Environment & Energy
Thermal Cycles
Conversion of Energy
Valentim M B Nunes
Unidade Departamental de Engenharias
Polytechnic Institute of Tomar, March, 2015
Introduction
The development of the steam engine, an invention that secured the first two
centuries of the industrial revolution, preceded the discovery of scientific
principles involved, in particular the production of mechanical work on a
machine that uses combustion with air.
The scientific knowledge that explains the
“production” of work (energy) from
different types of combustion is derived
from the laws of thermodynamics.
James Watt (1736 – 1819)
We will review how the laws of thermodynamics govern the operation of these
sources of mechanical work and particularly how those laws limit the amount
of mechanical work that can be obtained from the combustion of a given
amount of fuel.
Work
Thermodynamics studies the interaction between a given material system and
its surroundings or exterior. It is through these interactions that we are able to
produce mechanical work or other useful effects on the exterior. There are two
forms of interaction between a system and its exterior, called work and heat.
Each of these is a process in which the system and its exterior suffers chemical
or physical modifications related to the type of interaction, heat, work or both
simultaneously.
There are many examples of interaction for performing work. Consider a gas
contained in a cylinder, closed at one end and fitted with a movable piston.
Heat
The other form of interaction of the system with the surroundings its by heat
transfer. A variation in temperature, ΔT, corresponds to a heat transfer Q given
by:
Q  CT
where C is the heat capacity.
Usually we call this interaction by heat transfer, although the energy is changed
in a process of this type.
Zeroth Law of thermodynamics
The Zeroth Law of thermodynamics is a law of thermal equilibrium. The
thermal energy flows from a region of high temperature to another at lowest
temperature, with a diathermic wall between the two regions.
T/K = t/°C + 273.15
The 1st Law of Thermodynamics
One of the fundamental laws of Nature is the law of conservation of energy.
The energy of a system can take several forms (for example, kinetic, potential,
heat, light), but cannot be created nor destroyed.
Etotal  EC  EP  U
For closed systems, macroscopically at rest and without changes in the
gravitational field:
U  Q  W
The internal energy of an isolated system is constant. In a closed
system it can only be transferred by heat flux or work performed.
The 2nd Law of Thermodynamics
When designing a thermal power station the aim is to create a system that
converts the energy of a fuel into work. If we consider the combustion of a
fossil fuel, so the aim is to convert all the energy of the fuel in work, such as
the first law allows.
However, the Second Law of Thermodynamics states that a cyclical process in
which heat from a single source is entirely converted to work cannot exist.
Instead, only part of the heat can be converted to work; the remainder has to
be rejected to a reservoir of heat at lower temperature than the heat source.
The 2nd Law of Thermodynamics
The 2nd law of thermodynamics recognizes that there are fundamental
asymmetries in Nature. For example, bodies warmer than the environment
will cool spontaneously, but objects at room temperature do not become
warmer spontaneously.
The heat transfers spontaneously from hot bodies to cold bodies.
Cold body
Hot body
Q
The transformation of heat into work must be accompanied by the transfer of
part of the heat to a cold source.
Formulations of the 2nd Law
The Kelvin formulation of the second Law states that it is impossible to have a
process in which the only result is the absorption of heat from a reservoir and
its complete conversion to work.
The second law says that the transformation of
heat into work must be accompanied by the
transfer of part of the heat to a cold source.
Another asymmetry of Nature: it is impossible
to convert heat fully in work, but there is no
restriction on conversion of work into heat.
Combustion of fossil fuels
The source of energy that is used in the combustion of fossil fuels systems is
the chemical energy that is released when the fuel is oxidized by burning with
air. The most common fossil fuels are hydrocarbons, mixtures of molecules
composed of carbon and hydrogen. After the complete combustion, the fuel is
oxidized to carbon dioxide and water vapor, releasing energy.
Designating the fuel molecules by CnHm, where n and m are the number of
atoms of carbon and hydrogen in the molecule of fuel, the molecular
rearrangement that accompanies the complete oxidation can be
represented by the reaction:
Fuel Heating Value
When a mixture of fuel and air is burned, the temperature of combustion
products formed is much higher than the mixture. In many cases, the heat can
be transferred from hot combustion products to a colder fluid; for example, a
boiler heats water and then bring it to ebullition by converting it into water
vapor. The amount of heat available for this process is the calorific value of the
fuel (fuel heating value) and is usually expressed in units of energy per unit
mass of fuel.
Ideal thermal cycles
To understand the implications of the laws of thermodynamics to the
conversion of fuel energy into mechanical work, it is necessary to analyze
ideal devices, in which a fluid is heated and cooled and produces or consumes
work as it completes a cycle. A device of this type can be called a heat
engine, since exchanges heat with the exterior while produces work in a
cyclic process. The combustion of the fuel is represented in this ideal cycle by
the addition of heat from a hot source. Some practical machines, such as gas
turbines and car engines, are not heated by an external source. These are
called internal combustion engines. However much of its operation can be
modeled as ideal thermal machines to understand its operation.
Thermodynamic efficiency
Particularly important is the amount of work produced (W) in relation to the
amount of heat added (Q), to represent the combustion of fuel. To this reason
we call thermodynamic efficiency:
w
 
Q
Carnot´s Cycle
The Carnot cycle is the prototype of a cycle that has little practical importance
but is elegantly illustrative of the limitations of the 2nd Law on conversion of
heat into work. This is the simplest cycle of a heat engine. Consists of two
thermal reservoirs, a hot reservoir at temperature Th and a cold reservoir at
temperature Tc. (we can imagine the hot source held at that temperature for
heat transfer from the combustion of a fossil fuel and the cold one as the
atmosphere).
Consider then the thermal machine as a cylinder equipped with a moveable
piston and containing a fluid of unit mass. The cycle consists of four steps: an
isothermal expansion, during which a quantity of heat Qh is added to the
machine (1 → 2 in the figure); an isentropic adiabatic expansion during which
the temperature of the fluid decreases from Th to Tc (2 → 3); an isothermal
compression while the system transfers a quantity of heat Qc for the cold sink
(3 → 4); and finally an isentropic compression to the initial state (4 → 1). For
this cycle the piston work per cycle is:
Combining the two previous relationships we can calculate the
thermodynamic efficiency of the Carnot cycle:
The most important aspect of this result is that the thermodynamic efficiency
depends on the temperature of the two reservoirs and not dependent on any
of the properties of the fluid used in the heat engine.
Carnot´s Principles
The Second Law imposes limits on the operation of cyclic devices: a cyclic
Thermal engine cannot operate by exchanging heat with a single source.
We can draw two conclusions (principles of Carnot)
1. The performance of an irreversible heat engine is always lower than that of
a reversible heat engine that runs from the same sources (temperatures).
2. The thermal efficiency of all reversible machines operating between the
same two sources are equal.
The maximum efficiency of a thermal
power station operating with steam vapor
that runs between TH = 750 K and TC = 300
K is 60%. The actual thermal efficiency is
around 38-40%.
The Rankine cycle
The Carnot´s cycle is a important process to understand how it works a simple
thermal machine, but it's not useful in practical terms.
Since the beginning of the industrial revolution until the 20th century (and
still today), most of the mechanical power generated by burning fossil fuels
utilizes a steam cycle, called Rankine cycle. In a thermal power station with
steam cycle, the fuel mixed with air is burned to a vaporizer to convert water
into steam, which then feeds into a turbine. This is an external combustion
system where the working fluid, water-steam, is heated in tubes that are in
contact with the hot gases formed in the combustion chamber. In an efficient
thermal power station, virtually all the calorific value of the fuel is transferred
to the steamer, but only a portion is converted to work on turbine.
Rankine cycle
Scheme of a Thermoelectric Power Station
In a thermal power station, room-temperature water is pumped at high
pressure and injected into the vaporizer (1 → 2 in the figure) and is heated to
its boiling point (3), completely converted into steam (4), and then typically
heated to a higher temperature (5). This vaporizer heating occurs at constant
pressure, Pb. The steam flows through a turbine (5 → 6) where undergoes a
pressure reduction to a much lower value, Pc, while the turbine produces
power. The low-pressure steam that leaves the turbine is cooled to a liquid at
room temperature in the condenser (6 → 1) and pumped into vaporizer where
completes the cycle.
In the ideal cycle of Rankine, adiabatic work in continuous flow per unit mass of
steam, wt produced in turbine is equal to the change of enthalpy h5 − h6 through
the turbine, in virtue of the first law. As this is an isentropic process, the change
of enthalpy can be expressed through:
There is a similar expression to calculate the work required to operate the
pump. The total work w produced in the cycle can be expressed by:
where vs and vw are the specific volume of steam in the turbine and water in
the pump and Pb and Pc are the pressures in the vaporizer and condenser. Once
the specific volume of liquid water is vastly less than the steam, the pump
power is a small fraction of the power produced in the turbine, which is one of
the great attributes of the Rankine cycle. Once the steps of heating and cooling
of the ideal cycle of Rankine (2 → 5, 6 → 1) occur at constant pressure, while
the step in the turbine is isentropic thermal efficiency can be expressed by:
We must highlight some aspects relating to the Rankine cycle. First, unlike the
Carnot cycle, the thermal efficiency depends on the properties of the working
fluid, water. Second, the efficiency of the cycle increases if the pressure in the
boiler (and steam temperature) increases. At the same time, high pressure in
the evaporator increases the amount of work produced per unit mass of water
flowing in the system, and reducing turbine costs per unit of power produced.
The cycle can be further improved with efficiency gains through the use of
heat exchangers at the intermediate pressure levels.
For Rankine cycles using water as working fluid vaporizer temperatures rarely
exceed 550 ◦ C. A cycle of more high pressure and high temperatures is one for
which the steam pressure and temperature exceeds the critical point of water.
The thermodynamic efficiency of the optimal cycle of Rankine varies in the
range from 30 to 45%, depending on the details and complexity of the cycle.
The current steam cycle power stations have lower efficiencies for various
reasons. Turbines and pumps are not 100% efficient, resulting in less power
produced.
Otto cycle
The most common fossil fuel powered engine is the automobile engine.
Unlike steam plants, automobile engines do not depend on the heat transfer
of a working fluid from a combustion source. Instead, the fuel is burned
inside the engine, adiabatically, and the combustion products produce more
work during the expansion, than that which is used in the compression step.
The combustion products that are rejected to the atmosphere are replaced
by an air-fuel mixture to give origin to a new cycle. This is referred to as
open cycle, unlike steam cycle that is closed.
Otto cycle
The Otto cycle is the ideal cycle for gasoline engines. In most gasoline engines
the piston performs four complete courses within the cylinder. The crankshaft
complete two rotations for each thermodynamic cycle.
1-2: Adiabatic compression; 2-3: Addition of heat at constant volume
3-4: Adiabatic expansion; 4-1: Rejection of heat at constant volume.
Otto cycle efficiency increases depending on the compression ratio, ve/vc, and
depends on the thermodynamic properties of the working fluid. Can be
expressed by:
For a typical gasoline engine the compression ratio is about 9 and Cp/Cv =
1.26, then η = 43.5%.
Automobile engines efficiencies are quite smaller than that value. The friction
in the piston, power required to operate the valves, cooling pump, fuel supply
system, losses of pressure in the intake and exhaust systems and heat loss
during the compression and expansion, all contribute to reducing the
efficiency. The best thermal efficiencies of automobile engines vary between
28 and 39% for petrol engines and diesel engines.
Brayton cycle
Since the mid-20th century, the gas turbine has become the dominant
technology for large aircraft engines, because their fitness for high speeds of
propulsion, lightness, fuel economy and reliability. Also has application in
propulsion of large ships and more recently in thermoelectric power plants.
The ideal cycle that models the gas combustion process through a central gas
turbine is the Brayton cycle. Consists of an isentropic compression of the air
in the compressor inlet pressure Pi for the compressor outlet pressure, Pc
(1 → 2 in the figure), followed by a constant pressure heating (2 → 3) that
rises the temperature of gas for temperature T3 at the turbine inlet. The gases
expand isentropicaly while flow through turbine, being the reduced pressure
from Pc to Pi (3 → 4).
Per unit mass of the fluid, the resulting work, w, in gas turbine power station is
the difference between the work produced in the turbine and compressor
work:
The heat added to the fluid coming from the compressor, q, which is due to
the temperature rise caused by adiabatic combustion, is equal to the change
of enthalpy in the process at constant pressure:
Thus, the efficiency η of the Brayton cycle is :
The efficiency of the cycle depends on the ratio between the two pressures
P2/P1 = P3/P4 and the thermodynamic properties of air and combustion gases.
This efficiency is expressed by:
What shows that efficiency increases with compression ratio. As an example,
for P2/P1= 10 and Cp/Cv = 1.3 then η = 41.2%. For the Brayton cycle the best
efficiencies are around 33%.
Combined cycle
The exhaust gases coming out of a gas turbine transport part of the calorific
value of fuel that may have been converted to work. This hot gas stream can
be used to produce steam in a boiler and produce additional work without
burning more fuel. The use of a gas turbine and steam plant to produce more
work from a given amount of fuel is called combined cycle.
Thermodynamic efficiency, ηcc of a combined cycle thermal power station can
be determined depending on the efficiencies, ηg and ηs, of the gas turbine and
steam cycle. For the gas turbine, the wg is equal to ηg × qf, where qf is the heat
added per unit mass of combustion products. The amount of heat that can be
used in the steam cycle is qf – wg = qf ×(1 − ηg). The work produced in the steam
cycle ws is so ηs times this heat, or ηs × qf ×(1 − ηg).
The efficiency of the combined cycle is always lower than the sum of the
efficiencies of the two cycles (Brayton and Rankine). However the combination
is always more efficient than any one of its components. For example if ηg =
30% and ηs = 25%, then ηcc = 47.8%.
Combined cycle thermal power plants that burn natural gas or jet fuel are
often a good choice, instead of coal-fired power stations, despite the
favorable price of coal. The reasons are environmental and financial,
including a lower emission of gaseous pollutants, including CO2.
Problem
1
Are required 2.2 million tons of coal per year to feed a 1000-MW power
station, which operates with a capacity factor of 70%. If the calorific value of
coal is 12000 Btu/lb, calculate the thermal efficiency of the plant.
Problem
2
Given a compression reason of P2/P1 = 12 along a gas turbine and a ratio of
specific heats of Cp/Cv = 1.35 concerning the working fluid, calculate the
thermal efficiency of the Brayton cycle. Explain why the power plants with gas
turbines reach thermal efficiencies of just 25 to 35%.
Problem 3
A combined cycle power station has a gas turbine efficiency of 30% and a
steam cycle efficiency of 30%. Calculate the combined cycle efficiency.
Problem 4
A 1000-MW power station, with a thermal efficiency of 35%, during 100 % of
the time, uses coal with the formula CH and a calorific value of 30 MJ/kg. How
much CO2 emits this unit in ton/year?
Bibliography
Fay, J., Golomb, D.S., Energy and the Environment, Oxford University Press and
Open University, Oxford, UK, 2004
Azevedo, E.G., Termodinâmica Aplicada, 3ºed., Escolar Editora, Lisboa, 2011