Theoretical Investigation Of Flame Propagation Process In An Si Engine Running On Gasoline–ethanol Blends

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Renewable Energy 32 (2007) 758–771 www.elsevier.com/locate/renene

Theoretical investigation of flame propagation process in an SI engine running on gasoline–ethanol blends Hakan Bayraktar Mechanical Engineering Department, Faculty of Engineering, Karadeniz Technical University, Trabzon 61080, Turkey Received 5 October 2005; accepted 26 March 2006 Available online 24 May 2006

Abstract Turbulent flame propagation process in a spark-ignition (SI) engine is theoretically investigated. Fueling with gasoline, ethanol and different gasoline–ethanol blends is considered. A quasidimensional SI engine cycle model previously developed by the author is used to predict the thermodynamic state of the cylinder charge during the cycle. The flame is assumed to be spherical in shape and centered at the spark plug. Computations are carried out for an automobile SI engine having a disc-shaped combustion chamber, for which the compression ratio and the nominal speed are 9.2 and 5800 rpm, respectively. Geometrical features (flame radius, flame front area and enflamed volume) of the flame, combustion characteristics (mass fraction burned and burn duration), and cylinder pressure and temperature are predicted as a function of the crank angle. Three different positions of the crank angle are studied: 101, TC and +101. It was concluded that ethanol addition to gasoline up to 25 vol% accelerated the flame propagation process. r 2006 Elsevier Ltd. All rights reserved. Keywords: Faster burning; Spherical flame; Gasoline–ethanol blends

1. Introduction Combustion is the most important process taking place in spark-ignition (SI) engines, through which chemical energy of fuel is converted into sensible internal energy of the Tel.: +90 462 3773149.

E-mail address: [email protected]. 0960-1481/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.03.017

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Nomenclature a Af (F/A)s LHV lt m mb me Sl TC Ut V Xb XE

distance between centers of flame sphere and cylinder (mm) area of spherical flame front (m2) stoichiometric fuel–air ratio (dimensionless) lower heating value (MJ kg1) characteristic length scale of turbulent flame (m) mass (kg) burned mass (kg) mass entrained by the flame front into the flame zone (kg) laminar flame speed (m s1) top center characteristic turbulent speed (m s1) instantaneous cylinder volume (m3) mass fraction burned (dimensionless) volume percentage of ethanol in the blend (%)

Greek letters e f y r tb

compression ratio (dimensionless) fuel-air equivalence ratio (dimensionless) crank angle (deg) density (kg m3) characteristic reaction time to burn an eddy of size lt (s)

Subscripts b bl E F f G s u

burned gases blend pure ethanol conditions at the end of flame propagation process flame gasoline stoichiometric unburned gases

cylinder charge [1]. During this process, a turbulent flame,which is a roughly spherical in shape, propagates across the combustion chamber and burns the premixed fuel–air mixture [2,3]. Therefore, combustion can be considered as a turbulent flame propagation process. Details of the flame propagation have substantial effect on combustion, and therefore on energy conversion process [4]. If the flame propagation becomes faster, i.e. faster burning is achieved, more efficient engine operation can be obtained. Faster burning can reduce engine knock, because there would be less time for spontaneous ignition to develop. Reduced knock can lead to operation with higher compression ratios and with leaner mixtures; thus, higher efficiency, higher power output

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and more stable engine operation could be obtained [5]. Furthermore, improved combustion and operation with leaner mixtures may also reduce hydrocarbon emissions from the engine. Two methods are commonly suggested for faster burning. The first is to generate a more turbulent charge motion via the use of intake flow restrictions or combustion chambers with large ‘‘squish’’ regions [6]. The second is to increase the flame front area by minimizing the contact between the flame and chamber walls. This requires using a more compact (small surface-to-volume ratio) combustion chamber and moving the spark plug electrodes toward the chamber center [7]. It is obvious that such methods necessitate some modifications on intake system and combustion chamber design. However, using fuels such as hydrogen [8] and alcohols [9], which have higher octane number and higher flame speeds compared to conventional gasoline, could allow operation with higher compression ratios without any modification on engine design and fuel system. Among the various alcohols, ethyl alcohol is suggested as the most suited one for use in SI engines [10]. It can be produced from renewable energy resources, such as agricultural feedstocks, and it has some relevant properties, such as high knock resistance, high flame speed and low stoichiometric air–fuel ratio [9–11]. Ethanol can be used in SI engines as pure fuel or as gasoline–ethanol blends. Although using it alone requires some modifications on engine design and fuel system [12,13], it can be used without any modification by blending with gasoline at appropriate proportions [14,15]; the engine performance and exhaust emissions can be improved by this way [15–19]. The purpose of this study is to theoretically investigate turbulent flame propagation process in an SI engine fueled with gasoline, ethanol and various gasoline–ethanol blends using a quasi-dimensional SI engine cycle model previously developed by the author [15,19]. The variations of geometrical features of the spherical flame, burned mass fraction, combustion duration, and cylinder pressure and temperature are determined depending on the crank angle for each fuel and different blends. 2. SI engine cycle simulation 2.1. Cycle model The SI engine cycle model previously developed by the author [15] is used to predict the thermodynamic state of the cylinder charge throughout the cycle. The governing equations of this model have been derived by applying the first law of thermodynamics on cylinder charge, which are time-dependent first-order ordinary differential equations. In this model, cylinder charge is considered as an ideal gas mixture. During intake and compression, cylinder content is regarded as a non-reacting ideal gas mixture of air, fuel vapor and residual burned gases. Throughout the combustion, the cylinder is considered to consist of two thermodynamic regions which are separated by a thin spherical flame front: the unburned-gas region and the burned-gas region. During expansion, only burned gases are assumed to exist in the cylinder. In both the combustion and the expansion, composition of the burned gases is determined by considering the chemical equilibrium. For more detailed information on the SI engine model, readers are referred to Refs. [1,15,19,20]. 2.2. Combustion model The combustion model used here is originally based on the model developed by Blizard and Keck [21], and later extended by Keck [22] and the author [15,20]. The burning of

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cylinder charge is considered as a turbulent flame propagation process. Throughout this process, unburned eddies of radius lt are entrained into the flame zone at the entrainment velocity Ue (which is taken as sum of the characteristic speed Ut and laminar flame speed Sl), and then burned at the laminar flame speed Sl in a characteristic time tb ¼ lt/Sl. Combustion is described by the following set of ordinary differential equations: _ e ¼ ru Af ðU t þ S l Þ, m _ b ¼ ru Af S l þ m

ðme  mb Þ , tb

(1) (2)

where the dots denote the differentiation with respect to time t or the crank angle y. These equations are coupled with the thermodynamic cycle model mentioned above. The following assumptions, which are essentially based on the experimental observations [2–5,8,22] are made. During the early stage of the combustion, the ignition delay period, the expansion speed of the flame front is close to that of laminar flame [3,8,22] and therefore, laminar combustion is assumed (Ut ¼ 0; me ¼ mb). After this period, the main stage of combustion starts and the flame becomes turbulent due to the interaction with incylinder flow field [4]. In this case, instantaneous values of Ut and lt are determined using empirical correlations given by Keck [22]. Experimental findings have also suggested that combustion continues after all the charge in the chamber has been fully entrained into the flame front [4,22]. This stage of combustion is approximated by the following exponentially decreasing burning rate: _b m ¼ eðyyF Þ=tb . _ bF m

(3)

In all the cases, the instantaneous specific volumes of the unburned and burned gases, and corresponding densities, are supplied from the thermodynamic model. The flame front area is calculated from the geometric sub-model whose details are given below, and the laminar flame speed Sl is determined using correlations for isooctane, ethanol and isooctane–ethanol blends given by Gu¨lder [9] and Bayraktar [15,19]. At any crank angle, geometrical features of the spherical flame are determined as follows. The total enflamed volume Vf can be determined using the known values of mb, me, and ru: Vf ¼ Vb þ

me  mb . ru

(4)

The sphere radius Rf corresponding to this volume is determined by means of Newton–Raphson iteration method. The initial value of Rf is chosen approximately. At any iteration step, the flame front area Afi and enflamed volume Vfi for a given Rfi are calculated from the following geometric model. The calculation method applied here is similar to that given in Refs. [6,21,23] and is described in detail by the author in Ref. [15]. The spherical flame within a disc-shaped combustion chamber is illustrated schematically in Fig. 1. The chamber is a right circular cylinder of diameter D and variable height h. In calculating the flame geometry, for the case of Rfipa and when the chamber is fully enveloped by the flame, Afi and Vfi can easily be determined. When the flame is at the position shown in Fig. 1, Afi and Vfi are defined

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a

y

Rf

h

flame front

α

β

Fig. 1. Schematic representation of the spherical flame in a disc-shaped combustion chamber.

from the following integrals: Z X Afi ¼ 2ðp  aÞRfi dy,

(5)

0

Z

X

V fi ¼ 0

  D2 ½p  a þ 0:5 sinð2aÞ R2fi  y2 þ ½2b  sinð2bÞ dy, 8

(6)

where variable x varies depending on Rfi (x ¼ Rfi for Rfiph and x ¼ h for other cases), while angles a and b can easily be obtained from the geometric relations. Here, integrals (5) and (6) have been calculated numerically by using the Simpson’s integration method. After Vfi is determined in this fashion, it is compared with its exact value calculated from Eq. (4). If there exists an acceptable agreement between Vf and Vfi, Rf is taken as Rfi and iteration is terminated; otherwise, Rf is estimated again as follows: Rf iþ1 ¼ Rfi 

Vf  Vf i . Af i

(7)

Rfi is taken as Rfi+1 and the above procedure is repeated until convergence is achieved. Once Rf is determined, exact value of the flame front area for this radius can be calculated from the geometric model given above.

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2.3. Numerical solution procedure During the entire cycle computation, Eqs. (1)–(3) are solved in conjunction with the thermodynamic cycle model. The combustion calculation is started at the spark angle before TC toward the end of the compression stroke. The first approximation to the mass fraction burned and the mass burning rate is obtained by using the cosine burn rate formula [15]. The initial value of the burned gas temperature is determined as the adiabatic flame temperature [15]. After the combustion calculation is started, the mass of burned gas, the cylinder pressure, and temperatures of the burned and unburned gases are determined assuming two thermodynamic regions to exist in the combustion chamber. At each calculation step, thermodynamic properties, such as specific volumes of burned and unburned gases, and corresponding densities, are supplied from the thermodynamic model. After calculating the instantaneous enflamed volume from Eq. (4), the geometrical properties of the flame are obtained from the geometric sub-model given above. During early stage of combustion (the ignition delay period), laminar-like burning is assumed and this process is considered to continue along the time for burning an eddy of radius lt. After the ignition delay period is terminated, Eqs. (1) and (2) are solved regarding the fully developed flame propagation process. When the enflamed volume Vf equals that of total chamber volume, the final stage of the combustion initiates and the mass burning rate is calculated from Eq. (3). The combustion calculation is completed when 99% of the total mass within the cylinder is burned. In this model, governing equations have been numerically integrated by using the Euler–Predictor–Corrector method taking the crank angle increments as 11 [15]. 3. Numerical applications In this section, initially the accuracy and the validity of the presented model are verified. Numerical applications have been performed for an automotive SI engine with a discshaped combustion chamber. The geometric specifications of this engine are: the bore D ¼ 86.4 mm, the stroke H ¼ 67.4 mm, the distance between the spark plug and the chamber center a ¼ 14.44 mm and the compression ratio e ¼ 9.2. All the computations have been carried out for the nominal speed nN ¼ 5800 rpm and fuel–air equivalence ratio for gasoline-fuelled engine fG and the spark advance ys at this speed are taken as 1.15 and 281, respectively. The molecular formula of gasoline is assumed to be C7H17 and the values of (F/A)sG, LHVG and rG for this fuel are in turn taken as 0.0659, 44 MJ kg1 and 0.690 g cm3. The values of (F/A)E, LHVE and rE for the pure ethanol (C2H5OH) are taken as 0.1111, 27 MJ kg1 and 0.785 g cm3, respectively. Calculations have been performed for gasoline, ethanol and gasoline-ethanol blends containing 2, 4, 6, 8, 12, 25, 50 and 75 vol% ethanol. The properties of the blends, such as the stoichiometric fuel–air ratio, the lower heating value and the density, are calculated based on the concentrations of gasoline and ethanol as in Ref. [19]. The fuel–air equivalence ratios for different blends have been determined from the following formula given by Bayraktar [15,19]: rffiffiffiffiffiffi ðF =AÞsG rbl fbl ¼ fG . (8) ðF =AÞsbl rG The values of fbl calculated for different blends under consideration are shown in Fig. 4.

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3.1. Validity of the combustion model and the geometrical flame propagation model The accuracy of the computer model is verified by comparing the predicted results with those given in Refs. [7,21]. Fig. 2 compares the predicted dimensionless flame front area Af/D2 versus dimensionless flame radius Rf/D with that given by Poulos and Heywood [7]. Fig. 3 compares the variation of the burned mass fraction by the crank angle with that given by Blizard and Keck [21]. As seen, there exists a good agreement.

0.45 Ref. [7] Model a = 40 mm  = 8.5

Af / D2

0.30

0.15

0.00 -0.2

0.0

0.2

0.4

0.6

0.8

Rf /D Fig. 2. Comparison of the predicted dimensionless flame front areas with those given in literature.

1.0 Ref. [21] Mass fraction burned, Xb

0.8

0.6

Model a = 21 mm =5 n = 2100 rpm s =-30°

0.4

0.2

0.0 -40

-20

0 Crank angle, deg.

20

40

Fig. 3. Comparison of the predicted mass fraction burned with those given in literature.

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3.2. Comparison and discussion of the predicted results The fuel–air equivalence ratios of different blends under consideration were determined by means of Eq. (8) and variation of fbl with XE is plotted in Fig. 4. This figure clearly indicates that ethanol addition to gasoline leads to leaner operation. As shown, fbl approaches unity as the proportion of ethanol closes to 25 vol%. Therefore, combustion may become more complete or more stoichiometric at this blending ratio. Consequently, improvements in combustion characteristics may be anticipated. Results predicted for gasoline, ethanol and various gasoline–ethanol blended fuels are compared in Figs. 5–14. The flame radii and the flame front areas predicted for gasoline, ethanol and different blends are compared in Figs. 5 and 6, respectively. As shown, during 1.2 G = 1.15

1.1

 bl

1.0

0.9

0.8

0.7 0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 4. Fuel–air equivalence ratio as a function of ethanol concentration in the blend.

100  = -10°;

Flame radius, mm

80

TC;

 = +10°

60 40 20 0 -20

0

20

40 60 80 Volume percentage of ethanol, %

100

Fig. 5. Comparison of flame radii computed for different blends.

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15  = -10°;

TC;

 = +10°

Af x10-2, mm2

12

9

6

3

0 0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 6. Comparison of flame front areas computed for different blends.

8  = -10°;

TC;

 = +10°

Vf x 10-4, mm3

6

4

2

0 0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 7. Comparison of the enflamed volumes.

the initial burning phase or ignition delay period (around y ¼ 101), the flame size is not considerably affected by the fuel type. However, after this period (i.e. along the faster burning phase and at the final stage of combustion), ethanol addition to gasoline has noticeable influence on the flame geometry. At TC and 10o after TC, ethanol addition to gasoline up to 25% increases the flame radius. The flame front areas predicted at y ¼ 101 and TC increase up to 25% ethanol. As seen from Fig. 1, as the flame grows, it is intersected by the chamber walls, due to which the flame front area gradually decreases while the enflamed volume increases. This is clearly shown in Figs. 6 and 7. In both figures, 101 after TC, which corresponds to nearly the last stage of combustion, Af decreases and Vf increases as the ethanol proportion approaches 25%. Decrease in Af is a result of faster flame propagation. Namely, the flames of the gasoline–ethanol blends make contact with the cylinder walls earlier than those of gasoline alone. Briefly, it can be concluded that the

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Mass fraction burned, Xb

1.0 Gasoline

0.8

E06 E12

0.6

E25 E50

0.4

E75 Ethanol

0.2

0.0 -40

-20

0

20 40 Crank angle, deg.

60

80

Fig. 8. The effect of ethanol concentration on the mass fraction burned.

0.5  = -10°;

TC;

 = +10°

Mass fraction burned, Xb

0.4 0.3 0.2 0.1 0.0 0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 9. The effects of ethanol concentration on mass fractions burned computed at different piston positions.

growth of the flame becomes faster when gasoline–ethanol blends containing ethanol up to 25% are used. The effect of the ethanol concentration on the burned mass fraction Xb (which equals the ratio of the burned mass to the total mass in the chamber) is shown in Figs. 8 and 9. Here, the letter ‘‘E’’ designates ethanol and the numbers next to E refer to the volume percentage of ethanol in the blended fuel. At the beginning of combustion (around y ¼ 101), the mass fraction burned is negligibly affected by the ethanol amount in the blend. However, during the main stage (around TC) and final stage (around y ¼ +101) of combustion, Xb substantially increases with increase in ethanol amount up to 25%. The value of the mass fraction burned Xb predicted at TC and 101 after TC reaches a maximum at about 25%

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Combustion duration, deg.

110

100

 = 9.2 n = 5800 rpm s = -28°

90

80

70 0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 10. Variation of combustion duration with ethanol concentration.

50

Cylinder pressure, bar

 = -10°;

TC;

 = +10°

40

30

20

10 -20

0

20 40 60 80 Volume percentage of ethanol, %

100

120

Fig. 11. The effect of ethanol concentration on combustion pressure.

ethanol. As a consequence of increase in mass burning rate, it is expected that combustion takes place in shorter time, i.e. a shorter burning times can be obtained with gasoline–ethanol blends. This is confirmed by the comparisons in Fig. 10. As shown, combustion duration receives a minimum at about 25% ethanol, and then rises. As known, ethanol has lower calorific value, higher latent heat of vaporization and higher stoichiometric fuel–air ratio than gasoline [19]. As a result of such properties, it can produce a cooling effect on intake charge. Therefore, engine volumetric efficiency can rise. Although the leaning effect on intake charge and the lower calorific value of ethanol, the cylinder pressure and temperature may increase due to both improving combustion and higher volumetric efficiency when gasoline–ethanol blends are used. Figs. 11 and 12 show the effects of ethanol concentration on the cylinder pressure and the peak combustion

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Peak comb. pressure, bar

50

40

30  = 9.2 n = 5800 rpm s = -28°

20

0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 12. The effect of ethanol concentration on peak combustion pressure.

Combustion temperature, K

2700

2500

2300

2100  = -10°;

TC;

 = +10°

1900 0

20 40 60 80 Volume percentage of ethanol, %

100

Fig. 13. The effect of ethanol concentration on combustion temperature.

pressure, respectively. Both figures indicate that ethanol addition to gasoline up to 25% raises combustion pressure. Increasing cylinder pressure can result in higher mean indicated work and the mean indicated pressure; therefore, engine power output and thermal efficiency may also increase. Improvements in combustion also result in higher combustion temperatures. The burned gas temperatures are compared in Figs. 13 and 14. As stated in Section 2.3, the burned gas temperature at the beginning of combustion is calculated approximately as the adiabatic flame temperature by neglecting the heat losses. For this reason, temperatures predicted at 10o before TC are higher and close to those predicted at TC. As shown, combustion temperatures calculated at each piston position reach a maximum for the blend of 25 vol% ethanol.

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Peak cylinder temp., K

2800

2600

2400

2200

 = 9.2 n = 5800 rpm s = -28°

2000 0

20

40

60

80

100

Volume percentage of ethanol, % Fig. 14. The effect of ethanol concentration on peak combustion temperature.

In summary, above comparisons indicate that blending ethanol with gasoline up to 25% by volume results in positive effects on the flame development process, and therefore, on combustion. This can be attributed to relevant combustion properties of ethanol as an engine fuel. As known, ethanol has high flame speed and blending it with gasoline raises engine volumetric efficiency and causes leaner operation. For these reasons, combustion becomes more complete or more stoichiometric when gasoline–ethanol blends are used. 4. Conclusions and recommendations In the present study, the turbulent flame propagation process and combustion in an automobile SI engine fuelled with gasoline, ethanol and various gasoline–ethanol blends have been investigated by means of a quasi-dimensional SI engine combustion model. Comparisons performed between the results obtained from the presented model and those given by several literatures confirm that this model has an ability of accurately computing SI engine combustion. Blending ethanol with gasoline up to 25% by volume positively affects the geometric properties of flame and the mass burning rate, leading to faster burning. It also produces higher cylinder pressures and temperatures compared with gasoline. As a result, the mean indicated work, and therefore engine output power and thermal efficiency, may also increase. Higher combustion temperatures can result in higher dissociation rates. Hence, NO concentrations may increase when gasoline–ethanol blends are used in SI engines. Rising pressure and temperature can cause damages on engine structural components such as piston, cylinder and valves. In this case, engine components should be manufactured to resist higher pressure and temperature. These results have been obtained theoretically. Therefore, some shortcomings of ethanol could not be considered here. In an engine operating under real conditions, the improvements obtained here are somewhat offset by the unfavorable properties of

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ethanol, such as water contamination and volatility problems, leading to phase separation problem in the blended fuels. If such effects are examined in an actual engine, more sensitive results would be obtained. References [1] Bayraktar H, Durgun O. Development of an empirical correlation for combustion durations in spark ignition engines. Energy Convers Manage 2004;45:1419–31. [2] Namazian M, Hansen S, Lyford PE, Sanchez BJ, Heywood J, Rife J. Schlieren visualization of the flame and density fields in the cylinder of a spark-ignition engine. SAE 1980;Paper no. 800044:276–303. [3] Tagalian J, Heywood JB. Flame initiation in a spark-ignition engine. Combust Flame 1986;64:243–6. [4] Gatowski JA, Heywood JB, Deleplace C. Flame photographs in a spark-ignition engine. Combust Flame 1984;56:71–81. [5] Thomas A. Flame development in spark-ignition engines. Combust Flame 1983;50:305–22. [6] Lucas GG, Brunt MFJ. The effect of combustion chamber shape on the rate of combustion in a spark ignition engine. SAE 1982;Paper no. 820165:714–29. [7] Poulos SG, Heywood JB. The effect of chamber geometry on spark-ignition engine combustion. SAE 1983;Paper no. 830334:1106–29. [8] Heywood JB, Vilchis FR. Comparison of flame development in a spark-ignition engine fueled with propane and hydrogen. Combust Sci Technol 1984;38:313–24. [9] Gu¨lder O¨ L. Correlations of laminar combustion data for alternative SI engine fuels. SAE 1984;Paper no. 841000:1–23. [10] Wagner TO, Gray DS, Zarah BY, Kozinski AA. Practicality of alcohols as motor fuel. SAE 1979;Paper no. 790429:1591–607. [11] Bayraktar H. Using gasoline–ethanol–isoprophanol blends in engines. MS thesis, Karadeniz Technical University, Trabzon, Turkey, 1991 [in Turkish]. [12] Thring RH. Alternative fuels for spark-ignition engines. SAE 1983;Paper no. 831685:4715–25. [13] Clancy JS, Dunn PD, Chawawa B. Ethanol as fuel in small stationary spark ignition engines for use in developing countries. IMechE 1988;C67(88):191–4. [14] Kreith F. Mechanical engineering handbook. Boca Raton, FL: CRC Press; 1999. [15] Bayraktar H. Theoretical investigation of the effects of using ethanol–gasoline blends on SI engine combustion and performance. PhD thesis, Karadeniz Technical University, Trabzon, Turkey, 1997 [in Turkish]. [16] Bayraktar H, Durgun O. Theoretical investigation of the effects of using ethanol–gasoline blends on SI engine combustion and performance. In: Proceedings of the 10th international conference on thermal engineering and thermogrammetry, Budapest, Hungary, 1997. p. 240–9. [17] Hsieh WD, Chen RH, Wu TL, Lin TH. Engine performance and pollutant emission of an SI engine using ethanol–gasoline blended fuels. Atmos Environ 2002;36:403–10. [18] Al-Hasan M. Effect of ethanol–unleaded gasoline blends on engine performance and exhaust emissions. Energy Convers Manage 2003;44:1547–61. [19] Bayraktar H. Experimental and theoretical investigation of using gasoline–ethanol blends in spark-ignition engines. Renew Energy 2005;30(11):1733–47. [20] Bayraktar H, Durgun O. Mathematical modeling of spark-ignition engine cycles. Energy Sour 2003;25(7):651–66. [21] Blizard NC, Keck JC. Experimental and theoretical investigation of turbulent burning model for internal combustion engines. SAE 1974;Paper no. 740191:846–64. [22] Keck JC. Turbulent flame structure and speed in spark-ignition engines. In: 19th international symposium on combustion, The Combustion Institute 1982:1451–66. [23] Morel T, Rackmil CI, Keribar R, Jennings MJ. Model for heat transfer and combustion in spark ignited engines and its comparison with experiments. SAE 1988;Paper no. 880198:6348–62.