3. combustion thermodynamics

8/13/2019 3. Combustion Thermodynamics

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Prof. MohananDepartment of Mechanical Engg,

NITK Surathkal


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Thermodynamics : Deals with quantities of state at equilibrium

Temperature

Internal energy

Enthalpy Entropy

Availability and so on

Chemical Thermodynamics :

Deals with concentration of Reactants and chemicalinteractions.

Rate of reaction -- > how fast the reaction takes place.


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First Law Analysis for Reacting SystemConsider a constant pressure process in which nfmoles of fuel react withnamoles of air to produce npmoles of product:

PnAnFn paf

Applying First Law with state 1 being the reactants at P1, T1and state 2being products at P2, T2:

Reactants Products

Reactants Products

ReactionState 1 State 2

Q

W

)()( 121221 VVPUUQ

WUQ


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RRii

PpiiRP ThnThnHH

HH

VPUVPU

)()(

)()(

12

111222

HP< HR Q< 0 exothermic reaction

HP> HR Q> 0 endothermic reaction

)()( 1212 VVPUUQ

First Law Analysis for Reacting System


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Enthalpy of ReactionConsider the case where the final temperature of the products is the same asthe initial temperature of the reactants (e.g., calorimeter is used to measure Q).

Reaction Q

W

P1=P2=PoT1=T2=To

The heat released under this situation is referred to as the enthalpy ofreaction, HR ,

fuelofkmolorkgperkJ:units)()(

)()(

Roii

Poii

RRii

PpiiR

ThnThn

ThnThnH

To


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Enthalpy Scale for a Reacting System

By international convention, the enthalpy of every element in its natural state(e.g., O2(g), N2(g), H2(g), C(s)) at STP has been set to zero

0)298,1( ofhKatmh

We need to take into account that for a reacting system the working fluidchanges molecularly from reactants to products while undergoing a process.

Consider the following identity:

)]298,1(),([)298,1(),( KatmhTPhKatmhTPh

(note the notation convention)

at STP

i.e,


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The enthalpy of all other substances at STP is simply the heat of formation

of the substance, since it is formed from its elements, for example:

)]298,1(),([),(,

KatmhTPhhTPhii

o

ifi

sensible enthalpychemical enthalpy T

K ipdTc

298 ,

Therefore, the enthalpy of the ith component in a mixture is:

Enthalpy Scale for a Reacting System

olOHflOH

o

lOHfgHgOlOH

hh

hhhhQSTPrecall

lOHgHgO

)(,)(

)(,)()()(

222

22

2222

2/1@

)()()(2/1


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It is the heat of reaction, in a reaction inwhich species alone is the product & thecomponent elements of the species are theonly reactants at standard state.(298.16k, 0.1

Mpa)

Heat of formation of the reactants are set tozero at standard state.


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Heat of Formation for Different Fuels


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Heat of formation = Heat of combustion (refers to species) = (refers to reaction)


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For any reaction aiAi -- > aiAi Where ai& aiare stoichiometric coefficients and Ai

refer to species.

Heat of Combustion =


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The maximum amount of energy is released from a fuel when reacted with astoichiometric amount of air and all the hydrogen and carbon contained in thefuel is converted to CO

2and H

2O

This maximum energy is referred to as the heat of combustionor the heatingvalue and it is typically given per mass of fuel

Heat of Combustion

222224

76.32

)76.3(4

NOHCONOHC

HR(298K)

alcohols


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Fuel Energy

density

(MJ/L)

Air-

fuel

ratio

Specific

energy

(MJ/kg air)

Heat of

vaporizatio

n

Gasolineand

biogasoline

32 14.6 2.9 0.36 MJ/kg

Butanol fuel 29.2 11.2 3.2 0.43 MJ/kg

Ethanol fuel 19.6 9.0 3.0 0.92 MJ/kg

Methanol 16 6.5 3.1 1.2 MJ/kg
http://en.wikipedia.org/wiki/Energy_densityhttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Specific_energyhttp://en.wikipedia.org/wiki/Heat_of_vaporizationhttp://en.wikipedia.org/wiki/Heat_of_vaporizationhttp://en.wikipedia.org/wiki/Heat_of_vaporizationhttp://en.wikipedia.org/wiki/Biogasolinehttp://en.wikipedia.org/wiki/Biogasolinehttp://en.wikipedia.org/wiki/Ethanol_fuelhttp://en.wikipedia.org/wiki/Methanolhttp://en.wikipedia.org/wiki/Methanolhttp://en.wikipedia.org/wiki/Ethanol_fuelhttp://en.wikipedia.org/wiki/Biogasolinehttp://en.wikipedia.org/wiki/Gasolinehttp://en.wikipedia.org/wiki/Heat_of_vaporizationhttp://en.wikipedia.org/wiki/Heat_of_vaporizationhttp://en.wikipedia.org/wiki/Heat_of_vaporizationhttp://en.wikipedia.org/wiki/Specific_energyhttp://en.wikipedia.org/wiki/Specific_energyhttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Air-fuel_ratiohttp://en.wikipedia.org/wiki/Energy_densityhttp://en.wikipedia.org/wiki/Energy_densityhttp://en.wikipedia.org/wiki/Fuel


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Heat of CombustionThere are two possible values for the heat of combustion depending onwhether the water in the products is taken to be saturated liquid or vapour.

Tp

T

S

hghfFrom steam tables:

hfg= hghf > 0

HR= HPHR < 0 (exothermic)

The term higher heat of combustionis used when the water in the productsis taken to be in the liquid state (hH20= hf)

The term lower heat of combustionis used when the water in the productsis taken to be in the vapour state (hH20= hg)


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0

h kJ/kg fuel)

T

Products with H2O (g)

Products with H2O (l)

Reactants

hfg,H2Oper kgfuel

hlo

whhigh

Heat of Combustion, graphical

298K


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Adiabatic Flame TemperatureConsider the following adiabatic constant pressure process:

)()(

0)()(

1

Rii

Paii

RRii

Ppii

ThnThn

ThnThnQ

For a constant pressure process, the final products temperature, Ta, is known

as the adiabatic flame temperature (AFT).

For a given reaction where the nis are known for both the reactants and theproducts, Tacan be calculated explicitly.

FuelAir Productseactants


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Adiabatic Flame Temperature

P R

o

ifi

o

ifiR iiiP iaii

Rii

o

ifiP

iai

o

ifi

Rii

Paii

hnhnKhThnKhThn

KhThhnKhThhn

ThnThn

,,1

1,,

1

)298()()298()(

)298()()298()(

)()(

o

RHSensible heat of reactants(equal to 0 if T1= 298K)

Sensible heat of products

P R

o

ifi

o

ifiR

T

ipiP

T

ipi hnhndTcndTcn ia

,,298 ,298 ,OR


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The flame temperatureis attained as in anadiabatic situation.

Reactants are kept inan isolated cylinder

with a piston tosimulate the pressure. They are sparked to

initiate ignition. Reaction proceeds to

completion. Temperature rises toadiabatic flametemperaure.


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STEPS:

Composition of the products is to be found out .

Heat of combustion (HOC) is to be calculated. HOC is used to raise the temp from Toto Tf This rise in temp is in the form of sensible enthalpy

rise.

If all the HOC is used up to raise the temp to Tf, thenthe adiabatic flame temp can be obtained.

Tfis assumed first.

If some heat is left in balance or heat absorbed islarger than available, keep computing the

composition & checking the balance till heat balanceis satisfied to the required degree of accuracy.


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Ta,

Constant Pressure Adiabatic Flame Temperaturewith products at equilibrium


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Constant Pressure Adiabatic Flame Temperaturewith products at equilibrium

nitromethane

octaneethanol

hydrogen


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Estimate the constant-pressure adiabatic

flame temperature for the combustion of astoichiometric CH4-air mixture. The pressureis 1 atm and the initial reactant temperatureis 298 K.

Use the following assumptions:1.Complete combustion(no dissociation) i.e.,the product mixture consists of onlyCO2,H2O,and N2.

2. The product mixture enthalpy is estimatedusing constant specific heats evaluated at1200K(~0.5(Ti+Tad),where Tadis guessed tobe about 2100K)


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Mixture composition:

Properties(Appendices A and B)

52.7,2,1

52.721)76.3(2

222

222224

NOHCO NNN

NOHCONOCH


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Species Enthalpy of Formation @298K

h0f,i(kJ/kmol)

Specific Heat@1200K

cP,i(kJ/kmol-K)

CH4 -74,831 -----

CO2 -393,546 56.21

H2O -241,845 43.87

N2 0 33.71

O2 0 ----


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298)]-33.71((7.52)[0

)]298(87.43845,241)[2(

)298(21.56546,393)[1(

)]298([

831,74)0(52.7)0(2)831,74)(1(

,

0

,

ad

ad

ad

adipifiprod

react

i

prod

iprod

react

iireact

T

T

T

TchNH

kJH

hNHhNH

Equating Hreactto Hprodand solvingfor Tad yieldsTad=2318K


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Constant Volume AFT

Reaction Q

W

Consider the case where the piston is fixed and the cylinder is perfectly

insulated so the process is adiabatic (Q= 0)

)()(

0)()(

1

Rii

Paii

RRii

Ppii

TunTun

TunTunQ

Note h = u + pv = u + RT, so

T)R)(Th(nTRThnR

iiP

aii 1))((


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p Riai

iP

iP R

o

ifi

o

ifiR

iiiP

aii

TRnTRn

KhnhnhnKhThnThn

1

,,1

)298()298()()(

Extra term compared to constant pressure AFT ( term > 0)

The AFT for a constant volume process is larger than for a constantpressure process.

The AFT is lower for constant pressure process since there is Pdvworkdone

Constant Volume AFT

R

iii

o

ifiP

iiai

o

ifi TRKhThhnTRKhThhn )298()()298()( 1,,


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Estimate the constant-volume adiabatic flametemperature for a stoichiometric CH4-airmixture using the same assumptions as inExample 2.5. Initial conditions are T i=298K,P=1 atm 101,325Pa).


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The same composition and properties used inExample 3 apply here. We note, however, thatthe cp,ivalues should be evaluated at atemperature somewhat greater than 1200K,

since the constant-volume Tadwill be higherthan the constant-pressure Tad. Nevertheless,we will use the same values as before.


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First Law:

0)(

0)(

adprodinitreacuprod

ii

reac

ii

adprodinitreacuprodreac

TNTNRhNhN

orTNTNRHH


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kJT

T

T

TH

kJH

ad

ad

ad

adprod

reac

)298(5.397236,877

)]29833.71((7.52)[0

)]298(87.43845,241)[2(

)]298(21.56546,393)[1(

831,74)0(52.7)0(2)831,74)(1(


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And

where reac=prod=10.52kmol.Reassembling and solving for Tadyields Tad=2889K

)298)(52.10(315.8)( adadprodinitreacu TTNTNR


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Combustion by Irvin Glassman Fuels and combustion by Sharma and

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3. combustion thermodynamics

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