In this example we wish to evaluate the following:
The following example is that of a basic steam
power plant as presented by Potter & Somerton - Problem 4-29
(Solved Problems). Unless otherwise specified we assume that the
turbine and the pump (as well as all the interconnecting tubing)
are adiabatic, and the condenser exchanges all of its heat with
the cooling water. We wish to evaluate the performance of this
system under the conditions shown in the diagram, including the
power of the turbine and pump, heat transfer rates of the boiler
and condenser, and thermal efficiency of the system.
In this example we wish to evaluate the following:
th), defined as the net work done by the system divided
by the heat supplied to the boiler.
Do not be intimidated by the complexity of this system. We will find that we can solve each component of this system separately and independently of all the other components, always using the same approach and the same basic equations. We first use the information given in the above schematic to plot the four processes (1)-(2)-(3)-(4)-(1) on the P-h diagram. Notice that the fluid entering and exiting the boiler is at the high pressure 10 MPa, and similarly that entering and exiting the condenser is at the low pressure 10 kPa. State (1) is given by the intersection of 10 kPa and 40°C, process (1)-(2) follows the constant temperature line, since T2 = T1 = 40°C, state (3) is given by the intersection of 10 MPa and 600°C, and state (4) is given as 10 kPa at 100% quality (saturated vapor).
We will cover in class the methods of evaluating
the solution of this exercise using the steam tables. The usefulness
of plotting the system processes on the P-h diagram is
that we can obtain a convenient visual check of our calculations
and estimate the performance of this system by inspection.
The analysis follows
Thus the P-h diagram is a powerful tool for quantitatively evaluating the approximate performance of the system to a high degree of accuracy. Unfortunately what it does not show is that this power plant is in fact a poorly designed plant. Actual power plants have efficiencies in the upper thirties. In this case the turbine has a very poor performance, however if we improve the performance of the turbine then it will self destruct because of large amounts of water droplets condensing on the turbine blades (can you see from the P-h diagram why this would happen?). This is a real, practical problem. On a previous tour of the Gavin Power Plant we were shown that the large low pressure turbine blades had to be replaced because of inefficiency due to pitting (see picture).We will have to wait patiently until we consider entropy and the h-s diagram in Chapter 6 in order to do a qualitative evaluation of the turbine, as well as of the entire steam power plant.
