with the fuel remains after accounting for the stack loss and combustion exergy destruction.
5. T_{0}=22^{\circ} C , p_{0}=1 atm.
Analysis The rate of exergy destruction can be found by reducing the exergy rate balance or by use of the relationship \dot{ E }_{ d }=T_{0} \dot{\sigma}_{ cv }, where \dot{\sigma}_{ cv } is the rate of entropy production from an entropy rate balance. With either approach, the rate of exergy destruction for the turbine can be expressed as
\dot{ E }_{ d }=\dot{m} T_{0}\left(s_{2}-s_{1}\right)
From Table A-3, s_{1}=5.7432 kJ / kg \cdot K . \text { Using } h_{2}=1939.3 kJ / kg from the solution to Example 8.2, the value of s_{2} can be determined from Table A-3 as s_{2}=6.2021 kJ / kg \cdot K. Substituting values
\dot{ E }_{ d }=\left(4.449 \times 10^{5} kg / h \right)(295 K )(6.2021-5.7432)( kJ / kg \cdot K )
=\left(0.602 \times 10^{8} \frac{ kJ }{ h }\right)\left|\frac{1 h }{3600 s } \right| \left|\frac{1 MW }{10^{3} kJ / s }\right|=16.72 MW
From the solution to Example 8.7, the net rate at which exergy is supplied by the cooling combustion gases is 231.28 MW. The turbine rate of exergy destruction expressed as a percentage of this is (16.72/231.28)(100%) = 7.23%. However, since only 69% of the entering fuel exergy remains after the stack loss and combustion exergy destruction are accounted for, it can be concluded that 0.69 × 7.23% = 5% of the exergy entering the plant with the fuel is destroyed within the turbine. This is the value listed in Table 8.4.
| TABLE 8.4 Vapor Power Plant Exergy Accounting^{a} | |
| Outputs | |
| Net power out^{b} | 30% |
| Losses | |
| Condenser cooling water^{c} | 1% |
| Stack gases (assumed) | 1% |
| Exergy destruction | |
| Boiler | |
| Combustion unit (assumed) | 30% |
| Heat exchanger unit^{d} | 30% |
| Turbine^{e} | 5% |
| Pump^{f} | – |
| Condenser^{g} | 3% |
| Total | 100% |
| ^{a} All values are expressed as a percentage of the exergy carried into the plant with the fuel. Values are rounded to the nearest full percent. Exergy losses associated with stray heat transfer from plant components are ignored. | ^{b}Example 8.8. |
| ^{c}Example 8.9. | |
| ^{d}Example 8.7. | |
| ^{e}Example 8.8. | |
| ^{f}Example 8.8. | |
| ^{g}Example 8.9. | |
Similarly, the exergy destruction rate for the pump is
\dot{ E }_{ d }=\dot{m} T_{0}\left(s_{4}-s_{3}\right)
With s_{3} from Table A-3 and s_{4} from the solution to Example 8.7
\dot{ E }_{ d }=\left(4.449 \times 10^{5} kg / h \right)(295 K )(0.5957-0.5926)( kJ / kg \cdot K )
=\left(4.07 \times 10^{5} \frac{ kJ }{ h }\right)\left|\frac{1 h }{3600 s }\right| \left|\frac{1 MW }{10^{3} kJ / s }\right|=0.11 MW
Expressing this as a percentage of the exergy entering the plant as calculated above, we have (0.11/231.28)(69%) = 0.03%. This value is rounded to zero in Table 8.4.
The net power output of the vapor power plant of Example 8.2 is 100 MW. Expressing this as a percentage of the rate at which exergy is carried into the plant with the fuel, (100/231.28) (69%) = 30%, as shown in Table 8.4.
Skills Developed
Ability to…
• perform exergy analysis of a power plant turbine and pump.
Quick Quiz
What is the exergetic efficiency of the power plant? Ans. 30%.
