
9. Daemons>Vapor Power Cycles> Examples 
EXAMPLE1 
In a steam power plant operating on a reheat Rankine cycle, steam
enters the HP turbine at 15 MPa and 620^{o}C and is condensed in
the condenser at a pressure of 15 kPa. If the moisture content in the turbine
is not to exceed 10%, determine (a) the reheat pressure and (b) the thermal
efficiency of the cycle.
Whatif scenario: (c) How would the answers change if the moisture content in the turbine were not to exceed 15%? 
Time Saver: To reproduce the visual solution, copy and paste these TESTcodes on the I/O Panel of the appropriate daemon, then click the Load and SuperCalculate buttons. This is
one of the cases, where you have to use the SuperIterate button after SuperCalculate
to continue iterations between the state and device panels.


Step 1: Launch the appropriate open cycle daemon. Step 2: Set up the cycle. Step 3: Calculate the states.

Solution
Launch the open cycle daemon located at the page TEST. Daemons. Systems. Open. Steady. Specific. PowerCycles. PhaseChange. Let us set up the cycle as follows: DeviceA: isentropic pumping from State1 to State2 ; DeviceB : constant pressure boiler with State2 and State4 as inlets and State3 and State5 as exits; DeviceC : high pressure isentropic turbine from State3 to State4 ; DeviceD : low pressure isentropic turbine from State4 to State5 ; DeviceE : constant pressure heat rejection from State4 to State1 . State1: Enter mdot1 (assume 1 kg/s), p1 (15 kPa) and x1 (0%). Calculate . State2: Enter p2 (15 MPa), s2 ('=s1'), and Calculate. State3: Enter p3 ('=p2'), T3 (620C) and Calculate. State4: Enter p4 ('=p5'), s4 ('=s3'), and Calculate. Note that p5 is not yet known. State5: Enter T5 ('=T3'), s5 ('=s6') and Calculate . Note that s6 is not yet known. State6: Choose 'More...' from the state selector to add more states to the menu. Choose State6. Enter p6 ('=p1'), x6 (90%) and Calculate. SuperCalculate to propagates s6 back to State5
and then p5 back to State4, thus completing evaluation of all states. It
is always a good practice to draw a Ts or some other thermodynamic plot
to visualize the calculated states before proceeding to other panels.

Fig. 1 Image of State4. Only after State6 is Calculated, is State4 updated by SuperCalculate. 
Step 4: Analyze the open steady devices. 
On Device Panel work on the
five devices.
DeviceA: Select State1 and State2 as the i1 and e1States , enter Qdot=0, and Calculate. The pumping power is calculated as 15.17 kW. DeviceB: Select State2 and State4 as the i1 and e1States , and State3 and State5 as the e1 and e2States , Calculate. Click on the 'nonmixing' radio button. Enter Wdot_ext=0. The heat transfer is 3831 kW (note that we could have broken the boiler into two devices, steam generator and superheater) . DeviceC: Select State3 and State4 as the i1 and e1States , enter Qdot=0, and Calculate. The work is calculated as Wdot_ext=360 kW. DeviceD: Select State5 and State6 as the i1 and e1States , enter Qdot=0 kW and Calculate. The work is calculated as Wdot_ext=1349 kW. On the Cycle panel, no further work is necessary. The thermal efficiency is calculated as eta_th=44.2% . Use SuperCalculate to produce detailed output and the TESTCode. Use SuperIterate for further iteration if the solution is not complete. This is one of the rare instances where the SuperIterate button has been used. One could avoid that by working in modules. Working on State1,3,4 and Deviced (a SuperCalculate among them will completely evaluate State1) first will reduce the need for iterations. 
Step 5: For the whatif study, change a variable, Calculate and SuperCalculate. 
For the parametric study,
change x6 to 85%, Calculate and SuperCalculate to obtain the new efficiency as 43.24% (the efficiency
increases with moisture content for cycles without superheat). 
Fig. 2 Image of Device Panel (DeviceB, the boiler).
Notice that the NonMixing option must be turned on for the nonmixing flow of a heat exchanger. 
EXAMPLE2 
A combined gas turbinesteam power plant.has a net power
output of 50 MW. Air enters the compressor of the gas turbine at 100 kPa,
300 K, and has a compression ratio of 12 and an isentropic efficiency of
85%. The turbine has an isentropic efficiency of 90% and has the inlet conditions
of 1200 kPa and 1400 K, and an exit pressure of 100 kPa. The air from the
turbine exhaust passes through a heat exchanger and exits at 400 K. On the
steam turbine side, steam at 8 MPa, 400^{o}C enters the turbine,
which has an isentropic efficiency of 85%, and expands to the condenser
pressure of 8 kPa. Saturated water enters the pump, which has an isentropic
efficiency of 80% at 8 kPa. Determine (a) the ratio of mass flow rates in
the two cycles, (b) the mass flow rate of air if the net power is 50 MW,
(c) the thermal efficiency.
Whatif scenario: (d) How would the thermal efficiency change if the compression
ratio is increased to 15? Solution
See Ex3 in Gas Power Cycle chapter. 
More examples! 
For more solved examples on this topic, visit the TEST>Slides and TEST.Problems pages. If you would like more examples on a particular topic, please send us a note using the TEST.Comments page. 
Copyright 1998: Subrata Bhattacharjee 