We introduced the basic Steam Power Plant in **Chapter
4b**, however we could only evaluate the
turbine and feedwater pump after we introduced the concept of entropy
in **Chapter
6**a. In this Chapter
we will consider ideal steam power cycles including isentropic
turbines and pumps. This will allow us to determine the maximum
performance of these systems, and evaluate the influence of various
components on this performance.

**The pressure-enthalpy ( P-h) diagram**

The common method of describing steam power plant
systems is by plotting them on a *T-s*
(temperature-entropy) diagram for steam. This is done
exclusively in all thermodynamic text books that I have evaluated
over many years. We find this approach cumbersome, non-intuitive and
even incorrect in the description of feedwater pumps. We will make
exclusive use of *P-h*
(pressure-enthalpy) diagrams (which we inroduced in
**Chapter
4b**) to describe the various steam power
systems and we will require that all problems to be solved should
first be drawn on the *P-h* diagram.

A typical *P-h*
diagram for steam is shown below. One aspect of the
diagram that we have ignored until now are the various constant
entropy lines drawn in the superheated and high quality section of
the diagram. We will use these lines to indicate the path of an
isentropic turbine for the ideal cycles described below. We do not
require this for the feedwater pumps since, as we determined in
**Chapter
6a**, the isentropic pump follows the
constant temperature line.

This is shown below as an **Ideal
Rankine cycle**, which is the simplest
of the steam power cycles. We have specifically split the turbine
into a High Pressure (HP) turbine and a Low Pressure (LP) turbine
since it is impractical for a single turbine to expand from 15MPa to
10kPa.

As stated above, our approach is that prior to doing
any analysis we will always first sketch the complete cycle on a *P-h*
diagram based exclusively on the pressure and temperature data
presented, as follows:

Notice that since both turbines are considered ideal,
they follow the isentropic curve (1)-(2). From the *P-h*
diagram we see that the LP turbine output (station (2))
has a quality of 80%. This is unacceptable. The condensed water will
cause erosion of the turbine blades, and we should always try to
maintain a quality of above 90%. One example of the effects of this
erosion can be seen on the blade tips of the final stage of the **Gavin
LP turbine**. During 2000, all four LP
turbines needed to be replaced because of the reduced performance
resulting from this erosion.

Thus once we have determined from the *P-h*
diagram that this cycle is impractical we have no reason to continue
with the analysis, and prefer to extend this into an Ideal Reheat
steam power cycle as follows.

**A High Pressure Ideal Reheat Steam Power Cycle**

We extend the above example to the more practical
**Ideal Reheat**
cycle as shown below. In this example the HP turbine
expands the steam from 15 MPa to 1 MPa, and the steam is subsequently
reheated back to 600°C before being expanded in the LP turbine to 10
kPa.

Again we plot this cycle on the *P-h* diagram
and compare it to the previous situation of no reheat, as shown
below:

We notice that reheating the output of the HP turbine back to 600°C (process (2)-(3)) allows both significantly more power output as well as increasing the quality at the LP turbine output (4) to 98%.

The method of analysis is similar to that developed
in **Chapter
4b**, in which we consider each component
as a separate control volume.

1) Assuming both turbines are isentropic (adiabatic and reversible), and neglecting kinetic energy effects we use the

**steam tables**to determine the combined work output of both turbines.

2) In this ideal cycle we assume that the feedwater pump is isentropic. Furthermore, since the suction temperature of the water is 46°C, we assume that it behaves as an incompressible liquid, even at 15 MPa. Recall the section from

**Chapter 4b**where we derived the**energy equation for an incompressible liquid**.

3) The total heat transfer to the boiler, including the reheat system:

4) The thermal efficiency of the ideal Rankine reheat system, defined as the net work done (turbines, pump) divided by the total heat supplied to the boiler:

Notice that we could have also determined the thermal efficiency by the simpler method of evaluating the condenser heat transferred to the cooling water, thus:

This is an excellent check and should always be done
to validate your answer. The reason why we have preferred to evaluate
the output power directly is that it *is* the primary purpose of
a steam power plant, thus we are always interested in the various
components (turbines, pumps) that directly influence its value.
Thermal efficiency is important in its own right, however only on
condition that we can satisfy the output power requirements of the
steam power plant.

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Engineering Thermodynamics by Israel
Urieli is licensed under a Creative
Commons Attribution-Noncommercial-Share Alike 3.0 United States
License