One approach to increasing the efficiency of
steam power cycle is by extracting some of the steam from various
stages of the turbine and using it to preheat the compressed liquid
before it enters the boiler. This is done either by direct mixing
of the fluids (Open Feedwater Heater) or through a heat exchanger
(Closed Feedwater Heater), In many practical steam power plants
various combinations of open and closed feedwater heaters are
used, and systems using them are generally referred to as **Regenerative Cycles**.

We continue with the Reheat cycle developed
in **Chapter 8a** and examine
the performance effects of adding open and closed feedwater heaters.

**The Ideal Regenerative Reheat Cycle using
an Open Feedwater Heater**

We continue with the Reheat cycle developed
in **Chapter 8a**, and examine
the effect of adding a regenerative heat exchanger in the form
of an **Open Feedwater
Heater**, as shown below. We will find
that this system does result in an increase in thermal efficiency
by preheating the water before it enters the boiler, however at
the expense of a reduced power output. In the schematic diagram
we notice that many of the state and enthalpy values (indicated
in red)
have already been evaluated in **Chapter
8a**. The mass fraction of the steam bled at the outlet
of the HP turbine (2) as well as the state and enthalpy values
at stations (6) through (9) will be evaluated below.

For this example we have chosen the mixture pressure of the open feedwater heater as 200kPa. Notice that a portion of the steam is bled off the outlet of the HP turbine at a pressure of 1MPa, passed through a throttling valve reducing its pressure to 200kPa, and then mixed with the compressed liquid (also at 200kPa), ultimately resulting in saturated liquid at station (8). We first need to determine the mass flow fraction y of the bled steam required to bring the output of the open feedwater heater (8) to a saturated liquid state.

Notice that the work output is reduced by having
bled off a fraction y of the steam, and the boiler heat input
is reduced by the increased temperature of the compressed liquid
entering the boiler T_{9}. Thus:

We always confirm our results by the alternate evaluation of efficiency using the heat flow out from the condenser to the cooling water:

Thus we see a slight increase in efficiency
and reduction in power compared to the reheat system that we solved
in **Chapter 8a** (45%, 1910 kJ/kg).
Can we justify this added complexity for such a small gain in
efficiency? This was discussed in **Solved
Problem 4.2** in which we noted that a de-aerator is a necessary
vital component of a steam power plant with a condenser pressure
of 10 kPa - air leaking into the system causes corrosion as well
as a reduction in performance. The open feedwater heater naturally
includes a de-aerator. On a previous visit to the Gavin power
plant we were informed that the open feedwater heater can also
conveniently include a liquid water storage tank which enables
the feedwater pump to be the main power control of the system
by varying the mass flow rate of the steam. We were also informed
that using a single feedwater pump to increase the water pressure
from 10 kPa to 15 MPa is impractical, and in the Gavin power plant,
in addition to the condensate pump there is a booster pump to
bring the pressure from 10 kPa to the de-aerator pressure.

**Problem
8.1 - A 10 MPa Steam Power Plant with an
Open Feedwater Heater**

**Problem
8.2 - A Cogeneration Steam Power Plant
with an Open Feedwater Heater**

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**The Ideal Regenerative Reheat Cycle using
a Closed Feedwater Heater**

We again extend the Reheat cycle developed
in **Chapter 8a**, and examine
the effect of adding a regenerative heat exchanger in the form
of a **Closed Feedwater
Heater**, as shown below. We have not
included an open feedwater heater even though we learned in the
previous example that it is a necessary component of a high pressure
steam cycle, since we are using this example to develop the techniques
for analyzing closed feedwater heaters. The various state values
shown on the schematic (in red) have been evaluated in previous sections.

From the schematic diagram we see that a portion
of the steam is bled off from the output of the HP turbine at
state (2), and then used to heat the high pressure liquid, ultimately
condensing to a subcooled liquid at state (8). A finite temperature
difference is a necessary condition for heat transfer to occur,
and from the temperature distribution plot shown above we see
that the closed feedwater heater behaves as a counterflow heat
exhanger, in which the compressed liquid water entering at state
(6) is heated to the saturation temperature of the bled steam
(T_{sat@1MPa} = 180°C). In typical closed feedwater
heaters (such as those used at the Gavin Power Plant) there are
three distinct zones of heat transfer as shown in the simplified
schematic diagram below:

The bled steam first enters the **desuperheating zone enclosure** and is cooled while raising the temperature of the
feedwater leaving the heater to a level approaching or equal to
the steam saturation temperature. The **condensing zone** is the largest
heat transfer region within the heater shell. The major portion
of heat transfer takes place here as the steam condenses and gives
up its latent heat. The **subcooling
zone**, which is enclosed in a separate
shrouded area within the shell, further cools the condensed steam
while heating the incoming feedwater. The following photograph
shows one of the seven sets of closed feedwater heaters used in
the Gavin Power Plant Typically we find that the subcooled liquid
is reduced to within around 4°C to 6°C above the incoming
feedwater temperature.

The *P-h* diagram plot of this system
follows, and we notice on the diagram that the high pressure feedwater
is heated from state (6) to state (7) before entering the boiler,
while a mass fraction y of the bled steam is cooled from the HP
turbine outlet state (2) to a subcooled liquid at state (8). The
subcooled liquid is then passed through a throttling valve before
being returned to the condenser at state (9). As we have learned
from our studies of refrigerators, a throttling valve is simply
represented on the *P-h* diagram by a vertical line, since
from the energy equation we find that h_{8} equals h_{9}.

We consider first the evaluation of the mass flow fraction y, which is bled from the output of the HP turbine on order to heat the compressed water at state (8) to the saturation temperature of the steam at station (2):

Once again we notice that the work output is
reduced by having bled off a fraction y of the steam, and the
boiler heat input is reduced by the increased temperature of the
compressed liquid entering the boiler T_{7}. Thus:

Thus the system thermal efficiency becomes:

The alternative evaluation of thermal efficiency using the heat transfer from the condenser to the cooling water:

Notice that the thermal efficiency is slightly more than that of the previous example with an open feedwater heater, however with even less power output. In practice one normally finds a combination of open and closed feedwater heaters, and in the Gavin power plant there are seven closed feedwater heaters and one de-aerator/open feedwater heater. In the following section we develop the analysis technique of this type of system.

**Problem
8.3 - A Reheat Steam Power Plant with a
Closed Feedwater Heater**

________________________________________________________________________

**The Ideal Regenerative Reheat Cycle using
both an Open and a Closed Feedwater Heater**

In a practical power plant one may find various
combinations of closed and open feedwater heaters. For example
the **Gavin Power Plant** has
one open- and 7 closed-feedwater heaters in each of the two sections
of the plant (refer to the Case Study at the end of this section).
In the following example we have chosen one open and one closed
feedwater heaters in order to illustrate the method of analysis,
however the same approach will apply to any combination of feedwater
heaters.

Once again we evaluate the required mass flow
fractions y_{1} and y_{2} of the bled steam in
order to bring the compressed water at the entrance to the boiler
(state (10)) to the correct state. An enthalpy inventory and energy
balance on both the closed and open feedwater heaters leads to
the following:

The resultant net work output and heat input now become:

And finally we obtain the thermal efficiency of the overall system as follows:

As always, we check this result against the equivalent method of considering only heat in and heat rejected in the condenser to the cooling water

.

**Case
Study - The General James M. Gavin Steam Power Plant**

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