Thermodynamic Irreversibilities and Exergy Balance in Combustion Processes

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Progress in Energy and Combustion Science 34 (2008) 351–376

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Thermodynamic irreversibilities and exergy balancein combustion processes

S.K. Soma,�, A. Dattab

aDepartment of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302, IndiabDepartment of Power Engineering, Jadavpur University, Salt Lake Campus, Kolkata 700 098, India

Received 30 March 2007; accepted 4 September 2007

Available online 23 October 2007

Abstract

The growing concern for energy, economy and environment calls for an efficient utilization of natural energy resources in developing

useful work. An important thermodynamic aspect in gauging the overall energy economy of any physical process is the combined energy

and exergy analysis from the identification of process irreversibilities. The present paper makes a comprehensive review pertaining to

fundamental studies on thermodynamic irreversibility and exergy analysis in the processes of combustion of gaseous, liquid and solid

fuels. The need for such investigations in the context of combustion processes in practice is first stressed upon and then the various

approaches of exergy analysis and the results arrived at by different research workers in the field have been discussed. It has been

recognized that, in almost all situations, the major source of irreversibilities is the internal thermal energy exchange associated with high-

temperature gradients caused by heat release in combustion reactions. The primary way of keeping the exergy destruction in a

combustion process within a reasonable limit is to reduce the irreversibility in heat conduction through proper control of physical

processes and chemical reactions resulting in a high value of flame temperature but lower values of temperature gradients within the

system. The optimum operating condition in this context can be determined from the parametric studies on combustion irreversibilities

with operating parameters in different types of flames.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Combustion; Chemical reaction; Transport processes; Exergy; Irreversibility

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

2. Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

2.1. Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

2.2. Irreversibility and its causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

2.3. Exergetic efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

3. Exergy analysis approach in combustion systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

3.1. Different combustion systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

3.2. Physical processes in a combustion system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

3.3. Exergetic performance analysis based on exergy balance: approach 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

3.3.1. Equilibrium approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

3.3.2. Analysis in well-stirred reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

3.3.3. Intrinsic analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

3.4. Exergetic performance analysis using entropy generation equation: approach 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

e front matter r 2007 Elsevier Ltd. All rights reserved.

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ing author. Tel.: +913222 282978; fax: +91 3222 282278.

ess: [email protected] (S.K. Som).

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ARTICLE IN PRESSS.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376352

4. State of art in exergy analysis in combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

4.1. Gaseous fuel combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

4.2. Liquid fuel combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

4.2.1. Droplet exergy models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

4.2.2. Spray exergy models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

4.3. Solid fuel combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

1. Introduction

The world energy consumption is largely dependent onfossil fuels even today where combustion plays a key role inthe energy utilization process. Combustion of fuel finds itsimportance in heating, power production, transportationand process industries. The energy-intensive industries likepetroleum refining, steel, chemical, glass, metal casting,aluminum, etc. are also heavily dependent on combustionprocesses. In 2003, almost 86% of a total 421 quadrillion kJenergy produced from the primary energy resources camefrom the combustion sources [1]. In this, the shares of oil,natural gas and coal, which are the three principal pillarsfor energy supply, were 162, 99 and 100.5 quadrillion kJ,respectively. The high share of combustion associatedenergy production is maintained in all the four majorenergy utilization sectors, viz. residential, commercial,industrial and transportation. This trend is believed tocontinue in the coming years. A projection of data to 2030shows a 71% increase in the total energy consumptionfigure from that in 2003. However, the share of fossil fuel-based resources has been predicted to remain at the samerange of 86% as is in 2003. Despite the on-going depletionin the fossil fuel reserves and the ever-increasing concerntowards the conservation of the environment, the growth inthe use of oil in the time span of 2003–2030 has beenenvisaged to be 47.5%, that in natural gas to be 91.6% andin coal to be 94.7%. The figures reveal that the combustionsystem and combustors will maintain their importance inthe energy sector in the next several decades to come.

On this backdrop, the question of efficient operation ofthe combustors finds importance. Both the limited com-bustible fossil fuel reserve and the damage that combustioncauses to the environment, e.g. through the liberation ofthe GHGs, calls for an increase in efficiency of the systemthrough the minimization of the losses. In a gross sense, theefficiency of a device whose primary purpose is theconversion of energy is given by the ratio of the energyin the converted form to that before conversion. In acombustor, the chemical energy of the fuel is convertedinto thermal energy. Therefore, the conventional definitionof efficiency of a combustor indicates how much thermalenergy is available for use from the stored chemical energyof the fuel. The losses in a combustor that accounts for thedecrease in the efficiency are due to unburnt fuel,incomplete combustion and heat loss to the surroundingacross the combustor wall.

The conventional definition of combustion efficiency,however, does not pay any attention to the quality atwhich the thermal energy from the combustor is availablein the hot products of combustion. For example,if we consider combustion of a fuel with air at atmospherictemperature in a well-stirred combustor, the final tempera-ture of the product upon complete combustion ofthe fuel will depend on the extent of the air supplied. Anincrease in the excess air will lower the product gastemperature, even when the energy content of the gasremains the same in consideration of adiabatic wallsof the combustor. Thus, the work producing potentialof the product gas decreases, as given by the secondlaw of thermodynamics. So complete conversion ofenergy in the combustor cannot be its sole performanceindicator.Probably the most important use of combustion in

practice is for the production of work. The transportationsector and the electricity generating plants use the energyobtained from combustion for the generation of work.Many applications in the process industries also employcombustors for the purpose of getting work. In all theseapplications, the work producing potential of the productsof combustion should be the performance indicator for thecombustion process. Exergy is the term coined [2] todescribe the work producing potential of energy, andhence, an exergy-based analysis of combustors should findimportance in optimizing the design.Many works are available in the literature advocating

the importance of exergy-based analysis for the perfor-mance evaluation of thermodynamic systems [3–5].According to them, energy-based performance analysisare often misleading as they fail to identify the deviationfrom ideality. An ideal process is reversible and doesnot incur any destruction of exergy. The practicalprocesses generate thermodynamic irreversibilities internalto them and result in a loss of exergy even when thereis no loss of energy external to the system. Several studieshave indicated that the conventional combustion processinvolves inherent thermodynamic irreversibility, whichsignificantly limits the conversion of fuel energy intowork [6]. For typical atmospheric combustion systems,about 1/3rd of the fuel exergy becomes unavailabledue to the inherent irreversibilities in the combustor. Mostof this irreversibility is associated with the internalheat transfer within the combustor between the productsand reactants. Such heat transfer becomes inevitable in

ARTICLE IN PRESS

H

HH

H

H

H

H

HH

H

O

O O

O

O O

O

O

O

H

H

H

H

OH

H

O

H

H

O

H

H

O

O

H

H OH

H

O

H H

Tcool Tmax Tadiabatic

Flame Front

Fig. 1. Schematic of how entropy is generated in H2–O2 flame front due to

internal heat transfer. Energetic product molecules dissipate its energy in

collision with surrounding cool reactant molecules. After Daw et al. [73].

Nomenclature

A area (m2)_A rate of exergy flow (J/s)

a specific exergy (J/kg)ach specific chemical exergy (J/kg)B transfer numberCk mass fraction of species k

cp specific heat (J/kgK)f ki

body force per unit mass on species k (N/kg)h specific enthalpy (J/kg)_I rate of exergy destruction (J/s)jki

mole flux of species k (kmol/m2 s)K specific kinetic energy (J/kg)k thermal conductivity (W/mK)M molecular weight_m mass flow rate (kg/s)_m000 volumetric rate of mass generation (kg/m3 s)

Pr Prandtl numberp pressure (N/m2)_Q rate of heat transfer (W)_qi conduction heat flux vector (W/m2)R̄ universal gas constant (J/kmolK)Re Reynolds number_Sg rate of entropy generation (W/K)s specific entropy (J/kgK)_s000g volumetric entropy generation rate (W/m3K)T temperature (K)t time (s)Uki

diffusion velocity of species k (m/s)u specific intermolecular energy (J/kg)ui velocity vector (m/s)

uofl adiabatic laminar flame speed (m/s)

V volume (m3)v specific volume (m3/kg)

Greek letters

a thermal diffusivity (m2/s)w chemical potential (J/kg)dij Kronecker deltaf equivalence ratioj overall potential energy of all species (J/kg)ZII exergetic efficiencym viscosity (kg/m s)r density (kg/m3)tij stress tensor (N/m2)_ok volumetric rate of formation of species k

(kg/m3 s)

Subscripts

a aircv control volumeex exitf fuelk species indexin inletr exergy reference environment

Superscripts

ex exitin inlet

S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376 353

both premixed and diffusion flames, where highly energeticproduct molecules are free to exchange energy withunreacted fuel and air molecules. Fig. 1 depicts howentropy is generated due to internal heat transfer in ahydrogen–oxygen reaction. However, the entropy genera-tion in a combustion process is attributed to both internalheat and mass transfers and chemical reactions. Internalheat transfer within the combustor is often difficult to berecognized as an issue affecting the performance, because itdoes not result in a direct energy loss from the combustionzone to the surrounding. Instead, internal heat transferonly degrades the exergy of the product flue gas andreduces its work potential. Therefore, the actual energypenalty does not become apparent until the work genera-tion step, which is separated from the combustion step, istaken into account.

The losses due to process irreversibilities can becalculated using the second-law analysis, either from theunbalanced rate of exergy input or from the rate of entropygeneration. Accordingly two different approaches forsecond-law-based process performance evaluation andoptimization studies have evolved—exergy analysis ap-

proach and minimization of entropy generation approach.The concept of minimizing the irreversible production ofentropy is inherent in reducing the exergy loss in a process


for improving the efficiency. Accordingly, the most efficientperformance is achieved when the exergy loss in the processis the minimum. Both the approaches find wide accept-ability in heat transfer engineering, e.g. in the optimizationof heat exchangers, fins, thermal insulation, electronicpackage cooling, etc. and have been chronologicallyreviewed in many references [7–11].

Yilmaz et al. [12] presented an exhaustive review of theapplication of various second-law-based analyses for theoptimal design of heat exchangers. They described the needfor the systematic design of heat exchangers using second-law-based procedure. Accordingly, the design of heatexchangers based on low first cost approach dictating theminimum size leads to higher irreversibilities, as it requiresa larger temperature difference between the streams toaffect the heat transfer. Such designs are inefficient fromthe exergy standpoint, as they do not preserve the qualityof energy during the transformation. The authors pro-claimed that the exergy-based performance evaluation isworthy as it gives a measure of the perfection of thethermal process.

Historically, second-law-based analysis was developed toevaluate the process of power generation from heat.Applications of exergy analysis for the performanceevaluation of power-producing cycles have increased inthe recent years. A lot of works are now available in theliterature where the second-law-based analyses have beenapplied for optimizing performance on coal-based electri-city generation using conventional [13–19], fluidized bedand combined cycle technology [20] as well as for gasturbine [21–24], internal combustion engine [25–32] andblast furnace [33] applications. It can be concluded from allthese studies that in power plants involving combustion,the major part of the exergy loss takes place in the processof combustion.

Lior [34] and Lior et al. [35] outlined the necessity ofsecond-law-based analysis of combustion processes withthe following objectives:

(1)
identification of the specific phenomena/processes thathave large exergy losses or irreversibilities,
(2)
understanding of why these losses occur, (3) evaluation of how they change with the changes in the
process parameters and configuration, and
(4) as a consequence of all the above, suggestions on how
the process could be improved.

The present review will throw light on the state of artknowledge on thermodynamic irreversibility and exergyloss that occur in fundamental physical processes in thecombustion of solid, liquid and gaseous fuels. The differentapproaches adopted by the researchers to achieve the goalhave been reviewed with their relative merits and demerits.A final conclusion has been drawn to give direction onfuture research needed for more efficient utilization offuel’s useful energy through a trade-off between the energyand exergy-based efficiencies.

2. Basic concepts

2.1. Exergy

The concept of exergy is a direct outcome of second lawof thermodynamics. The exergy of a system is defined to beits work potential with reference to a prescribed environ-ment known as ‘exergy reference environment’. The term‘work potential’ implies physically the maximum theore-tical work obtainable if the system of interest and theprescribed environment interact with each other and reachthe equilibrium. The term exergy is sometimes referred bythermodynamically synonymous term ‘availability’ and is acomposite property of the system and the referenceenvironment. In general, the specific exergy is defined as

a ¼ K þ jþ u� urð Þ þ pr v� vrð Þ � Tr s� srð Þ þ ach, (1)

where K is the specific kinetic energy of the system and j isthe potential energy per unit mass due to the presence of anyconservative force field. T, p, u, v and s are the temperature,pressure, specific intermolecular energy, specific volume andspecific entropy, respectively, while ach represents the specificchemical exergy. The terms with the subscript r are theproperties of the exergy reference environment.

2.2. Irreversibility and its causes

Any natural process depletes the total exergy of allinteracting systems in the process (i.e. the exergy reserve ofthe universe decreases). This is known as law of degradationof energy. The destruction of exergy is termed as irreversi-bility, which is considered to be a thermodynamic character-istic of a physical process. All natural processes areirreversible. The causes of irreversibility lie in the basicrequirement of a natural process to occur and can beclassified broadly as: (i) lack of thermodynamic equilibriumand (ii) dissipative effects associated with a natural process.The thermodynamic irreversibility in a process is character-ized by the entropy generation in the process. For continuousprocesses performed by a system, it can be written that

_I ¼ Tr_Sg, (2)

where _I is the rate of exergy destruction or dissipation and _Sg

is the rate of entropy generation. Eq. (2) is known as theGouy–Stodola equation [8].An engineering system, in general, involves a number of

coupled physical processes. The entropy generation due toall these processes together determines the system irrever-sibility. The general expression for entropy generation in acontinuous field described by a system is derived from theequation of change of entropy (entropy transport equa-tion). This is discussed in Section 3.4.

2.3. Exergetic efficiency

The parameter that gauges the effectiveness of a systemin preserving its exergy in performing a physical process is

ARTICLE IN PRESS

Q

Ain Aex

Inlet

ReactantsProducts

Combustion System

Outlet

. .

Fig. 2. Schematic of a combustion system showing the exergy transfer.


known as exergetic efficiency. This is also called as second-law efficiency. Lower is the irreversibility, higher is theexergetic efficiency and vice versa. In determining theexergetic efficiency of a process performed by a system, onehas to consider the exergy quantities that cross the systemboundaries either as flow exergy associated with mass flux,or as exergy transfer built in with the transfer of energyquantities (heat and work).

A combustion system in general performs a number ofcoupled transport processes like convection and diffusionof mass, momentum and energy along with the process ofchemical reactions. All of them can be realized either in alaminar or in a turbulent flow regime. In both cases, theexpression for exergetic (or second law) efficiency of acombustion system (see Fig. 2) can be written as

ZII ¼_Aex

_Ain � _Qð1� ðTr=TÞÞ, (3)

where _Ain and _Aex are the rate of flow availability at inletand exit to the combustor, respectively. _Q is the rate of heatloss from the combustion system and T is the representa-tive temperature at the boundary surface of combustor.

From an exergy balance, we can write

_I ¼ _Ain � _Aex � _Q 1�Tr

T

� �. (4)

Hence, it becomes

ZII ¼ 1�_I

_Ain � _Qð1� ðTr=TÞÞ. (5)

For an adiabatic combustor ( _Q ¼ 0):

ZII ¼_Aex

_Ain

¼ 1�_I_Ain

. (6)

3. Exergy analysis approach in combustion systems

3.1. Different combustion systems

In the practical world, combustion is used in variousdevices from the simplest one like a candle to the mostcomplex ones like rocket and scramjet engines. However,there are fundamental differences in the physical processesinvolved in combustion in different devices in more thanone aspect. Borman and Ragland [36] cited and analyzedexamples of combustion in many important devices.

One way of distinguishing the combustion behavior inpractical systems is based on the fuel that is burnt. Thoughthe major share of the fuels used for combustion is thehydrocarbons, the composition of the fuel differs andaccordingly the fuel can be either in the gaseous, liquid orsolid phase. The gaseous fuels can homogeneously mixwith the oxidizer very easily for burning. The need of fuelpreparation is the minimum and the combustion reactionproceeds rapidly with little formation of the pollutingspecies. However, the cost of the fuel is high and thestorage and handling systems are voluminous and elabo-rate. The convenient burning of the gaseous fuels mostlypertains to small combustion applications including thedomestic use. However, the present day concern of theenvironment calls for the use of gaseous fuels even in largecombustors to keep the emission levels within the statutorylimits. The solid fuels are suitably gasified to obtainsynthetic gas and liquid fuels are pre-vaporized andpremixed with air to get a lean vapor–air mixture in thegas phase for burning.The liquid fuel burning is mainly promoted in the

transportation sector for its easy storage and relativelyclean handling. Various forms of liquid hydrocarbon fuelsare used in automobile engines, diesel engines, aircraft gasturbines, etc. The heavier fractions of the liquid hydro-carbons, which are relatively less expensive, are used infurnaces and boilers. The fuel preparation is necessary forthe high viscous species, where heating is required tocontrol the fuel viscosity for reducing the pumping powerand for better atomization. The atomization of the liquidinto minute droplets is always necessary to enhance theevaporation process, which precedes the combustion.Different types of atomizers are used depending upon theapplication. Combustion of liquid fuel sprays is an intricateaffair involving various inter-related phenomena, likeatomization, penetration, evaporation, interference, mixingand chemical reaction. Multi-component nature of most ofthe practical fuels further complicates the situation.Solid fuel burning is always heterogeneous in nature

occurring at the surface of the fuel and inside the poreswhen the fuel particles are porous. Mainly coal, lignite andbiomass fuels come under this category. These fuels requirean elaborate fuel preparation process, e.g. in case ofpulverized coal-fired boiler the fuel is required to bepulverized from the coarse size to fine powder having meansize of 50–75 mm. The utility boilers and heat treatmentfurnaces are the two major applications using solid fuels.

3.2. Physical processes in a combustion system

A number of coupled interacting physical processes takeplace in a combustion system to initiate and sustain thecombustion reactions. The primary requirement for acombustion reaction is the mixing of fuel and oxidizer sothat they come in contact at the molecular level. Except forsolid fuel combustion, all combustion reactions take placein the gaseous phase. Therefore, for liquid fuel combustion,


vaporization of fuel and its mixing with the air (oxidizer)are the controlling processes in sustaining the combustionreactions. A combustion system, in general, is a multi-component and multiphase system. The physical processesoccurring in the system can be classified broadly in twogroups, namely: (i) transport processes and (ii) chemicalreactions. The transport processes pertain to the transportof mass momentum and energy, which involve theprocesses of diffusion and convection of those quantities.The turbulence plays an additional key role by transportingmass momentum and energy through turbulent eddiesalong with the transport of the quantities throughmolecular diffusion and flow-aided convection. The phy-sical aspects of transport processes are governed by threebasic conservation equations as follows:

Mass conservation equation of individual species:

qCk

qtþ

qqxj

rCkuj þ rCkUk;j

� �¼ _ok, (7)

where Ck is the mass fraction of the species k in themixture, and uj and Uk,j are the mass average velocity andthe mass diffusion velocity for the species k, respectively._ok is the rate of formation of the kth species. In a generalmulticomponent system comprising N components, thereare N equations of this kind. The addition of these N

equations gives the equation for conservation of bulk massand is known as the continuity equation.

Momentum conservation equation:

qqt

ruið Þ þqqxj

rujui

� �¼ �

qp

qxj

þqtji

qxj

,

þ rXN

k¼1

Ckf ki

!. ð8Þ

Energy conservation equation:

qqt

rhð Þ þqqxj

rujh� �

¼qp

qtþ uj

qp

qxj

þ tij

qui

qxj

�q _qj

qxj

�qqxj

XN

k¼1

rCkUk;j

� hk

!þ r

XN

k¼1

Ckf k;jUk;j . ð9Þ

There are numerous physical models and approachesfollowed by several computational methods to solve theabove equations in determining the velocity, temperatureand species concentration fields in a combustion system.The field variables define the thermodynamic potentials forrespective diffusive and convective fluxes of mass momen-tum and energy. The rate equations of the fluxes are givenby the phenomenological laws of respective processes. Thetransport processes are inherently irreversible due tothermodynamic dissipation in the processes occurringunder a finite potential gradient.

One major process in a combustion system is the chemicalreaction. The word combustion is usually defined in itssimplest form as the rapid oxidation reaction generatingheat or both heat and light. The definition itself emphasizesthe intrinsic importance of chemical reactions to combus-tion. The oxidation between fuel and oxidizer in acombustion system takes place through a number ofreaction steps involving the production of intermediatespecies in the form of compounds, elements, radicals,molecules and atoms. The number and details of the stepsfor a given reaction is provided by the combustionchemistry. A detailed reaction mechanism involving inter-mediate reaction steps is very complex and the combustionchemistry of many reactions is not fully understood eventoday. The use of global or quasi-global reactions to expressthe combustion chemistry is a ‘black box’ approach, since itdoes not provide a basis for understanding what actuallyhappens chemically in the system. However, for oxidation ofhydrocarbon fuels, particularly of higher paraffin or alkanegroup, global or quasi-global steps can capture the overallbehavior of the reaction processes, and may be used forengineering approximations with due regard to theirlimitations. Westbrook and Dryer [37] present and evaluateone-step, two-step and multi-step global kinetics for a widevariety of hydrocarbon oxidations. The chemical reactionsfor gaseous and liquid fuel combustions are referred to ashomogeneous reactions, which take place in gas phase as aresult of the collisions of gas-phase molecules of the reactingspecies (fuel and oxidizer). Therefore, the primary step inliquid fuel combustion is the vaporization of liquid fuel. Onthe other hand, the solid fuel combustion involves hetero-geneous reactions, where gas-phase oxidizer reacts withsolid-phase fuel at the surface of the solid fuel. The rate ofany chemical reaction is guided either by the kinetics of thereaction or by the rate of diffusive transport of the reactingmolecules to come in contact for possible collision forreaction. The rate equation of either kinetic-controlled ordiffusion-controlled reactions are developed with the helpof the physics of the governing process, and involveempirical model parameters, which are tuned to the bestagreement with the actual reaction rates found fromexperiments.The direction of a chemical reaction is provided by the

second law of thermodynamics, and is determined by thedifference between the sum of the products of chemicalpotential and stoichiometric coefficient of the reactingspecies and that of the product species. Similar to transportprocesses, thermodynamic irreversibility is incurred by achemical reaction and is determined by the chemicalaffinity (potential driving the chemical reaction) and thespecific rate of the reaction.

3.3. Exergetic performance analysis based on exergy

balance: approach 1

One way of analyzing the performance of a combustor isby the exergy balance across the combustor. Considering

ARTICLE IN PRESSS.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376 357

the fuel and air entering the combustor either separately, orin the form of a mixture, it is possible to calculate theexergy flow rate at the inlet to the combustor. It willcomprise the chemical exergy of the fuel and the thermo-mechanical (or physical) exergy of the fuel and air. Thecombustion analysis in the combustor results in theproduct stream at a particular pressure, temperature andcomposition, from which the exergy of the outlet stream isevaluated. The accuracy of the result depends upon theaccuracy of the combustion analysis performed by themodels with different degrees of complexity.

3.3.1. Equilibrium approach

The simplest method of calculation considers a zero-dimensional model with the product stream leaving as anequilibrium mixture of all the product species at a singlepressure and temperature. The analysis adopts the laws ofthermochemistry, without considering specific transportand kinetic rates. In other words, both the transport andchemistry are assumed to be infinitely fast. Such a methodis widely used in all thermodynamic analyses of cycles andsystems involving a combustor.

Let us consider, as an example, a simplified adiabatic,well-stirred combustor burning a stream of fuel (methane(CH4)) in air. The rate of exergy flow at the inlet isassociated with the inflow of air and fuel to the system andcan be written as

_Ain ¼ _maaina þ _mf ain

f , (10)

where _ma and _mf are the mass flow rates of air and fuel,respectively, into the combustor and ain

a and ainf are the

specific exergy of air and fuel at the inlet. In considerationof air as an ideal gas, the specific flow exergy of air,considering only the thermomechanical contribution, isdetermined from the following equation:

aina ¼ hin

a � hr

� �� Tr sin

a � sr

� �. (11)

In the equation, h and s refer to the specific enthalpy andspecific entropy, respectively, with the subscript a referringto air and r referring to the exergy reference environment.The superscript in refers to the inlet condition.

The terms on the right-hand side can be evaluated as

hina � hr

� �¼

Z Tina

Tr

cpaðTÞdT , (12)

and

sina � sr

� �¼

Z Tina

Tr

cpaðTÞ

TdT �

R̄

Ma

Z pina

pr

dp

p. (13)

In the above equations, cpaðTÞ is the specific heat of air as

a function of temperature, R̄ and Ma are the universal gasconstant and the molecular weight of air, respectively. Tin

a

and pina are the temperature and pressure of air at the inlet,

while Tr and pr are the exergy reference temperature andpressure, respectively.

The specific exergy of the fuel stream may comprise boththe thermomechanical and chemical exergy components.The thermomechanical component is calculated as aboveconsidering the corresponding properties and state of thefuel instead of air and assuming the fuel as an ideal gas.The chemical exergy component depends upon the type offuel and is based on stoichiometric reaction of completecombustion of the fuel and a reference state of concentra-tion of the constituent products [38].The chemical reaction of the fuel with air is considered

through single-step global reaction chemistry as follows,when there is sufficient supply of air for completecombustion

CH4 þ2

fO2 þ 3:76N2ð Þ ! CO2 þ 2H2O

þ2

f� 2

� �O2 þ

2

f� 3:76N2. ð14Þ

In Eq. (14), f represents the equivalence ratio, which has tobe less than or equal to unity to ensure sufficient air forcomplete reaction.In case of insufficient air, it may be assumed that the

oxygen of air preferentially reacts with hydrogen of the fuelto form the water. The oxygen then converts the carbon tocarbon monoxide, a part of which is converted to carbondioxide depending upon the availability of oxygen. Theabove assumption for writing the stoichiometric chemicalequation is logical since the relative affinities of hydrogen,carbon and carbon monoxide for oxygen are in thatrespective order. The reaction can therefore be expressed as

CH4 þ2

fO2 þ 3:76N2ð Þ !

4

f� 3

� �CO2

þ 4�4

f

� �COþ 2H2Oþ

2

f� 3:76N2. ð15Þ

As the combustor is adiabatic, there is no energy transferacross it. The energy equation therefore gives the productgas temperature at the combustor exit (Tex) as the adiabaticflame temperature considering the variation of the specificheat of the product components with temperature. Theexergy flow rate at the exit to the combustor is evaluated as

_Aex ¼X

k

_mexk hex

k � hr

� �� Tr Sex

k � sr

� �� , (16)

where k is the index for each species present in the productstream at the exit. The exit properties (temperature andpressure) are used for evaluating the Eq. (16).The exergetic efficiency of combustion is then given as in

Eq. (6), i.e. ZII ¼_Aex= _Ain. Fig. 3 shows the variation of the

exergetic efficiency, calculated using the above formula-tion, with the equivalence ratio and inlet air temperature.The fuel is considered to enter the combustor at atemperature of 298K and the combustor operates at1 atm pressure. The results show that the second-lawefficiency is the maximum for the stoichiometric supply ofair. The lower product gas temperature at the exit for

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Ain

Ci, in

Tin

m

Aex

Ci, ex

Tex

m

mi

Reactantin

Productout

Well - stirred Reactors

′′′.

.

. .

.

Fig. 4. Analysis in a well-stirred reactor model: Entire combustor is

divided into a number of well-stirred reactors.

1

1

Exerg

etic E

ffic

iency

300 K450 K600 K750 K900 K

1.41.20.80.60.4

Equivalence Ratio

0.4

0.5

0.6

0.7

0.8

0.9

Fig. 3. Variation of exergetic efficiency with equivalence ratio of the

reactant mixture at different inlet air temperature calculated with the

equilibrium approach.

S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376358

a lean mixture as a result of the excess air supply reducesthe second-law efficiency of the combustor. This is despitethe fact that all the energy stored in the fuel is contained inthe product gas with the complete combustion of the fuel incase of a lean fuel–air mixture in the adiabatic combustor.Therefore, it is clear that neither the completeness ofcombustion nor the energy content of the product gasdetermines the exergy-based performance of the combus-tor. As the product gas temperature at the combustor exitdecreases with the increase in the excess supply of air, themaximum ability of it to perform useful work decreases.Therefore, the second-law efficiency decreases.

The same decrease in exergetic efficiency is also observedwith the insufficient supply of air, when the exit tempera-ture decreases because of the incomplete release of fuel’sstored energy. The maximum efficiency, which is obtainedwith the stoichiometric supply of air, may be considered asthe ideal situation for every inlet air temperature. This idealefficiency again increases with the increase in the inlet airtemperature which increases the temperature of theproduct gas.

Adebiyi [39] showed from a similar analysis in anadiabatic combustor, assuming complete combustion with-out dissociation and constant specific heats of air andproduct gas, that the maximum second-law efficiencyattainable for a combustion engine is 70% with CH4 asthe fuel and keeping the product temperature within theacceptable limit guided by the metallurgical constraint.

3.3.2. Analysis in well-stirred reactor

The above approach considering both infinite speed oftransport and kinetics does not in any way involve the timescale for determining the performance of the process. Animprovement may consider a well-stirred reactor model forthe combustor. A well-stirred reactor considers an infiniterate of transport, while taking into account the speed ofreaction. In a practical reactor, high level of turbulence

increases the rate of transport and such an assumption mayoften be acceptable. The reaction speed is determined usingthe kinetic parameters of the reactions for the assumedreaction scheme. Depending on the size of the combustor,the entire combustor may be assumed as a single well-stirred reactor. Otherwise, if the size is large, it can bedivided into several such reactors in series, with the outletof one entering the next reactor (Fig. 4). The analysis inevery single reactor control volume considers the solutionof the governing equations for getting the concentrations ofdifferent species of interest and the temperature [40].The mass conservation equation of an arbitrary species i

may be written as

dmcvk

dt¼ _min

k � _mexk þ _m000k V , (17)

where _m000k is the rate of mass generation of the species k perunit volume of the reactor and V is the reactor volume.Assuming steady-state operation of the reactor, the aboveequation may be written as

_m Cink � Cex

k

� �þ _okMkV ¼ 0, (18)

where _m is the total mass flow rate of the entire reactant orproduct streams and Ck is the mass fraction of the speciesk. _ok is the chemical rate of formation of species k per unitvolume, expressed in kmol/m3 s, obtained from the kineticsof reaction. For the well-stirred reactor, the chemicalreaction rate may be expressed as a function of thetemperature and the species concentration in the controlvolume (i.e. at the outlet).The steady state, steady flow conservation of energy

equation considering adiabatic reactor gives

_mXN

k¼1

Cexk hk Texð Þ �

XN

k¼1

Cink hk Tinð Þ

!¼ 0, (19)

where the upper limit N of the index k denotes the numberof species involved. The simultaneous solution of the above


equations gives the species mass fraction and the tempera-ture at the exit of the reactor, when the inlet values areknown. Using the expressions for exergy (thermomechani-cal as well as chemical), as shown in the previous section,the exergy values at the inlet and exit of the reactor can beobtained from which the second-law efficiency can becalculated.

This method includes in the calculation the volume ofthe reactor, as well as the chemical reaction rate for thespecies from the kinetic parameters. Therefore, the resultsfrom the method will be more realistic.

3.3.3. Intrinsic analysis

As pointed out by Lior [34], the system level develop-ment based on exergy calculation mostly use the equili-brium approach that employs equilibrium state data at theinlet and exit of the combustor for the exergy calculation.However, such equilibrium may not prevail in realitywithin the actual combustor. The exact distribution of thevelocity, temperature and species concentrations in thecombustor can be numerically obtained from the detailedsolution of reacting flow inside the combustor. Thisrequires the coupled solution of the full field and stateequations consisting of the Navier–Stokes, energy, speciesconservation and thermodynamic property equationsalong with the equations of reaction kinetics. The fieldparameters are then used in the transport equation ofexergy to find out the change in exergy flux between theinlet and outlet amounting to the loss of exergy. Theindividual contribution of the kinetic, potential, thermal,strain and chemical exergy loss can also be obtained fromthe calculation. The expanded forms of individual compo-nents are given in Lior [34] and Lior et al. [35].

The calculation of exergy loss, as indicated in thereferred papers, are complicated because of the complex-ities of the equations involved. However, the intrinsicanalysis for the exergy loss calculation can be performed inan alternative way [41]. The solution of the conservation ofmass, momentum, energy and species concentrations in thecombustor along with suitable kinetic rates of reactiongenerates information at the exit, typically for the velocity,temperature and concentration of various species. Theexergy flow rate at the inlet to the combustor can beobtained from the Eq. (10). While at the exit, the exergyflow rate is expressed as

_Aex ¼

ZAreaex

Xk

Cexk aex

k rexuexz dA, (20)

where the exit variables are obtained as the output of thenumerical solution of the reacting flow. This methodconsiders the local specific availability ‘a’ to bear the samefunctional relationship with the pertinent thermodynamicproperties as in case of equilibrium thermodynamics.

The second-law efficiency obtained from the exergyapproach gives a direct measurement of the performance ofthe combustor. The larger the irreversibilities, lower will be

the value of the second-law efficiency. However, thisapproach does not throw any light on the causes of theirreversibilities. In a combustor, several transport andchemical processes take place simultaneously, which areirreversible. The contribution of the processes towardsentropy generation at different locations within thecombustor is required to be known to investigate theprimary causes of exergy loss. It is also not practicallypossible to improve the performance of a combustorwithout such information. The present approach fails toprovide this data and calls for a methodology, whichconsiders the irreversibility as a field variable to find itsdistribution within the entire combustor.

3.4. Exergetic performance analysis using entropy

generation equation: approach 2

The irreversibility present in the actual processesoccurring in a combustor results in the generation ofentropy following the second law of thermodynamics. Therate of entropy generation may be used to calculate the rateof irreversibility or exergy destruction using the well-known Gouy–Stodola equation (Eq. (2)). The determina-tion of the total rate of entropy generation is an involvedprocess in an intrinsic analysis in the combustor. This isdone by calculating separately the rate of entropygeneration in each physical and chemical process thattakes place.In the flow field of a combustor, the nonequilibrium

conditions are due to the exchange of momentum, energyand mass of different species (multicomponent) within thefluid and at the solid boundaries. These nonequilibriumphenomena cause a continuous generation of entropy inthe flow field. The entropy generation is due to theirreversible nature of heat transfer, mass diffusion, viscouseffects within the fluid and at the solid boundaries,chemical reaction, coupling effects between heat and masstransfers and body force effects. Every irreversible processcan be viewed as the relevant flux driven by thecorresponding potential, e.g. the flux of heat is driven bythe temperature gradient. The entropy production rates indifferent processes can be explicitly obtained consideringthe conservation of multicomponent species mass inpresence of chemical reaction, conservation of momentumand energy along with the local entropy balance equation.The local entropy generation per unit volume has beenderived by Hirschefelder et al. [42] and is given by:

_s000g ¼tijðqui=qxjÞ

T�

_qi

T2

qT

qxi

�

PKk¼1 jki

ðqwk=qxiÞ

T

�

PKk¼1 s̄k jki

ðqT=qxiÞ

Tþ

PKk¼1 jki

f ki

T

�

PRc¼1 _oc

PKk¼1 g00kr � g0kr

� �wk

T, ð21Þ

where tij is the stress tensor, _qi is the heat flux vector andjki, wk and s̄k are the species mole flux per unit area,


chemical potential and partial molal entropy of the kthspecies, respectively. g0kr and g00kr are the stoichiometriccoefficients on the reactant side and product side,respectively, for the kth species in the cth reaction, and_oc is the reaction rate of the cth chemical reaction. In theabove equation, the first term is due to fluid friction, thesecond due to heat transfer, the third due to mass transfer,the fourth is a result of the coupling between heat and masstransfer, the fifth term is due to the body force effects andthe last term results from chemical reaction.

Observation of the Eq. (21) shows that knowledge of thefield parameters like velocity (and hence tij), temperature(and hence qi), species concentration (and hence jk, mk), ofthe state equations of the species used to determine thethermophysical properties (density, viscosity and thermalconductivity), and of the chemical reactions involved (todetermine the rate) allow the computation of the entropygeneration fields and exergy destruction. All these fieldparameters are obtained from the solution of the full fieldand state equations, consisting of the Navier–Stokes,energy, species conservation, entropy generation, andthermodynamic properties equations, combined in acombustion process with the reaction kinetics equations,all tightly coupled.

The rate of exergy destruction calculated from theentropy generation rate in this approach, gives the localcontribution of each individual process over the entirecombustor. It therefore helps in identifying the process,which has to be improved to reduce the loss. The aboveequation, given by Hirschfelder et al. [42] has been laterused by other researchers for the calculation of entropygeneration in non-reacting as well as reacting flows. Teng etal. [43] further considered the contribution of the diffusive-viscous effect towards entropy generation in a multi-component reacting fluid flow in addition to the othercontributions as shown in Eq. (21).

4. State of art in exergy analysis in combustion

Both the approaches, described above have been used inthe literature for the analysis of exergy destruction incombustion. The calculation of exergy destruction inconsideration of the equilibrium states at inlet and outletis mainly used for the analysis of system design and doesnot help in identifying the root causes of exergy destructionin the combustor. We shall exclude the review of such workand only consider those works, which give somewhatdetailed information regarding the causes and locations ofirreversibility in different combustion situations.

Tracking entropy generation in a flowing fluid is used foranalyzing the energy conversion systems in many industrialprocesses. Investigations of entropy generation in flowshave been reported in the literature related to momentumtransfer [7], heat transfer [7,8,10,11,44], mass transfer[45,46], combined heat and mass transfer [47,48] andchemical reaction [49]. Analysis during combustion is themost challenging because it involves the transport pro-

cesses of momentum, heat and mass as well as includeschemical reaction. Therefore, for a sufficiently detailedanalysis, in addition to considering the contribution ofevery process towards entropy generation, it is firstrequired to solve the combustion phenomenon itself,considering the maximum possible details. The accuracyin the simulation of combustion has a big role in correctlypredicting the exergy destruction.Arpaci and Selamet [50] calculated the entropy genera-

tion in a premixed flame established on a flat flame burner.They developed an equation for local entropy productionconsidering the conservation equations of mass, momen-tum and energy as well as the local entropy balanceequation as follows:

_s000g ¼1

T

k

T

qT

qxi

� �2

þ tij

qui

qxj

þ u000

" #. (22)

The terms in the bracket on the RHS show the contribu-tions of thermal diffusion, mechanical energy dissipationand the dissipation of other forms of energy towardsentropy production (u000), respectively. In a flat flameestablished on a burner, the authors considered one-dimensional variation of temperature and obtained thelocal entropy production from the dimensional considera-tion of the thermal part. They defined a non-dimensionalentropy production rate as Ps ¼ _s000g l2=k, where l is acharacteristic length given as l ¼ a=uo

fl (a being the thermaldiffusivity and uo

fl the adiabatic laminar flame speed at theunburned gas temperature). It was shown from the analysisthat the non-dimensional entropy generation rate is aninverse quadratic function of the flame Peclet number,given as Peo

D ¼ uoflD=a, where D is the quench distance of

the laminar flame, which was expressed as the distance ofthe flame from the burner [50]. Using the tangencycondition ðq=qybÞðPeo

DÞ ¼ 0 during flame quenching (whereyb is the burned gas temperature normalized against theadiabatic flame temperature), the authors showed that theminimum quench distance corresponds to an extremum inthe entropy production.The distribution of rate of entropy production between

the flame and the burner was also shown in terms of theburned gas temperature and the distance from the burner.The entropy production rate between the flame and theburner appears to remain almost constant spatially, foryboð1� yuÞ, where yu is the unburned gas temperaturenormalized against the adiabatic flame temperature. Thisresult was not surprising considering the small quenchdistance, which varies only between 0.5 and 1mm. However,when ybXð1� yuÞ, an unusually rapid change in thedistribution of entropy production was found from theanalysis. This result was indicated by the authors as alimitation of their model, which predicted a large deviationfrom the experimental results for this condition. The workof Arpaci and Selamat finds importance as it was probablythe first one, which applied the entropy generation approachin combustion application. However, the simplistic physical


situation and model adopted in the work failed to generatedetailed information from it.

In the literature of exergy analysis in combustionsystems, the work of Dunbar and Lior [6] receives a specialmention, because they for the first time evaluated theprimary causes for irreversibility using some heuristic finiteincrement exergy analysis method for the simple hydrogenand CH4 fuel combustors. The method adopted in thework was not fully intrinsic as the authors did not solve thefull conservation equations with the reaction kinetics in thecombustion chamber to obtain the flux and gradient termsfor the different processes involved. Instead they dividedthe entire combustion phenomenon into a number ofhypothetical sub-processes and applied them along theprescribed process paths. The sub-processes considered bythe authors are:

(i)
a diffusion process where the fuel and oxygenmolecules are drawn together,
(ii)
a chemical reaction process leading to oxidation of thefuel,
(iii)
an internal thermal energy exchange between high-temperature product and the unburned reactant,
(iv)
a physical mixing process where the system constitu-ents mix uniformly.
The sub-processes are arranged differently in the processpaths resulting in different types of combustion phenomena.

In one case (path 1), the authors considered anincremental quantity of fuel to be mixed with itscorresponding stoichiometric quantity of oxygen to resultthe chemical reaction, internal energy exchange andproduct mixing (Fig. 5a). Such incremental processcontinued along the length of the combustor in smallcompartments till the gas constituents reached the fuelignition temperature after which the oxidation of theremaining fuel was assumed to be instantaneous. The pathaccording to the authors corresponds to the behavior of adiffusion flame.

In an alternative case (path 2), the entire fuel and airwere first mixed thoroughly (Fig. 5b). Subsequently,incremental amount of the mixture was reacted followedby the internal energy exchange and mixing. Such a pathmay exhibit the behavior of a premixed flame.

Dunbar and Lior performed their analysis separatelywith hydrogen and hydrocarbon (CH4) fuels. It was foundthat fixing the number of increments beyond an optimumnumber does not change the results any further. Despitethe simplification, the analysis yielded consistent results. Itwas observed that, in each of the hypothetical paths, themajor share of exergy destruction took place due to theinternal energy exchange. In the process path 1, the overallexergetic efficiency was reported to be within 66.5% and77.3% in hydrogen combustion for a range of excess air of0–100%, decreasing with the increasing amount of excessair. Out of the total exergy destruction, 72–77% wasreported to be due to the internal heat exchange, 15–18%

due to chemical oxidation reaction and 8–10% due to gasmixing. In the process path 2, 66–73% of the total exergydestruction was accounted to internal heat exchange,18–25% to chemical reaction and 8–10% to the mixingprocesses. Therefore, Dunbar and Lior concluded noperceptible difference in the causes of exergy destructiondue to the premixing of the reactants. Between hydrogenand CH4, a relatively higher percentage of irreversibilityresulted due to chemical reaction in the latter case than thatin the former. However, even with CH4 combustion thelargest share of irreversibility resulted due to heat transferonly. They also studied the effects of preheating usingsuitable choice of the process path.The analysis of Dunbar and Lior was able to provide

important information through a hypothetical approach.Subsequent to this, additional works have been reported inthe literature dealing with the detailed exergy analysis invarious combustion phenomenon. In the following sub-sections these works have been briefly reviewed based onthe type of fuel on which they have been applied.

4.1. Gaseous fuel combustion

Exergy analysis in gaseous jet flames have been studiedby Datta [51,52], Stanciu et al. [53], Nishida et al. [54],Datta and Leipertz [55] and Yapici et al. [56,57]. Thestudies include both non-premixed and premixed flames aswell as laminar and turbulent jet flames. All these workspertain to the numerical solution of the conservationequations to predict the combustion process and calcula-tion of the volumetric entropy generation on a local basisfrom the field values. The accuracy of the prediction iscertainly a key factor in the determination of the exergyloss, as the flux and gradient of the field variablesdetermine the entropy generation rate. The assumptionsemployed in the models, including those in the transportand thermodynamic properties (e.g. unity Lewis number),chemical reaction equation, etc. play important role tothis effect. Following the approach given in Section 3.4,the Gouy–Stodola equation is used for the calculation ofexergy loss. A complete field picture of the entropygeneration rate using Eq. (21) helps to identify thekey locations causing the exergy loss as well as the rootcause of it.Datta [51] performed a numerical analysis of CH4–air

laminar non-premixed flame in a confined environment(Fig. 6) and evaluated the volumetric rate of entropygeneration. A single-step chemical reaction and unity Lewisnumber were the key assumptions in the model. The effectof viscous dissipation was found to be negligible andthermal diffusion, chemical reaction and mass diffusionwere found to contribute to the entropy generation in theorder of their enumeration. A study of parametricvariation on the entropy generation rate was performedby varying the air inlet temperature, the thermal conditionat the confined wall (isothermal at 298K, and adiabatic)and the air–fuel supply ratio (by changing the fuel flow rate

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Fuel Feed

Air Feed

IncrementalFuel

Stoich. amount O2

UnreactedFuel

H2O H2O

Q

Q

Restamount

Productmixing

Stoich.amount O2

Incre. Fuel

H2OH2O

Q

Q

Restamount

Productmixing

Unreac.Fuel

First Incremental Extent of Reaction

Second IncrementalExtent of Reaction

Fuel

Product

FuelFeed

Air Feed

Fuel-AirMixing

IncrementalReaction

Thermal Energy

Exchange

IncrementalReaction

Thermal Energy

Exchange

First Incremental Extent of Reaction

Second Incremental Extent of Reaction

Fig. 5. (a) Hypothetical combustion chamber for process path 1 with H2 as fuel [6]. (b) Hypothetical combustion chamber for process path 2 [6].


while keeping the airflow constant) in gauging the relativerole of chemical reaction, internal heat and mass transfer inentropy production within the combustor only. However,the entropy production in combustor together with that inair pre-heater determines the energy economy of thecombustion system comprising both the combustor andair pre-heater. It can be mentioned in this context that anexergy analysis of an air pre-heater requires informationabout the thermodynamic states of air and hot gas at entryand exit to the heater which in turn depend upon itsphysical location in the plant.

Stanciu et al. [53] showed that in a constant pressurelaminar non-premixed flame the irreversibilities due toviscous dissipation, heat conduction, mass diffusion andchemical reaction are uncoupled. The authors also showedthat in a CH4–air combustion process, the thermal,chemical and diffusive irreversibilities represent, in orderof enumeration, the predominant irreversibilities in thelaminar diffusion reacting flows.

Nishida et al. [54] studied a typical unconfined laminarnon-premixed flame for the analysis of the local entropygeneration. The conservation equation of entropy wassolved with a source term containing contributions ofviscous dissipation, heat conduction, mass diffusion andchemical reaction. The radial distribution of species molefraction and temperature at a single axial height as also thelocal entropy generation rate for each irreversible processat the same height were presented. The contribution ofthermal conduction was seen to far outweigh the contribu-tion of chemical reaction towards entropy generation. Theauthors reasoned that the high temperature in the zone ofchemical reaction in a non-premixed flame is the cause ofits lower contribution to entropy generation.Though the work of Nishida et al. [54] gave the radial

distribution of entropy generation rate at a single axiallocation, a complete representation of the irreversibleprocesses over the entire field is absent in it. Such acomplete irreversible field could be envisaged in a later

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Fig. 7. Temperature distribution in a laminar methane–air jet diffusion

flame with the flame contour shown in black line [52].

di

din

d

dout

L

FuelAir Air

Fig. 6. Schematic of the co-flow confined burner used for the computation

of thermodynamic irreversibilities in jet diffusion flame [51,52].


work of Datta [52], which studied the role of gravity on theentropy generation in a laminar non-premixed CH4–airflame in the same configuration as in Fig. 6. The numericalmodel employed a two-step chemical reaction and thevariation in the property values based on local temperatureand species concentration. The kinetic parameters wereadjusted to give a reasonably correct prediction in the fieldvariables, which was ascertained by comparing thedistribution of the field variables against the experiment.It was assumed that the low flux of the intermediate speciesbecause of their low concentration, would not contributemuch towards entropy generation and the major species,whose concentrations were predicted in the model, weresolely responsible to the entropy production process.

Fig. 7 typically illustrates the structure of a laminar non-premixed flame predicted by the numerical model [52]. Thefigure plots the temperature distribution in the confineddomain near the core, where the flame exists. The plot nearthe wall is not shown as there is almost no variation oftemperature there. The flame contour is also plotted in thefigure by drawing the heat release zone. The highest

temperature zone is located within the flame in an annularregion somewhat above the burner port. The hightemperature causes a buoyant acceleration to the flow inthe flame zone and thereby entrains air from thesurrounding resulting in a flow field that generatesthe over-ventilated structure of the flame. Moreover, dueto the continued entrainment towards the core, thepressure near the periphery drops resulting in an ingressof air from the atmosphere through the exit plane. Theingress causes the formation of a recirculation over theouter wall and results in a low temperature shield overthe wall. The complete picture of flow may be available inthe original work [52]. At the core, the temperaturegradually reduced downstream to the flame zone due tothe transport of heat due to internal heat exchange.Figs. 8a–e show the concentration distributions of

the major species like fuel (CH4) and O2, which are thereactants, and CO, CO2 and H2O, which are theintermediate and final products. The distributions arethe result of the transport process of the species mass in amulticomponent environment as well as chemical reaction.The fuel coming from the central jet is consumed at theflame and its concentration gets rapidly reduced. There-fore, the fuel species exist only inside the flame region. Theoxygen supplied from air enters as the co-flow andtransports towards the flame from the peripheral side. Itgets consumed at the flame surface and therefore within theflame region only a trace of it is located. CO is found insidethe flame. It is formed on the inside surface of the flame,which burns in a rich atmosphere because of the shortfallof oxygen. The CO that comes towards the outer surface ofthe flame front gets readily consumed with oxygen. On the

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Fig. 8. Distribution of concentration of different species in methane–air jet diffusion flame: (a) CH4, (b) O2, (c) CO, (d) CO2 and (e) H2O.


contrary, absence of oxygen inside the flame allows CO todiffuse inside showing its existence inside the flame. CO2

and H2O are formed in the flame front and are transportedin all directions based on the advective and diffusive rates.The transport of the product species continues downstreamto the flame till the exit plane is reached. However, themajor mass transport occurs in the flame region, where the

sudden reduction in concentrations of the reactants andgeneration of products result in large rates of transport ofthe species. The transport processes of heat and mass as aresult of the temperature and concentration distributionsoccur through irreversible processes and result in entropygeneration. The entropy generation rate is high at locationswhere the field gradient and the resulting fluxes are high.

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Fig. 9. Rate of volumetric entropy generation in methane–air laminar jet diffusion flame due to (a) chemical reaction, (b) heat transfer, (c) mass transfer.


Figs. 9a–c illustrate the plots of the local volumetricentropy generation rate contours due to chemical reaction,heat transfer (thermal diffusion) and mass transferrespectively, for the non-premixed flame. It is evident fromthe figure that the entropy generation due to chemicalreaction (Fig. 9a) takes place within the flame front. Thevolumetric entropy generation rate due to chemicalreaction is higher near the base of the flame. It revealsthat the flame is more intense near its base. At the tip, theflame is weak and the volumetric entropy generation rate isless than 1/20th of the peak contour value shown in thefigure. The concentration gradient of the fuel is more atlower elevation and results in higher rate of diffusion offuel towards the flame front. This makes the flame moreintense there. With the consumption of fuel, the fuelconcentration gradient reduces at higher elevation. Thisdecreases the fuel transfer rate to the flame and the flameintensity also decreases. An inner reaction zone is alsoevident from the chemical entropy generation plot, whichhowever is much weaker. In a jet diffusion flame, the flameis little lifted from the burner depending upon the jetmomentum. Through the gap some air diffuses in to form aweak premixed flame in the core. Therefore, the entropygeneration field portrays a good picture of the flamestructure.

Fig. 9b shows the volumetric entropy generation rate dueto thermal diffusion in the confined domain. The strongtemperature gradient close to the burner rim, where theflame is stabilized, increases the entropy generation there.The peak volumetric entropy generation rate due to heat

diffusion is less than that due to chemical reaction.However, the entropy generation due to heat diffusionoccurs over a much greater volume compared to thevolume of the flame, where entropy is generated due tochemical reaction. In the flame zone, heat diffusion occursfrom the high-temperature flame. Moreover, the buoyancy-induced acceleration increases the flow velocity at the coreand results in a high entrainment of fluid towards thecenter. The flow structure generates a thermal stratificationwith the high-temperature gas near the core. Due to theaxi-symmetric nature of the flow the gradient of tempera-ture remains low near the axis. The ingress of atmosphericair through the outlet plane and formation of therecirculation zone around the peripheral wall maintains alow temperature shield at the periphery. There exists anannular region between the core and the wall, where thetemperature falls rapidly causing a high rate of heattransfer. The stratification of the flow and the formation ofthe recirculating zone due to atmospheric air ingressmaintain the annular region of high-temperature gradienttill the exit plane. Therefore, high diffusion of heatcontinues over a much larger volume to cause a highoverall entropy generation rate.The entropy generation due to mass transfer of all the

species is depicted in the Fig. 9c. It is observed that themass transfer results in entropy generation mainly aroundthe flame. In a diffusion flame the reactants diffuse intothe flame from the opposite sides of the flame surface andthe products transport from the flame in all directions.Beyond the flame, though transport of heat continues,

ARTICLE IN PRESS

Fig. 10. Variation of the rate of entropy generation (total as well as for

individual processes) and exergetic efficiency in a confined laminar

diffusion flame at different gravity levels [52].

Table 1a

Inlet operating parameters for different numerical experiments in non-

premixed gaseous jet flames [51]

Sl. no. Inlet section

0orpR1 R1orpR2

Fuel jet

velocity (cm/s)

Fuel jet

temp. (K)

Air jet velocity

(cm/s)

Air jet temp.

(K)

1 4.5 298 9.88 298

2 4.5 298 14.55 450

3 4.5 298 19.89 600

4 6.0 298 9.88 298

5 7.5 298 9.88 298

Diameter of the central fuel port (R1) ¼ 12.7mm.

Diameter of the annular co-flow tube (R2) ¼ 50.8mm.

Pressure ¼ 1 atm.

Wall condition: adiabatic.


mass diffusion ceases to play any major role. The figurereveals that the magnitude of the rate of entropygeneration per unit volume due to mass transfer issignificantly lower compared to the other two majorcontributors even in the flame zone. Though generationand consumption of different species occur in the flame, thegradient of species concentrations never takes a large valueand the transport process always bring a uniformity in thedistribution of the species around the flame. The only highrate of entropy generation due to mass transfer is observedjust above the entry plane and around the interfacebetween the fuel and air jets.

The field values of the rate of entropy generation give acomplete picture of the causes of irreversibilities and theirlocation in the flame. It was observed that the gravity has amajor role in controlling the entropy generation rate in theflame. In a reduced gravity environment, the flame andflow characteristics experience a major change. At zerogravity, the buoyancy-induced flow is totally absentreducing the entrainment of air from the surroundingtowards the flame. The flame therefore becomes less intenseand the volume of the flame increases as it achieves asomewhat spherical shape instead of the elongated over-ventilated shape at normal gravity. The volumetric entropygeneration rate due to chemical reaction shows a reductionin its peak value at zero gravity than at normal gravity dueto reduced intensity of the flame. However, the total rate ofentropy generation due to chemical reaction is not muchdifferent because the volume of the flame front at zerogravity level is more due to the increased width of theflame. The higher volume of the flame front compensatesthe decrease in the volumetric entropy generation rate thattakes place at zero gravity. On the other hand, the entropygeneration rate due to heat transfer is reduced considerablyat zero gravity compared to that at normal gravity. This isbecause in a zero gravity non-premixed flame the reducedentrainment from the co-flow results in a more uniformradial temperature distribution. The entropy generationdue to mass transport, which is in effect low, is not muchdifferent at reduced gravity from the corresponding valueat normal gravity.

Fig. 10 shows a plot of the total rate of entropygeneration in the confined domain and the rate of entropygeneration due to individual processes in non-premixedflame at various gravity levels varying from normal gravityto zero gravity [52]. The corresponding Froude number(Fr ¼ gdi=u2

f , where g is the acceleration due to gravity, di

the fuel port diameter in the burner and uf the fuel jetvelocity at burner exit) varies in the range of zero (at zerogravity) to 61.33 (at normal gravity). The entropygeneration due to fluid friction is not included in the figuredue to its very low value. It is seen that out of all theindividual processes, the most dominant role towardsentropy generation in non-premixed flame is played byheat conduction under all gravity conditions. Chemicalreaction is the next significant contributor and masstransfer comes as the third important. With the change in

gravity level, the entropy generation due to reaction andmass transfer hardly changes in magnitude. However, theentropy generation due to heat transfer is grossly affectedby gravity. It is already explained that as the gravity level isreduced the temperature field becomes more uniform andthe entropy generation due to heat transfer decreases. Thisdecrease in the entropy generation is also reflected in thetotal entropy generation rate and results in a decrease inthe total entropy generation.Tables 1a and 1b show the details of the operating

conditions studied and the entropy generation valuesobtained in the non-premixed laminar gaseous jet flamein a confined environment [51]. The effect of preheated airon entropy generation showed that the total rate of entropygeneration decreases with the increase in inlet air tempera-ture. The variation is principally attributed to the decreasein the contributions of the thermal diffusion and chemicalreaction. The higher value of air temperature increases theflame temperature but decreases the temperature gradientoccurring in most of the region of the domain resulting in

ARTICLE IN PRESS

Table 1b

Rate of entropy generation (W/K) at different inlet conditions given in Table 1a

Sl.

no.

Inlet air

temp.

Air–fuel

ratio

Entropy generation rate due to transport Entropy gen. rate

in chem. reaction

Total rate of

entropy

generationHeat

transport

Mass

transport

Combined heat-

mass transport

Total in

transport

1 298 59.29 0.3650 0.0440 0.1004 0.5094 0.1429 0.6523

2 450 59.29 0.3120 0.0464 0.0796 0.4380 0.1376 0.5757

3 600 59.29 0.3017 0.0489 0.0670 0.4177 0.1341 0.5519

4 298 44.46 0.3999 0.0503 0.1158 0.5661 0.1675 0.7337

5 298 35.57 0.4356 0.0670 0.1294 0.6224 0.1935 0.8159


a reduction in the diffusive heat flux. These together are theprimary cause of the lower contribution of thermaldiffusion towards entropy generation. The chemical reac-tion occurring in the high-temperature flame reduces itscontribution to the entropy generation rate.

The effect of increase in the fuel flow rate was found toincrease the total entropy generation rate in the domain.The contribution of both the transport processes andchemical reaction was found to increase. The height of thenon-premixed flame increases with the increase in the fuelflow rate. The increased volume of the flame is the primarycause of the increased rate of entropy generation.

The other class of gaseous fuel combustion is thepremixed flame, where the fuel is considered to behomogeneously mixed with the oxidizer before reachingthe reaction front. Caton [23] performed a somewhatsimplified analysis in an adiabatic, constant volumechamber, where the exergy loss in a combustion processis analyzed based on thermodynamic calculations con-sidering equilibrium. Though the fuel considered wasoctane, the author assumed a pre-vaporized mixture of itwith air. The features of liquid fuel combustion, likeevaporation and mixing of the fuel vapor and air were notconsidered. We have therefore included the work here asgaseous fuel combustion.

As there was neither heat and work transfer across thesystem boundary nor any additional mass exchange duringthe process, the author claimed the difference of exergybefore and after the chemical reaction was solely due tocombustion. A homogeneous mixture of species in thecombustor was assumed giving spatially uniform proper-ties. The combustion reaction was assumed to be completeand the product concentrations were calculated fromchemical equilibrium consideration at high temperature.The first and second laws of thermodynamics were used tocalculate the properties before and after the reaction. Theexergy quantities before and after the reaction werecalculated considering the thermomechanical contributionof all the species and the additional chemical exergycontribution of the fuel species. The chemical exergy of thefuel was obtained from the difference between the Gibb’sfree energy of the product and reactant at the referencestate. The exergy destruction was further checked intern-ally against the process irreversibility calculated using the

entropy generation from the entropy balance equationgiven by the second law of thermodynamics.The highest exergy exists in the fuel, which represents the

maximum potential of the fuel to perform work. When thischemical energy is transformed into thermal energy, someportion (which depends on the final temperature) of theinitial availability is destroyed. The amount of the exergythat is destroyed increases for lower final temperatures ofthe product, i.e. for lower flame temperature. The higherinitial temperature of the reactant decreases the destructionin exergy in the combustion process due to the highertemperature of the product, which retains more exergycontained in it. Regarding the effect of the equivalenceratio, the author found that the destruction of exergy perunit mass of the fuel increased as the reactant mixturebecame leaner than stoichiometric. This may be attributedto the lower temperature of the flame in a lean mixture andthe inherent irreversibility associated with the mixing of thecombustion products with the excess air present in thecombustor. As a recommendation from the study, Catonobserved that in an internal combustion engine the reactanttemperature should be kept high to ensure less exergydestruction. However, the author also reminded that therealization of the exergy depends on the applicationfollowing the combustor. For example, he suggested thatto recover the maximum work from the high exergycontent of exhaust gases, exhaust devices like turbo-compounding have to be employed in the engine. Theauthor also pointed out that the high initial temperaturefor recovering maximum exergy in combustion may resultin other issues like increased NO emission.Nishida et al. [54] performed a detailed numerical

analysis for the study of exergy loss in a laminar premixedflame. The conservation equations of mass, momentum,energy and species were solved taking into account thedetailed chemical kinetics and multi-component diffusion.The thermodynamic and transport properties were ob-tained from the CHEMKIN database. Premixed flameswere simulated using the steady, one-dimensional flow atatmospheric pressure and with hydrogen and CH4 as thefuels. The entropy generation rate was calculated using thefield variables and considering the contributions of viscousdissipation, heat diffusion, mass diffusion and chemicalreaction. It has been shown that the total rate of entropy


generation becomes large in the region of the main reactionzone denoted by the high-temperature gradient. Chemicalreaction accounted for the maximum entropy generationboth in hydrogen and CH4 flames, while heat conductioncontributed the second largest. While in a stoichiometrichydrogen–air flame with 25 1C reactant temperature,72.6% of the total entropy generation rate was contributedby chemical reaction, in a stoichiometric CH4–air flame thepercentage contribution of chemical reaction was 55.3%.The contribution of heat conduction for the two cases werefound to be 21.6% and 37.9%, respectively. The effect ofmass diffusion was found to be much smaller and the effectof viscous dissipation is negligible.

From the spatial distribution of the entropy generationrate shown by the authors, it is evident that in the hydrogenflame the steep rise in the entropy generation rate due tochemical reaction and heat conduction initiates at the sameaxial location, though the peak for the chemical reactionoccurs at a little downstream location. However, thetemperature where the entropy generation due to chemicalreaction reaches the peak was found to be sufficiently low.In the CH4 flame, however, the entropy generation due tochemical reaction increased much later compared to theentropy generation due to heat conduction. Therefore, thepeak in the entropy generation due to chemical reactionshifted to a much downstream location compared to thepeak due to heat conduction. The temperature at thelocation where the entropy generation rate due to chemicalreaction peaked was much higher in CH4 flame than inhydrogen flame. This was attributed to the increasedconcentration of the radical species in the flame. Accordingto the authors, the high temperature in the flame region ofCH4 combustion reduced the entropy generation rate dueto chemical reaction and its contribution towards totalentropy generation was less than that in hydrogen flame. Itindicated the importance of the flame chemistry indetermining the exergy destruction in combustion.

In a study of parametric variation [54], the authorsfound that the total destruction of fuel’s exergy increasedwhen the premixed mixture was leaner than stoichiometric,while an increase in the reactant temperature was found todecrease the percentage of total exergy destruction. In alean mixture, the temperature in the reaction zone wasfound to rise more gradually resulting in a wider reactionzone than that in stoichiometric mixture. Consequently, theentropy generation zone of each process in the flamebecame wider. Though the fraction of entropy generationdue to each individual irreversible process was similar tothat in a stoichiometric flame, the wider flame zone resultedin the increase in total rate of entropy generation increasingthe exergy loss. With an increase in reactant temperature,the flame temperature was increased correspondingly. Theflame became narrower reducing the prime zone of entropygeneration. The entropy generation due to heat conductionbecame smaller as the inlet and outlet fluid temperaturerose. The high-temperature flame reduced the entropygeneration due to chemical reaction also. Thus, the total

entropy generation decreased and the exergy destruction asa fraction of fuel’s exergy was reduced. However, thecontribution of chemical reaction towards the total entropygeneration increased.A contrasting feature of the predictions of Nishida et al.

[54] and those of Dunbar and Lior [6] in premixed flame isthat while the former found the chemical reaction as themost significant contributor the latter attributed the sameto heat diffusion. Though Dunbar and Lior performed ahypothetical analysis, they considered chemical reaction inincremental quantities followed by internal heat exchangein the mixture. On the other hand, Nishida et al. considereda one-dimensional analysis typical for a flat flame situation.In a flat flame, the temperature varies from the reactanttemperature to the product temperature within a smallthickness of about 0.5–1mm, outside which the tempera-ture gradient is reasonably flat. Therefore, the entropygeneration due to heat diffusion is only effective within ashort volume and the effect of irreversibility remains low.Most of the reacting flows occurring in the engineering

devices are turbulent. In this case, the fluctuating field ismaintained by the turbulent production terms. At thelarger scales of turbulence, they extract a part of energy (orexergy) from the mean flow field and through the vortexstretching mechanism continuously transfer it to thesmallest turbulent scales, where the molecular diffusivitiesof multicomponent fluid perform its dissipation. Followingthis idea, Stanciu et al. [53] split the turbulent reacting flowirreversibility not only into the viscous, thermal anddiffusion components but also into its mean and turbulentparts. They used the phenomenological multi-speciesapproach and proved that 98% of the exergy destructionresulted due to the last part.Yapici et al. [56,57] studied the entropy generation in a

turbulent swirl flow axisymmetric combustor with CH4 asthe fuel. The fuel and air streams entered the combustor ascoflow, with swirl imparted to the airflow using inletswirler. The former work [56] studied the effects ofequivalence ratio and swirl ratio on the entropy generationrate, while the latter work [57] studied the influence of fueltype. The turbulent quantities were evaluated using theRNG-k–e model, while the eddy dissipation model wasused for the calculation of the reaction rates. The CH4–airreaction was assumed to proceed in two steps, with theintermediate formation of CO. The entropy generation ratewas considered to contain terms related to viscousdissipation and heat conduction only. Such considerationis applicable in heat transfer problem but fails to give thecomplete picture of exergy destruction in combustion sincethe irreversibilities associated with mass transfer andchemical reaction are not considered. It remains the majordrawback in the works.The numerical solution of combustion gave a tempera-

ture field with very high-temperature gradient. Swirl in theflow was found to affect the temperature gradient at lowvalue of fuel jet velocity, while at high fuel jet velocity thiseffect was minimal. In all the cases studied, the entropy


generation due to heat transfer was found to dominate overthat due to viscous dissipation. The highest local entropygeneration rate was observed at the entry plane and nearthe wall.

Parametrically the swirl number, equivalence ratio andthe fuel flow rate were all found to be affecting the entropygeneration rate in the combustor [56]. The authorsproclaimed that, at no swirl, the entropy generation ratedecreased exponentially with the increase of equivalenceratio (in the lean side between 0.5 and 1.0) for high fuelinjection rate, whereas they had quadratic profiles withminima in the case of low fuel flow rate. However, itappeared from their results that the variation is similar forall the fuel flow rates. Only difference being that at highfuel flow rates the said minima did not come in the range ofequivalence ratio of 0.5–1. At a constant fuel flow rate of10 lpm, the entropy generation rate was found to decreasewith the increase of swirl number.

The variation in the entropy generation rate shoulddepend on the peak temperature reached in the flame andthe structure of the flame in the combustor. In astoichiometric flame, the peak temperature is higher thana lean flame while, in a lean flame due to the higher flowrate of air, the flame can not spread radially, giving a highgradient of temperature and a high rate of entropygeneration. It shows that the flame structure has a strongeffect on the entropy generation rate due to heat transfer.The merit factor, which is the ratio of the useful exergytransfer rate through the wall and to the fluid to the sum ofthe exergy transfer rate and the rate of irreversibility, wasalso calculated in the work. It was shown that for high fuelflow rate, the merit factor continually increased with theincrease in equivalence ratio, showing the reduced influenceof the irreversibility. While, for low mass flow rate, themerit factor reached a maximum at a particular equiva-lence ratio and then sharply decreased with a furtherincrease in the equivalence ratio. A marginal increase in themerit factor was observed with the increase in swirl at afixed fuel flow rate and equivalence ratio.

The second study [57] calculated the entropy generationrate with a large number of fuels, e.g. hydrogen, CH4,C2H2, C2H4, C2H6, C3H8, C4H10, C6H6 burning in air. Forthe sake of comparison, the fuel flow rates were adjusted togive the same heat transfer rate in the combustionchamber. In all the studies it was found that the maximumreaction rates decreased with the increase in the equiva-lence ratio in the lean side of mixture stoichiometry. Theincrease in the equivalence ratio also reduced the tempera-ture gradients in the combustor. Therefore, the volumetriclocal entropy generation rate was found to decrease withthe increase in equivalence ratio from 0.5 to 1. Bejannumber (ratio of entropy generation due to heat conduc-tion to that due to both heat conduction and viscousdissipation) remained high (around 0.995) for all the casesindicating the negligible influence of viscous dissipationtowards entropy generation, compared to heat conduction.The overall rate of entropy generation for any fuel

decreased exponentially with the increase in equivalenceratio for the conditions of fuel flow rate studied. However,at a particular equivalence ratio, the total entropygeneration in the combustor increased with the increasein the fuel flow rate and therefore the heat transfer rate.The incremental increase in the entropy generation for thesame incremental increase in the heat transfer rate wasmore at lower values of equivalence ratio. For the varioushydrocarbons studied, it was observed that the entropygeneration excepting with C2H4 and C2H2 were very closeto each other. Merit number was found to increase byabout 16% for the increase in the equivalence ratio from0.5 to 1.0.

4.2. Liquid fuel combustion

4.2.1. Droplet exergy models

The work of Dash et al. [58] is probably the pioneeringwork in ascertaining the sources of irreversibility in course ofevaporation of a single component liquid fuel droplet in ahigh-temperature convective gaseous medium. The thermo-dynamic irreversibilities were characterized by the rate ofentropy production in the transport processes and weredetermined from the field values of volumetric entropygeneration rate as described in approach in Section 3.4.A break-up of entropy generation rate due to different modesof transport processes in gas and liquid (droplet) phasesdepicted that the entropy generation rate due to viscousdissipation was negligibly small because of low flow velocities.Irreversibilities in droplet phase were also found to be quiteinsignificant compared to those in the gas phase. The mostsignificant contribution in the total entropy generation ratewas due to the conduction of heat and its coupled effect withmass transfer in the gas phase. The rate of entropyproduction decreased continuously at a rate lower than thedecreasing rate of droplet surface area. A numericalcorrelation of entropy generation rate with pertinentdimensionless input parameters was developed as [58]

_S0

g

r02¼ 714:5

M1=Mv

� �1:02B1:29

RePr0:66ð Þ0:72

, (23)

where _S0

g ¼_Sg

�r1Rur2i

� �is the dimensionless entropy

generation rate, r is the density, R is the gas constant, u isthe flow velocity, r0 is the dimensionless droplet radius ( ¼ r/ri),Re is the Reynolds number of flow past the droplet, Pr isthe Prandtl number of gas flowing around the droplet, andB is the transfer number. The subscripts N and i refer tothe free-stream condition and initial state of the droplet,respectively. MN and Mv are, respectively the molecularweights of free-stream gas and droplet liquid. The relation-ship given by Eq (23) provides the fundamental informa-tion in exergy-modeling of spray combustion, in a similarfashion, Nusselt number relation of single droplet does inheat transfer modeling of spray combustion.The identification of irreversibility components and

subsequent exergy analysis in droplet combustion require

ARTICLE IN PRESS

1

CurveI

4.0

T

Dai = 12.22 x 106

I

II

100100.001

0.01

0.1

1

10

t

I che

m /

I-I c

hem

0.1

II3.0

Fig. 11. Temporal histories of the ratio of irreversibility due to chemical

reaction alone to that of the diffusion processes taken together in a droplet

combustion [59].

Curve

IIIIII

T∞

1

0.8

0.6

0.4

0.21001010.10.01

I II

III

� II

Dai × 10-6

4.0

3.0

2.0

Fig. 12. The exergetic efficiency of a droplet combustion process [59].


the determination of entropy generation in a chemicallyreacting flow. The pertinent information in this regard hasbeen reported by Hiwase et al. [59], Dash and Som [60],and Puri [61]. It was observed [59] that in spherico-symmetric droplet combustion, the entropy generation ratedue to chemical reaction was of the same order as those dueto heat conduction and combined heat and mass convec-tion. However, the entropy generation rate due to heatconduction in gas phase was still the dominant factor,though the entropy generation rate due to chemicalreaction shot up to a higher value at the instant of ignition.The interesting outcome of this fact is that, in a typicaldiffusion-controlled droplet combustion process, the irre-versibility rate due to chemical reaction is lower than thatdue to diffusion processes taken together, except at theinstant of ignition. This is shown in Fig. 11. In a convectiveambience, the total entropy generation rate (or irreversi-bility) per unit droplet surface area increases as the burningof droplet progresses and reaches its highest value at theend of droplet life when the droplet surface area becomesextremely small [60].

A typical variation in second-law efficiency, for theprocess of a n-hexane droplet combustion in a quiescentambient of air, with initial Damkohler number (Dai) atvarious free-stream temperatures is shown in Fig. 12. Theparameter Dai physically signifies the ratio of characteristicthermal diffusion time to chemical-reaction time.A variation in Dai for any given fuel, under fixed valuesof initial gas-phase properties, implies a variation in theinitial diameter of the droplet. The upper flat portions ofthe curves (Fig. 12) correspond to the process of puredroplet vaporization without combustion in the gas phase,while the lower flat portions pertain to the steady-statedroplet combustion process. It is observed from the figurethat a low value of Dai and a high value of free-streamtemperature for the process of droplet combustion areneeded from the view point of energy economy in relationto efficient utilization of energy resources. In a convectiveambience, the minimum entropy generation for the burningof a fuel droplet corresponds to an optimum transfernumber, which is directly proportional to the square of therelative velocity and inversely proportional to the heatrelease rate and the temperature difference between thedroplet and its surrounding flow [61]. For flow with smallReynolds number, the expression for optimum transfernumber can be written after Puri [61] as

BM ;opt ¼O2

� �5

� 1, (24)

where

O ¼3

5

U2r

hfg

Qþ hf

hfg

� 1

� �1�

T1

Tf

� �

�1

Mf

wp;1;�wp;fT1

Tf

� �. ð25Þ

In the expression, Ur is the relative velocity between thedroplet and ambient. hfg is the latent heat of evaporationand Q is the heat release from the fuel droplet. TN and Tf

are the free-stream temperature and fuel droplet tempera-ture, respectively.In a real system there is a little control over the transfer

number and the heat release. The specific enthalpyassociated with the products is fixed by the choice ofliquid fuel and the stoichiometry related to the oxidizercontent in the gas. Under the circumstances, Eq. (24)describes an optimum relative velocity that minimizesthe entropy generation or exergy loss for a given gasflow rate and temperature ratio (ratio of free-streamtemperature to flame temperature). It should be mentionedin this context that the irreversibility analysis of dropletevaporation and combustion as discussed above pertains tothe laminar flow of the gas phase past the liquid fueldroplet.

ARTICLE IN PRESS

Rei = 60

Rei = 30

n = 3

2.75

0.700

0.725

0.750

0.775

0.800

0.825

0.850

1.50

T∞

� II

1.75 2.00 2.25 2.50 3.00

Fig. 13. Exergetic efficiency of a spray evaporation process with

Rosin–Rammler function as initial drop size distribution [63].


4.2.2. Spray exergy models

The identification of irreversibility components fromentropy generation rate in a spray combustion process iscomposed of two parts, namely: (i) the entropy generationin the evaporation of individual droplets in their localsurroundings due to interphase transport processes and(ii) the entropy generation due to transport processes andchemical reaction in the continuous carrier phase. A break-up of the source of irreversibilities in a spray combustionprocess shows equal order of magnitudes for the irreversi-bility contributed by local interphase transport processesand that contributed by the transport processes and chemicalreactions in continuous gas phase. The exergy balance andthe second-law analysis of a spray evaporation process in agaseous surrounding with uniform free stream were reportedby Som et al. [62] and Som and Dash [63]. The entropygeneration rate in the evaporation of a liquid spray is initiallyvery large and then decreases with the axial distance of thevaporizing spray. The rate of entropy generation increaseswith an increase in the ratio of free stream to initial droplettemperature or with a decrease in the initial Reynoldsnumber of the spray based on initial droplet velocity andSauter mean diameter of the initial PDF of the spray.

The variation in second-law efficiency of a sprayevaporation process with governing parameters, as predictedby Som et al. [62] and Som and Dash [63] depictsdifferent kinds of picture. The second-law efficiency ZII,evaluated using ‘‘discrete droplet model’’, shows an initialincrease in ZII with the free-stream temperature TN followedby an almost constant value thereafter. This impliesphysically an optimum value of TN above, which theevaporation of spray is not thermodynamically justified,since the increase in the rates of exergy transfer and that inits destruction become almost equal. However, the picture isdifferent when the ‘‘two-phase- separated-flow model’’ isused [63] to evaluate the second-law efficiency (ZII). Underthis situation, ZII shows a monotonically decreasing functionof free-stream temperature and an increasing trend withinitial Reynolds number of the spray (Fig. 13). Thequalitative difference in the results of [62] and [63] can beattributed to the fact that in the ‘‘discrete droplet model’’adopted by Som et al. [62] for spray calculation, thetransport processes in the carrier phase was neglected as itwas considered to be a homogeneous gas phase with free-stream properties. On the other hand, the separated-flowmodel for spray calculation [63] considered all the transportprocesses in the carrier phase along with the interphasetransport processes between the gas phase and theevaporating droplet phase. Therefore, the earlier work [62]underestimated the total entropy generation in sprayevaporation process due to the lack of additional contribu-tion towards entropy generation due to the gas-phaseprocesses. The optimum values of free-stream temperatureand spray Reynolds number should be chosen as suggestedby Som and Dash [63] on the basis of an overall economywhich is a trade-off between the length of evaporation andtotal irreversibility of the process.

The recent investigations of Datta and Som [64], Datta[65] and Som and Sharma [66] provide comprehensiveinformation on energy and exergy balance in a spraycombustion process in a gas-turbine combustor. Theanalyses employed a spray combustion model based onstochastic separated flow (SSF) approach. The gas-phaseconservation equations were solved in an Eulerian frame,while the droplet phase equations were computed in aLagrangian frame. The interphase source terms wereevaluated during the droplet phase computation andintroduced in the gas phase. The turbulent quantities weremodeled using a standard k–e model and the chemicalreaction employed the eddy dissipation model. It wasfound that the inlet air pressure had a marked influence indecreasing the irreversibility due to interphase transportprocesses (Id), while the irreversibility in the continuousgas-phase (Ig) was almost uninfluenced by the air pressure.At high air pressure, the value of Id is relatively lower thanthe value of Ig, while the picture was reversed at lowerpressure of ambient air. This can be attributed to areduction in droplet vaporization rate because of areduction in mole fraction of fuel vapor at droplet surfacewith an increase in local pressure at a given localtemperature. An increase in inlet air temperature increasesthe irreversibility in the interphase transport process, whilethe gas phase irreversibility remains almost the same.The exergetic efficiency in a typical spray combustion

process lies between 50% and 70%, while the combustionefficiency in case of gas turbine combustion lies between90% and 98% under usual operating conditions.A comparative picture of exergetic efficiency and combus-tion efficiency in spray combustion in a typical gas turbinecombustion process at different operating conditions isshown in Table 2 [64]. The interesting feature observed, inthis context, is that the qualitative trends of the influence ofinlet swirl number of incoming air on both second-lawefficiency and combustion efficiency are exactly theopposite when the combustor pressure is changed from

ARTICLE IN PRESS

Table 2

Comparison of combustion efficiency (%) and exergetic efficiency (%) in

spray combustion [64]

(a) Influence of inlet pressure

Inlet conditions: _mina ¼ 0:1kg=s, Rein ¼ 52,100, SMD ¼ 52 mm, spray cone

angle ¼ 801, swirl no. ¼ 0.76, Tina ¼ 600K, air–fuel ratio ¼ 60

Inlet pressure (kPa) Combustion efficiency Exergetic efficiency

100 95.34 57.21

300 93.56 61.53

600 91.32 71.82

1000 83.31 79.93

(b) Influence of inlet air temperature


angle ¼ 801, swirl no. ¼ 0.76, pin ¼ 100 kPa, air–fuel ratio ¼ 60

Inlet air temperature

(K)

Combustion efficiency Exergetic efficiency

400 86.03 55.24

600 95.34 57.21

800 99.53 55.60

(c) Influence of inlet swirl number


angle ¼ 801, Tina ¼ 600K, air–fuel ratio ¼ 60

Inlet pressure

(kPa)

Inlet swirl

number

Combustion

efficiency

Exergetic

efficiency

100 0.37 97.59 54.86

100 0.76 95.34 57.21

600 0.37 87.24 75.70

600 0.76 91.32 71.82

(d) Influence of initial mean droplet diameter in injected spray

Inlet conditions: _mina ¼ 0:1kg=s, Rein ¼ 52,100, spray cone angle ¼ 801,

swirl no. ¼ 0.76, Tina ¼ 600K, pin ¼ 100 kPa, air–fuel ratio ¼ 60

Initial SMD (mm) Combustion

efficiency

Exergetic efficiency

34 94.37 59.63

52 95.34 57.21

67 95.61 53.43

96 94.11 51.13

(e) Influence of spray cone angle

Inlet conditions: _mina ¼ 0:1kg=s, Rein ¼ 52,100, SMD ¼ 52 mm, swirl

no. ¼ 0.76, Tina ¼ 600K, pin ¼ 100 kPa, air–fuel ratio ¼ 60

Spray cone angle (1) Combustion

efficiency

Exergetic efficiency

60 91.49 62.67

80 95.34 57.21

100 98.58 48.85


a lower to a higher value. While, at a low pressure of100 kPa, an increase in inlet swirl increases the second-lawefficiency (ZII) and reduces the combustion efficiency, (Zc),the trends are reversed when the combustor pressure isincreased to a value of 600 kPa. At low pressure, theadverse effect of reduced droplet penetration due to anincrease in inlet air swirl plays the dominant role inreducing Zc and increasing ZII. However, at higher pressurethe droplet penetration is as such low and hence thefavorable effect of enhanced mixing of fuel vapor in the gasphase due to an increase in inlet air swirl plays theprominent role in increasing the value of Zc and reducingthe value of ZII. It has also been observed [64,65] (Table 2)that an increase in the cone angle of spray increases thecombustion efficiency and decreases the second-law effi-ciency. A higher spray cone angle results in a larger radialdispersion and hence a better mixing of fuel vapor in thegas phase. This causes an increase in the rate of combustionand accordingly in the total irreversibility in the process.

Som and Sharma [66] predicted from an energy andexergy balance of spray combustion process in a gas-turbine combustor, that an increase in fuel volatilityincreased the combustion efficiency only at higherpressures for any given inlet temperature and air swirl(Table 3), while the second-law efficiency decreased with anincrease in fuel volatility at any operating condition. Thephysical explanations for these typical variations in Zc andZII, put forward by Som and Sharma [66] are as follows:

The success for complete combustion depends on thepenetration of fuel droplets, their rate of vaporization, andmixing of fuel vapor with air. At low pressures, for a giventemperature, all these three physical processes are relativelyfast and combustion efficiency is usually very high.Therefore, the change in the rate of droplet vaporizationwith fuel volatility does not make any marked influence incombustion efficiency. However, on the other hand, whenthe pressure in the combustion chamber is high, at a giveninlet temperature, there occur (i) a reduction in dropletpenetration due to increased density of ambient air, and(ii) a reduction in the rate of droplet vaporization due to adecrease in fuel–air diffusivity with pressure. Therefore, fora given fuel, an increase in combustion pressure for a fixedinlet temperature always reduces the combustion efficiency.Under this situation, the favorable effects of enhanceddroplet vaporization and its mixing with ambient air due toan increase in fuel volatility is felt sharply through amarked increase in the combustion efficiency. The increasein second-law efficiency with pressure can be attributed tosimultaneous increase in flow availability of incoming air ata high pressure and less process irreversibility due toreduced droplet vaporization.

4.3. Solid fuel combustion

Coal is the most important solid fuel and is widely usedin generating electricity. It will be the principal fuel to meetthe future demand of electricity since coal reserves are

much greater than the other fossil fuels. Most of the coal-fired power stations use pulverized coal for combustion.Coal is also used in the operation of a blast furnace, which

ARTICLE IN PRESS

Table 3

Influences of inlet pressure and swirl on combustion efficiency (%) and exergetic efficiency (%) in spray combustion for fuels with different volatilities [66]

Inlet conditions: _mina ¼ 0:1 kg=s, Rein ¼ 52,400, SMD ¼ 52 mm, spray cone angle ¼ 801, Tin

a ¼ 600K, air–fuel ratio ¼ 60

Inlet pressure (kPa) Inlet swirl number Combustion efficiency (%) Exergetic efficiency (%)

n-Hexane Kerosene n-Dodecane n-Hexane Kerosene n-Dodecane

100 0.36 95.37 96.06 94.34 54.54 65.84 71.14

100 0.76 95.40 96.92 94.81 56.11 70.64 74.44

1000 0.36 91.14 82.92 64.43 74.04 83.27 86.43

1000 0.76 84.21 78.47 45.90 67.12 72.27 82.73


employs pulverized coal injection along with the blast airthrough its tuyere to reduce the coke feed rate. From theview point of energy economy, an efficient process of coalcombustion should be guided not only by the combustionefficiency of the process but also by its second-lawefficiency.

Fundamental research in the field of coal combustion forthe determination of the reaction rate parameters andmodeling of reaction chemistry is going on for the last threedecades. Both experimental and numerical works areavailable and exhaustive reviews of all these works aremade in Smoot [67,68]. Som et al. [69] first attempted adetailed second-law-based analysis in a cylindrical com-bustor burning pulverized coal particles. The full Navier–-Stokes equations are solved along with the conservation ofmass and energy, with the standard k–e model employedfor the solution of the turbulent quantities. A pdf-basedconserved scalar equation was solved for the speciesconcentrations as well as the reaction rates. Followingthe earlier spray model of Datta and Som [64], the coalparticle tracking was done in a Lagragian frame andcoupled with the Eulerian fluid flow through the carefullycomputed source terms. The exergy analysis is donecalculating the inlet and exit exergy components followingapproach 1 given in Section 3.3. The second-law efficiencyfor the combustion process is computed using Eq. (7). Theeffect of variation in air temperature, airflow rate, particlesize and inlet swirl level of airflow on the second-lawefficiency were studied. The outcome of the studies are asfollows:

An increase in air temperature decreases the combustionefficiency for a shorter length of combustor, but increasesthe combustion efficiency for a higher length of combustor.The second-law efficiency follows a trend that bears aninverse relationship to that in combustion efficiency withair temperature. At low values of inlet air swirl(S ¼ 0.0–0.32), an increase in SMD of coal particledecreases the combustion efficiency. At a higher value ofinlet air swirl (S ¼ 0.77) combustion efficiency increaseswith an increase in SMD from 50 to 95 mm, and thereafterdecreases with a further increase in SMD of coal particlefrom 95 to 145 mm. The second-law efficiency alwaysincreases with an increase in the particle diameter, whereas,at high swirl of S ¼ 0.77, this trend shows an optimum

particle diameter with an initial decreasing trend of ZII

followed by an increasing one with the particle diameter.The optimum design of the combustor is based on a trade-off between Zc and ZII for an overall energy economy. Therelative weight of Zc and ZII to be assigned in the process ofoptimization depends on the relative savings in the cost ofenergy quantity over the energy quality for a specificapplication, which is a task of energy management inpractice.Prins and Ptasinski [70], following the line of Dunbar

and Lior [6], studied the exergy losses in the gasificationand combustion process of solid carbon in a gasificationreactor by dividing the process into several subprocesses,like chemical reaction, internal thermal energy exchangebetween reaction products and unburnt reactants, productmixing, etc. The irreversibilities associated with theindividual subprocesses have been calculated using thethermodynamic parameters for the isothermal and adia-batic combustion of carbon in the reactor. The overallefficiency is computed as the gain in exergy of the gas as afraction of the change in exergy of the solid fuel (expressedas the difference of exergy in the fuel input and the exergyof the unburned fuel). Alternately a term called efficiencydefect is defined as the sum of the irreversibilities due to allprocesses as a fraction of the exergy difference of the solidfuel across the reactor. For stoichiometric combustion ofcarbon with air, exergy losses due to internal thermalenergy exchange (14–16% of expended exergy) are largerthan those due to the chemical reaction (9–11% ofexpended exergy). The overall exergetic efficiency ingasification process, employing partial combustion, isfound to be higher than that in combustion. In acombustion process the fuel’s exergy is totally convertedinto the theromechanical exergy of the high-temperatureproduct gas, while gasification retains a large part ofchemical exergy in the generated fuel gas. In gasification,the reaction remains very efficient while the exergy lossesrelated to internal thermal energy exchange (5–7% ofexpended exergy) are reduced due to the lower tempera-ture. The efficiency in the gasification process can beimproved by gasifying with oxygen instead of air, but theirreversibilities incurred in separating oxygen from airnullify this advantage. In order to maximize the chemicalexergy present in the product gas, for oxygen-blown


gasification of fuels like solid carbon, it was advised tomoderate the temperature with steam and operate between1200 and 1400K for atmospheric pressure and1300–1500K for elevated pressures. In this way, up to75% of the exergy contained in solid fuels can be convertedinto chemical exergy of carbon monoxide and hydrogen.

Lior [34] presented the exergy analysis in a Radiatively/Conductively Stabilized Pulverized Coal Combustor(RCSC) earlier modeled by Kim and Lior [71,72]. Theanalysis used the computer simulation results, whichconsisted of the solution of the conservation of mass,momentum, energy and species conservation equationswith the standard k–e equations. The radiative transferequation was solved using spherical harmonics method.The particle trajectories were solved in the Lagrangianframe. A 13-equation chemical kinetic model for reactionand separate models for devolatilization, volatile combus-tion were used. The solution gives three-dimensionaldistribution of gas, particle and wall temperature, radiationintensity, gas and particle velocity and species concentra-tions. These results are used for the spatial determinationof all the components of exergy. It was found from theorder of magnitude of different components of exergy that

Z / R

127 109 91

73 55 37 19

1 1

3

5

7

911

Exerg

y, kJ / k

g c

oal

24000

18000

12000

6000

0

24000

18000

12000

6000

0

Z / R

7255 37 19 1

51000.0

15000.0

1

35

79

Exerg

y,

kJ /

kg c

oal

Fig. 14. (a) Thermomechanical exergy distribution in a pulverized coal combu

[34]. (c) Total exergy distribution in a pulverized coal combustor [34].

potential exergy, strain exergy and kinetic exergy are toosmall and can be ignored. Consequently, the major exergycomponents were reported to be thermal and chemical.The thermomechanical and chemical exergy fields and

the total exergy field as reported by the authors are shownin Figs. 14a–c. About 30% of the fuel exergy is found to bedestroyed in the combustion process. The maximum exergydestruction was found in the thin flame zone, and onlyabout 10% of the destruction was found to occur down-stream to the flame due to heat transfer to the wall and exit.Increasing the air inlet temperature was found to slightlydecrease the exergy efficiency.

5. Conclusion

The optimum operating conditions of a combustor inpractice depend on an overall fuel economy and otherdesirable combustion characteristics like combustionchamber wall temperature and emissions. However, theimportant consideration of fuel economy for a combustorof a power-producing unit pertains to the trade-off betweenthe efficient conversion of energy quantity and minimumdestruction of energy quality (exergy). This is determined

127109

91735537

191 Z / R1

3

5

7

911

2000

8500

15000

21500

28000

2000

8500

15000

21500

28000

127 109 91

15000.0

24000.0

33000.0

42000.0

51000.0

Exerg

y,

kJ /

kg c

oal

stor [34]. (b) Chemical exergy distribution in a pulverized coal combustor


from the knowledge of the relationship of combustionefficiency and exergetic efficiency with the operatingparameters. This information are furnished by the funda-mental studies on the identification of irreversibilities andsubsequent exergy analysis in a combustion process, whichhas been reviewed in the present paper. The majorobservations relating to the reduction of thermodynamicirreversibilities in combustion processes are as follows:

�
Chemical reaction and physical transport processes arethe sources of irreversibilities in combustion. In manysituations, the major part played among all physicalprocesses is the internal thermal energy exchange. � All combustion reactions are thermodynamically irre-
versible. However, the rate of exergy destruction bychemical reaction can be reduced if the flame tempera-ture is kept high. It can be done by oxygen enrichmentof air through an exergy efficient method.
� The most important way of keeping exergy destruction
in combustion within limit is to reduce the irreversibilityin heat conduction due to internal mixing. Combustionshould be controlled to occur with less temperaturegradient in the combustor. This can be attained by airpreheating, fuel–air staging, and controlling the jetvelocities.
� For the design and development of energy and exergy
efficient combustion systems, further fundamental stu-dies are required to understand the influences ofturbulence and vorticity on entropy production indifferent types of flames and also the influence ofpressure on exergetic efficiency of combustion process inhigh-pressure flames.
� Finally, the work extraction devices should be properly
designed to extract the maximum exergy contained inthe product gas.

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