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):
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.
|
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.
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.