ME301 Final Project
Mannat Gill, Olivia Chamberlain, Keegan King, David Godun
Introduction/Background
The Rankine cycle is the fundamental thermodynamic cycle for large-scale electricity generation.
By converting thermal energy to motion, the phase change to superheated steam can use the water’s large
latent heat of vaporization to transfer energy more efficiently while keeping the temperature constant
during phase changes. Unlike the air-standard cycle, the Rankine cycle is highly efficient while also being
non-toxic, inexpensive, and widely available. This combination of high efficiency, practical working fluid
properties, and scalability makes the Rankine cycle the most suitable choice for power generation. This
report will focus on coal-powered generation plants, though these principles apply to many other forms of
power generation.
Cycle Description
Coal plants use Rankine Cycles to generate
power from heat. A standard Rankine Cycle starts by
pumping saturated liquid water (State 1) to a higher
pressure (State 2) and enters a boiler. Coal
combustion superheats the water into steam (State 3),
then expands through a turbine (State 4) to perform
work. A condenser then returns it to a lower-pressure
liquid (State 1). This cycle repeats.
While efficient, there are still unavoidable losses, such as combustion inefficiencies and heat
escape, which can be handled with insulation. The condenser is the primary source of loss, which ejects
heat from the water to bring it back to liquid form. The pump can then repressurize it much more
efficiently than a gas. This is necessary as the process of driving the turbine increases entropy and causes
the steam to lose pressure. If the ejected heat can be reduced or repurposed, this inefficiency can be
reduced.
Many modern plants don’t use a simple
Rankine Cycle. They use a variation called a
Reheating Rankine Cycle. Instead of condensing the
water right after the turbine, the cycle pushes the
steam back into the boiler to reheat and push another
turbine. However, each turbine you add generates
entropy and drops the pressure, causing diminished
returns.
This method requires a few things to work
well. As the pressure of the steam drops after every turbine, different turbines that are more suited to each
pressure state are required to maximize efficient energy production. It would also be beneficial to lower
entropic inefficiencies in each turbine to minimize pressure losses and allow it to be repeated further.
While requiring additional considerations with the turbines, it allows for more work to be
produced per unit of heat energy put into the system. It also extracts more work for the heat energy added
into the system before the condenser ejects heat. This can theoretically be scaled infinitely, but energy
gains would quickly diminish, and the extra cost, complexity, and size would become unrealistic. In
current coal plant applications, the most that has been achieved is a double reheat.
Design Considerations
In a coal-fired Rankine cycle for electricity generation, the central design objective is to
maximize thermal efficiency, since this directly determines how much electrical power is produced per
unit of fuel. Thermal efficiency is defined as 𝜂�𝑡�ℎ=𝑊�𝑛�𝑒�𝑡�/𝑄�𝑖�𝑛�. Using standard Rankine cycle analysis,
this can be written in terms of enthalpies as:
𝜂�𝑡�ℎ=(ℎ3−ℎ4) −(ℎ2−ℎ1) / (ℎ3−ℎ2)
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Because pump work is relatively small, efficiency is primarily affected by how much
useful work is extracted during turbine expansion relative to the heat added in the boiler. Thus, the design
criteria focus on increasing turbine work and raising the average temperature at which heat is added,
while minimizing irreversibility.
Two of the most important parameters in achieving high thermal efficiency in a standard Rankine
Cycle are boiler pressure and turbine inlet temperature. Increasing the boiler pressure increases the
average temperature of the heat that is added into the boiler, therefore increasing efficiency: higher boiler
pressure increases h3 (for superheated steam), leading to greater turbine work (Wt = h3 - h4). However, this
introduces risk of excessive moisture and blade erosion.
Similarly, increasing the turbine inlet temperature significantly improves thermal efficiency by
increasing the maximum cycle temperature. This raises the enthalpy at turbine entry h3 and increases the
enthalpy drop across the turbine, therefore increasing work output. A greater �������� increases the
numerator of the efficiency equation more rapidly than the denominator, resulting in a higher thermal
efficiency. However, increasing turbine inlet pressure is limited by material performance at high
temperatures.
Overall, the design of a coal-fired Rankine cycle is a balance between maximizing thermal
efficiency and respecting practical limitations. These are all separate from any reheating considerations,
which would increase efficiency even more. As a result, modern plants typically have an efficiency of
around 41% to maintain safe and durable operation.
Graph 1:
Graph 2:
Comparing Thermal Efficiency (metric) to Boiler Pressure and Turbine Inlet Temperature (parameters): generated
by AI prompts to create Python matplotlib plots, while also comparing a basic Rankine cycle to one modified or with
additions for better thermal efficiency.
Conclusion
The Rankine cycle is a very efficient system for converting heat to usable work. However,
because it involves transforming heat into a higher-quality energy in electricity, there is a loss in total
energy. There are several limited ways to reduce wasted energy. By superheating the water and
pressurizing it further, you can generate more power per cycle. In the same vein, the principle of heating
the water multiple times per cycle, each one can generate even more power.
However, the condenser remains the biggest inefficiency in the cycle, and there isn’t a way to
avoid it entirely. You can repurpose that heat in some other system, but even that is just kicking the bucket
down the street. Each cycle can be optimized, but there is a certain amount of unavoidable waste in each
iteration. We are just working around that inevitability.
References
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https://usea.org/sites/default/files/032015_High-efficiency%20power%20generation%20%20review%20of%20alternative%20systems_ccc247.pdf
https://www.sciencedirect.com/topics/engineering/steam-rankine-cycle
https://www.sciencedirect.com/org/science/article/pii/S0199859525000375
file:///Users/mannat/Downloads/a-rankine-cycle-design-project-for-assessment-of-abetstudent-outcome-1.pdf
(7) How the Rankine Cycle Powers Lakvijaya Coal Power Plant | LinkedIn
https://www.sciencedirect.com/science/article/pii/S0360544221013165
https://www.researchgate.net/figure/Double-reheat-cycle-layout-a-and-thecorresponding-T-s-diagram-b_fig5_228969222
Python Visual Code Studio (Graphs 1 and 2)