9. Daemons>Vapor Power Cycles> Examples
|| In a steam power plant operating on a reheat Rankine cycle, steam
enters the HP turbine at 15 MPa and 620oC 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.
What-if 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 TEST-codes on the I/O Panel of the appropriate daemon, then click the Load and Super-Calculate buttons.
one of the cases, where you have to use the Super-Iterate button after Super-Calculate
to continue iterations between the state and device panels.
Step 1: Launch
the appropriate open cycle
Step 2: Set up the cycle.
Step 3: Calculate the states.
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: 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.
|Fig. 1 Image of State-4. Only after State-6 is Calculated, is State-4 updated by Super-Calculate.|
Step 4: Analyze the open steady devices.
|On Device Panel work on the
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-Code. 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.
Step 5: For the what-if study, change a variable, Calculate and Super-Calculate.
|For the parametric study,
change x6 to 85%, Calculate and Super-Calculate to obtain the new efficiency as 43.24% (the efficiency
increases with moisture content for cycles without superheat).
|Fig. 2 Image of Device Panel (Device-B, the boiler).
Notice that the Non-Mixing option must be turned on for the
non-mixing flow of a heat exchanger.
|| A combined gas turbine-steam 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, 400oC 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.
What-if scenario: (d) How would the thermal efficiency change if the compression
ratio is increased to 15?
See Ex-3 in Gas Power Cycle chapter.
|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|