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Cycle Calculations

To see how to set up and analyze thermodynamic cycles, consider a typical textbook problem (Problem 11.31, "Fundamentals of Thermodynamics", Sonntag, Borgnakke, and van Wylen, 5th edition, John Wiley):

"A steam power plant has a high pressure of 5 MPa and maintains 50 C in the condenser. The boiler exit temperature is 600 C. All the components are ideal except the turbine which has an actual exit state of saturated vapor at 50 C. Find the cycle efficiency with the actual turbine and the turbine isentropic efficiency."

Solution:

First, set the units in TPX to C and MPa.

It is a good practice to draw a sketch of the cycle (on paper - you can't do everything on a computer), and assign numbers to the states where you will need to find property information.

For this problem, there are 5 relevant states:

State 1: condenser outlet, pump inlet. Saturated liquid: T1 = 50 C, X1 = 0.

State 2: pump outlet at P2 = 5 MPa. The pump is ideal, so s2 = s1.

State 3: boiler exit. T3 = 600 C, P3 = P2.

State 4s: turbine exit state for ideal isentropic turbine. S4s = S3, P4s = P1.

State 4: real turbine exit state. P4 = P4s = P1, X4 = 1.

The table below was generated using the Property Calculator as follows.

p1131.jpg (31633 bytes)

First, a blank table was laid out on the worksheet by labeling the columns with the states, and the rows with the desired properties. Cell B4 was selected and the Property Calculator opened.

State 1:  "T X" was selected as the specified pair, and T, P, h, s, and x were written (as functions) in column B. All functions in the column were written in one step by simply pressing Calculate. After writing the functions, TPX automatically selected cell C4 as the default starting cell for the next calculation. The remaining columns were written in a similar way.

State 2: "P S" was selected, with P = 5, and S constant (double-click)

State 3: "T P" was selected, with T = 600, and P constant (double-click)

State 4s: "P S" was selected, the equation  "=B5" was entered in the P box, and S was held constant (double-click)

State 4: "P X" was selected, with X = 1, and P constant (double-click)

If you were to select a cell in the table above and look at its contents in the Formula bar, you would find that in fact TPX entered functions, not just numbers. Click here to see what is really in the cells.

After the table was laid out using the Property Calculator, the Calculator was closed and spreadsheet formulas were entered below the property table (not shown) for the   turbine work (h3 - h4 = 1074.4 kJ/kg) and the ideal work (h3 - h4s = 1338.9 kJ/kg). The turbine isentropic efficiency is defined as the actual work divided by the ideal work, so the isentropic efficiency is 0.802.

The cycle efficiency is the net work (turbine work out - pump work in, 1069.4 kJ/kg) divided by the heat input in the boiler (h3 - h2 = 3452.1 kJ/kg). Therefore, the overall cycle efficiency is 0.31.

That's the end of the problem as stated, and if you were doing it by hand (looking up properties on tables or in charts) it would be quite tedious to repeat the solution for other conditions. But with TPX and Excel it is trivial, so let's do it.

eff.gif (3831 bytes)In Excel, a "Data Table" can be created (on the Data menu), which is a table of one computed cell value vs. a range of values for an input cell. Let us ask the following question:

How does the cycle efficiency depend on the temperature at the boiler exit T3?

A data table was set up to answer this question, with the results shown below. This illustrates both the ease of answering "what-if" questions using TPX/Excel, and the desirability of a high boiler exit / turbine inlet temperature. (Unfortunately, real steam turbines cannot take temperatures as high as shown here, due to materials problems.) The entire process of generating this plot took less than 1 minute, with most of the time used to format the graph.

 

Once a data table is generated, TPX can add the data points to multiple process representation plots in one step, which is the subject of the next section.

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