204 Int. J. Exergy, Vol. 5, No. 2, 2008

Copyright © 2008 Inderscience Enterprises Ltd.

Exergy analysis of SI engines

İsmet Sezer and Atilla Bilgin* Mechanical Engineering Department, Karadeniz Technical University, 61080 Trabzon, Turkey Fax: +9 0462 325 55 26 E-mail: isezer@ktu.edu.tr E-mail: bilgin@ktu.edu.tr *Corresponding author

Abstract: In this study, exergy (availability) analysis of a Spark Ignition (SI) engine has been performed theoretically during compression, combustion and expansion processes of the engine cycle. For this purpose, a thermodynamic-based engine cycle model is developed without considering the geometric features of fluid motion. Through the analysis, the effects of changing some design and operating parameters, such as compression ratio, fuel-air equivalence ratio and spark timing on the variation and destruction of exergy have been investigated. It was obtained that design and operation conditions have considerable effects on the variation of exergy and irreversibilities during investigated parts of the cycle.

Keywords: spark ignition engine; thermodynamic-based modelling; the second law of thermodynamics; exergy analysis; availability; irreversibility.

Reference to this paper should be made as follows: Sezer, İ. and Bilgin, A. (2008) ‘Exergy analysis of SI engines’, Int. J. Exergy, Vol. 5, No. 2, pp.204–217.

Biographical notes: İsmet Sezer graduated from the Mechanical Engineering Department of Karadeniz Technical University (KTU), Trabzon, Turkey in 1997. He is presently pursuing his PhD and his Thesis is on the Exergetic Analysis of the SI engine cycle.

Atilla Bilgin graduated from the Mechanical Engineering Department of Karadeniz Technical University (KTU), Trabzon, Turkey in 1985. He received his PhD from KTU in 1994. His PhD thesis was on the numerical (CFD) Modelling of the Flow in an Engine Cylinder. His current research interests include thermodynamic modelling of the internal combustion engine cycles, alternative fuels and combustion.

1 Introduction

Thermodynamic models of engine cycles are useful tools because of its results in reduction in time and costs. These models have been commonly used since the early 1960s for analysis of engine performance and investigation of the effects of various parameters on it. Most of the earlier studies were based only on the use of the first law of thermodynamics. However, in the last two decades, it has been clearly understood that

Exergy analysis of SI engines 205

the first law of thermodynamics alone is not capable of providing a suitable insight into the engine operations (Caton, 2002; Rakopoulos and Giakoumis, 2006). For this reason, the interest in the use of the second law of thermodynamics has been intensified in the field of Internal Combustion Engines (ICEs). Analysis of a process or a system in terms of the second law of thermodynamics is termed exergy or availability analysis. The application of exergy analysis for engineering systems proves to be very useful because it provides quantitative information about irreversibilities and exergy losses in the system. In this way, the thermodynamic efficiency can be quantified, poor efficiency areas can be identified, and thus processes can be designed and operated to be more efficient (Moran and Shapiro, 2000). Therefore, exergy analysis is a suitable tool for researchers to investigate processes and systems. On the other hand, there are still a few works on exergy analysis of ICEs in the existing literature. One of the earliest studies was a brief report presented by Trapuel (1957). Patterson and van Wylen reported another early work on this topic in 1964 (Caton, 2000a). In the 1980s, a group of more detailed investigations were reported on the use of second law analysis for ICEs (Flynn et al., 1984; Alkidas, 1988; Kumar et al., 1989; Shapiro and van Gerpen, 1989). The work by Alkidas was different from the other investigations because he defined the thermodynamic system as being outside the engine cylinder. The investigations on exergy analysis have been continued with increasing in the field of ICEs in recent years (Bozza et al., 1991; Gallo and Milanez, 1992; Rakopoulos, 1993; Rakopoulos and Giakoumis, 1997a, 1997b; Alasfour, 1997; Caton, 1999a, 2000a, 2000b).

In this study, exergy analysis was performed for the compression, combustion and expansion phases of an SI engine cycle. A two-zone thermodynamic-based combustion model was developed for this purpose. The details of the model and analysis were given in the following sections.

2 Thermodynamic model

The most important part of the engine cycle model is the combustion phase. In general, there are two types of thermodynamic-based approximations for modelling of combustion in SI engines. The first is the finite heat release model, in which the heat release rate is modelled as empirical equations such as cosine or Wiebe functions. The second is the mass fraction burned model, in which burned mass fraction is calculated in conjunction with an appropriate flame propagation model.

In this study, the first of the above models was used and the heat release rate was determined by using the cosine burn rate formula, which is given in equation (1)

s( )1 1 cos .2

bb

b

mx

mπ θ θ

θ − = = − ∆

(1)

Simulation starts at Bottom Dead Center (BDC) at the beginning of compression stroke and ends at the end of the expansion stroke at BDC. The cylinder content is assumed to be a homogenous unburned mixture of fuel, air and residual gases during the compression stroke while it consists of only burned gases during the expansion stroke. The composition of the unburned mixture during the compression period does not change significantly, and it is sufficiently accurate to assume that it is frozen or unchanged. The combustion products are also assumed to be in chemical equilibrium during the

206 İ. Sezer and A. Bilgin

combustion and expansion periods. The composition and thermodynamic properties of gas mixtures throughout the compression and combustion periods are calculated by using FORTRAN subroutines Fuel-Air-Residual Gas (FARG) and Equilibrium-Combustion-Products (ECP), respectively, developed originally by Ferguson (1985). These subroutines use least-squares polynomials fitted to the tabulated JANAF data to give expressions for the thermodynamic properties of species, such as specific heat, enthalpy and entropy depend on temperature.

Through the simulation, the cylinder pressure, burned and unburned gas temperatures, work output, heat loss and enthalpy loss are calculated by numerically integrating the differential equations simultaneously. These equations are given below in a closed form.

1d ( , , , )d b u

p f p T Tθθ

= (2)

2d

( , , , )d

bb u

Tf p T Tθ

θ= (3)

3d

( , , , )d

ub u

Tf p T Tθ

θ= (4)

4d ( , )dW f pθθ

= (5)

5d ( , , , )d

Lb u

Q f p T Tθθ

= (6)

6d ( , , , ).d

Lb u

H f p T Tθθ

= (7)

The thermodynamic details of the current cycle model can be seen in Altin (2004). Normally, burn duration is input data for heat release models. But, in this study, burn durations for various design and operation parameters are determined by using empirical correlations to perform more realistic calculations. These correlations are as in equations (8)–(12) (Bayraktar and Durgun, 2004).

11

21( ) 3.2989 3.3612( / ) 1.0800( / )c c c c cc r r r r r= − + (8)

22 1 1( ) 0.1222 0.9717( / ) 0.05051( / )c n n n n n= + − (9)

23 1 1( ) 4.3111 5.6383( / ) 2.3040( / )c φ φ φ φ φ= − + (10)

1 1

24 ( ) 1.0685 0.2902( / ) 0.2545( / )s s s s sc θ θ θ θ θ= − + (11)

11 2 3 4( , , , ) ( ) ( ) ( ) ( ) .b c s c s br n c r c n c cθ φ θ φ θ θ∆ = ∆ (12)

Here, 1

∆ bθ is known as combustion duration for 1c

r , n1, φ1, 1sθ . These operating

conditions were taken as; 1

7.5,cr = n1 = 1000 rpm, 1φ = 1.0, 1

30 CA,sθ = − ° and for these conditions

1∆ 24 CA.bθ = ° Computed burn durations for various operating conditions are

given in Table 1.

Exergy analysis of SI engines 207

Table 1 Effects of various operating conditions on burn durations

rc φ θs (°CA) n (rpm) f ∆θb (°CA)

8 0.8 –45 1500 0.0 65 10 1.0 –35 2000 0.1 46 12 1.2 –25 2500 0.2 43

3 Exergetic calculations

3.1 Exergy concept

Exergy (or availability) is defined as the maximum theoretical work that can be obtained from a combined system (combination of a system and its environment) when the system comes into equilibrium (thermally, mechanically and chemically) with the environment (Zhang, 2002). The maximum available work from a closed system emerges as the sum of two contributions: thermomechanical exergy (Atm) and chemical exergy (Ach) (van Gerpen and Shapiro, 1990). Thermomechanical exergy is defined as the maximum work extractable from the combined system, as the system comes into thermal and mechanical equilibrium with the environment, and it is given as in equation (13)

0 0 ,tm o i ii

A E p V T S mµ= + − −∑ (13)

where E = U + Ekin + Epot, V and S are the total (internal, kinetic and potential) energy, volume and entropy of the system contents; mi and µ 0,i are the mass and chemical potential of species i calculated at restricted dead state conditions, and p0 and T0 are the fixed pressure and temperature of the environment. At the restricted dead state conditions, the system is in thermal and mechanical equilibrium with the environment and no work potential exists between the system and environment due to temperature and pressure differences. But the system does not reach the chemical equilibrium with the environment, because the contents of the system are not permitted to mix with the environment or enter into chemical reaction with environmental components (Zhang, 2002). In principle, the difference between the compositions of the system at the restricted dead state conditions and that of the environment can be used to obtain additional work, in order to reach chemical equilibrium. The maximum work obtained in this way is called as chemical exergy, given as in equation (14)

00,( )ch i i i

i

A mµ µ= −∑ (14)

where, 0iµ is the chemical potential of species i calculated at true dead state conditions.

Thus, the true dead state conditions are the conditions in which the system is in thermal, mechanical and chemical equilibrium with the environment.

By using equations (13) and (14), the total exergy (A) can be calculated as 0

0 0 .tm ch i ii

A A A E p V T S mµ= + = + − −∑ (15)

208 İ. Sezer and A. Bilgin

3.2 Application to the engine cylinder

Exergy balance equation for the engine cylinder in differential form on a crank angle basis is given in equation (16)

42 315

00 , tot

dd d d d1 .d d d d d

f bf ch

mT xA Q W Vp a IT mθ θ θ θ θ

= − − − + − (16)

The first term in equation (16) is the rate of change in the total exergy of cylinder contents. The second term represents exergy transfer with heat. The third term shows exergy transfer by means of indicated work transfer, where dV/dθ is the rate of change of cylinder volume with crank angle. The fourth term corresponds to the burned fuel exergy, where mf and m are the masses of fuel and total cylinder contents, respectively, and af,ch is the fuel chemical exergy. In this study, the fuel is gasoline (C7H17) and af,ch = 47870 kJ/kg (Ferguson, 1985). The last term in the equation illustrates exergy destruction in the cylinder due to combustion and heat transfer. It is calculated as:

0tot genI T S= (17)

where, genS is the rate of entropy production in the cylinder due to irreversibilities. It is calculated by using second law of thermodynamics (entropy balance) in accordance with the two-zone combustion model:

( )d d ( )d d

b ugen b b u u

b u

Q QS m s m sT Tθ θ

= + + + (18)

where, mb and mu are burned and unburned masses of the cylinder contents, sb and su are entropy values of the burned and unburned gases, Qb and Qu are heat losses from burned and unburned gasses, and Tb and Tu are temperatures of the burned and unburned gas zones, respectively.

3.3 The first and second law efficiencies

The efficiency is defined in order to be able to compare different engine size applications or evaluate various improvement effects from the perspective of either the first or the second law (Rakopoulos and Giakoumis, 2006). By the first law (or energy-based), efficiency is defined as:

ILHV

indEnergy out (as work)Energy in f

Wm Q

η = = (19)

where, Wind is indicated work output and QLHV = 44510 kJ/kg is lower heating value of gasoline.

Various second law efficiencies (exergetic or availability efficiency, or effectiveness) have been defined in the literature. In this study the following definition is used for second law efficiency:

IIind ind

max ind

Exergy out (as work)= = = .Maximum extractable exergy (as work) +

W WW W I

η (20)

Exergy analysis of SI engines 209

The second law efficiency gives a finer understanding of performance than the first law efficiency. Moreover, the second law efficiency stresses both exergy transfer losses and internal exergy destruction due to the need of dealing with irreversibilities to improve performance (Zhang, 2002).

4 Results and discussions

Once the thermodynamic conditions of the cylinder contents have been determined for any crank angle during the cycle, then the terms in the exergy balance equation can be easily determined simultaneously. Figure 1 shows variations of the mentioned terms and total cylinder exergy (atot) during the investigated part of the cycle for the selected base conditions. As can be seen in this figure, thermomechanical exergy (atm) increases gradually during the first part of the compression stroke up to the start of combustion, while fuel chemical exergy (af,ch) remains constant. During this process, increase in the thermomechanical exergy is related directly to the work transfer (aw) into the system, which is shown in the figure as a symmetrical variation in the thermomechanical exergy with a negative sign. Since there are no remarkable irreversibilities (i) due to a negligible level of heat transfer, the variation in the total cylinder exergy directly reflects the behaviour of the thermomechanical exergy variation. With the start of combustion, at a crank angle of –35° Before Top Dead Center (BTDC), chemical exergy of the fuel decreases rapidly due to the conversion to heat. According to this conversion, i.e., combustion of fuel, temperature and pressure increase in the cylinder, which results in a steep increase in the thermomechanical exergy. Increase in temperature also be caused by increase in exergy transfer from the cylinder’s contents to the walls by means of heat transfer (aQ). Both heat transfer and, especially, combustion give a rapid increase in irreversibilities. Combination of all the mentioned effects results in a steep decrease in total exergy during the combustion phase of the cycle as shown in the figure Combustion ends at a crank angle of 25 degrees after top dead centre (ATDC) while the expansion process continues until the piston reaches the BDC. During this last part of the cycle, decrease in atot continues due to the extracted work and heat transfer, while irreversibilities stand almost at a constant level.

Figure 2 shows the effects of varying compression ratios on exergy variations. Variation of compression ratio has little effect on exergy transfer with heat, which is seen only during the expansion (including combustion) period. The increase in compression ratio increases exergy transfer with work during both compression and expansion period. This is due to the increases in cylinder pressure and temperature with increasing compression ratio. The increase in temperature also results in decrease in irreversibilities as reported in the literature (Caton, 1999b). However, the rises in temperature and pressure cause an increase in thermomechanical exergy during combustion. On the other hand, less exergy is exhausted at end of the expansion period because more exergy is transferred from the system as work with increasing compression ratio. Fuel chemical exergy curves are getting steeper due to faster burning with increasing compression ratio.

210 İ. Sezer and A. Bilgin

Figure 1 Typical variations of the exergetic terms in the balance equation with respect to crank angle

Figure 2 Effects of compression ratio on exergetic terms in balance equation

(a) (b)

(c) (d)

Exergy analysis of SI engines 211

Figure 2 Effects of compression ratio on exergetic terms in balance equation (continued)

(e) (f)

Figure 3 shows the effects of varying spark timing on various terms of exergy balance equation. If ignition is started too early, according to fuel chemical exergy variation, there will be too much thermomechanical exergy rise before the end of compression stroke, which cause increase in exergy transfer to the system as compression work. This is a waste of exergy and does not contribute to the exergy output as work. In addition to this, earlier start of combustion results in increase in exergy transfer from the cylinder contents to the walls, with heat transfer due to the extending of the contact duration of hot gases with the cylinder walls. Conversely, if ignition is started too late, increase in thermomechanical exergy is reduced due to the decrease in peak values of pressure and temperature of cylinder contents during combustion. This also causes reduction in the extracted exergy from the system as work during the expansion process. As shown in the figure, there is no significant effect on the total irreversibility by varying the spark advance. Therefore, ignition timing has to be optimised to give the least exergy transfer by means of heat and to extract maximum exergy during the expansion as work.

Figure 3 Effects of spark timing on exergetic terms in balance equation

(a) (b)

212 İ. Sezer and A. Bilgin

Figure 3 Effects of spark timing on exergetic terms in balance equation (continued)

(c) (d)

(e) (f)

Figure 4 shows the effects of fuel-air equivalence ratio on terms of exergy during compression, combustion and expansion strokes. The maximum exergy transfers associated with heat and work occur for an equivalence ratio of 1.0 while they decrease to lesser values for both the lean mixture (equivalence ratio of 0.8) and the rich mixture (equivalence ratio of 1.2). This is because the stoichiometric mixture (equivalence ratio of 1.0) gives the maximum flame temperature and cylinder pressure as compared to rich or lean mixtures. Differently from exergy transfers, irreversibilities have maximum values for an equivalence ratio of 1.2 and they decrease for stoichiometric and lean mixtures. This is directly related to the entropy generation by combustion. As the fuel-air mixture gets leaner, combustion occurs completely which results in a decrease in irreversibilities. There is a gradual increase in thermomechanical availability until the spark timing, and variation of equivalence ratio has no effect on variation of thermomechanical exergy along this stage of cycle. Then a steep variation takes place with the advent of combustion, and thermomechanical exergy reaches a maximum value for the equivalence ratio of 1.0 during combustion and expansion. Closer but somewhat lower values than those of stoichiometric mixtures are obtained with rich mixtures while

Exergy analysis of SI engines 213

lean mixtures give considerably lower thermomechanical exergy values. These variations can be explained by the fact that increased exergy contribution for rich mixtures by excess fuel cannot be converted to work due to incomplete combustion and the reduced cylinder pressures and temperatures appear for lean mixtures due to fuel deficiency. Thus, the stoichiometric mixture gives the maximum thermomechanical exergy values. Enriching of the fuel-air mixture increases the chemical exergy of the cylinder content, but, as mentioned above, excess fuel, which more than what is required for the stoichiometric mixture, cannot be converted to useful work and the remaining fuel is wasted with the exhaust. The main contribution to variations of total exergy is supplied by the fuel chemical exergy during the compression period while both thermomechanical exergy and fuel chemical exergy dominate the rest of the cycle.

Figure 4 Effects of equivalence ratio on exergetic terms in balance equation

(a) (b)

(c) (d)

214 İ. Sezer and A. Bilgin

Figure 4 Effects of equivalence ratio on exergetic terms in balance equation (continued)

(e) (f)

Figure 5 shows the variation of the first and second law efficiencies, depending on compression ratio, spark timing and equivalence-ratio, respectively. Variations of first and second law efficiencies are usual and similar in trend for compression ratio and spark advance. But variations for the equivalence ratio are different in character. That is, the first law efficiency increases with decreasing equivalence ratio while the second law efficiency reaches a maximum at about the equivalence ratio of 1.0. Variation of the second law efficiency is suitable for the exergetic variations in Figure 4. On the other hand, variation of the first law efficiency with respect to equivalence ratio is also suitable for the definition of the first law efficiency. Decrease in equivalence ratio, i.e., leaning of the fuel-air mixture beyond the stoichiometric mixture, results in increase in combustion efficiency, which causes a maximum in the lean region (Alasfour, 1997).

Figure 5 Variations of the first and second law efficiencies with respect to: (a) compression ratio; (b) spark advance and (c) equivalence ratio

(a) (b) (c)

5 Conclusions

In order to investigate the compression, combustion and expansion processes of a spark-ignition engine from a second law perspective, a thermodynamic-based cycle

Exergy analysis of SI engines 215

model was developed in the presented study. By using this model, the effects of some important design and operating conditions, such as compression ratio, fuel-air equivalence ratio and spark timing, on the variation of exergy transfers between cylinder contents and the environment, and irreversibilities have been investigated during the mentioned part of the cycle. The total exergy of the cylinder contents is divided into two components as thermomechanical and chemical exergy, to determine the contribution of each one on the variation of total exergy over the investigated processes.

The following general conclusions have been drawn from the results of the study:

• A parametric exergetic analysis provides a better understanding of interactions between some design and operating conditions, and energy conversion and transfer processes; permits the revelation of the magnitude of work potential lost during the cycle in a more realistic way than the first law analysis can; and points to several possible ways for improving engine performance.

• Increasing the compression ratio results in increase in the first and second law efficiencies due to the increase in combustion speed and extracted work during the expansion, and decrease in irreversibilities.

• Variation of spark timing affects the efficiencies mainly by means of the variation of the location of the maximum, and the magnitude of the thermomechanical exergy, and changing the duration of exergy transfer via heat transfer.

• Fuel-air equivalence ratio has significant effects on the variation of the chemical and thermomechanical exergy evolution, and variation of irreversibilities. The largest thermomechanical exergy value is obtained for the stoichiometric mixture. Enriching of the fuel-air mixture beyond the stoichiometric mixture does not make any contribution to the extracted useful exergy as work output, while leaning of the mixture results in decrease in irreversibilities.

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Nomenclature

A Availability, exergy (J) a Specific availability, exergy (J/kg) CA Crank Angle c Correlation coefficient E Total energy f Residual gas fraction H Enthalpy (J)

Exergy analysis of SI engines 217

I Irreversibility (J) i Specific irreversibility (J/kg) m Mass (kg) n Engine speed (rpm) p Pressure (bar) Q Heat (J) QLHV Lower heating value of fuel (J/kg) rc Compression ratio S Entropy (J/K) SI Spark ignition s Specific entropy (J/kg K) T Absolute temperature (K) U Internal energy (J) V Volume (m3)

W Work (J) xb Burned mass fraction Greek letters

φ Equivalence ratio

θ Crank angle (deg)

θs Spark timing angle (deg)

∆θb Burn duration (deg)

ηI First law efficiency (%)

ηII Second law efficiency (%)

µ0 Chemical potential

Subscripts 0 Restricted dead state b Burned ch Chemical com Combustion f Fuel gen Generation, production ind Indicated L Lost max Maximum tm Thermomechanical tot Total u Unburned