Solution Detailed analysis of cycles, executed by a fluid flowing through open devices, is carried out by the open cycle daemons located in the specific branch of the open steady daemons. Launch the open cycle daemon located at the page  TEST. Daemons. Systems. Open. Steady. Specific. PowerCycles.  PC Model.

Let us set up the cycle as follows: Device-A (turbine): isentropic expansion from State-1 to State-2 ; Device-B (condenser): constant pressure heat rejection from State-2 and State-3; Device-C (pump): isentropic compression from State-3 to State-4; Device-D (boiler): constant pressure heat addition from State-4 to State-1 .

Evaluate the states as follows. Assume a mass flow rate of 1 kg/s as a basis. H2O is the default fluid. For each state enter the known properties, and press the Enter key.

State-1: Enter p1, T1, and mdot1 (assume 1 kg/s), and Calculate. 

State-2: Enter p2, s2 ('=s1'), mdot2 ('=mdot1'), and Calculate.

State-3: Enter p3 ('=p2'), x3 (=0 for saturated liquid), mdot3 ('=mdot1'), and Calculate.

State-4: Enter p4 ('=p1'), s4 ('=s3'), mdot4 ('=mdot1'), and Calculate.

Verify the calculated states graphically on a T-s diagram (as shown below). Notice that state-4 is coincident with state-3 (can you explain why?).

Having evaluated the principle states, it is time for setting up the four devies. Switch to the device panel and analyze each device as follows.

Device-A (Turbine): Load state-1 as the i1-state and state-2 as the e1-state, enter Qdot=0, and Calculate. Wdot_ext is calculated as 758 kW.

Device-B (Condenser): Load state-2 as the i1-state and state-3 as the e1-state, enter Wdot_ext=0, and Calculate. Qdot is calculated as -2037 kW.

Device-C (Pump): Load state-3 as the i1-state and state-4 as the e1-state, enter Qdot=0, and Calculate. Wdot_ext is calculated as -4.07 kW.

Device-D (Boiler): Load state-4 as the i1-state and state-1 as the e1-state, enter Wdot_ext=0, and Calculate. Qdot is calculated as 2792 kW.

Now switch to the cycle panel to find the thermal efficiency and net output calculated as 27.0% and 754.1 kJ/kg. (because mdot was chosen as 1 kg/s, the magnitude of Wdot_net/mdot is same as that of Wdot_net).

 For the parametric study, change p2 to 10 kPa, press the Enter key, and Super-Calculate to update all calculations. The new answers are calculated on the cycle panel as 35.3% and 1065 kJ/kg (see below). The minimum temperature in the cycle, 45.8 deg-C, is still high enough for the condenser to be cooled by circulating water at ambient temperature.

The TEST-codes, generated by the Super-Calculate operation, are listed below. Note how closely the codes follow the solution procedure.

Let us set up the cycle as follows: Device-A: isentropic pumping from State-1 to State-2 ; Device-B : constant pressure boiler with State-2 and State-4 as inlets and  State-3 and State-5 as exits; Device-C : high pressure isentropic turbine from State-3 to State-4 ; Device-D : low pressure isentropic turbine from State-4 to State-5 ; Device-E : constant pressure heat rejection from State-4 to State-1 .

State-1: Enter mdot1 (assume 1 kg/s),  p1 (15 kPa) and x1 (0%). Calculate . 

State-2: Enter p2  (15 MPa), s2 ('=s1'), and Calculate.

State-3: Enter p3 ('=p2'), T3 (620C) and Calculate.

State-4: Enter p4 ('=p5'), s4 ('=s3'), and Calculate. Note that p5 is not yet known.

State-5: Enter T5 ('=T3'), s5 ('=s6') and Calculate . Note that s6 is not yet known.

State-6: Choose 'More...' from the state selector to add more states to the menu. Choose State-6. Enter p6 ('=p1'), x6 (90%) and Calculate. 

Super-Calculate to propagates s6 back to State-5 and then p5 back to State-4, thus completing evaluation of all states. It is always a good practice to draw a T-s or some other thermodynamic plot to visualize the calculated states before proceeding to other panels.
 

Device-A: Select State-1 and State-2 as the i1- and e1-States , enter Qdot=0, and   Calculate.   The pumping power  is calculated as -15.17 kW. 

Device-B:  Select State-2 and State-4 as the i1- and e1-States ,  and  State-3 and State-5 as the e1- and e2-States , Calculate.   Click on the 'non-mixing' 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) . 

Device-C: Select State-3 and State-4 as the i1- and e1-States , enter Qdot=0, and   Calculate.   The work is calculated as Wdot_ext=360 kW.

Device-D: Select State-5 and State-6 as the i1- and e1-States ,  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  Super-Calculate to produce detailed output and the TEST-codes. Use  Super-Iterate   for further iteration if the solution is not complete. 

This is one of the rare instances where the Super-Iterate button has been used. One could avoid that by working in modules.  Working on State-1,3,4 and Device-d  (a Super-Calculate among them will completely evaluate State-1) first will reduce the need for iterations.

Solution Launch the open cycle daemon located at the page  TEST. Daemons. Systems. Open. Steady. Specific. PowerCycles.  PC Model.

Let us set up the cycle as follows: Device-A (turbines): Instead of treating the two turbines separately, let us analyze them as a composite device with two exits, State-3 and State 5, and one inlet, State-1. Note that State-2 and 4 are isentropic states, which are necessary to evaluate the actual exit states. Device-B (condenser): Constant pressure heat rejection from State-5 to State-6. Device-C (pump-I): Compression from State-6 to State-8 (with State-7 being the isentropic state). Device-D (FWH): Constant pressure mixing between State-3 and State-8, producing State-9. Device-E (pump-II): Compression from State-9 to State-11; (with State-10 being the isentropic state). Device-F (boiler): constant pressure heat addition from State-11 to State-1.

Let us assume a mass flow rate of 1 kg/s through the boiler and leave mdot3 (the rate of bleeding) unknown, expressing all other mass flow rates in terms of mdot1 and mdot3. Evaluate the states as follows.

State-1: Enter p1, T1, and mdot1 (assume 1 kg/s), and Calculate. 

State-2: Enter p2, s2 ('=s1'), mdot2 ('=mdot1'), and Calculate.

State-3: Enter p3 ('=p2'), h3 ('=h1+(h2-h1)*0.88'), and Calculate (mdot3 is unkown at this point).

State-4: Enter p4 ('=p1'), s4 ('=s3') and Calculate (mdot4 is never used and so can be left unknown).

State-5: Enter p5 ('=p4'), h5 ('=h3+(h4-h3)*0.88'), mdot5 ('=mdot1-mdot3'), and Calculate (mdot5 is unkown at this point).

State-6: Enter p6 ('=p4'), x6 ('=0', saturated liquid), mdot6 ('=mdot1-mdot3'), and Calculate (mdot6 is unkown at this point).

State-7: Enter p7 ('=p2'), s7 ('=s6') and Calculate (mdot7 is never used and so can be left unknown).

State-8: Enter p8 ('=p2'), h5 ('=h6-(h6-h7)/0.8'), mdot8 ('=mdot1-mdot3'), and Calculate (mdot8 is unkown at this point).

State-9: Enter p9 ('=p2'), x9 ('=0', saturated liquid), mdot9 ('=mdot1'), and Calculate.

State-10: Enter p10 ('=p1'), s10 ('=s9') and Calculate (mdot10 is never used and so can be left unknown).

State-11: Enter p11 ('=p1'), h11 ('=h9-(h9-h10)/0.8'), mdot11 ('=mdot1'), and Calculate.

Having evaluated the principle states as best as possible, it is time for setting up the devies. Switch to the device panel and analyze each device as follows.

Device-A (Turbine): Load state-1 as the i1-state, and state-3 and 5 as the e1 and e2 states respectively. Enter Qdot=0, and Calculate. Wdot_ext cannot be calculated at this time as mdot3 is still an unknown.

Device-B (Condenser): Load state-5 as the i1-state and state-6 as the e1-state, enter Wdot_ext=0, and Calculate. Qdot is unknown at this point.

Device-C (Pump): Load state-6 as the i1-state and state-9 as the e1-state, enter Qdot=0, and Calculate. Wdot_ext is is unknown at this point.

Device-D (Heater): Load state-3 and 8 as the i1 and i2 states and state-9 as the e1-state. Enter Qdot=0 and Wdot_ext=0, and Calculate. The energy equation produces mdot3 and posts it back to state-3 as shown below. The fraction of steam that is extracted at state-3 is, therefore, 0.1924.

At this point we can do a Super-Calculate to update all calculations. However, a few more devices remain to be analyzed.

Device-E (Pump-II): Load state-9 as the i1-state and state-11 as the e1-state, enter Qdot=0, and Calculate. Wdot_ext is calculated as -10.11 kW.

Device-F (Boiler): Load state-11 as the i1-state and state-1 as the e1-state. Enter Wdot_ext=0, and Calculate Qdot=2814 kW.

Super-Calculate one more time to update the cycle panel. The thermal efficiency and net output are calculated as 39.44% and 1109.6 kW respectively.

For the what-if scenario, change p2 to 500 kPa, press the Enter key, and Super-Calculate. The new answers are found to be mdot3=0.1764 kg/s, eta_th=39.35%, and Wdot_net= 1129.6 kW.

The TEST-Codes for the problem are reproduced below, which can be used to instanly regeneratre the solution (simply paste the TEST-codes into the I/O panel, click the Load button and then Super-Calculate).