Advanced thermodynamics for engineers part 2

10 Thermodynamics of Combustion Combustion is an oxidation process and is usually exothermic (i.e releases the chemical (or bond) energy contained in a fuel as thermal energy) The most common combustion processes encountered in engineering are those which convert a hydrocarbon fuel (which might range from pure hydrogen to almost pure carbon, e.g coal) into carbon dioxide and water This combustion is usually performed using air because it is freely available, although other oxidants can be used in special circumstances, e.g rocket motors The theory that will be developed here will be applicable to any mixture of fuel and oxidant and any ratio of components in the products; however, it will be described in terms of commonly available hydrocarbon fuels of the type used in combustion engines or boilers The simplest description of combustion is of a process that converts the reactants available at the beginning of combustion into producrs at the end of the process This model presupposes that combustion is a process that can take place in only one direction and it ignores the true statistical nature of chemical change Combustion is the combination of various atoms and molecules, and takes place when they are close enough to interact, but there is also the possibility of atoms which have previously joined together to make a product molecule separating to form reactants again The whole mixture is really taking part in a molecular ‘barn dance’ and the tempo of the dance is controlled by the temperature of the mixture The process of molecular breakdown is referred to as dissociation; this will be introduced in Chapter 12 In reality a true combustion process is even more complex than this because the actual rate at which the reactions can occur is finite (even if extremely fast) This rate is the basic cause of some of the pollutants produced by engines, particularly NO, In fact, in most combustion processes the situation is even more complex because there is an additional factor affecting combustion, which is related to the rate at which the fuel and air can mix These ideas will be introduced in Chapter 15 Hence, the approach to combustion in this chapter is a simplified one but, in reality, it gives a reasonable assessment of what would be expected under good combustion conditions It cannot really be used to assess emissions levels but it can be extended to this simply by the introduction of additional equations: the basic approach is still valid The manner in which combustion takes place is governed by the detailed design of the combustion system The various different types of combustion process are listed in Table 10.1, and some examples are given of where the processes might be found There is an interdependence between thermodynamics and fluid mechanics in combustion, and this interaction is the subject of current research This book will concentrate on the thermo- Thermodynamics of combustion 183 dynamics of combustion, both in equilibrium and non-equilibrium states The first part of the treatment of combustion will be based on equilibrium thermodynamics, and will cover combustion processes both with and without dissociation It will be found that equilibrium thermodynamics enables a large number of calculations to be performed but, even with dissociation included, it does not allow the calculation of pollutants, the production of which are controlled both by mixing rates (fluid mechanics) and reaction rates (thermodynamics) Table 10.1 Factors affecting combustion processes Conditions of combustion Classification Examples Time dependence steady unsteady gas turbine combustion chamber, boilers petrol engine, diesel engine Spatial dependence zero-dimensional only used for modelling purposes, wellstirred reactors approximated in pipe flows, flat flame burners axisymmetric flames, e.g Bunsen burner general combustion one-dimensional two-dimensional three-dimensional Mixing of initial reactants premixed non-premixed petrol, or spark ignition, engine diesel engine, gas turbine combustion chamber Flow laminar turbulent special cases for measuring flame speed most real engine cases, boilers Phase of reactants single spark-ignited gas engines, petrol engines with fuel completely evaporated; gas-fired boilers diesel engines, gas turbines, coal- and oilfired boilers multiphase Reaction sites homogeneous heterogeneous spark-ignition engines diesel engines, gas turbines, coal fired boilers Reaction rate equilibrium chemistry (infinite rate) approached by some processes in which the combustion period is long compared with the reaction rate all real processes: causes many pollutant emissions finite rate Convection conditions natural forced Bunsen flame, gas cooker, central heating boiler gas turbine combustion chamber, large boilers Compressibility incompressible compressible free flames engine flames Speed of combustion deflagration detonation most normal combustion processes ‘knock’ in spark ignition engines, explosions I84 Thermodynamics of combustion 10.1 Simple chemistry Combustion is a chemical reaction and hence a knowledge of basic chemistry is required before it can be analysed An extremely simple reaction can be written as c o + 0, (j2 c , (10.1) This basically means that two molecules of carbon monoxide (CO) will combine with one molecule of oxygen (0,)to create two molecules of carbon dioxide (CO,) Both CO and 0, are diatomic gases, whereas CO, is a triatomic gas Equation (10.1) also indicates that two molecules of CO, will always break down into two molecules of CO and one molecule of 0,; this is signified by the symbol e which indicates that the processes can go in both directions It is conventional to refer to the mixture to the left of the arrows as the reactants and that to the right as the products; this is because exothermic combustion (i.e in which energy is released by the process) would require CO and 0, to combine to give CO, Not all reactions are exothermic and the formation of NO during dissociation occurring in an internal combustion (i.c.) engine is actually endothermic It should be noted from the combustion eqn (10.1) that three molecules of reactants combine to produce two molecules of products, hence there is not necessarily a balance in the number of molecules on either side of a chemical reaction However, there is a balance in the number of atoms of each constituent in the equation and so mass is conserved 10.1.1 FUELS Hydrocarbon fuels are rarely single-component in nature due to the methods of formation of the raw material and its extraction from the ground A typical barrel of crude oil contains a range of hydrocarbons, and these are separated at a refinery; the oil might produce the constituents defined in Fig 10.1 None of the products of the refinery is a single chemical compound, but each is a mixture of compounds, the constituents of which depend on the source of the fuel Light distillates (chemical feedstock) Fuel to run refinery / Heavy fuel, or A Kerosene (paraffin, aviation fuel) Middle distillates (gas oil diesel, heating oil) Gases (butane, propane) Fig 10.1 Typical constituents of a barrel of crude oil Combustion of simple hydrocarbons fuels 185 One fuel which approaches single-component composition is ‘natural gas’, which consists largely of methane (CH,) Methane is the simplest member of a family of hydrocarbons referred to as paraffins or, more recently, alkanes which have a general The lower alkanes are methane (CH,), ethane (C,H,), propane (C,H,) formula C,,HZn+, and butane (C,H,,) etc Two other alkanes that occur in discussion of liquid fuels are heptane (C,H,,) and octane (CEHIE) The alkanes are referred to as saturated hydrocarbons because it is not physically possible to add more hydrogen atoms to them However, it is possible to find hydrocarbons with less than 2n + hydrogen atoms and these are referred to as unsaturated hydrocarbons A simple unsaturated hydrocarbon is acetylene (C,H,), which belongs to a chemical family called alkenes Some fuels contain other constituents in addition to carbon and hydrogen For example, the alcohols contain oxygen in the form of an OH radical The chemical symbol for methanol is CH,OH, and that for ethanol is C,H,OH; these are the alcohol equivalents of methane and ethane Often fuels are described by a mass analysis which defines the proportion by mass of the carbon and hydrogen, e.g a typical hydrocarbon fuel might be defined as 87% C and 13% H without specifying the actual components of the liquid Solid fuels, such as various coals, have a much higher carbon/hydrogen ratio but contain other constituents including oxygen and ash The molecular weights (or relative molecular masses) of fuels can be evaluated by adding together the molecular (or atomic) weights of their constituents Three examples are given below: (m,),, Methane (CH,) = 12 + x = 16 (mw)CsH,s = x 12 + 18 x = 114 Octane (CEH18) Methanol (CH,OH) (mw)CH30H = 12 + x + 16 + = 32 10.2 Combustion of simple hydrocarbon fuels The combustion of a hydrocarbon fuel takes place according to the constraints of chemistry The combustion of methane with oxygen is defined by CH, kmol 12+4 16kg + 2Q kmol 2x32 64kg CQ kmol 12x32 44 kg + 2H,O kmol 2x(2+16) 36 kg (10.2) In this particular case there is both a molar balance and a mass balance: the latter is essential but the former is not Usually combustion takes place between a fuel and air (a mixture of oxygen and nitrogen) It is normal to assume, at this level, that the nitrogen is an inert gas and takes no part in the process Combustion of methane with air is given by a kmol 12+4 16 kg 9.52 kmol 2x(32+105.2) 274.4 kg CO, kmol 12+32 44 kg + 2H2O kmol 2x(2+16) 36 kg 79 +2~-”, 21 7.52 kmol 7.52~28 210.67 kg (10.3) 186 Thermodynamics of combustion 10.2.1 STOICHIOMETRY There is a clearly defined, and fixed, ratio of the masses of air and fuel that will result in complete combustion of the fuel This mixture is known as a stoichiometric one and the ratio is referred to as the stoichiometric air- fuel ratio The stoichiometric air-fuel ratio, for methane can be evaluated from the chemical equation (eqn 10.3) This gives & StOlC = x (32 + 105.33) mass of air mass of fuel 16 = 17.17 This means that to obtain complete combustion of kg CH, it is necessary to provide 17.17 kg of air If the quantity of air is less than 17.17 kg then complete combustion will not occur and the mixture is known as rich If the quantity of air is greater than that required by the stoichiometric ratio then the mixture is weak 10.2.2 COMBUSTION WITH WEAK MIXTURES A weak mixture occurs when the quantity of air available for combustion is greater than the chemically correct quantity for complete oxidation of the fuel; this means that there is excess air available In this simple analysis, neglecting reaction rates and dissociation etc, this excess air passes through the process without taking part in it However, even though it does not react chemically, it has an effect on the combustion process simply because it lowers the temperatures achieved due to its capacity to absorb energy The equation for combustion of a weak mixture is 7.52 + - (0,+ 3.76Nz) CH, ( 10.4) NZ $J where @ is called the equivalence ratio, and @= actual fuel-air ratio stoichiometric air-fuel ratio stoichiometric fuel-air ratio actual air-fuel ratio For a weak mixture q5 is less than unity Consider a weak mixture with CH, 10.2.3 + 2.5(0, + 3.76N2)3CO, + 2H,O + 0.50, + 9.4Nz (10.5) c$ = 0.8; then (10.6) COMBUSTION WITH RICH MIXTURES A rich mixture occurs when the quantity of air available is less than the stoichiometric quantity; this means that there is not sufficient air to bum the fuel In this simplified approach it is assumed that the hydrogen combines preferentially with the oxygen and the carbon does not have sufficient oxygen to be completely burned to carbon dioxide; this results in partial oxidation of part of the carbon to carbon monoxide It will be shown in Chapter 12 that the equilibrium equations, which control the way in which the hydrocarbon fuel oxidizes, govern the proportions of oxygen taken by the carbon and hydrogen of the fuel and that the approximation of preferential combination of oxygen and Heats of formation and heats of reaction 187 hydrogen is a reasonable one In this case, to define a rich mixture, @ is greater than unity Then CH4 + - ( @ + 3.76N2) * ( :@)co2 + _ H + 4(@ - 1) @ 7.52 co+- @ N2 (10.7) If the equivalence ratio is 1.2, then eqn (10.7) is CH, + 1.667(0, + 3.76N2)3 0.333C0, + 2H,O + 0.667CO + 6.267N2 (10.8) It is quite obvious that operating the combustion on rich mixtures results in the production of carbon monoxide (CO), an extremely toxic gas For this reason it is now not acceptable to operate combustion systems with rich mixtures Note that eqn (10.7) cannot be used with values of @ >4/3, otherwise the amount of CO, becomes negative At this stage it must be assumed that the carbon is converted to carbon monoxide and carbon The resulting equation is CH4+-(02+3.76N2)*2H20+ @ Equation (10.9) is a very hypothetical one because during combustion extensive dissociation occurs and h s liberates oxygen by breaking down the water molecules; this oxygen is then available to create carbon monoxide and carbon dioxide rather than carbon molecules In reality it is also possible to produce pollutants even when the mixture is weaker than stoichiometric, simply due to poor mixing of fuel and air, quenching of flames on cold cylinder or boiler walls, trapping of the mixture in crevices (fluid mechanics effects) and also due to thermodynamic limitations in the process 10.3 Heats of formation and heats of reaction Combustion of fuels takes place in either a closed system or an open system The relevant property of the fuel to be considered is the internal energy or enthalpy, respectively, of formation or reaction In a naive manner it is often considered that combustion is a process of energy addition to the system This is not true because the energy released during a combustion process is already contained in the reactants, in the form of the chemical energy of the fuel (see Chapter 11) Hence it is possible to talk of adiabatic combustion as a process in which no energy (heat) is transferred to, or from, the system - the temperature of the system increases because of a rearrangement of the chemical bonds in the fuel and oxidant Mechanical engineers are usually concerned with the combustion of hydrocarbon fuels, such as petrol, diesel oil or methane These fuels are commonly used because of their ready availability (at present) and high energy density in terms of both mass and volume The combustion normally takes place in the presence of air In some other applications, e.g space craft, rockets, etc, fuels which are not hydrocarbons are burned in the presence of other oxidants; these will not be considered here Hydrocarbon fuels are stable compounds of carbon and hydrogen which have been formed through the decomposition of animal and vegetable matter over many millennia It is also possible to synthesise hydrocarbons by a number of processes in which hydrogen is 188 Thermodynamics of combustion added to a carbon-rich fuel The South African Sasol plant uses the Lurgi and Fischer-Tropsch processes to convert coal from a solid fuel to a liquid one The chemistry of fuels is considered in Chapter 11 10.4 Application of the energy equation to the combustion process - a macroscopic approach Equations (10.3) to (10.6) show that combustion can take place at various air-fuel ratios, and it is necessary to be able to account for the effect of mixture strength on the combustior process, especially the temperature rise that will be achieved It is also necessary to be able to account for the different fuel composition: not all fuels will release the same quantity of energy per unit mass and hence it is required to characterise fuels by some capacity to release chemical energy in a thermal form Both of these effects obey the First Law of Thermodynamics, i.e the energy equation 10.4.1 INTERNAL ENERGIES AND ENTHALPIES OF IDEAL GASES It was shown previously that the internal energies and enthalpies of ideal gases are functions of temperature alone ( c pand c, might still be functions of temperature) This means that the internal energy and enthalpy can be represented on U - T and H-T diagrams It is then possible to draw a U-T or H-T line for both reactants and products (Fig 10.2) The reactants will be basically diatomic gases (neglecting the effect of the fuel) whereas the products will be a mixture of diatomic and triatomic gases - see eqn (10.3) Temperature, T Fig 10.2 Enthalpy (or internal energy) of reactants and products The next question which arises is: what is the spacing between the reactants and products lines? This spacing represents the energy that can be released by the fuel 10.4.2 HE.4TS OF REACTION AND FORMATION The energy contained in the fuel can also be assessed by burning it under a specified condition; this energy is referred to as the heat of reaction of the fuel The heat of reaction Application of the energy equation to the combustion process 189 for a fuel is dependent on the process by which it is measured If it is measured by a constant volume process in a combustion bomb then the internal energy of reaction is obtained If it is measured in a constant pressure device then the enthalpy of reaction is obtained It is more normal to measure the enthalpy of reaction because it is much easier to achieve a constant pressure process The enthalpy of reaction of a fuel can be evaluated by burning the fuel in a stream of air, and measuring the quantity of energy that must be removed to achieve equal reactant and product temperatures (see Fig 10.3) Control surface I T,= T, eQP Fig 10.3 Constant pressure measurement of enthalpy reaction Applying the steady flow energy equation ( : ) ( : +) Q - W s= liz, he + - + gz, - ri2; hi - + gz, (10.10) and neglecting the kinetic and potential energy terms, then (QPh - ( H R ) T = nP(hP)T - n R ( h d ~ = (1G.11) where n denotes the amount of substance in either the products or reactants; this is identical to the term n which was used for the amount of substance in Chapter The suffix T defines the temperature at which the enthalpy of reaction was measured is a function of this temperature and normally it is evaluated at a standard temperature of 25°C (298 K) When is evaluated at a standardised temperature it will be denoted by the symbol Most values of Qpthat are used in combustion calculations are the ones (In a similar way, (Q,), will be used for internal energy of reaction at the standard temperature.) The sign of Qp is negative for fuels because heat must be transferred from the ‘calorimeter’ to achieve equal temperatures for the reactants and products (it is positive for some reactions, meaning that heat has to be transferred to the calorimeter to maintain constant temperatures) The value of the constant volume heat of reaction, the internal energy of reaction, can be calculated from as shown below, or measured using a constant volume combustion ‘bomb’; again (Q,), has a negative value and (Q,), are shown in Figs 10.4(a) and (b) respectively The term calorific value of the fuel was used in the past to define the ‘heating’ value of the fuel: this is actually the negative value of the heat of reaction, and is usually a positive number It is usually associated with analyses in which ‘heat’ is added to a system during the combustion process, e.g the air standard cycles Applying the first law for a closed system to constant volume combustion gives (ep), (e,),, (ep), (ep), (ep), (10.12) 190 Thermodynamics of combustion If both the products and reactants are ideal gases then h = J c ~dT,, and ~ u = J cy,,, dT, which can be evaluated from the polynomial expressions derived in Chapter Thus (QpIs - (QvIs =~ P ( ~ P) T~ R ( ~ R ) T( ~ P ( ~ P ) Tn R ( u R ) T l = np( (hP)T- (up)TJ - nRI (hR)T- (uR)T} = % T ( n p- n R ) (10.13) (e,), This result is quite logical because the definitions of (Qp)sand require that Tp and TR are equal Hence the constant pressure and constant volume processes are identical if the amounts of substance in the products and the reactants are equal If the amounts of substance change during the reaction then the processes cease to be identical and, in the case of a combustion bomb, a piston would have to move to maintain the conditions The movement of the piston is work equal to % T ( n p- nR) It is also possible to relate the quantity of energy that is chemically bound up in the fuel to a value at absolute zero of temperature These values are denoted as -AHo and -AUo and will be returned to later 10.4.3 HEAT OF FORMATION - HESS' LAW The heat of formation of a compound is the quantity of energy absorbed (or released) during its formation from its elements (the end pressures and temperatures being maintained equal) For example, if CO, is formed from carbon and oxygen by the reaction c + 0, -+ co, (10.14) then in a constant pressure steady flow process with equal temperature end states the reaction results in heat transfer of ( given by