Download Thermodynamic Irreversibilities and Exergy Balance in Combustion Processes...
ARTICLE IN PRESS
Progress in Energy and Combustion Science 34 (2008) 351–376 www.elsevier.com/locate/pecs
Thermodynamic irreversibilities and exergy balance in combustion processes S.K. Soma,, A. Dattab a
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721 302, India Department of Power Engineering, Jadavpur University, Salt Lake Campus, Kolkata 700 098, India
b
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 hightemperature 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. 2.
3.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Exergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Irreversibility and its causes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Exergetic efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exergy analysis approach in combustion systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Different combustion systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Physical processes in a combustion system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Exergetic performance analysis based on exergy balance: approach 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Equilibrium approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Analysis in well-stirred reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Intrinsic analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Exergetic performance analysis using entropy generation equation: approach 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
Corresponding author. Tel.: +91 3222 282978; fax: +91 3222 282278.
E-mail address:
[email protected] (S.K. Som). 0360-1285/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.pecs.2007.09.001
352 354 354 354 354 355 355 355 356 357 358 359 359
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
352
4.
5.
State of art in exergy analysis in combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Gaseous fuel combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Liquid fuel combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Droplet exergy models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. Spray exergy models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Solid fuel combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction The world energy consumption is largely dependent on fossil fuels even today where combustion plays a key role in the energy utilization process. Combustion of fuel finds its importance in heating, power production, transportation and process industries. The energy-intensive industries like petroleum refining, steel, chemical, glass, metal casting, aluminum, etc. are also heavily dependent on combustion processes. In 2003, almost 86% of a total 421 quadrillion kJ energy produced from the primary energy resources came from the combustion sources [1]. In this, the shares of oil, natural gas and coal, which are the three principal pillars for energy supply, were 162, 99 and 100.5 quadrillion kJ, respectively. The high share of combustion associated energy production is maintained in all the four major energy utilization sectors, viz. residential, commercial, industrial and transportation. This trend is believed to continue in the coming years. A projection of data to 2030 shows a 71% increase in the total energy consumption figure from that in 2003. However, the share of fossil fuelbased resources has been predicted to remain at the same range of 86% as is in 2003. Despite the on-going depletion in the fossil fuel reserves and the ever-increasing concern towards the conservation of the environment, the growth in the use of oil in the time span of 2003–2030 has been envisaged to be 47.5%, that in natural gas to be 91.6% and in coal to be 94.7%. The figures reveal that the combustion system and combustors will maintain their importance in the energy sector in the next several decades to come. On this backdrop, the question of efficient operation of the combustors finds importance. Both the limited combustible fossil fuel reserve and the damage that combustion causes to the environment, e.g. through the liberation of the GHGs, calls for an increase in efficiency of the system through the minimization of the losses. In a gross sense, the efficiency of a device whose primary purpose is the conversion of energy is given by the ratio of the energy in the converted form to that before conversion. In a combustor, the chemical energy of the fuel is converted into thermal energy. Therefore, the conventional definition of efficiency of a combustor indicates how much thermal energy is available for use from the stored chemical energy of the fuel. The losses in a combustor that accounts for the decrease in the efficiency are due to unburnt fuel, incomplete combustion and heat loss to the surrounding across the combustor wall.
360 361 369 369 371 372 374 375
The conventional definition of combustion efficiency, however, does not pay any attention to the quality at which the thermal energy from the combustor is available in the hot products of combustion. For example, if we consider combustion of a fuel with air at atmospheric temperature in a well-stirred combustor, the final temperature of the product upon complete combustion of the fuel will depend on the extent of the air supplied. An increase in the excess air will lower the product gas temperature, even when the energy content of the gas remains the same in consideration of adiabatic walls of the combustor. Thus, the work producing potential of the product gas decreases, as given by the second law of thermodynamics. So complete conversion of energy in the combustor cannot be its sole performance indicator. Probably the most important use of combustion in practice is for the production of work. The transportation sector and the electricity generating plants use the energy obtained from combustion for the generation of work. Many applications in the process industries also employ combustors for the purpose of getting work. In all these applications, the work producing potential of the products of combustion should be the performance indicator for the combustion process. Exergy is the term coined [2] to describe the work producing potential of energy, and hence, an exergy-based analysis of combustors should find importance in optimizing the design. Many works are available in the literature advocating the importance of exergy-based analysis for the performance evaluation of thermodynamic systems [3–5]. According to them, energy-based performance analysis are often misleading as they fail to identify the deviation from ideality. An ideal process is reversible and does not incur any destruction of exergy. The practical processes generate thermodynamic irreversibilities internal to them and result in a loss of exergy even when there is no loss of energy external to the system. Several studies have indicated that the conventional combustion process involves inherent thermodynamic irreversibility, which significantly limits the conversion of fuel energy into work [6]. For typical atmospheric combustion systems, about 1/3rd of the fuel exergy becomes unavailable due to the inherent irreversibilities in the combustor. Most of this irreversibility is associated with the internal heat transfer within the combustor between the products and reactants. Such heat transfer becomes inevitable in
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
Nomenclature A A_ a ach B Ck cp f ki h I_ j ki K k M _ m _ 000 m Pr p Q_ q_ i ¯ R Re S_ g s s_000 g T t U ki u ui
area (m2) rate of exergy flow (J/s) specific exergy (J/kg) specific chemical exergy (J/kg) transfer number mass fraction of species k specific heat (J/kg K) body force per unit mass on species k (N/kg) specific enthalpy (J/kg) rate of exergy destruction (J/s) mole flux of species k (kmol/m2 s) specific kinetic energy (J/kg) thermal conductivity (W/m K) molecular weight mass flow rate (kg/s) volumetric rate of mass generation (kg/m3 s) Prandtl number pressure (N/m2) rate of heat transfer (W) conduction heat flux vector (W/m2) universal gas constant (J/kmol K) Reynolds number rate of entropy generation (W/K) specific entropy (J/kg K) volumetric entropy generation rate (W/m3 K) temperature (K) time (s) diffusion velocity of species k (m/s) specific intermolecular energy (J/kg) velocity vector (m/s)
both premixed and diffusion flames, where highly energetic product molecules are free to exchange energy with unreacted fuel and air molecules. Fig. 1 depicts how entropy is generated due to internal heat transfer in a hydrogen–oxygen reaction. However, the entropy generation in a combustion process is attributed to both internal heat and mass transfers and chemical reactions. Internal heat transfer within the combustor is often difficult to be recognized as an issue affecting the performance, because it does not result in a direct energy loss from the combustion zone to the surrounding. Instead, internal heat transfer only degrades the exergy of the product flue gas and reduces its work potential. Therefore, the actual energy penalty does not become apparent until the work generation step, which is separated from the combustion step, is taken into account. The losses due to process irreversibilities can be calculated using the second-law analysis, either from the unbalanced rate of exergy input or from the rate of entropy generation. Accordingly two different approaches for second-law-based process performance evaluation and optimization studies have evolved—exergy analysis ap-
uofl V v
353
adiabatic laminar flame speed (m/s) volume (m3) specific volume (m3/kg)
Greek letters thermal diffusivity (m2/s) chemical potential (J/kg) Kronecker delta equivalence ratio overall potential energy of all species (J/kg) exergetic efficiency viscosity (kg/m s) density (kg/m3) stress tensor (N/m2) volumetric rate of formation of species k (kg/m3 s)
a w dij f j ZII m r tij _k o
Subscripts a cv ex f k in r
air control volume exit fuel species index inlet exergy reference environment
Superscripts ex in
exit inlet
proach and minimization of entropy generation approach. The concept of minimizing the irreversible production of entropy is inherent in reducing the exergy loss in a process
Tmax
Tcool O O
H
O H H
H H
H
H
O
H H
H
H
O
O
Tadiabatic
H O
H H H H
O H
H
O H
O
H
O
O
H
O H
H
O
O H H
H O
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].
ARTICLE IN PRESS 354
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
for improving the efficiency. Accordingly, the most efficient performance is achieved when the exergy loss in the process is the minimum. Both the approaches find wide acceptability in heat transfer engineering, e.g. in the optimization of heat exchangers, fins, thermal insulation, electronic package cooling, etc. and have been chronologically reviewed in many references [7–11]. Yilmaz et al. [12] presented an exhaustive review of the application of various second-law-based analyses for the optimal design of heat exchangers. They described the need for the systematic design of heat exchangers using secondlaw-based procedure. Accordingly, the design of heat exchangers based on low first cost approach dictating the minimum size leads to higher irreversibilities, as it requires a larger temperature difference between the streams to affect the heat transfer. Such designs are inefficient from the exergy standpoint, as they do not preserve the quality of energy during the transformation. The authors proclaimed that the exergy-based performance evaluation is worthy as it gives a measure of the perfection of the thermal process. Historically, second-law-based analysis was developed to evaluate the process of power generation from heat. Applications of exergy analysis for the performance evaluation of power-producing cycles have increased in the recent years. A lot of works are now available in the literature where the second-law-based analyses have been applied for optimizing performance on coal-based electricity generation using conventional [13–19], fluidized bed and combined cycle technology [20] as well as for gas turbine [21–24], internal combustion engine [25–32] and blast furnace [33] applications. It can be concluded from all these studies that in power plants involving combustion, the major part of the exergy loss takes place in the process of combustion. Lior [34] and Lior et al. [35] outlined the necessity of second-law-based analysis of combustion processes with the following objectives: (1) identification of the specific phenomena/processes that have 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 art knowledge on thermodynamic irreversibility and exergy loss that occur in fundamental physical processes in the combustion of solid, liquid and gaseous fuels. The different approaches adopted by the researchers to achieve the goal have been reviewed with their relative merits and demerits. A final conclusion has been drawn to give direction on future research needed for more efficient utilization of fuel’s useful energy through a trade-off between the energy and exergy-based efficiencies.
2. Basic concepts 2.1. Exergy The concept of exergy is a direct outcome of second law of thermodynamics. The exergy of a system is defined to be its work potential with reference to a prescribed environment known as ‘exergy reference environment’. The term ‘work potential’ implies physically the maximum theoretical work obtainable if the system of interest and the prescribed environment interact with each other and reach the equilibrium. The term exergy is sometimes referred by thermodynamically synonymous term ‘availability’ and is a composite property of the system and the reference environment. In general, the specific exergy is defined as a ¼ K þ j þ ðu ur Þ þ pr ðv vr Þ T r ðs sr Þ þ ach ,
(1)
where K is the specific kinetic energy of the system and j is the potential energy per unit mass due to the presence of any conservative force field. T, p, u, v and s are the temperature, pressure, specific intermolecular energy, specific volume and specific entropy, respectively, while ach represents the specific chemical exergy. The terms with the subscript r are the properties of the exergy reference environment. 2.2. Irreversibility and its causes Any natural process depletes the total exergy of all interacting systems in the process (i.e. the exergy reserve of the universe decreases). This is known as law of degradation of energy. The destruction of exergy is termed as irreversibility, which is considered to be a thermodynamic characteristic of a physical process. All natural processes are irreversible. The causes of irreversibility lie in the basic requirement of a natural process to occur and can be classified broadly as: (i) lack of thermodynamic equilibrium and (ii) dissipative effects associated with a natural process. The thermodynamic irreversibility in a process is characterized by the entropy generation in the process. For continuous processes performed by a system, it can be written that I_ ¼ T r S_ g , (2) where I_ is the rate of exergy destruction or dissipation and S_ g is the rate of entropy generation. Eq. (2) is known as the Gouy–Stodola equation [8]. An engineering system, in general, involves a number of coupled physical processes. The entropy generation due to all these processes together determines the system irreversibility. The general expression for entropy generation in a continuous field described by a system is derived from the equation of change of entropy (entropy transport equation). This is discussed in Section 3.4. 2.3. Exergetic efficiency The parameter that gauges the effectiveness of a system in preserving its exergy in performing a physical process is
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
355
3. Exergy analysis approach in combustion systems
One way of distinguishing the combustion behavior in practical systems is based on the fuel that is burnt. Though the major share of the fuels used for combustion is the hydrocarbons, the composition of the fuel differs and accordingly the fuel can be either in the gaseous, liquid or solid phase. The gaseous fuels can homogeneously mix with the oxidizer very easily for burning. The need of fuel preparation is the minimum and the combustion reaction proceeds rapidly with little formation of the polluting species. However, the cost of the fuel is high and the storage and handling systems are voluminous and elaborate. The convenient burning of the gaseous fuels mostly pertains to small combustion applications including the domestic use. However, the present day concern of the environment calls for the use of gaseous fuels even in large combustors to keep the emission levels within the statutory limits. The solid fuels are suitably gasified to obtain synthetic gas and liquid fuels are pre-vaporized and premixed with air to get a lean vapor–air mixture in the gas phase for burning. The liquid fuel burning is mainly promoted in the transportation sector for its easy storage and relatively clean handling. Various forms of liquid hydrocarbon fuels are used in automobile engines, diesel engines, aircraft gas turbines, etc. The heavier fractions of the liquid hydrocarbons, which are relatively less expensive, are used in furnaces and boilers. The fuel preparation is necessary for the high viscous species, where heating is required to control the fuel viscosity for reducing the pumping power and for better atomization. The atomization of the liquid into minute droplets is always necessary to enhance the evaporation process, which precedes the combustion. Different types of atomizers are used depending upon the application. Combustion of liquid fuel sprays is an intricate affair involving various inter-related phenomena, like atomization, penetration, evaporation, interference, mixing and chemical reaction. Multi-component nature of most of the practical fuels further complicates the situation. Solid fuel burning is always heterogeneous in nature occurring at the surface of the fuel and inside the pores when the fuel particles are porous. Mainly coal, lignite and biomass fuels come under this category. These fuels require an elaborate fuel preparation process, e.g. in case of pulverized coal-fired boiler the fuel is required to be pulverized from the coarse size to fine powder having mean size of 50–75 mm. The utility boilers and heat treatment furnaces are the two major applications using solid fuels.
3.1. Different combustion systems
3.2. Physical processes in a combustion system
In the practical world, combustion is used in various devices from the simplest one like a candle to the most complex ones like rocket and scramjet engines. However, there are fundamental differences in the physical processes involved in combustion in different devices in more than one aspect. Borman and Ragland [36] cited and analyzed examples of combustion in many important devices.
A number of coupled interacting physical processes take place in a combustion system to initiate and sustain the combustion reactions. The primary requirement for a combustion reaction is the mixing of fuel and oxidizer so that they come in contact at the molecular level. Except for solid fuel combustion, all combustion reactions take place in the gaseous phase. Therefore, for liquid fuel combustion,
Q
Reactants
. Ain
Combustion System
. Aex Products
Inlet
Outlet
Fig. 2. Schematic of a combustion system showing the exergy transfer.
known as exergetic efficiency. This is also called as secondlaw efficiency. Lower is the irreversibility, higher is the exergetic efficiency and vice versa. In determining the exergetic efficiency of a process performed by a system, one has to consider the exergy quantities that cross the system boundaries either as flow exergy associated with mass flux, or as exergy transfer built in with the transfer of energy quantities (heat and work). A combustion system in general performs a number of coupled transport processes like convection and diffusion of mass, momentum and energy along with the process of chemical reactions. All of them can be realized either in a laminar or in a turbulent flow regime. In both cases, the expression for exergetic (or second law) efficiency of a combustion system (see Fig. 2) can be written as A_ ex , (3) _ _ Ain Qð1 ðT r =TÞÞ where A_ in and A_ ex are the rate of flow availability at inlet and exit to the combustor, respectively. Q_ is the rate of heat loss from the combustion system and T is the representative temperature at the boundary surface of combustor. From an exergy balance, we can write Tr I_ ¼ A_ in A_ ex Q_ 1 . (4) T
ZII ¼
Hence, it becomes ZII ¼ 1
I_ . _ ðT r =TÞÞ A_ in Qð1
(5)
For an adiabatic combustor (Q_ ¼ 0): ZII ¼
I_ A_ ex ¼1 . _ _ Ain Ain
(6)
ARTICLE IN PRESS 356
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
vaporization of fuel and its mixing with the air (oxidizer) are the controlling processes in sustaining the combustion reactions. A combustion system, in general, is a multicomponent and multiphase system. The physical processes occurring in the system can be classified broadly in two groups, namely: (i) transport processes and (ii) chemical reactions. The transport processes pertain to the transport of mass momentum and energy, which involve the processes of diffusion and convection of those quantities. The turbulence plays an additional key role by transporting mass momentum and energy through turbulent eddies along with the transport of the quantities through molecular diffusion and flow-aided convection. The physical aspects of transport processes are governed by three basic conservation equations as follows: Mass conservation equation of individual species: qC k q _ k, þ rC k uj þ rC k U k;j ¼ o qxj qt
(7)
where Ck is the mass fraction of the species k in the mixture, and uj and Uk,j are the mass average velocity and the mass diffusion velocity for the species k, respectively. _ k is the rate of formation of the kth species. In a general o multicomponent system comprising N components, there are N equations of this kind. The addition of these N equations gives the equation for conservation of bulk mass and is known as the continuity equation. Momentum conservation equation: q q qp qtji ðrui Þ þ ruj ui ¼ þ , qt qxj qxj qxj ! N X þr C k f ki .
ð8Þ
k¼1
Energy conservation equation: q q qp qp qui ðrhÞ þ þ uj ruj h ¼ þ tij qt qxj qt qxj qxj N qq_ j q X rC k U k;j qxj qxj k¼1 ! N X hk þ r C k f k;j U k;j .
ð9Þ
k¼1
There are numerous physical models and approaches followed by several computational methods to solve the above equations in determining the velocity, temperature and species concentration fields in a combustion system. The field variables define the thermodynamic potentials for respective diffusive and convective fluxes of mass momentum and energy. The rate equations of the fluxes are given by the phenomenological laws of respective processes. The transport processes are inherently irreversible due to thermodynamic dissipation in the processes occurring under a finite potential gradient.
One major process in a combustion system is the chemical reaction. The word combustion is usually defined in its simplest form as the rapid oxidation reaction generating heat or both heat and light. The definition itself emphasizes the intrinsic importance of chemical reactions to combustion. The oxidation between fuel and oxidizer in a combustion system takes place through a number of reaction steps involving the production of intermediate species in the form of compounds, elements, radicals, molecules and atoms. The number and details of the steps for a given reaction is provided by the combustion chemistry. A detailed reaction mechanism involving intermediate reaction steps is very complex and the combustion chemistry of many reactions is not fully understood even today. The use of global or quasi-global reactions to express the combustion chemistry is a ‘black box’ approach, since it does not provide a basis for understanding what actually happens chemically in the system. However, for oxidation of hydrocarbon fuels, particularly of higher paraffin or alkane group, global or quasi-global steps can capture the overall behavior of the reaction processes, and may be used for engineering approximations with due regard to their limitations. Westbrook and Dryer [37] present and evaluate one-step, two-step and multi-step global kinetics for a wide variety of hydrocarbon oxidations. The chemical reactions for gaseous and liquid fuel combustions are referred to as homogeneous reactions, which take place in gas phase as a result of the collisions of gas-phase molecules of the reacting species (fuel and oxidizer). Therefore, the primary step in liquid fuel combustion is the vaporization of liquid fuel. On the other hand, the solid fuel combustion involves heterogeneous reactions, where gas-phase oxidizer reacts with solid-phase fuel at the surface of the solid fuel. The rate of any chemical reaction is guided either by the kinetics of the reaction or by the rate of diffusive transport of the reacting molecules to come in contact for possible collision for reaction. The rate equation of either kinetic-controlled or diffusion-controlled reactions are developed with the help of the physics of the governing process, and involve empirical model parameters, which are tuned to the best agreement with the actual reaction rates found from experiments. The direction of a chemical reaction is provided by the second law of thermodynamics, and is determined by the difference between the sum of the products of chemical potential and stoichiometric coefficient of the reacting species and that of the product species. Similar to transport processes, thermodynamic irreversibility is incurred by a chemical reaction and is determined by the chemical affinity (potential driving the chemical reaction) and the specific rate of the reaction. 3.3. Exergetic performance analysis based on exergy balance: approach 1 One way of analyzing the performance of a combustor is by the exergy balance across the combustor. Considering
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
the fuel and air entering the combustor either separately, or in the form of a mixture, it is possible to calculate the exergy flow rate at the inlet to the combustor. It will comprise the chemical exergy of the fuel and the thermomechanical (or physical) exergy of the fuel and air. The combustion analysis in the combustor results in the product stream at a particular pressure, temperature and composition, from which the exergy of the outlet stream is evaluated. The accuracy of the result depends upon the accuracy of the combustion analysis performed by the models with different degrees of complexity. 3.3.1. Equilibrium approach The simplest method of calculation considers a zerodimensional model with the product stream leaving as an equilibrium mixture of all the product species at a single pressure and temperature. The analysis adopts the laws of thermochemistry, without considering specific transport and kinetic rates. In other words, both the transport and chemistry are assumed to be infinitely fast. Such a method is widely used in all thermodynamic analyses of cycles and systems 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 is associated with the inflow of air and fuel to the system and can be written as _ a ain _ f ain A_ in ¼ m a þm f ,
(10)
_ f are the mass flow rates of air and fuel, _ a and m where m in respectively, into the combustor and ain a and af are the specific exergy of air and fuel at the inlet. In consideration of air as an ideal gas, the specific flow exergy of air, considering only the thermomechanical contribution, is determined from the following equation: in in ain (11) a ¼ ha hr T r s a s r . In the equation, h and s refer to the specific enthalpy and specific entropy, respectively, with the subscript a referring to 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 Z T ina in ha h r ¼ cpa ðTÞ dT, (12) Tr
and
sin a
Z
T in a
sr ¼ Tr
¯ Z pina dp cpa ðTÞ R . dT M a pr p T
(13)
In the above equations, cpa ðTÞ is the specific heat of air as ¯ and Ma are the universal gas a function of temperature, R constant and the molecular weight of air, respectively. T in a and pin a are the temperature and pressure of air at the inlet, while Tr and pr are the exergy reference temperature and pressure, respectively.
357
The specific exergy of the fuel stream may comprise both the thermomechanical and chemical exergy components. The thermomechanical component is calculated as above considering the corresponding properties and state of the fuel instead of air and assuming the fuel as an ideal gas. The chemical exergy component depends upon the type of fuel and is based on stoichiometric reaction of complete combustion of the fuel and a reference state of concentration 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 complete combustion 2 CH4 þ ðO2 þ 3:76N2 Þ ! CO2 þ 2H2 O f 2 2 2 O2 þ 3:76N2 . þ f f
ð14Þ
In Eq. (14), f represents the equivalence ratio, which has to be less than or equal to unity to ensure sufficient air for complete reaction. In case of insufficient air, it may be assumed that the oxygen of air preferentially reacts with hydrogen of the fuel to form the water. The oxygen then converts the carbon to carbon monoxide, a part of which is converted to carbon dioxide depending upon the availability of oxygen. The above assumption for writing the stoichiometric chemical equation is logical since the relative affinities of hydrogen, carbon and carbon monoxide for oxygen are in that respective order. The reaction can therefore be expressed as 2 4 CH4 þ ðO2 þ 3:76N2 Þ ! 3 CO2 f f 4 2 þ 4 ð15Þ CO þ 2H2 O þ 3:76N2 . f f As the combustor is adiabatic, there is no energy transfer across it. The energy equation therefore gives the product gas temperature at the combustor exit (Tex) as the adiabatic flame temperature considering the variation of the specific heat of the product components with temperature. The exergy flow rate at the exit to the combustor is evaluated as X ex _ ex A_ ex ¼ (16) hk hr T r S ex m k sr , k k
where k is the index for each species present in the product stream at the exit. The exit properties (temperature and pressure) are used for evaluating the Eq. (16). The exergetic efficiency of combustion is then given as in Eq. (6), i.e. ZII ¼ A_ ex =A_ in . Fig. 3 shows the variation of the exergetic efficiency, calculated using the above formulation, with the equivalence ratio and inlet air temperature. The fuel is considered to enter the combustor at a temperature of 298 K and the combustor operates at 1 atm pressure. The results show that the second-law efficiency is the maximum for the stoichiometric supply of air. The lower product gas temperature at the exit for
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
358
Well - stirred Reactors
1 300 K 450 K 600 K 750 K 900 K
Exergetic Efficiency
0.9 0.8
Product out
Reactant in
0.7 0.6 0.5
. m Tin Ci, in . Ain
0.4 0.4
0.6
0.8
1
1.2
1.4
Equivalence Ratio Fig. 3. Variation of exergetic efficiency with equivalence ratio of the reactant mixture at different inlet air temperature calculated with the equilibrium approach.
a lean mixture as a result of the excess air supply reduces the second-law efficiency of the combustor. This is despite the fact that all the energy stored in the fuel is contained in the product gas with the complete combustion of the fuel in case of a lean fuel–air mixture in the adiabatic combustor. Therefore, it is clear that neither the completeness of combustion nor the energy content of the product gas determines the exergy-based performance of the combustor. As the product gas temperature at the combustor exit decreases with the increase in the excess supply of air, the maximum ability of it to perform useful work decreases. Therefore, the second-law efficiency decreases. The same decrease in exergetic efficiency is also observed with the insufficient supply of air, when the exit temperature decreases because of the incomplete release of fuel’s stored energy. The maximum efficiency, which is obtained with the stoichiometric supply of air, may be considered as the ideal situation for every inlet air temperature. This ideal efficiency again increases with the increase in the inlet air temperature which increases the temperature of the product gas. Adebiyi [39] showed from a similar analysis in an adiabatic combustor, assuming complete combustion without dissociation and constant specific heats of air and product gas, that the maximum second-law efficiency attainable for a combustion engine is 70% with CH4 as the fuel and keeping the product temperature within the acceptable limit guided by the metallurgical constraint. 3.3.2. Analysis in well-stirred reactor The above approach considering both infinite speed of transport and kinetics does not in any way involve the time scale for determining the performance of the process. An improvement may consider a well-stirred reactor model for the combustor. A well-stirred reactor considers an infinite rate of transport, while taking into account the speed of reaction. In a practical reactor, high level of turbulence
. mi′′′
. m Tex Ci, ex . Aex
Fig. 4. Analysis in a well-stirred reactor model: Entire combustor is divided into a number of well-stirred reactors.
increases the rate of transport and such an assumption may often be acceptable. The reaction speed is determined using the kinetic parameters of the reactions for the assumed reaction scheme. Depending on the size of the combustor, the entire combustor may be assumed as a single wellstirred reactor. Otherwise, if the size is large, it can be divided into several such reactors in series, with the outlet of one entering the next reactor (Fig. 4). The analysis in every single reactor control volume considers the solution of the governing equations for getting the concentrations of different species of interest and the temperature [40]. The mass conservation equation of an arbitrary species i may be written as dmcv k _ in _ ex _ 000 ¼m (17) k m k þm k V, dt _ 000 where m k is the rate of mass generation of the species k per unit volume of the reactor and V is the reactor volume. Assuming steady-state operation of the reactor, the above equation may be written as ex _ k M k V ¼ 0, _ C in m (18) k Ck þ o _ is the total mass flow rate of the entire reactant or where m product streams and Ck is the mass fraction of the species _ k is the chemical rate of formation of species k per unit k. o volume, expressed in kmol/m3 s, obtained from the kinetics of reaction. For the well-stirred reactor, the chemical reaction rate may be expressed as a function of the temperature and the species concentration in the control volume (i.e. at the outlet). The steady state, steady flow conservation of energy equation considering adiabatic reactor gives ! N N X X _ m C ex C in ¼ 0, (19) k hk ðT ex Þ k hk ðT in Þ k¼1
k¼1
where the upper limit N of the index k denotes the number of species involved. The simultaneous solution of the above
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
equations gives the species mass fraction and the temperature at the exit of the reactor, when the inlet values are known. Using the expressions for exergy (thermomechanical as well as chemical), as shown in the previous section, the exergy values at the inlet and exit of the reactor can be obtained from which the second-law efficiency can be calculated. This method includes in the calculation the volume of the reactor, as well as the chemical reaction rate for the species from the kinetic parameters. Therefore, the results from the method will be more realistic. 3.3.3. Intrinsic analysis As pointed out by Lior [34], the system level development based on exergy calculation mostly use the equilibrium approach that employs equilibrium state data at the inlet and exit of the combustor for the exergy calculation. However, such equilibrium may not prevail in reality within the actual combustor. The exact distribution of the velocity, temperature and species concentrations in the combustor can be numerically obtained from the detailed solution of reacting flow inside the combustor. This requires the coupled solution of the full field and state equations consisting of the Navier–Stokes, energy, species conservation and thermodynamic property equations along with the equations of reaction kinetics. The field parameters are then used in the transport equation of exergy to find out the change in exergy flux between the inlet and outlet amounting to the loss of exergy. The individual contribution of the kinetic, potential, thermal, strain and chemical exergy loss can also be obtained from the calculation. The expanded forms of individual components are given in Lior [34] and Lior et al. [35]. The calculation of exergy loss, as indicated in the referred papers, are complicated because of the complexities of the equations involved. However, the intrinsic analysis for the exergy loss calculation can be performed in an alternative way [41]. The solution of the conservation of mass, momentum, energy and species concentrations in the combustor along with suitable kinetic rates of reaction generates information at the exit, typically for the velocity, temperature and concentration of various species. The exergy flow rate at the inlet to the combustor can be obtained from the Eq. (10). While at the exit, the exergy flow rate is expressed as Z X ex ex ex A_ ex ¼ C ex (20) k ak r uz dA, Areaex
k
where the exit variables are obtained as the output of the numerical solution of the reacting flow. This method considers the local specific availability ‘a’ to bear the same functional relationship with the pertinent thermodynamic properties as in case of equilibrium thermodynamics. The second-law efficiency obtained from the exergy approach gives a direct measurement of the performance of the combustor. The larger the irreversibilities, lower will be
359
the value of the second-law efficiency. However, this approach does not throw any light on the causes of the irreversibilities. In a combustor, several transport and chemical processes take place simultaneously, which are irreversible. The contribution of the processes towards entropy generation at different locations within the combustor is required to be known to investigate the primary causes of exergy loss. It is also not practically possible to improve the performance of a combustor without such information. The present approach fails to provide this data and calls for a methodology, which considers the irreversibility as a field variable to find its distribution within the entire combustor. 3.4. Exergetic performance analysis using entropy generation equation: approach 2 The irreversibility present in the actual processes occurring in a combustor results in the generation of entropy following the second law of thermodynamics. The rate of entropy generation may be used to calculate the rate of irreversibility or exergy destruction using the wellknown Gouy–Stodola equation (Eq. (2)). The determination of the total rate of entropy generation is an involved process in an intrinsic analysis in the combustor. This is done by calculating separately the rate of entropy generation in each physical and chemical process that takes place. In the flow field of a combustor, the nonequilibrium conditions are due to the exchange of momentum, energy and mass of different species (multicomponent) within the fluid and at the solid boundaries. These nonequilibrium phenomena cause a continuous generation of entropy in the flow field. The entropy generation is due to the irreversible nature of heat transfer, mass diffusion, viscous effects within the fluid and at the solid boundaries, chemical reaction, coupling effects between heat and mass transfers and body force effects. Every irreversible process can be viewed as the relevant flux driven by the corresponding potential, e.g. the flux of heat is driven by the temperature gradient. The entropy production rates in different processes can be explicitly obtained considering the conservation of multicomponent species mass in presence of chemical reaction, conservation of momentum and energy along with the local entropy balance equation. The local entropy generation per unit volume has been derived by Hirschefelder et al. [42] and is given by: PK j k ðqwk =qxi Þ tij ðqui =qxj Þ q_ i qT 000 s_g ¼ 2 k¼1 i T T T qxi PK PK s j ðqT=qx Þ j ¯ k ki i k fk þ k¼1 i i k¼1 T T PR PK 00 0 _ w g g o c k¼1 kr kr k , ð21Þ c¼1 T where tij is the stress tensor, q_ i is the heat flux vector and j ki , wk and s¯k are the species mole flux per unit area,
ARTICLE IN PRESS 360
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
chemical potential and partial molal entropy of the kth species, respectively. g0 kr and g00 kr are the stoichiometric coefficients on the reactant side and product side, respectively, for the kth species in the cth reaction, and _ c is the reaction rate of the cth chemical reaction. In the o above equation, the first term is due to fluid friction, the second due to heat transfer, the third due to mass transfer, the fourth is a result of the coupling between heat and mass transfer, the fifth term is due to the body force effects and the last term results from chemical reaction. Observation of the Eq. (21) shows that knowledge of the field parameters like velocity (and hence tij), temperature (and hence qi), species concentration (and hence jk, mk), of the state equations of the species used to determine the thermophysical properties (density, viscosity and thermal conductivity), and of the chemical reactions involved (to determine the rate) allow the computation of the entropy generation fields and exergy destruction. All these field parameters are obtained from the solution of the full field and state equations, consisting of the Navier–Stokes, energy, species conservation, entropy generation, and thermodynamic properties equations, combined in a combustion process with the reaction kinetics equations, all tightly coupled. The rate of exergy destruction calculated from the entropy generation rate in this approach, gives the local contribution of each individual process over the entire combustor. It therefore helps in identifying the process, which has to be improved to reduce the loss. The above equation, given by Hirschfelder et al. [42] has been later used by other researchers for the calculation of entropy generation in non-reacting as well as reacting flows. Teng et al. [43] further considered the contribution of the diffusiveviscous effect towards entropy generation in a multicomponent reacting fluid flow in addition to the other contributions as shown in Eq. (21). 4. State of art in exergy analysis in combustion Both the approaches, described above have been used in the literature for the analysis of exergy destruction in combustion. The calculation of exergy destruction in consideration of the equilibrium states at inlet and outlet is mainly used for the analysis of system design and does not help in identifying the root causes of exergy destruction in the combustor. We shall exclude the review of such work and only consider those works, which give somewhat detailed information regarding the causes and locations of irreversibility in different combustion situations. Tracking entropy generation in a flowing fluid is used for analyzing the energy conversion systems in many industrial processes. Investigations of entropy generation in flows have been reported in the literature related to momentum transfer [7], heat transfer [7,8,10,11,44], mass transfer [45,46], combined heat and mass transfer [47,48] and chemical reaction [49]. Analysis during combustion is the most challenging because it involves the transport pro-
cesses of momentum, heat and mass as well as includes chemical reaction. Therefore, for a sufficiently detailed analysis, in addition to considering the contribution of every process towards entropy generation, it is first required to solve the combustion phenomenon itself, considering the maximum possible details. The accuracy in the simulation of combustion has a big role in correctly predicting the exergy destruction. Arpaci and Selamet [50] calculated the entropy generation in a premixed flame established on a flat flame burner. They developed an equation for local entropy production considering the conservation equations of mass, momentum and energy as well as the local entropy balance equation as follows: " # 1 k qT 2 qui 000 000 s_g ¼ þ tij þu . (22) T T qxi qxj The terms in the bracket on the RHS show the contributions of thermal diffusion, mechanical energy dissipation and the dissipation of other forms of energy towards entropy production (u000 ), respectively. In a flat flame established on a burner, the authors considered onedimensional variation of temperature and obtained the local entropy production from the dimensional consideration of the thermal part. They defined a non-dimensional 2 entropy production rate as Ps ¼ s_000 g l =k, where l is a o characteristic length given as l ¼ a=ufl (a being the thermal diffusivity and uofl the adiabatic laminar flame speed at the unburned gas temperature). It was shown from the analysis that the non-dimensional entropy generation rate is an inverse quadratic function of the flame Peclet number, given as PeoD ¼ uofl D=a, where D is the quench distance of the laminar flame, which was expressed as the distance of the flame from the burner [50]. Using the tangency condition ðq=qyb ÞðPeoD Þ ¼ 0 during flame quenching (where yb is the burned gas temperature normalized against the adiabatic flame temperature), the authors showed that the minimum quench distance corresponds to an extremum in the entropy production. The distribution of rate of entropy production between the flame and the burner was also shown in terms of the burned gas temperature and the distance from the burner. The entropy production rate between the flame and the burner appears to remain almost constant spatially, for yb oð1 yu Þ, where yu is the unburned gas temperature normalized against the adiabatic flame temperature. This result was not surprising considering the small quench distance, which varies only between 0.5 and 1 mm. However, when yb Xð1 yu Þ, an unusually rapid change in the distribution of entropy production was found from the analysis. This result was indicated by the authors as a limitation of their model, which predicted a large deviation from the experimental results for this condition. The work of Arpaci and Selamat finds importance as it was probably the first one, which applied the entropy generation approach in combustion application. However, the simplistic physical
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
situation and model adopted in the work failed to generate detailed information from it. In the literature of exergy analysis in combustion systems, the work of Dunbar and Lior [6] receives a special mention, because they for the first time evaluated the primary causes for irreversibility using some heuristic finite increment exergy analysis method for the simple hydrogen and CH4 fuel combustors. The method adopted in the work was not fully intrinsic as the authors did not solve the full conservation equations with the reaction kinetics in the combustion chamber to obtain the flux and gradient terms for the different processes involved. Instead they divided the entire combustion phenomenon into a number of hypothetical sub-processes and applied them along the prescribed process paths. The sub-processes considered by the authors are: (i) a diffusion process where the fuel and oxygen molecules are drawn together, (ii) a chemical reaction process leading to oxidation of the fuel, (iii) an internal thermal energy exchange between hightemperature product and the unburned reactant, (iv) a physical mixing process where the system constituents mix uniformly. The sub-processes are arranged differently in the process paths resulting in different types of combustion phenomena. In one case (path 1), the authors considered an incremental quantity of fuel to be mixed with its corresponding stoichiometric quantity of oxygen to result the chemical reaction, internal energy exchange and product mixing (Fig. 5a). Such incremental process continued along the length of the combustor in small compartments till the gas constituents reached the fuel ignition temperature after which the oxidation of the remaining fuel was assumed to be instantaneous. The path according to the authors corresponds to the behavior of a diffusion flame. In an alternative case (path 2), the entire fuel and air were first mixed thoroughly (Fig. 5b). Subsequently, incremental amount of the mixture was reacted followed by the internal energy exchange and mixing. Such a path may exhibit the behavior of a premixed flame. Dunbar and Lior performed their analysis separately with hydrogen and hydrocarbon (CH4) fuels. It was found that fixing the number of increments beyond an optimum number does not change the results any further. Despite the simplification, the analysis yielded consistent results. It was observed that, in each of the hypothetical paths, the major share of exergy destruction took place due to the internal energy exchange. In the process path 1, the overall exergetic efficiency was reported to be within 66.5% and 77.3% in hydrogen combustion for a range of excess air of 0–100%, decreasing with the increasing amount of excess air. Out of the total exergy destruction, 72–77% was reported to be due to the internal heat exchange, 15–18%
361
due to chemical oxidation reaction and 8–10% due to gas mixing. In the process path 2, 66–73% of the total exergy destruction was accounted to internal heat exchange, 18–25% to chemical reaction and 8–10% to the mixing processes. Therefore, Dunbar and Lior concluded no perceptible difference in the causes of exergy destruction due to the premixing of the reactants. Between hydrogen and CH4, a relatively higher percentage of irreversibility resulted due to chemical reaction in the latter case than that in the former. However, even with CH4 combustion the largest share of irreversibility resulted due to heat transfer only. They also studied the effects of preheating using suitable 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 in the literature dealing with the detailed exergy analysis in various combustion phenomenon. In the following subsections these works have been briefly reviewed based on the type of fuel on which they have been applied. 4.1. Gaseous fuel combustion Exergy analysis in gaseous jet flames have been studied by Datta [51,52], Stanciu et al. [53], Nishida et al. [54], Datta and Leipertz [55] and Yapici et al. [56,57]. The studies include both non-premixed and premixed flames as well as laminar and turbulent jet flames. All these works pertain to the numerical solution of the conservation equations to predict the combustion process and calculation of the volumetric entropy generation on a local basis from the field values. The accuracy of the prediction is certainly a key factor in the determination of the exergy loss, as the flux and gradient of the field variables determine the entropy generation rate. The assumptions employed in the models, including those in the transport and thermodynamic properties (e.g. unity Lewis number), chemical reaction equation, etc. play important role to this effect. Following the approach given in Section 3.4, the Gouy–Stodola equation is used for the calculation of exergy loss. A complete field picture of the entropy generation rate using Eq. (21) helps to identify the key locations causing the exergy loss as well as the root cause 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 entropy generation. A single-step chemical reaction and unity Lewis number were the key assumptions in the model. The effect of viscous dissipation was found to be negligible and thermal diffusion, chemical reaction and mass diffusion were found to contribute to the entropy generation in the order of their enumeration. A study of parametric variation on the entropy generation rate was performed by varying the air inlet temperature, the thermal condition at the confined wall (isothermal at 298 K, and adiabatic) and the air–fuel supply ratio (by changing the fuel flow rate
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
362
First Incremental Extent of Reaction
Fuel Feed
H2O
Stoich. amount O2
Unreac. Fuel Incre. Fuel
Fuel
Unreacted Fuel Incremental Fuel
Air Feed
Second Incremental Extent of Reaction
H2O
Q H2O
Stoich. amount O2
Product mixing
Q
H2O Q
Product mixing
Rest amount
Product
Rest amount
Q
First Incremental Extent of Reaction
Second Incremental Extent of Reaction
Fuel Feed
Fuel-Air Mixing
Incremental Reaction
Thermal Energy Exchange
Incremental Reaction
Thermal Energy Exchange
Air Feed
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 relative role of chemical reaction, internal heat and mass transfer in entropy production within the combustor only. However, the entropy production in combustor together with that in air pre-heater determines the energy economy of the combustion system comprising both the combustor and air pre-heater. It can be mentioned in this context that an exergy analysis of an air pre-heater requires information about the thermodynamic states of air and hot gas at entry and exit to the heater which in turn depend upon its physical location in the plant. Stanciu et al. [53] showed that in a constant pressure laminar non-premixed flame the irreversibilities due to viscous dissipation, heat conduction, mass diffusion and chemical reaction are uncoupled. The authors also showed that in a CH4–air combustion process, the thermal, chemical and diffusive irreversibilities represent, in order of enumeration, the predominant irreversibilities in the laminar diffusion reacting flows.
Nishida et al. [54] studied a typical unconfined laminar non-premixed flame for the analysis of the local entropy generation. The conservation equation of entropy was solved with a source term containing contributions of viscous dissipation, heat conduction, mass diffusion and chemical reaction. The radial distribution of species mole fraction and temperature at a single axial height as also the local entropy generation rate for each irreversible process at the same height were presented. The contribution of thermal conduction was seen to far outweigh the contribution of chemical reaction towards entropy generation. The authors reasoned that the high temperature in the zone of chemical reaction in a non-premixed flame is the cause of its lower contribution to entropy generation. Though the work of Nishida et al. [54] gave the radial distribution of entropy generation rate at a single axial location, a complete representation of the irreversible processes over the entire field is absent in it. Such a complete irreversible field could be envisaged in a later
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
363
L
dout
di Fig. 7. Temperature distribution in a laminar methane–air jet diffusion flame with the flame contour shown in black line [52].
Air
Fuel
Air
din d
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 the entropy generation in a laminar non-premixed CH4–air flame in the same configuration as in Fig. 6. The numerical model employed a two-step chemical reaction and the variation in the property values based on local temperature and species concentration. The kinetic parameters were adjusted to give a reasonably correct prediction in the field variables, which was ascertained by comparing the distribution of the field variables against the experiment. It was assumed that the low flux of the intermediate species because of their low concentration, would not contribute much towards entropy generation and the major species, whose concentrations were predicted in the model, were solely responsible to the entropy production process. Fig. 7 typically illustrates the structure of a laminar nonpremixed flame predicted by the numerical model [52]. The figure plots the temperature distribution in the confined domain near the core, where the flame exists. The plot near the wall is not shown as there is almost no variation of temperature there. The flame contour is also plotted in the figure by drawing the heat release zone. The highest
temperature zone is located within the flame in an annular region somewhat above the burner port. The high temperature causes a buoyant acceleration to the flow in the flame zone and thereby entrains air from the surrounding resulting in a flow field that generates the over-ventilated structure of the flame. Moreover, due to the continued entrainment towards the core, the pressure near the periphery drops resulting in an ingress of air from the atmosphere through the exit plane. The ingress causes the formation of a recirculation over the outer wall and results in a low temperature shield over the wall. The complete picture of flow may be available in the original work [52]. At the core, the temperature gradually reduced downstream to the flame zone due to the 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 the reactants, and CO, CO2 and H2O, which are the intermediate and final products. The distributions are the result of the transport process of the species mass in a multicomponent environment as well as chemical reaction. The fuel coming from the central jet is consumed at the flame and its concentration gets rapidly reduced. Therefore, the fuel species exist only inside the flame region. The oxygen supplied from air enters as the co-flow and transports towards the flame from the peripheral side. It gets consumed at the flame surface and therefore within the flame region only a trace of it is located. CO is found inside the flame. It is formed on the inside surface of the flame, which burns in a rich atmosphere because of the shortfall of oxygen. The CO that comes towards the outer surface of the flame front gets readily consumed with oxygen. On the
ARTICLE IN PRESS 364
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
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 to diffuse inside showing its existence inside the flame. CO2 and H2O are formed in the flame front and are transported in all directions based on the advective and diffusive rates. The transport of the product species continues downstream to the flame till the exit plane is reached. However, the major mass transport occurs in the flame region, where the
sudden reduction in concentrations of the reactants and generation of products result in large rates of transport of the species. The transport processes of heat and mass as a result of the temperature and concentration distributions occur through irreversible processes and result in entropy generation. The entropy generation rate is high at locations where the field gradient and the resulting fluxes are high.
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
365
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 volumetric entropy generation rate contours due to chemical reaction, heat transfer (thermal diffusion) and mass transfer respectively, for the non-premixed flame. It is evident from the figure that the entropy generation due to chemical reaction (Fig. 9a) takes place within the flame front. The volumetric entropy generation rate due to chemical reaction is higher near the base of the flame. It reveals that the flame is more intense near its base. At the tip, the flame is weak and the volumetric entropy generation rate is less than 1/20th of the peak contour value shown in the figure. The concentration gradient of the fuel is more at lower elevation and results in higher rate of diffusion of fuel towards the flame front. This makes the flame more intense there. With the consumption of fuel, the fuel concentration gradient reduces at higher elevation. This decreases the fuel transfer rate to the flame and the flame intensity also decreases. An inner reaction zone is also evident from the chemical entropy generation plot, which however is much weaker. In a jet diffusion flame, the flame is little lifted from the burner depending upon the jet momentum. Through the gap some air diffuses in to form a weak premixed flame in the core. Therefore, the entropy generation field portrays a good picture of the flame structure. Fig. 9b shows the volumetric entropy generation rate due to thermal diffusion in the confined domain. The strong temperature gradient close to the burner rim, where the flame 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 diffusion occurs over a much greater volume compared to the volume of the flame, where entropy is generated due to chemical reaction. In the flame zone, heat diffusion occurs from the high-temperature flame. Moreover, the buoyancyinduced acceleration increases the flow velocity at the core and results in a high entrainment of fluid towards the center. The flow structure generates a thermal stratification with the high-temperature gas near the core. Due to the axi-symmetric nature of the flow the gradient of temperature remains low near the axis. The ingress of atmospheric air through the outlet plane and formation of the recirculation zone around the peripheral wall maintains a low temperature shield at the periphery. There exists an annular region between the core and the wall, where the temperature falls rapidly causing a high rate of heat transfer. The stratification of the flow and the formation of the recirculating zone due to atmospheric air ingress maintain the annular region of high-temperature gradient till the exit plane. Therefore, high diffusion of heat continues over a much larger volume to cause a high overall entropy generation rate. The entropy generation due to mass transfer of all the species is depicted in the Fig. 9c. It is observed that the mass transfer results in entropy generation mainly around the flame. In a diffusion flame the reactants diffuse into the flame from the opposite sides of the flame surface and the products transport from the flame in all directions. Beyond the flame, though transport of heat continues,
ARTICLE IN PRESS 366
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
mass diffusion ceases to play any major role. The figure reveals that the magnitude of the rate of entropy generation per unit volume due to mass transfer is significantly lower compared to the other two major contributors even in the flame zone. Though generation and consumption of different species occur in the flame, the gradient of species concentrations never takes a large value and the transport process always bring a uniformity in the distribution of the species around the flame. The only high rate of entropy generation due to mass transfer is observed just above the entry plane and around the interface between the fuel and air jets. The field values of the rate of entropy generation give a complete picture of the causes of irreversibilities and their location in the flame. It was observed that the gravity has a major role in controlling the entropy generation rate in the flame. In a reduced gravity environment, the flame and flow characteristics experience a major change. At zero gravity, the buoyancy-induced flow is totally absent reducing the entrainment of air from the surrounding towards the flame. The flame therefore becomes less intense and the volume of the flame increases as it achieves a somewhat spherical shape instead of the elongated overventilated shape at normal gravity. The volumetric entropy generation rate due to chemical reaction shows a reduction in its peak value at zero gravity than at normal gravity due to reduced intensity of the flame. However, the total rate of entropy generation due to chemical reaction is not much different because the volume of the flame front at zero gravity level is more due to the increased width of the flame. The higher volume of the flame front compensates the decrease in the volumetric entropy generation rate that takes place at zero gravity. On the other hand, the entropy generation rate due to heat transfer is reduced considerably at zero gravity compared to that at normal gravity. This is because in a zero gravity non-premixed flame the reduced entrainment from the co-flow results in a more uniform radial temperature distribution. The entropy generation due to mass transport, which is in effect low, is not much different at reduced gravity from the corresponding value at normal gravity. Fig. 10 shows a plot of the total rate of entropy generation in the confined domain and the rate of entropy generation due to individual processes in non-premixed flame at various gravity levels varying from normal gravity to zero gravity [52]. The corresponding Froude number (Fr ¼ gd i =u2f , where g is the acceleration due to gravity, di the fuel port diameter in the burner and uf the fuel jet velocity at burner exit) varies in the range of zero (at zero gravity) to 61.33 (at normal gravity). The entropy generation due to fluid friction is not included in the figure due to its very low value. It is seen that out of all the individual processes, the most dominant role towards entropy generation in non-premixed flame is played by heat conduction under all gravity conditions. Chemical reaction is the next significant contributor and mass transfer comes as the third important. With the change in
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 nonpremixed gaseous jet flames [51] Sl. no.
Inlet section R1orpR2
0orpR1
1 2 3 4 5
Fuel jet velocity (cm/s)
Fuel jet temp. (K)
Air jet velocity (cm/s)
Air jet temp. (K)
4.5 4.5 4.5 6.0 7.5
298 298 298 298 298
9.88 14.55 19.89 9.88 9.88
298 450 600 298 298
Diameter of the central fuel port (R1) ¼ 12.7 mm. Diameter of the annular co-flow tube (R2) ¼ 50.8 mm. Pressure ¼ 1 atm. Wall condition: adiabatic.
gravity level, the entropy generation due to reaction and mass transfer hardly changes in magnitude. However, the entropy generation due to heat transfer is grossly affected by gravity. It is already explained that as the gravity level is reduced the temperature field becomes more uniform and the entropy generation due to heat transfer decreases. This decrease in the entropy generation is also reflected in the total entropy generation rate and results in a decrease in the total entropy generation. Tables 1a and 1b show the details of the operating conditions studied and the entropy generation values obtained in the non-premixed laminar gaseous jet flame in a confined environment [51]. The effect of preheated air on entropy generation showed that the total rate of entropy generation decreases with the increase in inlet air temperature. The variation is principally attributed to the decrease in the contributions of the thermal diffusion and chemical reaction. The higher value of air temperature increases the flame temperature but decreases the temperature gradient occurring in most of the region of the domain resulting in
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
367
Table 1b Rate of entropy generation (W/K) at different inlet conditions given in Table 1a Sl. no.
1 2 3 4 5
Inlet air temp.
298 450 600 298 298
Air–fuel ratio
59.29 59.29 59.29 44.46 35.57
Entropy generation rate due to transport Heat transport
Mass transport
Combined heatmass transport
Total in transport
0.3650 0.3120 0.3017 0.3999 0.4356
0.0440 0.0464 0.0489 0.0503 0.0670
0.1004 0.0796 0.0670 0.1158 0.1294
0.5094 0.4380 0.4177 0.5661 0.6224
a reduction in the diffusive heat flux. These together are the primary cause of the lower contribution of thermal diffusion towards entropy generation. The chemical reaction occurring in the high-temperature flame reduces its contribution to the entropy generation rate. The effect of increase in the fuel flow rate was found to increase the total entropy generation rate in the domain. The contribution of both the transport processes and chemical reaction was found to increase. The height of the non-premixed flame increases with the increase in the fuel flow rate. The increased volume of the flame is the primary cause of the increased rate of entropy generation. The other class of gaseous fuel combustion is the premixed flame, where the fuel is considered to be homogeneously mixed with the oxidizer before reaching the reaction front. Caton [23] performed a somewhat simplified analysis in an adiabatic, constant volume chamber, where the exergy loss in a combustion process is analyzed based on thermodynamic calculations considering equilibrium. Though the fuel considered was octane, the author assumed a pre-vaporized mixture of it with air. The features of liquid fuel combustion, like evaporation and mixing of the fuel vapor and air were not considered. We have therefore included the work here as gaseous fuel combustion. As there was neither heat and work transfer across the system boundary nor any additional mass exchange during the process, the author claimed the difference of exergy before and after the chemical reaction was solely due to combustion. A homogeneous mixture of species in the combustor was assumed giving spatially uniform properties. The combustion reaction was assumed to be complete and the product concentrations were calculated from chemical equilibrium consideration at high temperature. The first and second laws of thermodynamics were used to calculate the properties before and after the reaction. The exergy quantities before and after the reaction were calculated considering the thermomechanical contribution of all the species and the additional chemical exergy contribution of the fuel species. The chemical exergy of the fuel was obtained from the difference between the Gibb’s free energy of the product and reactant at the reference state. The exergy destruction was further checked internally against the process irreversibility calculated using the
Entropy gen. rate in chem. reaction
Total rate of entropy generation
0.1429 0.1376 0.1341 0.1675 0.1935
0.6523 0.5757 0.5519 0.7337 0.8159
entropy generation from the entropy balance equation given 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 this chemical energy is transformed into thermal energy, some portion (which depends on the final temperature) of the initial availability is destroyed. The amount of the exergy that is destroyed increases for lower final temperatures of the product, i.e. for lower flame temperature. The higher initial temperature of the reactant decreases the destruction in exergy in the combustion process due to the higher temperature of the product, which retains more exergy contained in it. Regarding the effect of the equivalence ratio, the author found that the destruction of exergy per unit mass of the fuel increased as the reactant mixture became leaner than stoichiometric. This may be attributed to the lower temperature of the flame in a lean mixture and the inherent irreversibility associated with the mixing of the combustion products with the excess air present in the combustor. As a recommendation from the study, Caton observed that in an internal combustion engine the reactant temperature should be kept high to ensure less exergy destruction. However, the author also reminded that the realization of the exergy depends on the application following the combustor. For example, he suggested that to recover the maximum work from the high exergy content of exhaust gases, exhaust devices like turbocompounding have to be employed in the engine. The author also pointed out that the high initial temperature for recovering maximum exergy in combustion may result in other issues like increased NO emission. Nishida et al. [54] performed a detailed numerical analysis for the study of exergy loss in a laminar premixed flame. The conservation equations of mass, momentum, energy and species were solved taking into account the detailed chemical kinetics and multi-component diffusion. The thermodynamic and transport properties were obtained from the CHEMKIN database. Premixed flames were simulated using the steady, one-dimensional flow at atmospheric pressure and with hydrogen and CH4 as the fuels. The entropy generation rate was calculated using the field variables and considering the contributions of viscous dissipation, heat diffusion, mass diffusion and chemical reaction. It has been shown that the total rate of entropy
ARTICLE IN PRESS 368
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
generation becomes large in the region of the main reaction zone denoted by the high-temperature gradient. Chemical reaction accounted for the maximum entropy generation both in hydrogen and CH4 flames, while heat conduction contributed the second largest. While in a stoichiometric hydrogen–air flame with 25 1C reactant temperature, 72.6% of the total entropy generation rate was contributed by chemical reaction, in a stoichiometric CH4–air flame the percentage contribution of chemical reaction was 55.3%. The contribution of heat conduction for the two cases were found to be 21.6% and 37.9%, respectively. The effect of mass diffusion was found to be much smaller and the effect of viscous dissipation is negligible. From the spatial distribution of the entropy generation rate shown by the authors, it is evident that in the hydrogen flame the steep rise in the entropy generation rate due to chemical reaction and heat conduction initiates at the same axial location, though the peak for the chemical reaction occurs at a little downstream location. However, the temperature where the entropy generation due to chemical reaction reaches the peak was found to be sufficiently low. In the CH4 flame, however, the entropy generation due to chemical reaction increased much later compared to the entropy generation due to heat conduction. Therefore, the peak in the entropy generation due to chemical reaction shifted to a much downstream location compared to the peak due to heat conduction. The temperature at the location where the entropy generation rate due to chemical reaction peaked was much higher in CH4 flame than in hydrogen flame. This was attributed to the increased concentration of the radical species in the flame. According to the authors, the high temperature in the flame region of CH4 combustion reduced the entropy generation rate due to chemical reaction and its contribution towards total entropy generation was less than that in hydrogen flame. It indicated the importance of the flame chemistry in determining the exergy destruction in combustion. In a study of parametric variation [54], the authors found that the total destruction of fuel’s exergy increased when the premixed mixture was leaner than stoichiometric, while an increase in the reactant temperature was found to decrease the percentage of total exergy destruction. In a lean mixture, the temperature in the reaction zone was found to rise more gradually resulting in a wider reaction zone than that in stoichiometric mixture. Consequently, the entropy generation zone of each process in the flame became wider. Though the fraction of entropy generation due to each individual irreversible process was similar to that in a stoichiometric flame, the wider flame zone resulted in the increase in total rate of entropy generation increasing the exergy loss. With an increase in reactant temperature, the flame temperature was increased correspondingly. The flame became narrower reducing the prime zone of entropy generation. The entropy generation due to heat conduction became smaller as the inlet and outlet fluid temperature rose. The high-temperature flame reduced the entropy generation due to chemical reaction also. Thus, the total
entropy generation decreased and the exergy destruction as a fraction of fuel’s exergy was reduced. However, the contribution of chemical reaction towards the total entropy generation increased. A contrasting feature of the predictions of Nishida et al. [54] and those of Dunbar and Lior [6] in premixed flame is that while the former found the chemical reaction as the most significant contributor the latter attributed the same to heat diffusion. Though Dunbar and Lior performed a hypothetical analysis, they considered chemical reaction in incremental quantities followed by internal heat exchange in the mixture. On the other hand, Nishida et al. considered a one-dimensional analysis typical for a flat flame situation. In a flat flame, the temperature varies from the reactant temperature to the product temperature within a small thickness of about 0.5–1 mm, outside which the temperature gradient is reasonably flat. Therefore, the entropy generation due to heat diffusion is only effective within a short 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 is maintained by the turbulent production terms. At the larger scales of turbulence, they extract a part of energy (or exergy) from the mean flow field and through the vortex stretching mechanism continuously transfer it to the smallest turbulent scales, where the molecular diffusivities of multicomponent fluid perform its dissipation. Following this idea, Stanciu et al. [53] split the turbulent reacting flow irreversibility not only into the viscous, thermal and diffusion components but also into its mean and turbulent parts. They used the phenomenological multi-species approach and proved that 98% of the exergy destruction resulted due to the last part. Yapici et al. [56,57] studied the entropy generation in a turbulent swirl flow axisymmetric combustor with CH4 as the fuel. The fuel and air streams entered the combustor as coflow, with swirl imparted to the airflow using inlet swirler. The former work [56] studied the effects of equivalence ratio and swirl ratio on the entropy generation rate, while the latter work [57] studied the influence of fuel type. The turbulent quantities were evaluated using the RNG-k–e model, while the eddy dissipation model was used for the calculation of the reaction rates. The CH4–air reaction was assumed to proceed in two steps, with the intermediate formation of CO. The entropy generation rate was considered to contain terms related to viscous dissipation and heat conduction only. Such consideration is applicable in heat transfer problem but fails to give the complete picture of exergy destruction in combustion since the irreversibilities associated with mass transfer and chemical reaction are not considered. It remains the major drawback in the works. The numerical solution of combustion gave a temperature field with very high-temperature gradient. Swirl in the flow was found to affect the temperature gradient at low value of fuel jet velocity, while at high fuel jet velocity this effect was minimal. In all the cases studied, the entropy
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
generation due to heat transfer was found to dominate over that due to viscous dissipation. The highest local entropy generation rate was observed at the entry plane and near the wall. Parametrically the swirl number, equivalence ratio and the fuel flow rate were all found to be affecting the entropy generation rate in the combustor [56]. The authors proclaimed that, at no swirl, the entropy generation rate decreased exponentially with the increase of equivalence ratio (in the lean side between 0.5 and 1.0) for high fuel injection rate, whereas they had quadratic profiles with minima in the case of low fuel flow rate. However, it appeared from their results that the variation is similar for all the fuel flow rates. Only difference being that at high fuel flow rates the said minima did not come in the range of equivalence ratio of 0.5–1. At a constant fuel flow rate of 10 lpm, the entropy generation rate was found to decrease with the increase of swirl number. The variation in the entropy generation rate should depend on the peak temperature reached in the flame and the structure of the flame in the combustor. In a stoichiometric flame, the peak temperature is higher than a lean flame while, in a lean flame due to the higher flow rate of air, the flame can not spread radially, giving a high gradient of temperature and a high rate of entropy generation. It shows that the flame structure has a strong effect on the entropy generation rate due to heat transfer. The merit factor, which is the ratio of the useful exergy transfer rate through the wall and to the fluid to the sum of the exergy transfer rate and the rate of irreversibility, was also calculated in the work. It was shown that for high fuel flow rate, the merit factor continually increased with the increase in equivalence ratio, showing the reduced influence of the irreversibility. While, for low mass flow rate, the merit factor reached a maximum at a particular equivalence ratio and then sharply decreased with a further increase in the equivalence ratio. A marginal increase in the merit factor was observed with the increase in swirl at a fixed fuel flow rate and equivalence ratio. The second study [57] calculated the entropy generation rate with a large number of fuels, e.g. hydrogen, CH4, C2H2, C2H4, C2H6, C3H8, C4H10, C6H6 burning in air. For the sake of comparison, the fuel flow rates were adjusted to give the same heat transfer rate in the combustion chamber. In all the studies it was found that the maximum reaction rates decreased with the increase in the equivalence ratio in the lean side of mixture stoichiometry. The increase in the equivalence ratio also reduced the temperature gradients in the combustor. Therefore, the volumetric local entropy generation rate was found to decrease with the increase in equivalence ratio from 0.5 to 1. Bejan number (ratio of entropy generation due to heat conduction to that due to both heat conduction and viscous dissipation) remained high (around 0.995) for all the cases indicating the negligible influence of viscous dissipation towards entropy generation, compared to heat conduction. The overall rate of entropy generation for any fuel
369
decreased exponentially with the increase in equivalence ratio for the conditions of fuel flow rate studied. However, at a particular equivalence ratio, the total entropy generation in the combustor increased with the increase in the fuel flow rate and therefore the heat transfer rate. The incremental increase in the entropy generation for the same incremental increase in the heat transfer rate was more at lower values of equivalence ratio. For the various hydrocarbons studied, it was observed that the entropy generation excepting with C2H4 and C2H2 were very close to each other. Merit number was found to increase by about 16% for the increase in the equivalence ratio from 0.5 to 1.0. 4.2. Liquid fuel combustion 4.2.1. Droplet exergy models The work of Dash et al. [58] is probably the pioneering work in ascertaining the sources of irreversibility in course of evaporation of a single component liquid fuel droplet in a high-temperature convective gaseous medium. The thermodynamic irreversibilities were characterized by the rate of entropy production in the transport processes and were determined from the field values of volumetric entropy generation rate as described in approach in Section 3.4. A break-up of entropy generation rate due to different modes of transport processes in gas and liquid (droplet) phases depicted that the entropy generation rate due to viscous dissipation was negligibly small because of low flow velocities. Irreversibilities in droplet phase were also found to be quite insignificant compared to those in the gas phase. The most significant contribution in the total entropy generation rate was due to the conduction of heat and its coupled effect with mass transfer in the gas phase. The rate of entropy production decreased continuously at a rate lower than the decreasing rate of droplet surface area. A numerical correlation of entropy generation rate with pertinent dimensionless input parameters was developed as [58] 1:02 1:29 0 S_ g M 1 =M v B ¼ 714:5 , (23) 0:72 2 0 0:66 r ðRePr Þ 0 where S_ g ¼ S_ g r1 Rur2i is the dimensionless entropy generation rate, r is the density, R is the gas constant, u is the flow velocity, r0 is the dimensionless droplet radius ( ¼ r/ri), Re is the Reynolds number of flow past the droplet, Pr is the Prandtl number of gas flowing around the droplet, and B is the transfer number. The subscripts N and i refer to the free-stream condition and initial state of the droplet, respectively. MN and Mv are, respectively the molecular weights of free-stream gas and droplet liquid. The relationship given by Eq (23) provides the fundamental information in exergy-modeling of spray combustion, in a similar fashion, Nusselt number relation of single droplet does in heat transfer modeling of spray combustion. The identification of irreversibility components and subsequent exergy analysis in droplet combustion require
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
where O¼
U 2r Q þ hf T1 hfg 1 1 hfg Tf 1 T1 w ; wp;f . M f p;1 Tf
3 5
ð25Þ
10
Dai = 12.22 x 106 Curve T I 3.0 II 4.0
1
Ichem / I-Ichem
the determination of entropy generation in a chemically reacting flow. The pertinent information in this regard has been reported by Hiwase et al. [59], Dash and Som [60], and Puri [61]. It was observed [59] that in sphericosymmetric droplet combustion, the entropy generation rate due to chemical reaction was of the same order as those due to heat conduction and combined heat and mass convection. However, the entropy generation rate due to heat conduction in gas phase was still the dominant factor, though the entropy generation rate due to chemical reaction shot up to a higher value at the instant of ignition. The interesting outcome of this fact is that, in a typical diffusion-controlled droplet combustion process, the irreversibility rate due to chemical reaction is lower than that due to diffusion processes taken together, except at the instant of ignition. This is shown in Fig. 11. In a convective ambience, the total entropy generation rate (or irreversibility) per unit droplet surface area increases as the burning of droplet progresses and reaches its highest value at the end of droplet life when the droplet surface area becomes extremely small [60]. A typical variation in second-law efficiency, for the process of a n-hexane droplet combustion in a quiescent ambient of air, with initial Damkohler number (Dai) at various free-stream temperatures is shown in Fig. 12. The parameter Dai physically signifies the ratio of characteristic thermal diffusion time to chemical-reaction time. A variation in Dai for any given fuel, under fixed values of initial gas-phase properties, implies a variation in the initial diameter of the droplet. The upper flat portions of the curves (Fig. 12) correspond to the process of pure droplet vaporization without combustion in the gas phase, while the lower flat portions pertain to the steady-state droplet combustion process. It is observed from the figure that a low value of Dai and a high value of free-stream temperature for the process of droplet combustion are needed from the view point of energy economy in relation to efficient utilization of energy resources. In a convective ambience, the minimum entropy generation for the burning of a fuel droplet corresponds to an optimum transfer number, which is directly proportional to the square of the relative velocity and inversely proportional to the heat release rate and the temperature difference between the droplet and its surrounding flow [61]. For flow with small Reynolds number, the expression for optimum transfer number can be written after Puri [61] as 5 O BM;opt ¼ 1, (24) 2
I
II
0.1
0.01
0.001 0.1
1
10
100
t 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].
1
0.8 II
I
III
0.6 II
370
Curve T∞
0.4
0.2
I II III
2.0 3.0 4.0
0.01
0.1 Dai × 10-6
1
10
100
Fig. 12. The exergetic efficiency of a droplet combustion process [59].
In the expression, Ur is the relative velocity between the droplet and ambient. hfg is the latent heat of evaporation and Q is the heat release from the fuel droplet. TN and Tf are the free-stream temperature and fuel droplet temperature, respectively. In a real system there is a little control over the transfer number and the heat release. The specific enthalpy associated with the products is fixed by the choice of liquid fuel and the stoichiometry related to the oxidizer content in the gas. Under the circumstances, Eq. (24) describes an optimum relative velocity that minimizes the entropy generation or exergy loss for a given gas flow rate and temperature ratio (ratio of free-stream temperature to flame temperature). It should be mentioned in this context that the irreversibility analysis of droplet evaporation and combustion as discussed above pertains to the laminar flow of the gas phase past the liquid fuel droplet.
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376 0.850 Rei = 60
0.825
n=3
0.800 II
4.2.2. Spray exergy models The identification of irreversibility components from entropy generation rate in a spray combustion process is composed of two parts, namely: (i) the entropy generation in the evaporation of individual droplets in their local surroundings due to interphase transport processes and (ii) the entropy generation due to transport processes and chemical reaction in the continuous carrier phase. A breakup of the source of irreversibilities in a spray combustion process shows equal order of magnitudes for the irreversibility contributed by local interphase transport processes and that contributed by the transport processes and chemical reactions in continuous gas phase. The exergy balance and the second-law analysis of a spray evaporation process in a gaseous surrounding with uniform free stream were reported by Som et al. [62] and Som and Dash [63]. The entropy generation rate in the evaporation of a liquid spray is initially very large and then decreases with the axial distance of the vaporizing spray. The rate of entropy generation increases with an increase in the ratio of free stream to initial droplet temperature or with a decrease in the initial Reynolds number of the spray based on initial droplet velocity and Sauter mean diameter of the initial PDF of the spray. The variation in second-law efficiency of a spray evaporation process with governing parameters, as predicted by Som et al. [62] and Som and Dash [63] depicts different kinds of picture. The second-law efficiency ZII, evaluated using ‘‘discrete droplet model’’, shows an initial increase in ZII with the free-stream temperature TN followed by an almost constant value thereafter. This implies physically an optimum value of TN above, which the evaporation of spray is not thermodynamically justified, since the increase in the rates of exergy transfer and that in its destruction become almost equal. However, the picture is different when the ‘‘two-phase- separated-flow model’’ is used [63] to evaluate the second-law efficiency (ZII). Under this situation, ZII shows a monotonically decreasing function of free-stream temperature and an increasing trend with initial Reynolds number of the spray (Fig. 13). The qualitative difference in the results of [62] and [63] can be attributed to the fact that in the ‘‘discrete droplet model’’ adopted by Som et al. [62] for spray calculation, the transport processes in the carrier phase was neglected as it was considered to be a homogeneous gas phase with freestream properties. On the other hand, the separated-flow model for spray calculation [63] considered all the transport processes in the carrier phase along with the interphase transport processes between the gas phase and the evaporating droplet phase. Therefore, the earlier work [62] underestimated the total entropy generation in spray evaporation process due to the lack of additional contribution towards entropy generation due to the gas-phase processes. The optimum values of free-stream temperature and spray Reynolds number should be chosen as suggested by Som and Dash [63] on the basis of an overall economy which is a trade-off between the length of evaporation and total irreversibility of the process.
371
0.775 0.750 Rei = 30 0.725 0.700 1.50
1.75
2.00
2.25 T∞
2.50
2.75
3.00
Fig. 13. Exergetic efficiency of a spray evaporation process with Rosin–Rammler function as initial drop size distribution [63].
The recent investigations of Datta and Som [64], Datta [65] and Som and Sharma [66] provide comprehensive information on energy and exergy balance in a spray combustion process in a gas-turbine combustor. The analyses employed a spray combustion model based on stochastic separated flow (SSF) approach. The gas-phase conservation equations were solved in an Eulerian frame, while the droplet phase equations were computed in a Lagrangian frame. The interphase source terms were evaluated during the droplet phase computation and introduced in the gas phase. The turbulent quantities were modeled using a standard k–e model and the chemical reaction employed the eddy dissipation model. It was found that the inlet air pressure had a marked influence in decreasing the irreversibility due to interphase transport processes (Id), while the irreversibility in the continuous gas-phase (Ig) was almost uninfluenced by the air pressure. At high air pressure, the value of Id is relatively lower than the value of Ig, while the picture was reversed at lower pressure of ambient air. This can be attributed to a reduction in droplet vaporization rate because of a reduction in mole fraction of fuel vapor at droplet surface with an increase in local pressure at a given local temperature. An increase in inlet air temperature increases the irreversibility in the interphase transport process, while the gas phase irreversibility remains almost the same. The exergetic efficiency in a typical spray combustion process lies between 50% and 70%, while the combustion efficiency in case of gas turbine combustion lies between 90% and 98% under usual operating conditions. A comparative picture of exergetic efficiency and combustion efficiency in spray combustion in a typical gas turbine combustion process at different operating conditions is shown in Table 2 [64]. The interesting feature observed, in this context, is that the qualitative trends of the influence of inlet swirl number of incoming air on both second-law efficiency and combustion efficiency are exactly the opposite when the combustor pressure is changed from
ARTICLE IN PRESS 372
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
a lower to a higher value. While, at a low pressure of 100 kPa, an increase in inlet swirl increases the second-law efficiency (ZII) and reduces the combustion efficiency, (Zc), the trends are reversed when the combustor pressure is increased to a value of 600 kPa. At low pressure, the adverse effect of reduced droplet penetration due to an increase in inlet air swirl plays the dominant role in reducing Zc and increasing ZII. However, at higher pressure the droplet penetration is as such low and hence the favorable effect of enhanced mixing of fuel vapor in the gas phase due to an increase in inlet air swirl plays the prominent role in increasing the value of Zc and reducing the value of ZII. It has also been observed [64,65] (Table 2) that an increase in the cone angle of spray increases the combustion efficiency and decreases the second-law efficiency. A higher spray cone angle results in a larger radial dispersion and hence a better mixing of fuel vapor in the gas phase. This causes an increase in the rate of combustion and accordingly in the total irreversibility in the process. Som and Sharma [66] predicted from an energy and exergy balance of spray combustion process in a gasturbine combustor, that an increase in fuel volatility increased the combustion efficiency only at higher pressures for any given inlet temperature and air swirl (Table 3), while the second-law efficiency decreased with an increase in fuel volatility at any operating condition. The physical explanations for these typical variations in Zc and ZII, put forward by Som and Sharma [66] are as follows: The success for complete combustion depends on the penetration of fuel droplets, their rate of vaporization, and mixing of fuel vapor with air. At low pressures, for a given temperature, all these three physical processes are relatively fast and combustion efficiency is usually very high. Therefore, the change in the rate of droplet vaporization with fuel volatility does not make any marked influence in combustion efficiency. However, on the other hand, when the pressure in the combustion chamber is high, at a given inlet temperature, there occur (i) a reduction in droplet penetration due to increased density of ambient air, and (ii) a reduction in the rate of droplet vaporization due to a decrease in fuel–air diffusivity with pressure. Therefore, for a given fuel, an increase in combustion pressure for a fixed inlet temperature always reduces the combustion efficiency. Under this situation, the favorable effects of enhanced droplet vaporization and its mixing with ambient air due to an increase in fuel volatility is felt sharply through a marked increase in the combustion efficiency. The increase in second-law efficiency with pressure can be attributed to simultaneous increase in flow availability of incoming air at a high pressure and less process irreversibility due to reduced droplet vaporization.
Table 2 Comparison of combustion efficiency (%) and exergetic efficiency (%) in spray combustion [64] (a) Influence of inlet pressure _ in Inlet conditions: m a ¼ 0:1 kg=s, Rein ¼ 52,100, SMD ¼ 52 mm, spray cone angle ¼ 801, swirl no. ¼ 0.76, T in a ¼ 600 K, air–fuel ratio ¼ 60 Inlet pressure (kPa)
Combustion efficiency
Exergetic efficiency
100 300 600 1000
95.34 93.56 91.32 83.31
57.21 61.53 71.82 79.93
(b) Influence of inlet air temperature _ in Inlet conditions: m a ¼ 0:1 kg=s, Rein ¼ 52,100, SMD ¼ 52 mm, spray cone 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
400 600 800
86.03 95.34 99.53
55.24 57.21 55.60
(c) Influence of inlet swirl number _ in Inlet conditions: m a ¼ 0:1 kg=s, Rein ¼ 52,100, SMD ¼ 52 mm, spray cone in angle ¼ 801, T a ¼ 600 K, air–fuel ratio ¼ 60 Inlet pressure (kPa)
Inlet swirl number
Combustion efficiency
Exergetic efficiency
100 100 600 600
0.37 0.76 0.37 0.76
97.59 95.34 87.24 91.32
54.86 57.21 75.70 71.82
(d) Influence of initial mean droplet diameter in injected spray _ in Inlet conditions: m a ¼ 0:1 kg=s, Rein ¼ 52,100, spray cone angle ¼ 801, swirl no. ¼ 0.76, T in a ¼ 600 K, pin ¼ 100 kPa, air–fuel ratio ¼ 60 Initial SMD (mm)
Combustion efficiency
Exergetic efficiency
34 52 67 96
94.37 95.34 95.61 94.11
59.63 57.21 53.43 51.13
(e) Influence of spray cone angle _ in Inlet conditions: m a ¼ 0:1 kg=s, Rein ¼ 52,100, SMD ¼ 52 mm, swirl ¼ 600 K, pin ¼ 100 kPa, air–fuel ratio ¼ 60 no. ¼ 0.76, T in a Spray cone angle (1)
Combustion efficiency
Exergetic efficiency
4.3. Solid fuel combustion
60 80 100
91.49 95.34 98.58
62.67 57.21 48.85
Coal is the most important solid fuel and is widely used in generating electricity. It will be the principal fuel to meet the future demand of electricity since coal reserves are
much greater than the other fossil fuels. Most of the coalfired power stations use pulverized coal for combustion. Coal is also used in the operation of a blast furnace, which
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
373
Table 3 Influences of inlet pressure and swirl on combustion efficiency (%) and exergetic efficiency (%) in spray combustion for fuels with different volatilities [66] in _ in Inlet conditions: m a ¼ 0:1 kg=s, Rein ¼ 52,400, SMD ¼ 52 mm, spray cone angle ¼ 801, T a ¼ 600 K, air–fuel ratio ¼ 60
Inlet pressure (kPa)
100 100 1000 1000
Inlet swirl number
0.36 0.76 0.36 0.76
Combustion efficiency (%)
Exergetic efficiency (%)
n-Hexane
Kerosene
n-Dodecane
n-Hexane
Kerosene
n-Dodecane
95.37 95.40 91.14 84.21
96.06 96.92 82.92 78.47
94.34 94.81 64.43 45.90
54.54 56.11 74.04 67.12
65.84 70.64 83.27 72.27
71.14 74.44 86.43 82.73
employs pulverized coal injection along with the blast air through its tuyere to reduce the coke feed rate. From the view point of energy economy, an efficient process of coal combustion should be guided not only by the combustion efficiency of the process but also by its second-law efficiency. Fundamental research in the field of coal combustion for the determination of the reaction rate parameters and modeling of reaction chemistry is going on for the last three decades. Both experimental and numerical works are available and exhaustive reviews of all these works are made in Smoot [67,68]. Som et al. [69] first attempted a detailed second-law-based analysis in a cylindrical combustor burning pulverized coal particles. The full Navier–Stokes equations are solved along with the conservation of mass and energy, with the standard k–e model employed for the solution of the turbulent quantities. A pdf-based conserved scalar equation was solved for the species concentrations as well as the reaction rates. Following the earlier spray model of Datta and Som [64], the coal particle tracking was done in a Lagragian frame and coupled with the Eulerian fluid flow through the carefully computed source terms. The exergy analysis is done calculating the inlet and exit exergy components following approach 1 given in Section 3.3. The second-law efficiency for the combustion process is computed using Eq. (7). The effect of variation in air temperature, airflow rate, particle size and inlet swirl level of airflow on the second-law efficiency were studied. The outcome of the studies are as follows: An increase in air temperature decreases the combustion efficiency for a shorter length of combustor, but increases the combustion efficiency for a higher length of combustor. The second-law efficiency follows a trend that bears an inverse relationship to that in combustion efficiency with air temperature. At low values of inlet air swirl (S ¼ 0.0–0.32), an increase in SMD of coal particle decreases the combustion efficiency. At a higher value of inlet air swirl (S ¼ 0.77) combustion efficiency increases with an increase in SMD from 50 to 95 mm, and thereafter decreases with a further increase in SMD of coal particle from 95 to 145 mm. The second-law efficiency always increases 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 tradeoff between Zc and ZII for an overall energy economy. The relative weight of Zc and ZII to be assigned in the process of optimization depends on the relative savings in the cost of energy quantity over the energy quality for a specific application, which is a task of energy management in practice. Prins and Ptasinski [70], following the line of Dunbar and Lior [6], studied the exergy losses in the gasification and combustion process of solid carbon in a gasification reactor by dividing the process into several subprocesses, like chemical reaction, internal thermal energy exchange between reaction products and unburnt reactants, product mixing, etc. The irreversibilities associated with the individual subprocesses have been calculated using the thermodynamic parameters for the isothermal and adiabatic combustion of carbon in the reactor. The overall efficiency is computed as the gain in exergy of the gas as a fraction of the change in exergy of the solid fuel (expressed as the difference of exergy in the fuel input and the exergy of the unburned fuel). Alternately a term called efficiency defect is defined as the sum of the irreversibilities due to all processes as a fraction of the exergy difference of the solid fuel across the reactor. For stoichiometric combustion of carbon with air, exergy losses due to internal thermal energy exchange (14–16% of expended exergy) are larger than those due to the chemical reaction (9–11% of expended exergy). The overall exergetic efficiency in gasification process, employing partial combustion, is found to be higher than that in combustion. In a combustion process the fuel’s exergy is totally converted into the theromechanical exergy of the high-temperature product gas, while gasification retains a large part of chemical exergy in the generated fuel gas. In gasification, the reaction remains very efficient while the exergy losses related to internal thermal energy exchange (5–7% of expended exergy) are reduced due to the lower temperature. The efficiency in the gasification process can be improved by gasifying with oxygen instead of air, but the irreversibilities incurred in separating oxygen from air nullify this advantage. In order to maximize the chemical exergy present in the product gas, for oxygen-blown
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
374
potential exergy, strain exergy and kinetic exergy are too small and can be ignored. Consequently, the major exergy components were reported to be thermal and chemical. The thermomechanical and chemical exergy fields and the total exergy field as reported by the authors are shown in Figs. 14a–c. About 30% of the fuel exergy is found to be destroyed in the combustion process. The maximum exergy destruction was found in the thin flame zone, and only about 10% of the destruction was found to occur downstream to the flame due to heat transfer to the wall and exit. Increasing the air inlet temperature was found to slightly decrease the exergy efficiency.
gasification of fuels like solid carbon, it was advised to moderate the temperature with steam and operate between 1200 and 1400 K for atmospheric pressure and 1300–1500 K for elevated pressures. In this way, up to 75% of the exergy contained in solid fuels can be converted into 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]. The analysis used the computer simulation results, which consisted of the solution of the conservation of mass, momentum, energy and species conservation equations with the standard k–e equations. The radiative transfer equation was solved using spherical harmonics method. The particle trajectories were solved in the Lagrangian frame. A 13-equation chemical kinetic model for reaction and separate models for devolatilization, volatile combustion were used. The solution gives three-dimensional distribution of gas, particle and wall temperature, radiation intensity, gas and particle velocity and species concentrations. These results are used for the spatial determination of all the components of exergy. It was found from the order of magnitude of different components of exergy that
5. Conclusion The optimum operating conditions of a combustor in practice depend on an overall fuel economy and other desirable combustion characteristics like combustion chamber wall temperature and emissions. However, the important consideration of fuel economy for a combustor of a power-producing unit pertains to the trade-off between the efficient conversion of energy quantity and minimum destruction of energy quality (exergy). This is determined
12000
18000
6000 12000 0 11 9 7
6000
15000
21500
8500
15000
2000 11 9
8500 7
0
5 3 1
1
19
37
91
73
55
28000
21500
Exergy, kJ / kg
24000
coal
28000 18000
Exergy, kJ
/ kg coal
24000
109
5
127
3 1
Z/R
1
19
37
55
73 Z/R
2000 127 109 91
51000.0 Exergy, kJ / kg coal
51000.0
42000.0
5
15000.0 9 7
33000.0
3
24000.0
1 1
19
37
55 72 Z/R
15000.0 91
109
127
Fig. 14. (a) Thermomechanical exergy distribution in a pulverized coal combustor [34]. (b) Chemical exergy distribution in a pulverized coal combustor [34]. (c) Total exergy distribution in a pulverized coal combustor [34].
ARTICLE IN PRESS S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
from the knowledge of the relationship of combustion efficiency and exergetic efficiency with the operating parameters. This information are furnished by the fundamental studies on the identification of irreversibilities and subsequent exergy analysis in a combustion process, which has been reviewed in the present paper. The major observations relating to the reduction of thermodynamic irreversibilities in combustion processes are as follows:
Chemical reaction and physical transport processes are the sources of irreversibilities in combustion. In many situations, the major part played among all physical processes is the internal thermal energy exchange. All combustion reactions are thermodynamically irreversible. However, the rate of exergy destruction by chemical reaction can be reduced if the flame temperature is kept high. It can be done by oxygen enrichment of air through an exergy efficient method. The most important way of keeping exergy destruction in combustion within limit is to reduce the irreversibility in heat conduction due to internal mixing. Combustion should be controlled to occur with less temperature gradient in the combustor. This can be attained by air preheating, fuel–air staging, and controlling the jet velocities. For the design and development of energy and exergy efficient combustion systems, further fundamental studies are required to understand the influences of turbulence and vorticity on entropy production in different types of flames and also the influence of pressure on exergetic efficiency of combustion process in high-pressure flames. Finally, the work extraction devices should be properly designed to extract the maximum exergy contained in the product gas.
References [1] Derived from the website of Energy Information Administration (EIA) at /www.eia.doe.govS. [2] Rant Z. Exergy, a new word for technical available work. Forsch Ing Wes 1956;22(1):36–7 [in German]. [3] Rosen MA, Dincer I. Exergy as the confluence of energy, environment and sustainable development. Exergy Int J 2001;1(1):3–13. [4] Rosen MA. Clarifying thermodynamic efficiencies and losses via exergy. Exergy Int J 2002;2:3–5. [5] Rosen MA. Exergy conservation: an alternative to conserving the already conserved quantity energy. Exergy Int J 2002;2:59–61. [6] Dunbar WR, Lior N. Sources of combustion irreversibility. Combust Sci Technol 1994;103:41–61. [7] Bejan A. Second-law analysis in heat transfer and thermal design. Adv Heat Transfer 1982;15. [8] Bejan A. Entropy generation through heat and fluid flow. New York: Wiley; 1982. [9] Bejan A. Entropy generation minimization. New York: CRC Press; 1995. [10] Bejan A. Entropy generation minimization: the new thermodynamics of finite-size devices and finite-time processes. J Appl Phys 1996;79: 1191–218.
375
[11] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: Wiley; 1996. [12] Yilmaz M, Sara ON, Karsli S. Performance evaluation criteria for heat exchangers based on second law analysis. Exergy Int J 2001;1(4): 278–94. [13] Rosen MA, Dincer I. Survey of thermodynamic methods to improve the efficiency of coal-fired electricity generation. J Power Energy Proc Inst Mech Eng 2003;217A:63–73. [14] Yasni E, Carrington CG. The role for exergy auditing in a thermal power station. HTD Am Soc Mech Eng 1987;80:101–9. [15] Habib MA, Said SAM, Al-Zaharna I. Optimization of reheat pressures in thermal power plants. Energy—Int J 1995;20:555–65. [16] Habib MA, Said SAM, Al-Bagawi JJ. Thermodynamic performance analysis of the Ghazlan power plant. Energy—Int J 1995;20:1121–30. [17] Gaggioli RA, Yoon JJ, Patulski SA, Latus AJ, Obert EF. Pinpointing the real inefficiencies in power plants and energy systems. Proc Am Power Conf 1975;37:656–70. [18] Taniguchi H, Mouri K, Nakahara T, Arai N. Exergy analysis on combustion and energy conversion processes. Energy 2005;30:111–7. [19] Sengupta S, Datta A, DuttaGupta S. Exergy analysis of a coal based 210 MW thermal power plant. Int J Energy Res 2007;31(1):14–28. [20] Kwak HY, Kim DJ, Jeon JS. Exergetic and thermoeconomic analyses of power plants. Energy 2003;28:343–60. [21] Horlock JH, Young JB, Manfrida G. Exergy analysis of modern fossil-fuel power plants. Trans ASME J Eng Gas Turbines Power 2000;122:1–7. [22] Harvey S, Kane N. Analysis of a reheat gas turbine cycle with chemical recuperation using aspen. Energy Convers Manage 1997;38(15–17):1671–9. [23] Anheden M, Svedberg G. Exergy analysis of chemical looping combustion systems. Energy Convers Manage 1998;39(16–18): 1967–80. [24] Ertesvag IS, Kvamsdal HM, Bolland O. Exergy analysis of a gas turbine combined cycle power plant with precombustion CO2 capture. Energy 2005;30:5–39. [25] Caton JA. On the destruction of availability (exergy) due to combustion processes- with specific application to internal combustion engines. Energy 2000;25:1097–117. [26] Kanoglu M, Isik SK, Abusoglu A. Performance characteristics of a diesel engine power plant. Energy Convers Manage 2005;46: 1692–702. [27] Caton JA. A review of investigations using the second law of thermodynamics to study internal-combustion engines. In: SAE paper no. 2000-01-1081. Society of Automotive Engineers, 2000. [28] Primus RJ, Flynn PF. The assessment of losses in diesel engines using second law analysis. In: Gaggioli RA, editor. Computer-aided engineering of energy systems, AES-vol. 2–3. American Society of Mechanical Engineers, Advanced Energy Systems Division, December, 1986. [29] Alkidas AC. The application of availability and energy balances to a diesel engine. Trans ASME J Eng Gas Turbines Power 1988;110: 462–9. [30] Alkidas AC. The use of availability and energy balances in diesel engines. In: SAE paper no. 890822, Society of Automotive Engineers, 1989. [31] Caton JA. Operating characteristics of a spark-ignition engine using the second law of thermodynamics: effects of speed and load. In: SAE paper no. 2000-01-0952, Society of Automotive Engineers, 2000. [32] Rakopoulos CD, Giakoumis EG. Second law analysis applied to internal combustion engines operation. Prog Energy Combust Sci 2006;32:2–47. [33] Rasul MG, Tanty BS, Mohanty B. Modelling and analysis of blast furnace performance for efficient utilization of energy. Appl Therm Eng 2007;27:78–88. [34] Lior N. Irreversibility in combustion. Invited Keynote Paper. Proc ECOS, 2001, p. 39–48.
ARTICLE IN PRESS 376
S.K. Som, A. Datta / Progress in Energy and Combustion Science 34 (2008) 351–376
[35] Lior N, Sarmiento-Darkin W, Al-Sharqawi HS. The exergy fields in transport processes: their calculation and use. Energy 2006;31: 553578. [36] Borman GL, Ragland KW. Combustion engineering. New York: McGraw-Hill; 1998. [37] Westbrook CK, Dryer FL. Chemical kinetic modeling of hydrocarbon combustion. Prog Energy Combust Sci 1984;10:1–57. [38] Moran MJ, Shapiro HN. Fundamentals of engineering thermodynamics. 4th ed. Singapore: Wiley; 2000. [39] Adebiyi GA. Limits of performance for alternate fuel energy to mechanical work conversion systems. ASME J Energy Resources Technol 2006;128:229–35. [40] Turns SA. An introduction to combustion. 2nd ed. New York: McGraw-Hill; 2000. [41] Datta A, Som SK. Energy and exergy balance in a gas turbine combustor. J Power Energy—Proc Inst Mech Eng 1999;213A:23–32. [42] Hirschfelder JO, Curtiss CF, Bird RB. Molecular theory of gases and liquids. New York: Wiley; 1954. [43] Teng H, Kinoshita CM, Masutani SM, Zhou J. Entropy generation in multicomponent reacting flows. Trans ASME J Energy Resources Technol 1998;120:226–32. [44] Arpaci VS. Radiative entropy production—lost heat into entropy. Int J Heat Mass Transfer 1987;30:2115–23. [45] San JY, Worek WM, Lavan Z. Entropy generation in convective heat transfer and isothermal convective mass transfer. Trans ASME J Heat Transfer 1987;109:647–52. [46] San JY, Worek WM, Lavan Z. Entropy generation in combined heat and mass transfer. Int J Heat Mass Transfer 1987;30:1359–69. [47] Sun ZF, Carrington CG. Application of non-equilibrium thermodynamics in second law analysis. Trans ASME J Energy Resource Technol 1991;113:33–9. [48] Carrington CG, Sun ZF. Second law analysis of combined heat and mass transfer phenomena. Int J Heat Mass Transfer 1991;34:2767–73. [49] Gyftopoulos EP, Beretta GP. Entropy generation rate in a chemically reacting system. ASME J Energy Resources Technol 1993;115: 208–12. [50] Arpaci VS, Selamat A. Entropy production in flames. Combust Flame 1988;73:251–9. [51] Datta A. Entropy generation in a confined laminar diffusion flame. Combust Sci Technol 2000;159:39–56. [52] Datta A. Effects of gravity on structure and entropy generation of confined laminar diffusion flames. Int J Therm Sci 2005;44:429–40. [53] Stanciu D, Isvoranu D, Marinescu M, Gogus Y. Second law analysis of diffusion flames. Int J Appl Thermodynamics 2001;4:1–18. [54] Nishida K, Takagi T, Kinoshita S. Analysis of entropy generation and exergy loss during combustion. In: Proceedings of the 29th symposium (international) of the Combustion Institute, vol. 29, 2002, p. 869–74. [55] Datta A, Leipertz A. Thermodynamic optimization of a laminar diffusion flame. In: Proceedings of first heat transfer fluid mechanics and thermodynamics conference, vol. 1, South Africa, 2002, p. 111–6.
[56] Yapıcı H, Kayatas N, Albayrak B, Basturk G. Numerical calculation of local entropy generation in a methane–air burner. Energy Convers Manage 2005;46:1885–919. [57] Yapıcı H, Kayatas N, Albayrak B, Basturk G. Numerical study on local entropy generation in a burner fueled with various fuels. Heat Mass Transfer 2005;41:519–34. [58] Dash SK, Sengupta SP, Som SK. Transport processes and associated irreversibilities in droplet evaporation. AIAA J Thermo Phys Heat Transfer 1991;5(3):366–73. [59] Hiwase SD, Datta A, Som SK. Entropy balance and exergy analysis of the process of droplet combustion. J Phys D: Appl Phys 1998;31: 1601–10. [60] Dash SK, Som SK. Transport processes and associated irreversibilities in droplet combustion in a connective medium. Int J Energy Res 1991;15(7):603–19. [61] Puri IK. Second law analysis of convective droplet burning. Int J Heat Mass Transfer 1992;35:2571–8. [62] Som SK, Mitra AK, Sengupta SP. Second law analysis of spray evaporation. ASME J Energy Resources Technol 1990;112:130–5. [63] Som SK, Dash SK. Thermodynamics of spray evaporation. J Phys D: Appl Phys 1993;26(4):574–84. [64] Datta A, Som SK. Thermodynamic irreversibilities and second law analysis in a spray combustion process. Combust Sci Technol 1999; 142:29–54. [65] Datta A. Hydrodynamics of swirl spray atomizer and thermal dynamics of gas turbine combustion. PhD thesis, Indian Institute of Technology, Kharagpur 1998. [66] Som SK, Sharma NY. Energy and exergy balance in the process of spray combustion in a gas turbine combustor. ASME J Heat Transfer 2001;124:828–36. [67] Smoot LD. A decade of combustion research. Prog Energy Combust Sci 1997;23:203–32. [68] Smoot LD. Modeling of coal combustion processes. Prog Energy Combust Sci 1984;10:229–72. [69] Som SK, Mandal SS, Dash SK. Energy and exergy balance in the process of pulverized coal combustion in a tubular combustor. ASME J Heat Transfer 2005;127:1322–33. [70] Prins MJ, Ptasinski KJ. Energy and exergy analyses of the oxidation and gasification of carbon. Energy 2005;30:982–1002. [71] Kim C, Lior N. Combined-mode conjugate heat transfer in a radiatively/conductively stabilized pulverized coal combustor. ASME paper 93-WA/HT-37, ASME winter annual meeting, New Orleans, LA, 1993. [72] Kim C, Lior N. A numerical analysis of NOx formation and control in radiatively/conductively stabilized pulverized coal combustors. J Chem Eng 1998;71:221–31. [73] Daw SC, Chakravarthy K, Conklin CJ, Graves RL. Minimizing destruction of thermodynamic availability in hydrogen combustion. Int J Hydrogen Energy 2006;31:728–36.
