11

Flame Flame TemperatureTemperature

朱　信朱　信Hsin ChuHsin ChuProfessorProfessor

Dept. of Environmental EngineeringDept. of Environmental EngineeringNational Cheng Kung UniversityNational Cheng Kung University

22

1. Energy Balance on a 1. Energy Balance on a SystemSystem A simple steady-state thermal energy A simple steady-state thermal energy

balance can be constructed around a balance can be constructed around a constant-pressure combustion constant-pressure combustion system (such as a boiler).system (such as a boiler).

Next slide (Next slide (Fig. 4.1Fig. 4.1))The energy flows into and out of the The energy flows into and out of the systemsystem..

44

Before the energy balance is developed it is Before the energy balance is developed it is worth looking more closely at the terms involved:worth looking more closely at the terms involved:(a)(a) HHRR, H, HPP and CV (calorific value) are all related and CV (calorific value) are all related to to the standard temperature of 25℃. the standard temperature of 25℃.

The enthalpy of the entering air is The enthalpy of the entering air is considered considered to be sensible heat only (i.e., the to be sensible heat only (i.e., the fuel/air is fuel/air is considered to be a dry mixture).considered to be a dry mixture).(b) The enthalpy of the flue gas must be (b) The enthalpy of the flue gas must be consistent consistent with the calorific value of the fuel with the calorific value of the fuel which is used which is used in the balance.in the balance.

55

If the gross calorific value is used, then HIf the gross calorific value is used, then HRR should co should contain a latent heat term equal to the mass of water ntain a latent heat term equal to the mass of water produced per kilogram of fuel multiplied by the lateproduced per kilogram of fuel multiplied by the latent heat of evaporation of water at 25℃ (hnt heat of evaporation of water at 25℃ (hfgfg).).

If the net calorific value is used, then the flue gas entIf the net calorific value is used, then the flue gas enthalpy will consist of sensible heat terms only.halpy will consist of sensible heat terms only.

In this chapter we are concerned with predicting the In this chapter we are concerned with predicting the temperature reached within the flame, hence the netemperature reached within the flame, hence the net calorific value/sensible heat terms system is the mt calorific value/sensible heat terms system is the more appropriate.ore appropriate.

66

The energy balance about the system can be The energy balance about the system can be written as:written as:

CV + HCV + HRR = H = HPP + Q + Qcc + Q + Quu (1)(1) HHRR, the sensible heat in the air and fuel (ref. 25, the sensible heat in the air and fuel (ref. 25

℃) is very small and often neglected.℃) is very small and often neglected. The case loss from the outside of the plant, QThe case loss from the outside of the plant, Qcc, ,

is also generally small compared to the other eis also generally small compared to the other energy fluxes and is similarly often considered nergy fluxes and is similarly often considered negligible.negligible.

77

2. Adiabatic Flame 2. Adiabatic Flame TemperatureTemperature Table 4.1 shows flame temperatures for some Table 4.1 shows flame temperatures for some

common fuels. common fuels. The higher the flame temperature, the greater The higher the flame temperature, the greater should be the effectiveness of the heat exchanger should be the effectiveness of the heat exchanger section.section.Table 4.1 Flame temperatures for some common fuelsTable 4.1 Flame temperatures for some common fuels

FuelFuel Adiabatic flame temperature Adiabatic flame temperature (℃)(℃)

Natural gasNatural gasKerosine Kerosine Light fuel oilLight fuel oilMedium fuel oil Medium fuel oil Heavy fuel oil Heavy fuel oil Bituminous CoalBituminous CoalAnthraciteAnthracite

2,0702,0702,0932,0932,1042,1042,1012,1012,1022,1022,1722,1722,1802,180

88

We can use the idea of the energy balance aboWe can use the idea of the energy balance about the combustion system to derive a straightfut the combustion system to derive a straightforward way of estimating the temperature of a orward way of estimating the temperature of a flame.flame.

It is assumed that combustion takes place undIt is assumed that combustion takes place under adiabatic conditions, i.e. no heat transfer is er adiabatic conditions, i.e. no heat transfer is permitted across the boundary of the system.permitted across the boundary of the system.The implication of this is thatThe implication of this is that

QQcc = 0 = 0 and Qand Quu = 0 = 0 Hence equation (1) simplifies down to Hence equation (1) simplifies down to

CV + HCV + HRR = H = HPP (2)(2)

99

It will be taken that CV is the net specific heat It will be taken that CV is the net specific heat of the fuel, hence Hof the fuel, hence HPP contains only sensible he contains only sensible heat terms.at terms.

The terms on the left-hand side of equation (2) The terms on the left-hand side of equation (2) are simple to evaluate as CV will be known for are simple to evaluate as CV will be known for the fuel used and Hthe fuel used and HRR, the enthalpy of the fuel a, the enthalpy of the fuel and air (ref. 25℃nd air (ref. 25℃ ）） , can easily be calculated fr, can easily be calculated fromom

Where tWhere tii is the initial temperature. is the initial temperature.( 25) ( )R i P RH t mc

1010

The specific heats of the fuel, oxygen and nitrogen can The specific heats of the fuel, oxygen and nitrogen can be evaluated at the mean temperature be evaluated at the mean temperature (t(ti i + 25)/2 and the enthalpy of the reactants is thus easi+ 25)/2 and the enthalpy of the reactants is thus easily evaluated.ly evaluated.

The right-hand side of equation (2), however, is not so The right-hand side of equation (2), however, is not so easily evaluated as it is defined byeasily evaluated as it is defined by

where twhere tff is the flame temperature. This relationship ca is the flame temperature. This relationship cannot be solved explicitly for tnnot be solved explicitly for tff as there will be a consid as there will be a considerable difference between terable difference between tff and the reference temper and the reference temperature 25℃, hence the value of tature 25℃, hence the value of tff is required to evaluat is required to evaluate the specific heats of the combustion products.e the specific heats of the combustion products.

P f P PH = (t - 25) (mc )

1111

3. Specific Heats of 3. Specific Heats of GasesGases Simple ideal gas theory predicts that the speciSimple ideal gas theory predicts that the speci

fic heat of a gas is not a function of its temperafic heat of a gas is not a function of its temperature or pressure.ture or pressure.

While the latter implication is effectively true iWhile the latter implication is effectively true in practice, the specific heat of a gas does incren practice, the specific heat of a gas does increase with temperature above about 100℃. This ase with temperature above about 100℃. This effect arises because molecules have vibrationeffect arises because molecules have vibrational (internal) energy as well as kinetic energy dual (internal) energy as well as kinetic energy due to the motion of the complete molecule.e to the motion of the complete molecule.

1212

This additional mode of “storing” enerThis additional mode of “storing” energy will mean that the specific heat of a ggy will mean that the specific heat of a gas will increase as its temperature rises.as will increase as its temperature rises.

This cannot be modelled using the ideas This cannot be modelled using the ideas of classical mechanics but the effect can of classical mechanics but the effect can be predicted using quantum theory.be predicted using quantum theory.

1313

Empirical equations which allow the Empirical equations which allow the calculation of specific heats as a function of calculation of specific heats as a function of temperature have been in use for some time. temperature have been in use for some time. A polynomial expression is normally used, A polynomial expression is normally used, with either fractional or integer powers.with either fractional or integer powers.

A straightforward integer power series is A straightforward integer power series is most convenient:most convenient:

CCPP = a[0] + a[1]t +a[2]t = a[0] + a[1]t +a[2]t22 + a[3]t + a[3]t33 +…….. +…….. Values for the coefficients for the polynomials Values for the coefficients for the polynomials

for some gases are given in Table 4.2 (for some gases are given in Table 4.2 (next slide next slide and and second slidesecond slide).).Where 9.9739 eWhere 9.9739 e-4-4 means means 9.9739 × 109.9739 × 10-4-4

1616

In the case of the above values, the data was In the case of the above values, the data was obtained in the temperatures range 25-obtained in the temperatures range 25-2,000℃ and the polynomials should not be 2,000℃ and the polynomials should not be used outside these limits.used outside these limits.

For hand calculations, tables of specific heats For hand calculations, tables of specific heats are a more useful formulation and Table 4.3 (are a more useful formulation and Table 4.3 (next slidenext slide) gives values for the common ) gives values for the common combustion gases over a typical range of combustion gases over a typical range of temperatures for combustion in boilers.temperatures for combustion in boilers.

Straightforward linear interpolation should be Straightforward linear interpolation should be used for intermediate used for intermediate temperaturestemperatures..

1818

4. Calculation Algorithm4. Calculation Algorithm

A straightforward method for the calculation oA straightforward method for the calculation of adiabatic flame temperature is to execute thf adiabatic flame temperature is to execute the following steps:e following steps:(1)(1) evaluate the left-hand side of equation evaluate the left-hand side of equation (2), (2), i.e. (CV + Hi.e. (CV + HRR); ); (2)(2) guess a value for tguess a value for tff and use this to find and use this to find ththe specific heats of the combustion e specific heats of the combustion producproducts at the average between the ts at the average between the flame and thflame and the reference temperature, i.e. e reference temperature, i.e. [(t[(tff + 25)/2]℃; + 25)/2]℃;

1919

(3)(3) solve equation (2) for tsolve equation (2) for tff;;(4)(4) compare the new value of tcompare the new value of tff with th with the e original estimate and if there is a original estimate and if there is a ssubstantial difference use the new ubstantial difference use the new value tvalue to re-evaluate the specific o re-evaluate the specific heats, loopheats, looping back to step (2) until ing back to step (2) until satisfactory satisfactory convergence is achieved.convergence is achieved.

2020

With regard to step (2) above, taking the averaWith regard to step (2) above, taking the average temperature over the interval is only valid if ge temperature over the interval is only valid if the relationship between specific heat and tethe relationship between specific heat and temperature is linear. mperature is linear.

We have seen that this is not in fact the case aWe have seen that this is not in fact the case and an integrating calculation should be used. nd an integrating calculation should be used.

However, the accuracy of calculating the adiaHowever, the accuracy of calculating the adiabatic flame temperature by this simple procedbatic flame temperature by this simple procedure is constrained by a number of limitions, heure is constrained by a number of limitions, hence taking a simple arithmetical average is quince taking a simple arithmetical average is quite acceptable.te acceptable.

2121

While this method is not a particularly efficient algoritWhile this method is not a particularly efficient algorithm, it is stable and will generally converge to within 5hm, it is stable and will generally converge to within 5℃ in four iterations.℃ in four iterations.

Example 1:Example 1:Find the adiabatic flame temperature for a stoichiomeFind the adiabatic flame temperature for a stoichiometric methane/air flame if the initial temperature of the tric methane/air flame if the initial temperature of the fuel and air is 10℃. Take the net calorific value of metfuel and air is 10℃. Take the net calorific value of methane as 50.14 MJ/kg.hane as 50.14 MJ/kg.

Solution:Solution:The first step is to evaluate, for 1 kg fuel, the mass of eThe first step is to evaluate, for 1 kg fuel, the mass of each of the reactants and products. These steps have bach of the reactants and products. These steps have been covered in previous chapters and the result can been covered in previous chapters and the result can be summarized thus:e summarized thus:

2222

ReactantsReactants ProductsProducts1 kg CH1 kg CH44 2.75 kg CO2.75 kg CO22

4 kg O4 kg O22 2.25 kg H2.25 kg H22OO13.17 kg N13.17 kg N22 13.17 kg N13.17 kg N22

The initial temperature of the reactants is 10℃ and the value of HThe initial temperature of the reactants is 10℃ and the value of HRR is the sensible heat in the reactants (ref. 25℃): is the sensible heat in the reactants (ref. 25℃): H HRR = (10-25){1 = (10-25){1 ．． CCPPCHCH44 + (4 + (4 ．． CCPPOO22) + (13.17) + (13.17 ．． CCPPNN22)})}

The mean temperature of the reactants over the interval is 17.5The mean temperature of the reactants over the interval is 17.5℃. At this temperature the values of the specific heats are:℃. At this temperature the values of the specific heats are:

CHCH44 2.23 kJ/kg/K2.23 kJ/kg/KOO22 0.920.92NN22 1.041.04

soso HHRR = -293.9 kJ/kg methane = -293.9 kJ/kg methane

2323

Giving HGiving HPP = CV + H = CV + HRR =50,144 – 293.9 = 49,850 kJ/kg =50,144 – 293.9 = 49,850 kJ/kgThis value of HThis value of HPP represents the sensible heat in the c represents the sensible heat in the combustion products above the reference temperatuombustion products above the reference temperature of 25℃, i.e.re of 25℃, i.e.49,850 = (t49,850 = (tff - 25) {(13.17 - 25) {(13.17 ．． CCPPNN22) + (2.25) + (2.25 ．． CCPPHH22O) + (2.75O) + (2.75 ．． CCPPCOCO22)})}

To solve this equation by trial and error requires an iTo solve this equation by trial and error requires an initial guess for the flame temperature.nitial guess for the flame temperature.If we assume 1,575℃, the mean temperature of the If we assume 1,575℃, the mean temperature of the products above 25℃ is (1,575 + 25)/2, i.e. 800℃.products above 25℃ is (1,575 + 25)/2, i.e. 800℃.

2424

The specific heats of nitrogen, water vapor and cThe specific heats of nitrogen, water vapor and carbon dioxide at this temperature are arbon dioxide at this temperature are

NN22 1.18 kJ/kg/K1.18 kJ/kg/KHH22OO 2.332.33COCO22 1.261.26

so the energy equation is so the energy equation is 49,850 = (t49,850 = (tff-25){(13.17×1.18)+(2.25×2.33)+(2.75×1.26)}-25){(13.17×1.18)+(2.25×2.33)+(2.75×1.26)}ttff=2,081℃=2,081℃

The new mean temperature of the products is (2,The new mean temperature of the products is (2,081+25)/2=1,053℃081+25)/2=1,053℃

2525

The specific heats are now:The specific heats are now:NN22 1.22 kJ/kg/K1.22 kJ/kg/KHH22OO 2.502.50COCO22 1.301.30

solving the energy equation for the third time gives:solving the energy equation for the third time gives:ttff = 1,998℃ = 1,998℃

The mean temperature of the products now becomes (1,The mean temperature of the products now becomes (1,998+25)/2=1,012℃ giving998+25)/2=1,012℃ giving

NN22 1.22 kJ/kg/K1.22 kJ/kg/KHH22OO 2.482.48COCO22 1.301.30

A further evaluation of the energy equation givesA further evaluation of the energy equation givesttff = 2,001℃ # = 2,001℃ #

2626

5. Calculated Adiabatic Flame 5. Calculated Adiabatic Flame TemperaturesTemperatures

Values of the predicted adiabatic flame Values of the predicted adiabatic flame temperature for hydrocarbon fuels are temperature for hydrocarbon fuels are affected by the following factors:affected by the following factors:(1)(1) the calorific value (and chemical the calorific value (and chemical

composition) of the fuel;composition) of the fuel;(2)(2) the air-to-fuel ratio at which the air-to-fuel ratio at which combustion takes place; andcombustion takes place; and(3)(3) the initial temperature (preheat) of the initial temperature (preheat) of

the air and fuel.the air and fuel.

2727

CALORIFIC VALUECALORIFIC VALUE It would be expected that the higher the It would be expected that the higher the

calorific value of the fuel the higher the calorific value of the fuel the higher the final flame temperature produced.final flame temperature produced.The picture is, however, not quite as The picture is, however, not quite as simple as this since the chemical simple as this since the chemical composition of the fuel also plays a part.composition of the fuel also plays a part.

For example, natural gas has a carbon-to-For example, natural gas has a carbon-to-hydrogen ratio of around 3.1 and a hydrogen ratio of around 3.1 and a calorific value of 54 MJ/kg (gross). A typical calorific value of 54 MJ/kg (gross). A typical coal, on the other hand, has a carbon-to-coal, on the other hand, has a carbon-to-hydrogen ratio of around 18.0 and a hydrogen ratio of around 18.0 and a calorific value of 33.3 MJ/kg.calorific value of 33.3 MJ/kg.

2828

Fuels with a higher proportion of hydrogen wilFuels with a higher proportion of hydrogen will generate more water vapor in their combustil generate more water vapor in their combustion products; a glance at Table 4.3 shows that on products; a glance at Table 4.3 shows that water vapor has a higher specific heat than the water vapor has a higher specific heat than the other combustion products, which will lower tother combustion products, which will lower the adiabatic flame temperature.he adiabatic flame temperature.

The adiabatic flame temperature for a number The adiabatic flame temperature for a number of common hydrocarbon fuels are given beforof common hydrocarbon fuels are given before in Table 4.1. In each case combustion is stoice in Table 4.1. In each case combustion is stoichiometric and the initial temperature of the air hiometric and the initial temperature of the air and fuel is 25℃.and fuel is 25℃.

2929

It can be seen that there is quite a It can be seen that there is quite a small variation in the calculated small variation in the calculated flame temperature, given the wide flame temperature, given the wide variation between the calorific values variation between the calorific values of these fuels. of these fuels.

The “conformity” is due to the effect The “conformity” is due to the effect of the hydrogen in the fuel discussed of the hydrogen in the fuel discussed above.above.

3030

AIR-TO-FUEL RATIOAIR-TO-FUEL RATIO

Any excess air will increase the mass of flue gaAny excess air will increase the mass of flue gas relative to the mass of fuel, with a correspons relative to the mass of fuel, with a corresponding reduction in temperature.ding reduction in temperature.

With sub-stoichiometric air supply the flame tWith sub-stoichiometric air supply the flame temperature will also fall, as although the mass emperature will also fall, as although the mass of flue gas is reduced, the effective calorific valof flue gas is reduced, the effective calorific value of the fuel is also reduced by an amount eque of the fuel is also reduced by an amount equivalent to the calorific value of the carbon mouivalent to the calorific value of the carbon monoxide which is present in the flue gas.noxide which is present in the flue gas.

3131

The net calorific value of carbon The net calorific value of carbon monoxide is 10.11 MJ/kg.monoxide is 10.11 MJ/kg.

Next slide (Next slide (Fig. 4.2Fig. 4.2))It shows the temperature calculated It shows the temperature calculated for a natural gas flame as a function for a natural gas flame as a function of the excess air ratio, and of the excess air ratio, and demonstrates the effects described demonstrates the effects described aboveabove..

air fuel ratio

3333

Very high flame temperature can be Very high flame temperature can be achieved by oxygen enrichment of the achieved by oxygen enrichment of the flame, as the mass of flue gas is flame, as the mass of flue gas is considerably reduced.considerably reduced.

Oxygen flames are used in a number of Oxygen flames are used in a number of process applications, in particular welding, process applications, in particular welding, but the temperatures in oxygen-enriched but the temperatures in oxygen-enriched flames are so high that dissociation effects flames are so high that dissociation effects (discussed later) are highly significant. (discussed later) are highly significant.

3434

PREHEATPREHEAT

Common sense (and equation (2)) suggest Common sense (and equation (2)) suggest that preheating the air will increase the that preheating the air will increase the final temperature of the flame.final temperature of the flame.

This is a useful feature because by This is a useful feature because by increasing the temperature difference increasing the temperature difference between the flue gas and the heat between the flue gas and the heat extracting fluid, greater heat transfer will extracting fluid, greater heat transfer will be obtained for the same fuel input rate.be obtained for the same fuel input rate.

3535

This will result in an increase in the This will result in an increase in the thermal efficiency of the plant.thermal efficiency of the plant.

An example of the effect of preheat An example of the effect of preheat on the adiabatic temperature of a on the adiabatic temperature of a natural gas flame at 5% excess air is natural gas flame at 5% excess air is shown in Fig. 4.3 (next slide).shown in Fig. 4.3 (next slide).

3737

In practice, there are a number of reasons In practice, there are a number of reasons why the actual flame temperature will be why the actual flame temperature will be lower than the value predicted by this lower than the value predicted by this procedure.procedure.

The most significant of these is that at the The most significant of these is that at the high temperature achieved in flames the high temperature achieved in flames the combustion products will “dissociate” back combustion products will “dissociate” back into reactants or other higher reactive into reactants or other higher reactive species: this process is accompanied by an species: this process is accompanied by an absorption of energy, hence reducing the absorption of energy, hence reducing the actual flame temperature.actual flame temperature.

3838

The results of above calculations are then morThe results of above calculations are then more correctly referred to as “undissociated adiae correctly referred to as “undissociated adiabatic flame temperatures”, which acknowledbatic flame temperatures”, which acknowledges the simplifications inherent in them. ges the simplifications inherent in them.

In order to understand the more complete pictIn order to understand the more complete picture it is necessary to gain some insight into the ure it is necessary to gain some insight into the principles of chemical equilibrium, which are iprinciples of chemical equilibrium, which are introduced in the next chapter.ntroduced in the next chapter.