**6. Conclusions**

In [47], the exponential factors *α* and *β* are given the values 0.9 and -0.05, respectively; the unstretched laminar flame speed *S*L, <sup>0</sup> (units of m/s) is calculated through a modification of the functional expression proposed by Syed et al. [65], in which an increase of the ethanol volume fraction *x*˜ *ETH* between 0% (pure gasoline) and 100% (pure ethanol) produces a 10% increase

( ) ( ( ) ) <sup>2</sup> 0.3

The flame propagation type models presented above are physics-based and hence, in principle, can be generalised to engines of different geometries. Through the definition of the laminar flame velocity, they enable accounting for two very relevant influences on combustion, i.e. the charge diluent fraction and the composition and strength of the fuel mixture. In spite of their simplicity, partly due to the range of assumptions taken, this type of control-oriented models has been demonstrated to capture the rate of combustion of modern SI engines with acceptable level of confidence. Hall et al. [47] validate the model using experimental records from a turbo-

**Variable Units Values/Description**

Test-engine configuration - In-line four-cylinder Bore mm 82.7 Stroke mm 93.0

More than 500 test points were used, consisting of combinations of engine speed between 750 and 5500 rev/min, intake manifold pressure between 0.4 and 2.2 bar, ST between -12 and 60 CA degrees BTDC and valve overlap between -16 and 24 CA degrees (intake valve timing only). Four basic ethanol/gasoline blend ratios were tested, between E0 (pure gasoline) and E85 (0.85 ethanol and 0.15 gasoline, as volume fractions). In the vast majority of instances, the model predicted the duration of the interval between ST and 50% MFB (*Δϑ*50) with a maximum error of 10%. The influence of relevant engine parameters on combustion duration is sum‐ marized in figure 19. This shows the theoretical Spark Ignition Timing (SIT) which ensures optimal 50% MFB location (i.e. at 8 CA degrees ATDC), when variable amounts of charge dilution (here Burned Gas Fraction), and variable amounts of ethanol are used, at different

Connecting rod length mm 144 Compression ratio - 10.55 Total swept volume cm3 2100

**Table 3.** Specifications of the test engine used in reference [47].

 f


,0 0.4658 1 0.1 4.48 1.075 *<sup>L</sup> ETH S* = + *x EXP* % f

charged, PFI, flexible-fuel, SI engine, the specification of which are given in table 3.

in laminar flame speed:

42 Advances in Internal Combustion Engines and Fuel Technologies

*5.2.3. Discussion of results*

The present chapter explores the evolution of the combustion process in modern-design, premixed, gasoline engines, which feature the increasingly common technology of variable valve timing. The assessment of combustion rates and duration has been performed by looking at the effects of a set of significant engine operating variables, which were studied in isolation. The chapter also explores recently-proposed simplified thermodynamic combustion models, which can be in principle deployed within fast-execution control algorithms. The engine data used cover a large portion of the part-load envelope, reflecting typical urban and cruise driving conditions, but incorporate high load operating conditions enabling a more comprehensive evaluation of combustion. The results presented are relevant to port-fuel injection gasoline engines, which feature homogeneous SI combustion, but also to direct-injection gasoline engines, because these run in theoretically-homogeneous combustion mode for a large part of the operating envelope. Despite burn rates and duration are invariably a function of engine geometry, the data used throughout the study for combustion analysis and modelling refer to the very common modern-design of 4-valve pent-roof combustion chamber, which also ascribes relevance and generality to the findings.

combustion further into the expansion stroke. When engine speed is varied in isolation, both combustion angles are found to increase linearly with increasing engine speed, with gradients of variation which appear independent of engine load. When engine speed increases between

Premixed Combustion in Spark Ignition Engines and the Influence of Operating Variables

http://dx.doi.org/10.5772/55495

45

Functional expressions for the total combustion angle, *Δϑ*90, and the so-called form factor have been derived empirically as inputs of the Wiebe function to model the charge burn process of a premixed gasoline SI engine. The application of the model for *Δϑ*90 yields average changes in the total burn angle of 10 CA degrees when dilution mass fraction increases by 5 point percent or engine speed increases by 800 rev/min. The maximum errors in FDA, RBA and *Δϑ*50, calculated using the Wiebe function with modelled inputs, were within 13%, which is typical of simplified combustion models applied to complex engine architectures. Importantly, the analysis has shown that errors of magnitude up to 7% would be expected due to the inherent limitations of fitting a Wiebe function to an experimental MFB profile. The error analysis also shows that the influence of the Wiebe function form factor upon *Δϑ*50 is relatively small, suggesting the modelling approach presented may be applicable to combustion phasing

Straightforward methods of combustion modelling as the Wiebe function or simplified flame propagation models (also outlined in this chapter) lend themselves ideally for robust inclusion into feed-back or feed-forward combustion control algorithms. If appropriately calibrated, these models are able to capture the most relevant factors influencing the rate of combustion and may enable efficiency improvement also during transient or variable operation. The main issue with the application of such models comes from relying on accurate values of in-cylinder charge dilution. High frequency sampling and analysis of the quantity of burned gas within the combustible mixture cannot be performed. Faster indirect measurement techniques are currently being studied, but are still far from becoming established technology. Engine mapping work may allow the compilation of multi-level look-up tables where dilution mass fraction can be tabulated as a function of engine speed, load, as well as intake and exhaust valve timing setting; these tables can be used to yield model inputs during steady-state running, less so during variable operation when the boundary conditions determining the diluent fraction change on a cycle-to-cycle basis. Physical measurements can be replaced by charge dilution models, but compounding the uncertainties associated to the various models may compromise the validity of the general approach. The best alternative among the various possible methods of combustion control would be the one enabling measurable improvements in fuel economy over a representative drive-cycle and further studies are needed in this field.

Supported by a vast and efficient infrastructure, the SI engine running on gasoline fuels continue to power the vast majority of light-duty vehicles used today across the globe. Due to the present level of technological advancement, as well as to the ever more stringent emission regulations, the homogenous premixed mode of combustion remains the favourite choice for most production SI engines. The current scenario will not be altered easily, until new technol‐ ogies and new alternative fuels become widely available and truly sustainable. In such a context, the investigation of gasoline premixed combustion, which in recent years is increas‐

1500 and 3000 rev/min, FDA and RBA grow by about 1/3 and 1/2, respectively.

control.

In modern engine architectures, the analysis of combustion tends to be intrinsically rich in details and challenging, and the ability to identify the most influential variables is crucial. Four operating variables are deemed as *essential and sufficient* to model the charge burn process in the context of current-design SI engines; in decreasing rank of importance these are charge dilution by burned gas, engine speed, ignition timing and charge density. In the present work dilution mass fraction, which slows the burning rate by increasing the cylinder charge heat capacity, has been of particular interest as large dilution variations produced by both valve timing setting and external-EGR are part of current combustion and emissions control strategies. The second most relevant engine variable is engine speed; greater engine speeds stretch the burning process over increasing intervals in the CA domain, as well as having a direct marked influence upon the level of combustion chamber turbulence. Similarly to engine load, the spark timing determines the thermodynamic state of the mixture when combustion commences, as well as controlling combustion phasing across TDC. Charge density calculated at spark timing is taken as an indication of engine load or of the amount of trapped mass within the cylinder.

Especially at low to medium load, the valve timing strategy exerts a strong influence upon both engine breathing ability and amount of burned gas internally recirculated during the valve overlap interval. Combustion control strategies aimed at improved efficiency must carefully consider the extent to which the burning characteristics are modified by VVT. Owing primarily to the influence of charge dilution, both FDA and RBA increase consistently with increasing degree of positive overlap, though the increase in RBA is more pronounced, and proportionately greater as engine load is reduced. In the range of valve timings investigated (EVC and IVO were varied between -14 and 36 and between -24 and 36 CA degrees BTDC, respectively), the experimental data show that the influence on combustion duration is exerted primarily through the overlap extension, whereas the overlap phasing about TDC is not critical. At relatively high load and speed conditions, combustion duration is found to be virtually independent of the valve timing setting. The effect of valve timing exerted through modifications to bulk motion and turbulence is not apparent in the data.

When the level of charge dilution is varied in isolation, by using fixed valve timing and variable amounts of external-EGR, both FDA and RBA increase linearly with increasing dilution, and the variation of RBA is slightly biased towards greater engine speed as a result of extending combustion further into the expansion stroke. When engine speed is varied in isolation, both combustion angles are found to increase linearly with increasing engine speed, with gradients of variation which appear independent of engine load. When engine speed increases between 1500 and 3000 rev/min, FDA and RBA grow by about 1/3 and 1/2, respectively.

The chapter also explores recently-proposed simplified thermodynamic combustion models, which can be in principle deployed within fast-execution control algorithms. The engine data used cover a large portion of the part-load envelope, reflecting typical urban and cruise driving conditions, but incorporate high load operating conditions enabling a more comprehensive evaluation of combustion. The results presented are relevant to port-fuel injection gasoline engines, which feature homogeneous SI combustion, but also to direct-injection gasoline engines, because these run in theoretically-homogeneous combustion mode for a large part of the operating envelope. Despite burn rates and duration are invariably a function of engine geometry, the data used throughout the study for combustion analysis and modelling refer to the very common modern-design of 4-valve pent-roof combustion chamber, which also

In modern engine architectures, the analysis of combustion tends to be intrinsically rich in details and challenging, and the ability to identify the most influential variables is crucial. Four operating variables are deemed as *essential and sufficient* to model the charge burn process in the context of current-design SI engines; in decreasing rank of importance these are charge dilution by burned gas, engine speed, ignition timing and charge density. In the present work dilution mass fraction, which slows the burning rate by increasing the cylinder charge heat capacity, has been of particular interest as large dilution variations produced by both valve timing setting and external-EGR are part of current combustion and emissions control strategies. The second most relevant engine variable is engine speed; greater engine speeds stretch the burning process over increasing intervals in the CA domain, as well as having a direct marked influence upon the level of combustion chamber turbulence. Similarly to engine load, the spark timing determines the thermodynamic state of the mixture when combustion commences, as well as controlling combustion phasing across TDC. Charge density calculated at spark timing is taken as an indication of engine load or of the amount of trapped mass within

Especially at low to medium load, the valve timing strategy exerts a strong influence upon both engine breathing ability and amount of burned gas internally recirculated during the valve overlap interval. Combustion control strategies aimed at improved efficiency must carefully consider the extent to which the burning characteristics are modified by VVT. Owing primarily to the influence of charge dilution, both FDA and RBA increase consistently with increasing degree of positive overlap, though the increase in RBA is more pronounced, and proportionately greater as engine load is reduced. In the range of valve timings investigated (EVC and IVO were varied between -14 and 36 and between -24 and 36 CA degrees BTDC, respectively), the experimental data show that the influence on combustion duration is exerted primarily through the overlap extension, whereas the overlap phasing about TDC is not critical. At relatively high load and speed conditions, combustion duration is found to be virtually independent of the valve timing setting. The effect of valve timing exerted through

When the level of charge dilution is varied in isolation, by using fixed valve timing and variable amounts of external-EGR, both FDA and RBA increase linearly with increasing dilution, and the variation of RBA is slightly biased towards greater engine speed as a result of extending

modifications to bulk motion and turbulence is not apparent in the data.

ascribes relevance and generality to the findings.

44 Advances in Internal Combustion Engines and Fuel Technologies

the cylinder.

Functional expressions for the total combustion angle, *Δϑ*90, and the so-called form factor have been derived empirically as inputs of the Wiebe function to model the charge burn process of a premixed gasoline SI engine. The application of the model for *Δϑ*90 yields average changes in the total burn angle of 10 CA degrees when dilution mass fraction increases by 5 point percent or engine speed increases by 800 rev/min. The maximum errors in FDA, RBA and *Δϑ*50, calculated using the Wiebe function with modelled inputs, were within 13%, which is typical of simplified combustion models applied to complex engine architectures. Importantly, the analysis has shown that errors of magnitude up to 7% would be expected due to the inherent limitations of fitting a Wiebe function to an experimental MFB profile. The error analysis also shows that the influence of the Wiebe function form factor upon *Δϑ*50 is relatively small, suggesting the modelling approach presented may be applicable to combustion phasing control.

Straightforward methods of combustion modelling as the Wiebe function or simplified flame propagation models (also outlined in this chapter) lend themselves ideally for robust inclusion into feed-back or feed-forward combustion control algorithms. If appropriately calibrated, these models are able to capture the most relevant factors influencing the rate of combustion and may enable efficiency improvement also during transient or variable operation. The main issue with the application of such models comes from relying on accurate values of in-cylinder charge dilution. High frequency sampling and analysis of the quantity of burned gas within the combustible mixture cannot be performed. Faster indirect measurement techniques are currently being studied, but are still far from becoming established technology. Engine mapping work may allow the compilation of multi-level look-up tables where dilution mass fraction can be tabulated as a function of engine speed, load, as well as intake and exhaust valve timing setting; these tables can be used to yield model inputs during steady-state running, less so during variable operation when the boundary conditions determining the diluent fraction change on a cycle-to-cycle basis. Physical measurements can be replaced by charge dilution models, but compounding the uncertainties associated to the various models may compromise the validity of the general approach. The best alternative among the various possible methods of combustion control would be the one enabling measurable improvements in fuel economy over a representative drive-cycle and further studies are needed in this field.

Supported by a vast and efficient infrastructure, the SI engine running on gasoline fuels continue to power the vast majority of light-duty vehicles used today across the globe. Due to the present level of technological advancement, as well as to the ever more stringent emission regulations, the homogenous premixed mode of combustion remains the favourite choice for most production SI engines. The current scenario will not be altered easily, until new technol‐ ogies and new alternative fuels become widely available and truly sustainable. In such a context, the investigation of gasoline premixed combustion, which in recent years is increas‐ ingly focusing on control strategy optimisation in *high-degree-of-freedom* engines, continues to be of paramount importance.

**List of main symbols**

*A* / *F* Air to Fuel Ratio

*dm* / *d*τ Rate of Burning (kg/s)

*N* Engine Speed (rev/min)

*SP* Mean Piston Speed (m/s)

*V* In-Cylinder Volume (m3)

τ Instant of Time (s)

**Author details**

Fabrizio Bonatesta\*

sity, Oxford, UK

*x*˜ Molar or Volumetric Fraction

γ Ratio of Specific Heat Capacities

*u* ' In-Cylinder Turbulence Intensity (m/s)

*T* Temperature (K)

Δ*ϑ*

*A* Average Flame Front Surface (m2)

Δ*h* Combustion Chamber Mean Height (m)

*n* Wiebe Function Form Factor or Polytropic Index

*P* In-Cylinder Pressure (Δ*P*: In-Cylinder Pressure Variation) (Pa)

*m* Mass (*mb*: Mass of Burned Gas; *mtot*: Total In-Cylinder Trapped Mass) (kg)

*SL* Laminar Burning (or Flame Front) Velocity (*Sb*: Turbulent Velocity) (m/s)

*ϑ* Crank Angle Location (*ϑST* : CA Location of Spark Ignition) (CA degrees)

between ST and 90% MFB, Equal to FDA+RBA) (CA degrees)

Crank Angle Interval or Combustion Interval (Δ*ϑ*50: Interval between ST and 50% MFB; Δ*ϑ*90: Interval

Premixed Combustion in Spark Ignition Engines and the Influence of Operating Variables

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47

ρ Density (ρ*u*: Density of the Unburned Charge; ρ*ST* : In-Cylinder Density at Spark Timing) (kg/m3)

*x* Mass Fraction (*xb*: Total In-Cylinder Dilution Mass Fraction; *xMFB*: Fresh Charge Burned Fraction)

Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes Univer‐
