MCEN90041: Advanced Thermodynamics
Semester 2, 2022 Exam Notes
Introduction ... 2
Chemical Thermodynamics and Equilibrium ... 10
Chemical Kinetics ... 22
Important Reaction Mechanisms in Combustion ... 28
Ideal Reactors for Combustion Kinetics ... 32
Simplified Conservation Equations for Reacting Flows ... 35
Laminar Premixed Flames ... 38
The Internal Combustion Engine ... 45
Exam Specific Tips and Tricks ... 53
Introduction
1. Why Study Combustion?
1.1 World Energy Picture
Combustion is the most important energy conversion process at present, which provides 90% of energy the world uses today.
Combustion in burners, furnaces, engines, and gas turbines produces the energy required for residential and industrial heating, transport, and electricity generation, etc.
~ 60% of world electricity is currently generated from burning fossil fuels, in particular coal and natural gas.
Transport relies almost entirely on fossil fuels, in particular oil. Electric vehicles currently use ~ 1% of total transport energy but are growing quickly.
Looking into the future, various international energy agencies predict that the world total primary energy supply (TPES) will increase slowly or plateau where
combustion remains as the predominant way to use energy.
Certain energy sectors can replace combustion of fossil energy more readily, e.g.
electricity generation, than others, e.g. transport, industry, etc.
1.2 Combustion Generating Pollutants
Combustion emits pollutants, including primary pollutants such as carbon monoxide, volatile organic compounds (VOC), soot, nitrogen oxides (NO and NO2), sulfur oxides (SO2 and SO3), heavy metals etc., and secondary pollutants such as smog which are formed within the atmosphere from primary pollutants by chemical or photochemical reactions.
Fuel-bound pollutants: sulfur oxides, heavy metals, part of NOx and VOC. Combustion- generated pollutants: CO, most VOC and NOx, soot, etc.
1.3 Combustion Emitting Greenhouse Gases
Combustion releases greenhouse gases, including carbon dioxide, methane, nitrous oxide (N2O) etc.
Note that the global warming potentials (GWP) of methane and nitrous oxide are much higher than carbon dioxide, ~ 25 (methane) and 300 (nitrous oxide) vs. 1 (carbon dioxide). So their actual emission rates are much smaller than the above percentage numbers (which is CO2 equivalent). Because of this, attentions should be paid to even small amount of CH4 and N2O emissions. The GWP of chlorofluorocarbons (CFC), e.g.
Freon, can be extremely high, up to 10000 times of CO2, but their emissions are regulated (by Montreal Protocol).
1.4 Strategies to Control Green House Gas Emissions
Two strategies can be used to reduce man-made (anthropogenic) CO2 emissions.
1) Replace fossil fuels with renewable energy, e.g. wind, solar, biomass, geothermal, hydro, etc. These energies are considered renewable because their supply is inexhaustible, unlike fossil fuels. Using renewable energy also does not produce greenhouse gas emission in theory. Nuclear energy is also an option, but the currently used nuclear fission is not renewable (in addition to the many safety and security issues associated). The undergoing development for nuclear fusion would be renewable and could potentially solve the world energy problem if it can be achieved economically.
Projections in the above, however, indicate that renewable energies will not be able to replace fossil energy entirely, instead, they will be used together with fossil energy for a long period of time
An emerging area is to convert renewable energy to fuels that can be used in
combustion process. This is proposed for decarbonizing the energy sectors where no viable technology alternative to combustion exists, such as aviation, marine
transport, long-haul trucking, industrial heating and others.
2) Improve efficiency of existing technologies. Combustion converts chemical energy to heat, which is a low-quality form of energy, and then uses the heat directly or
converts it to other forms of energy, such as mechanical energy in a heat engine.
Because mechanical energy is of higher quality than heat, significant portion of the heat cannot be used due to the theoretical limit imposed by Carnot theorem, 𝜂 = 1 − .
Typical maximum energy conversion efficiency for heat engines ─ gas turbine in power plant, 35~40%, combined cycle 55~60% (using a steam turbine to recover waste heat). Gasoline spark-ignition engine, 25-30%, diesel engine, 35-40%.
Significant efficiency improvements can be done before reaching the Carnot limit.
A good example of high-efficiency energy conversion is fuel cell. A fuel cell converts chemical energy to electric energy, rather than heat, and then to mechanical energy.
Since electric energy is a high quality energy, it can thus be converted to other energy forms (such as mechanical energy to drive a car) at a high efficiency. The efficiency of a fuel cell is NOT limited by Carnot Theorem. Fuel cell technology is under active development where current technical hurdles include the cost of the catalytic material (noble metals used in the electrodes) and fuel supply (mainly how to produce and distribute hydrogen).
2. What is Combustion?
2.1 Definition
Simply put, combustion is just a form of chemical reactions, oxidation. This type of oxidation is very rapid and releases a large amount of heat in a short period of time and can be
accompanied by light emissions.
Combustion can occur with a flame, e.g. a burning candle. In this case, there exists a thin reaction zone in which the fuel and oxidizer react with each other. There is no reaction outside the reaction zone.
For combustion with the presence of a flame, it can be categorized as premixed flame or non-premixed (diffusion) flame, depending on whether the fuel and oxidizer are mixed prior to entering the reaction zone (flame). A flame can also be categorized as laminar flame or turbulent flame depending on the flow condition of the flame. Laminar flames have steady and regular shapes while the shape of turbulent flames is irregular, stochastic and
unpredictable.
Combustion can also occur without a flame, e.g. autoignition. In this case, the entire fuel / oxidizer mixture reacts simultaneously. Due to the volumetric heat-release process, this type of combustion can be very violent (like an explosion) and can generate strong pressure waves. Note that non-flame combustions require fuel and air to be premixed so that the reaction can occur.
Negative Temperature Coefficient (NTC).
In a well-stirred closed reactor, 1→2→3→4, reaction rate varies non-monotonically against temperature, switching between fast reaction (explosion) and slow reaction (steady reaction). In particular, the reaction rate from 2 to 3 decreases with higher temperature.
This is called negative temperature coefficient (NTC) behaviour, which is related to the combustion chemistry at the particular temperature, pressure and the fuel molecular structure.
3. Basic Definitions and Relations 3.1 Equation of State
𝑃𝑉 = 𝑛𝑅 𝑇 𝑃 = [𝑋]𝑅 𝑇
𝑃𝑉 = 𝑚(𝑅 /𝑀𝑊)𝑇 = 𝑚𝑅𝑇 𝑃 = 𝜌𝑅𝑇
𝑅 = 8.3145 𝐽/𝑚𝑜𝑙/𝐾 Ideal gas law applies to most combustion cases.
The State Postulate says that the thermodynamic state of a simple compressible system (a system in the absence of electrical, magnetic, gravitational, motion, and surface tension effects) can be defined by two independent intensive properties. We can write
𝑢 =𝑈
𝑚= 𝑢(𝑇, 𝑣) ℎ = 𝐻/𝑚 = ℎ(𝑇, 𝑃)
Note u and h are mass-specific internal energy and enthalpy. We use 𝑢 and ℎ to express molar-specific denotation.
With differential change of u and h, we have 𝑑𝑢 = 𝜕𝑢
𝜕𝑇 𝑑𝑇 + 𝜕𝑢
𝜕𝑣 𝑑𝑣 𝑑ℎ = 𝜕ℎ
𝜕𝑇 𝑑𝑇 + 𝜕ℎ
𝜕𝑝 𝑑𝑃
At constant volume or constant pressure, the corresponding specific heats can be defined 𝑐 ≡ 𝜕𝑢
𝜕𝑇 =𝑑𝑢 𝑑𝑇 𝑐 ≡ 𝜕ℎ
𝜕𝑇 =𝑑ℎ 𝑑𝑇 or
𝑑𝑢 = 𝑐 𝑑𝑇 𝑑ℎ = 𝑐 𝑑𝑇
Specific heats are functions of temperature. For a given temperature T, we can calculate u(T) and h(T) via
𝑢(𝑇) − 𝑢 = 𝑐 (𝑇)𝑑𝑇
ℎ(𝑇) − ℎ = 𝑐 (𝑇)𝑑𝑇
These equations express sensible internal energy and sensible enthalpy because they can be actually measured by temperature measurement and the knowledge of the specific heats (known for most compounds).
The ratio of specific heats, 𝛾 = 𝑐 /𝑐 , is a parameter having important application in internal combustion engines. For ideal gases, is 5/3 for monoatomic gases, 7/5 for diatomic gases, and 9/7 for triatomic gases (which can be theoretical derived from statistical thermodynamics). For internal combustion engines, the ideal-cycle thermal efficiency with ideal gas can be expressed as
𝜂 , = 1 − 1 𝐶𝑅
where CR is the engine compression ratio. Note that increasing CR and can both increase engine efficiency. So if one can afford running the engine with noble gases (He, Ar etc.) the engine efficiency could be considerably improved over running with air.
3.2 Mixture of Ideal Gases Molar fraction: 𝒙𝒊 = 𝑵𝒊
𝑵𝒕𝒐𝒕𝒂𝒍
Mass fraction: 𝒀𝒊 =𝒎𝒎𝒊
𝒕𝒐𝒕𝒂𝒍
∑ 𝑥 = 1 ∑ 𝑌 = 1 𝑀𝑊 = ∑ 𝑥 𝑀𝑊 𝒀𝒊 =𝑴𝑾𝒙𝒊𝑴𝑾𝒊
𝒎𝒊𝒙
For thermodynamic properties such as enthalpy, the mass-based and molar-based mixture enthalpies are respectively,
ℎ = 𝑌 ℎ
ℎ = 𝑥 ℎ
3.3 Combustion Stoichiometry
For a hydrocarbon fuel, 𝐶 𝐻 𝑂 , the stoichiometric combustion (means all the fuel and oxidizer are consumed in the reaction) with air can be expressed as
𝐶 𝐻 𝑂 + 𝑎(𝑂 + 3.76𝑁 ) → 𝑥𝐶𝑂 + 𝑦
2 𝐻 𝑂 + 3.76𝑎𝑁 where
𝑎 = 𝑥 + 𝑦/4 − 𝑧/2
Here we assume that air consists of 21 % of 𝑂 and 79% of 𝑁 by volume. Therefore, for every mole of 𝑂 there is 3.76 moles of 𝑁 . The molecular weight of air is thus
𝑀𝑊 = 𝑥 𝑀𝑊 = 0.21 × 32 + 0.79 × 28 = 28.84𝑔/𝑚𝑜𝑙
The stoichiometric air-fuel ratio can be found as 𝐴
𝐹 = 𝑚
𝑚 =4.76𝑎
1
𝑀𝑊 𝑀𝑊
The equivalence ratio, 𝜙, expresses the ratio of the stoichiometric A/F ratio to the actual A/F ratio.
𝜙 = 𝐴 𝐹 𝐴 𝐹
= 𝐹 𝐴 𝐹 𝐴
It is used to indicate quantitatively whether a fuel-air mixture is fuel lean ( < 1), rich ( > 1) or stoichiometric ( = 1).
Another expression of combustion stoichiometry is lambda, which is used more commonly in industry and defined as
𝜆 = 1/𝜙
Major combustion products for various 𝜙 are summarised below:
𝜙 Major Products
<1 (lean) 𝐶𝑂 , 𝐻 𝑂, 𝑁 , 𝑂
=1 (stoichiometric) 𝐶𝑂 , 𝐻 𝑂, 𝑁
>1 (rich) 𝐶𝑂 , 𝐻 𝑂, 𝑁 , 𝐶𝑂, 𝐻
Note that for fuel rich cases, additional information is needed to determine the stoichiometric coefficients of the reaction.
4. Nomenclature of Organic Compounds
One carbon atom can form (up to) four covalent bonds, because it has four unpaired
electrons. These bonds can be formed with four hydrogens (𝐶𝐻 ), or two oxygens (𝐶𝑂 ), or combination of hydrogens and oxygen (e.g. 𝐶𝐻 𝑂), or other atoms like N (e.g. HCN, cyanide), F (e.g. 𝐶 𝐹, teflon) etc. In most cases, a carbon also forms covalent bonds with other
carbons (e.g. 𝐶𝐻 𝐶𝐻 ).
4.1 Chain length
Chain length is indicated by the number of carbon atoms in the chain.
C number Pre-fix
1 Meth-
2 Eth-
3 Prop-
4 But-
5 Pent-
6 Hex-
7 Hep-
8 Oct-
9 Non-
10 Dec-
11 Undec-
12 Dodec-
4.2 Hydrocarbon classification
Alkane, also called paraffin conventionally, refers to saturated hydrocarbons, in which each carbon atom is connected to four single bonds (C-H or C-C). Molecular formula of alkanes can be expressed as 𝐶 𝐻
Example: methane, 𝐶𝐻 , and ethane, 𝐶𝐻 − 𝐶𝐻
An alkane with straight carbon chain is called normal alkane. An example is normal heptane, 𝐶𝐻 − (𝐶𝐻 ) − 𝐶𝐻 , which is one reference fuel defining the octane-number scale and has an octane number of zero.
