In an effort to decentralize the national power
distribution grid, the following supercritical (25 MPa), coal
fired steam power plant (modeled after the **Gavin
Power Plant** in Cheshire, Ohio) has been proposed to service
about 10,000 households in Athens, Ohio. It is to be placed close
to the sewage plant on the east side of Athens and cooled by water
from the Hocking river. We consider first a simplified system
as shown below. Notice that we have replaced the "Boiler"
with a "Steam Generator", since at supercritical pressures
the concept of boiling water is undefined. Furthermore we have
specifically split the turbine into a High Pressure (HP) turbine
and a Low Pressure (LP) turbine since we will find that having
a single turbine to expand from 25MPa to 10kPa is totally impractical.
Thus for example the Gavin Power Plant has a turbine set consisting
of 6 turbines - a High Pressure Turbine, an Intermediate Pressure
(Reheat) turbine, and 4 large **Low
Pressure turbines** operating in parallel.

Note that prior to doing any analysis we always
first sketch the complete cycle on a ** P-h diagram** based on the pressure, temperature, and quality data
presented. This leads to the following diagram:

On examining the *P-h* diagram plot we
notice that the system suffers from two major flaws:

- The outlet pressure of the LP turbine at port (3) is 10 kPa, which is well below atmospheric pressure. The extremely low pressure in the condenser will allow air to leak into the system and ultimately lead to a deteriorated performance.
- The quality of the steam at port (3) is 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. (Refer:**Tour of the Gavin Power Plant - Feb. 2000**)

The following revised system diagram corrects both flaws. The steam at the outlet of the HP turbine (port (2)) is reheated to 550 C before entering the LP turbine at port (3). Also the low pressure liquid condensate at port (5) is pumped to a pressure of 800 kPa and passed through a de-aerator prior to being pumped by the feedwater pump to the high pressure of 25 MPa.

This system is referred to as a **Reheat** cycle,
and based on the data above is plotted on the *P-h* diagram
as follows:

Thus we see that in spite of the complexity
of the system, the *P-h* diagram plot enables an intuitive
and qualitative initial understanding of the system. Using the
methods described in **Chapter 4b**
for analysis of each component, as well as the **steam
tables**, determine the following:

- 1) Assuming that both turbines are adiabatic and neglecting kinetic energy effects determine the combined output power of both turbines [10.6 MW].

- 2) Assuming that both the condensate pump and the feedwater pump are adiabatic, determine the power required to drive the two pumps [-204 kW].

- 3) Determine the total heat transfer to the steam generator, including the reheat system [26.1 MW].

- 4) Determine the overall thermal efficiency
of this power plant. (Thermal efficiency (
_{th}) is defined as the net work done (turbines, pumps) divided by the total heat supplied externally to the steam generator and reheat system) [40 %].

- 5) Determine the heat rejected to the cooling water in the condenser [-15.7 MW].
- 6) Assume that all the heat rejected in the condenser is absorbed by cooling water from the Hocking River. To prevent thermal pollution the cooling water is not allowed to experience a temperature rise above 10°C. If the steam leaves the condenser as saturated liquid at 40°C, determine the required minimum volumetric flow rate of the cooling water [22.6 cubic meters/minute].

- 7) Discuss whether you think that the proposed
system can be cooled by the Hocking river. You will need to do
some research to determine the minimal seasonal flow in the river
in order to validate your decision. (
*Hint-***Google**: Hocking River Flow)

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Engineering Thermodynamics by Israel Urieli is licensed under a
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