**4. Development of the 3D GDI engine model and its application in the design phase**

The effects of the injection strategy on the combustion process of a GDI engine are discussed in this section. In particular, a single cylinder engine, four-valve, four-stroke, 638 cc displacement, suitable for motorbike applications is analysed. A 3D numerical model of the cylinder and intake and exhaust ducts, using as initial and boundary conditions the results of a 1D simulation of the entire propulsion systems, is presented, as developed by authors within the AVL FireTM environment. Gasoline injection is simulated according to the previously discussed model, under both single and double strategies, as issuing form Injector #1. In positioning the injector within the combustion chamber, the *spray guided* mixture formation mode is preferred, since it offers the greatest possibilities of extending the limits of lean engine operation. In fact, low combustion efficiency losses and combustion phasing losses, resulting in a significant further improvement in fuel economy and noxious emissions with respect to the other two concepts are typical of this way of operation [Piock, 2003, Landenfeld *et al*., 2004]. The considered engine is at a design stage, therefore major choices improving the engine operation are discussed, as firstly derived on the ground of parametric analyses.

#### **4.1 Moving mesh generation**

The discretisation of the moving boundary computational domain is realized by means of the pre-processing software included in the same FireTM Graphical User Interface (GUI), called Fame Engine Plus (FEP). This allows performing a semi-automatic moving mesh generation, where the user can control the cell size by thickening nodes where particular geometric conformations of the outer surfaces are present, or where intense gradients of the thermo-fluid variables are expected. This is made through the choice of appropriate selections on the surfaces, or the surfaces edges, in the vicinity of which the spacing of the grid is determined ad hoc, depending on the particular crank angle position and differently from the rest of the domain.

The mesh relevant to the simulation of the four-stroke engine cycle is made by accounting for both the sequence of steps in which the cycle itself may be decomposed (intake, compression, expansion and exhaust stroke) and the subdivision of the domain in three main parts, namely the cylinder, the intake ducts and the exhaust ducts. The time sequence of the strokes is managed by building more grids, each used for a range of crank angles defined *a priori*, that avoids an excessive cell distortion. The transition from one grid to the next is carried out by re-mapping the thermo-fluidynamic variables on the nodes, according to a procedure called *rezone* in the FireTM environment. In order to maintain the computational time within reasonable limits, the grids are considered active only in physical domains of interest: when intake and exhaust valves are closed the grid is built only in the cylinder; the intake and exhaust ducts are added geometrically, and numerically solved, only at those crank angles for which these zones are actually put into contact with the cylinder by the valves opening. The error resulting from not having simulated the flow in the pipes when valves are closed, is controlled by setting appropriate conditions of pressure and temperature at the crank angles where these domains are connected with the cylinder.

Fig. 17 shows a view from the top of the surface of the complete computational domain, with the four pipes. The spark plug is assumed as mounted in central position, while the injector is positioned between the two intake pipes at a distance of 39.6 mm from the

**4. Development of the 3D GDI engine model and its application in the design** 

The effects of the injection strategy on the combustion process of a GDI engine are discussed in this section. In particular, a single cylinder engine, four-valve, four-stroke, 638 cc displacement, suitable for motorbike applications is analysed. A 3D numerical model of the cylinder and intake and exhaust ducts, using as initial and boundary conditions the results of a 1D simulation of the entire propulsion systems, is presented, as developed by authors within the AVL FireTM environment. Gasoline injection is simulated according to the previously discussed model, under both single and double strategies, as issuing form Injector #1. In positioning the injector within the combustion chamber, the *spray guided* mixture formation mode is preferred, since it offers the greatest possibilities of extending the limits of lean engine operation. In fact, low combustion efficiency losses and combustion phasing losses, resulting in a significant further improvement in fuel economy and noxious emissions with respect to the other two concepts are typical of this way of operation [Piock, 2003, Landenfeld *et al*., 2004]. The considered engine is at a design stage, therefore major choices improving the engine operation are discussed, as firstly derived on the ground of

The discretisation of the moving boundary computational domain is realized by means of the pre-processing software included in the same FireTM Graphical User Interface (GUI), called Fame Engine Plus (FEP). This allows performing a semi-automatic moving mesh generation, where the user can control the cell size by thickening nodes where particular geometric conformations of the outer surfaces are present, or where intense gradients of the thermo-fluid variables are expected. This is made through the choice of appropriate selections on the surfaces, or the surfaces edges, in the vicinity of which the spacing of the grid is determined ad hoc, depending on the particular crank angle position and differently

The mesh relevant to the simulation of the four-stroke engine cycle is made by accounting for both the sequence of steps in which the cycle itself may be decomposed (intake, compression, expansion and exhaust stroke) and the subdivision of the domain in three main parts, namely the cylinder, the intake ducts and the exhaust ducts. The time sequence of the strokes is managed by building more grids, each used for a range of crank angles defined *a priori*, that avoids an excessive cell distortion. The transition from one grid to the next is carried out by re-mapping the thermo-fluidynamic variables on the nodes, according to a procedure called *rezone* in the FireTM environment. In order to maintain the computational time within reasonable limits, the grids are considered active only in physical domains of interest: when intake and exhaust valves are closed the grid is built only in the cylinder; the intake and exhaust ducts are added geometrically, and numerically solved, only at those crank angles for which these zones are actually put into contact with the cylinder by the valves opening. The error resulting from not having simulated the flow in the pipes when valves are closed, is controlled by setting appropriate conditions of pressure and temperature at the crank angles where these domains are connected with the cylinder. Fig. 17 shows a view from the top of the surface of the complete computational domain, with the four pipes. The spark plug is assumed as mounted in central position, while the injector is positioned between the two intake pipes at a distance of 39.6 mm from the

**phase** 

parametric analyses.

**4.1 Moving mesh generation** 

from the rest of the domain.

Fig. 17. Top view of the complete engine surface.

cylinder axis. Fig. 18 represents one of the grids used for the range of valves overlap, particularly at 380°, together with a table reporting its geometrical characteristics. Note the thick part on the right of the exhaust ducts, which is a part added properly to avoid numerical errors due to reflections from the outlet surface.

Fig. 18. Computational grid (cells on surface) corresponding to a crank angle of 380° and characteristic data.

Numerical Modelling and Optimization of the

Total pressure (Pa)

8.0E+004

2.9E+002

3.0E+002

3.1E+002

Temperature (K)

0.00E+000

Model (ECFM) model [Colin *et al.*, 2003].

1.00E+006

2.00E+006

In-cylinder pressure (Pa)

3.00E+006

4.00E+006

3.2E+002

3.3E+002

9.0E+004

1.0E+005

1.1E+005

1.2E+005

1.3E+005

Mixture Formation Process by Multi-Hole Injectors in a GDI Engine 195

360 450 540 630 720 810 900 990 1080 Crank angle (°)

360 450 540 630 720 810 900 990 1080 Crank angle (°)

300 400 500 600 700 800 900 1000 Crank angle (°)

When simulating typical engine working cycles, spray dynamics is simulated by following the previously described approach, combustion according to the Extended Coherent Flame

Fig. 20. Inlet boundary conditions. Total pressure (top) and static temperature (bottom).

1D simulation 3D simulation

Fig. 21. 1D and 3D in-cylinder pressure cycles. Motored conditions.

For the sake of clarity, Table 3 reports the instants of intake and exhaust valves opening (intake valves opening, IVO, exhaust valves opening, EVO) and closing (intake valves closing, IVC, exhaust valves closing, EVC), and the position of the top dead centre (TDC).


Table 3. Relevant crank angle positions.

#### **4.2 Simulation of the in-cylinder processes**

Boundary and initial conditions for the 3D simulation are derived from a 1D model of the whole propulsion system, including all the elements from the intake mouth to the exhaust. The model is developed at the University of Naples - DIME, within the 1Dime code environment, by accurately schematising all the engine components [Bozza *et al.*, 2001]. The 1Dime code is a well assessed gas-dynamic tool, using the two-zone fractal combustion model and validated under various engine configurations by Bozza *et al.* [Bozza and Torella, 2004; Bozza *et al.*, 2008].

To give an example of the boundary conditions set at the intake pipes inlet and at the exhaust pipes outlet of the 3D model, Figs 19 and 20 are drawn. These show, respectively, the static pressure set at the exhaust and the total pressure and static temperature set at the intake at the engine speed of 7500 rpm, motored conditions. Note that the engine under investigation is characterized by the presence of intense pressure wave propagation in the intake system, strongly affecting the cylinder volumetric efficiency. Imposing a transient boundary condition at the intake ducts inlet is required to get a good prediction of the overall trapped mass. On the other hand, no problem derives from this assumption, as no unphysical/spurious oscillations arise, between the imposed 1D total pressure and the static pressure resulting from the 3D computations.

The comparison between the in-cylinder motored pressure cycle calculated by means of the 1D and the 3D models at 7500 rpm is reported in Fig. 21. The agreement is good, both as regards the charge substitution phase, and the compression and expansion strokes.

Fig. 19. Outlet boundary condition. Static pressure.

For the sake of clarity, Table 3 reports the instants of intake and exhaust valves opening (intake valves opening, IVO, exhaust valves opening, EVO) and closing (intake valves closing, IVC, exhaust valves closing, EVC), and the position of the top dead centre (TDC).

Boundary and initial conditions for the 3D simulation are derived from a 1D model of the whole propulsion system, including all the elements from the intake mouth to the exhaust. The model is developed at the University of Naples - DIME, within the 1Dime code environment, by accurately schematising all the engine components [Bozza *et al.*, 2001]. The 1Dime code is a well assessed gas-dynamic tool, using the two-zone fractal combustion model and validated under various engine configurations by Bozza *et al.* [Bozza and Torella,

To give an example of the boundary conditions set at the intake pipes inlet and at the exhaust pipes outlet of the 3D model, Figs 19 and 20 are drawn. These show, respectively, the static pressure set at the exhaust and the total pressure and static temperature set at the intake at the engine speed of 7500 rpm, motored conditions. Note that the engine under investigation is characterized by the presence of intense pressure wave propagation in the intake system, strongly affecting the cylinder volumetric efficiency. Imposing a transient boundary condition at the intake ducts inlet is required to get a good prediction of the overall trapped mass. On the other hand, no problem derives from this assumption, as no unphysical/spurious oscillations arise, between the imposed 1D total pressure and the static

The comparison between the in-cylinder motored pressure cycle calculated by means of the 1D and the 3D models at 7500 rpm is reported in Fig. 21. The agreement is good, both as

> 360 450 540 630 720 810 900 990 1080 Crank angle (°)

regards the charge substitution phase, and the compression and expansion strokes.

(valves overlap)

TDC

(combustion)

TDC

330° 608° 120° 390° 360° 720°

IVO IVC EVO EVC

2004; Bozza *et al.*, 2008].

Table 3. Relevant crank angle positions.

**4.2 Simulation of the in-cylinder processes** 

pressure resulting from the 3D computations.

8.0E+004 9.0E+004 1.0E+005 1.1E+005 1.2E+005 1.3E+005 1.4E+005 1.5E+005

Fig. 19. Outlet boundary condition. Static pressure.

Static pressure (Pa)

Fig. 20. Inlet boundary conditions. Total pressure (top) and static temperature (bottom).

Fig. 21. 1D and 3D in-cylinder pressure cycles. Motored conditions.

When simulating typical engine working cycles, spray dynamics is simulated by following the previously described approach, combustion according to the Extended Coherent Flame Model (ECFM) model [Colin *et al.*, 2003].

Numerical Modelling and Optimization of the

axis. A red arrow indicates injector position.

of 675° is reached for the inclination angle of 70°.

indicates injector position.

combustion chamber.

Mixture Formation Process by Multi-Hole Injectors in a GDI Engine 197

The analysis leading to the choice of the Injector #1 inclination angle is first discussed. The injection strategy shown in Fig. 3, characterised by an injected mass equal to 50mg at a pressure of 10 MPa, is chosen to effect the study. The injector is assumed mounted on the cylinder head in such a way that its axis and the cylinder axis form angles of 45°, 60° and 70°. SOI is set at 470°, angle of maximum intake valves lift, SI is fixed at 675°. Valves and spark plug wetting are avoided by choosing the best injector orientation with respect to its own axis, namely by directing the previously mentioned insulated jet, of the six composing the spray, towards the engine head. The dramatic effect of the injector inclination on the pressure cycle and the rate of heat release is shown in Fig. 22. An angle of 70° is demonstrated to increase the pressure cycle area by increasing the release of heat within the

(a) (b) (c)

(a) (b) (c)

Fig. 24. Gasoline vapour distribution on a plane passing through the spark plug at 675°. The injector axis is inclined at 45° (a), 60° (b) and 70° (c) w.r.t. the cylinder axis. A red arrow

This consideration is justified by the better quality of the mixture formation process relevant to the higher inclination angle, as demonstrated by Figs. 23 and 24. Fig. 23 reports the spray visualization in the cylinder at the crank angle of 600°. At this instant, which is 130° after the SOI, and only 25° before its end, only a small part of the fuel injected is evaporated, due to the low temperature existing in the cylinder during the intake stroke and at the initial stage of compression. As expected, the air motion significantly affects the droplets trajectory by deviation towards the spark plug, and reduces the penetration as a consequence of an increased dispersion. A large number of droplets impacts on the piston surface, particularly with the injector angles of 45° and 60°. A greater inclination indeed realises a more effective vapour distribution of gasoline. Fig. 24 demonstrates that the greater concentration of fuel vapour around the spark plug, on a plane passing through the spark axis, at the crank angle

Fig. 23. Spray droplets visualization at the crank angle corresponding to the end of the intake stroke. The injector axis is inclined at 45° (a), 60° (b) and 70° (c) w.r.t. the cylinder

Results relevant to different engine representative working conditions, including mixture formation and combustion processes, are discussed hereafter. Table 4 summarises data relevant to a full-load case and a moderate-load case: speed, air-to-fuel ratio A/F, injected gasoline mass and injection pressure and injection duration are reported.


Table 4. Numerical tests cases.

The first considered operating condition refers to an engine speed equal to 7500 rpm and full load, namely brake mean effective pressure BMEP=1.28 MPa and A/F=13, according to data derived from the 1D simulation. After the definition of the best inclination of the injector with respect to the cylinder axis, different crank angles of start of injection (SOI) at the injection pressure Pinj=10 MPa are discussed, for fixed instants of time of spark ignition (SI). In a second step, the injection pressure is changed with fixed SOI and fixed SI. As Pinj raises from 10 MPa to 20 MPa, the injection duration is reduced from 3.44 ms to 2.63 ms, hence from 155° to 118°.

Another considered representative operating condition is of moderate-load, for an engine speed equal to 5000 rpm, namely BMEP=0.3 MPa, with A/F=17. Injection pressure is assumed at 6 MPa, injected mass is mf= 19.4 mg, SI is varied to reach the maximum brake torque (MBT). This case is examined with the scope of highlighting advantages deriving from adopting overall lean stratified mixtures.

Fig. 22. In-cylinder pressure (a) and rate of heat release (b) for three different inclinations of the injector w.r.t. the cylinder axis.

Results relevant to different engine representative working conditions, including mixture formation and combustion processes, are discussed hereafter. Table 4 summarises data relevant to a full-load case and a moderate-load case: speed, air-to-fuel ratio A/F, injected

(MPa) A/F Pinj

Full-load 7500 1.28 13 10 50 3.44 155 Moderate-load 5000 0.3 17 6 19.4 2.07 62°

The first considered operating condition refers to an engine speed equal to 7500 rpm and full load, namely brake mean effective pressure BMEP=1.28 MPa and A/F=13, according to data derived from the 1D simulation. After the definition of the best inclination of the injector with respect to the cylinder axis, different crank angles of start of injection (SOI) at the injection pressure Pinj=10 MPa are discussed, for fixed instants of time of spark ignition (SI). In a second step, the injection pressure is changed with fixed SOI and fixed SI. As Pinj raises from 10 MPa to 20 MPa, the injection duration is reduced from 3.44 ms to 2.63 ms,

Another considered representative operating condition is of moderate-load, for an engine speed equal to 5000 rpm, namely BMEP=0.3 MPa, with A/F=17. Injection pressure is assumed at 6 MPa, injected mass is mf= 19.4 mg, SI is varied to reach the maximum brake torque (MBT). This case is examined with the scope of highlighting advantages deriving

0.00E+000

4.00E+001

8.00E+001

Rate of Heat Release (J/°)

Fig. 22. In-cylinder pressure (a) and rate of heat release (b) for three different inclinations of

1.20E+002

(MPa)

mf (mg) Injection duration (ms)

650 675 700 725 750 775 800 Crank Angle (°)

Injection duration (°)

> 45° 60° 70°

gasoline mass and injection pressure and injection duration are reported.

BMEP

Speed (rpm)

Table 4. Numerical tests cases.

hence from 155° to 118°.

0.0E+000

2.0E+006

4.0E+006

6.0E+006

Pressure (Pa)

8.0E+006

1.0E+007

from adopting overall lean stratified mixtures.

45° 60° 70°

650 675 700 725 750 775 800 Crank Angle (°)

the injector w.r.t. the cylinder axis.

(a) (b)

The analysis leading to the choice of the Injector #1 inclination angle is first discussed. The injection strategy shown in Fig. 3, characterised by an injected mass equal to 50mg at a pressure of 10 MPa, is chosen to effect the study. The injector is assumed mounted on the cylinder head in such a way that its axis and the cylinder axis form angles of 45°, 60° and 70°. SOI is set at 470°, angle of maximum intake valves lift, SI is fixed at 675°. Valves and spark plug wetting are avoided by choosing the best injector orientation with respect to its own axis, namely by directing the previously mentioned insulated jet, of the six composing the spray, towards the engine head. The dramatic effect of the injector inclination on the pressure cycle and the rate of heat release is shown in Fig. 22. An angle of 70° is demonstrated to increase the pressure cycle area by increasing the release of heat within the combustion chamber.

Fig. 23. Spray droplets visualization at the crank angle corresponding to the end of the intake stroke. The injector axis is inclined at 45° (a), 60° (b) and 70° (c) w.r.t. the cylinder axis. A red arrow indicates injector position.

Fig. 24. Gasoline vapour distribution on a plane passing through the spark plug at 675°. The injector axis is inclined at 45° (a), 60° (b) and 70° (c) w.r.t. the cylinder axis. A red arrow indicates injector position.

This consideration is justified by the better quality of the mixture formation process relevant to the higher inclination angle, as demonstrated by Figs. 23 and 24. Fig. 23 reports the spray visualization in the cylinder at the crank angle of 600°. At this instant, which is 130° after the SOI, and only 25° before its end, only a small part of the fuel injected is evaporated, due to the low temperature existing in the cylinder during the intake stroke and at the initial stage of compression. As expected, the air motion significantly affects the droplets trajectory by deviation towards the spark plug, and reduces the penetration as a consequence of an increased dispersion. A large number of droplets impacts on the piston surface, particularly with the injector angles of 45° and 60°. A greater inclination indeed realises a more effective vapour distribution of gasoline. Fig. 24 demonstrates that the greater concentration of fuel vapour around the spark plug, on a plane passing through the spark axis, at the crank angle of 675° is reached for the inclination angle of 70°.

Numerical Modelling and Optimization of the

load.

0.0E+000

MPa (a), full load.

2.0E+006

4.0E+006

6.0E+006

Pressure (Pa)

8.0E+006

1.0E+007

1.2E+007

Mixture Formation Process by Multi-Hole Injectors in a GDI Engine 199

(a)

(b)

0.0E+000

1.0E-003

2.0E-003

Mean NO mass fraction

Fig. 27. In-cylinder pressure (a) and mean NO mass fraction (b) for Pinj=10 MPa and Pinj=20

3.0E-003

4.0E-003

650 675 700 725 750 775 800 Crank Angle (°)

pinj=10 MPa pinj=20 MPa

Fig. 26. Spray droplets visualization at IVC for Pinj=10 MPa (a) and Pinj =20 MPa (b), full

650 675 700 725 750 775 800 Crank Angle (°)

(a) (b)

pinj=10 MPa pinj=20 MPa

Fig. 25. In-cylinder pressure for three vales of SOI at full load.

The effect of changes in SOI on the engine pressure cycle at full-load is shown in Fig. 25. Three values of SOI ranging between 450° and 490° are considered. As already noticed, the angle 470° corresponds to the maximum intake valves lift. Spark ignition, SI, is set at 676°. No appreciable variations are observed by anticipating SOI during the intake stroke. In other words, the numerical results highlights the need to fully exploit the turbulent motion of the entering air, and to initiate the mixture formation process before the starting of the intake valves reverse motion, due to the quite long duration of injection (155°) under full load conditions at the injection pressure Pinj= 10 MPa.

The comparison between simulations effected at high load under different injection pressures, Pinj= 10 MPa and Pinj= 20 MPa, is made in Figs. from 26 to 28. SI is assumed at 691°. Injection always starts at the crank angle of 470°. Fig. 26 represents the spray visualisation within the cylinder at the crank angle of valves closure. The stronger atomisation pertinent to Pinj= 20 MPa is well evident. The increased quality of the mixture formation process determines a better vapour distribution within the combustion chamber, whose effect is well evident on the resulting in-cylinder pressure cycle (Fig. 27.a). The faster release of heat in the case of higher injection pressure determines, on the other hand, far worst conditions for the in-cylinder NO formation, as highlighted in Fig. 27.b, that represents the mean NO mass fraction as a function of the crank angle. Hence, the choice of the injection pressure must consider different aspects, including the coupling with the exhaust after-treatment system. Fig. 28, indeed, reports the injected and the evaporated gasoline mass within the cylinder, as a function of the crank angle for the two injection pressures. It is evident that injection starts at 470° and has different durations, evaporation is faster for the case Pinj=20 MPa, but, anyway, it is practically complete at the time of spark ignition for both the cases.

SOI=450° SOI=470° SOI=490°

650 675 700 725 750 775 800 Crank Angle (°)

The effect of changes in SOI on the engine pressure cycle at full-load is shown in Fig. 25. Three values of SOI ranging between 450° and 490° are considered. As already noticed, the angle 470° corresponds to the maximum intake valves lift. Spark ignition, SI, is set at 676°. No appreciable variations are observed by anticipating SOI during the intake stroke. In other words, the numerical results highlights the need to fully exploit the turbulent motion of the entering air, and to initiate the mixture formation process before the starting of the intake valves reverse motion, due to the quite long duration of injection (155°) under full

The comparison between simulations effected at high load under different injection pressures, Pinj= 10 MPa and Pinj= 20 MPa, is made in Figs. from 26 to 28. SI is assumed at 691°. Injection always starts at the crank angle of 470°. Fig. 26 represents the spray visualisation within the cylinder at the crank angle of valves closure. The stronger atomisation pertinent to Pinj= 20 MPa is well evident. The increased quality of the mixture formation process determines a better vapour distribution within the combustion chamber, whose effect is well evident on the resulting in-cylinder pressure cycle (Fig. 27.a). The faster release of heat in the case of higher injection pressure determines, on the other hand, far worst conditions for the in-cylinder NO formation, as highlighted in Fig. 27.b, that represents the mean NO mass fraction as a function of the crank angle. Hence, the choice of the injection pressure must consider different aspects, including the coupling with the exhaust after-treatment system. Fig. 28, indeed, reports the injected and the evaporated gasoline mass within the cylinder, as a function of the crank angle for the two injection pressures. It is evident that injection starts at 470° and has different durations, evaporation is faster for the case Pinj=20 MPa, but, anyway, it is practically complete at the time of spark

0.0E+000

Fig. 25. In-cylinder pressure for three vales of SOI at full load.

load conditions at the injection pressure Pinj= 10 MPa.

ignition for both the cases.

2.0E+006

4.0E+006

6.0E+006

Pressure (Pa)

8.0E+006

1.0E+007

(b)

Fig. 26. Spray droplets visualization at IVC for Pinj=10 MPa (a) and Pinj =20 MPa (b), full load.

Fig. 27. In-cylinder pressure (a) and mean NO mass fraction (b) for Pinj=10 MPa and Pinj=20 MPa (a), full load.

Numerical Modelling and Optimization of the

analysis (starting point).

**5. The optimization problem** 

limiting the interval of variation of this last quantity.

mean indicated pressure in the closed valves period.

flow-chart of the optimization problem, in the case of split injection.

Mixture Formation Process by Multi-Hole Injectors in a GDI Engine 201

Injection is realized in a single event, as characterized by an injection pressure equal to 6 MPa, hence by a duration, at the considered engine speed, of about 60°. SOI is fixed at 450° and SI is varied between 670° and 710°, step 5°. The value of SOI is assumed on the ground of the physical consideration that the injection has to fully exploit the motion of the air entering the cylinder, hence by accounting for the fact that the maximum intake valves lift occurs at 470°. The indicated mean pressure, relevant to the closed valves period and normalized with respect to its maximum value, is reported in Fig. 8 as a function of SI. The maximum value of the curve, hence the maximum brake torque (MBT), is attained in correspondence of SI at 680°, namely 40° before the top dead centre (BTDC). This situation is hereafter considered as a reference case to be used as a term of comparison for the following

Reducing costs, improving performances and system reliability and shortening the time to market is of crucial importance in the design of technical systems and components. The use of rigorous methods of decision-making, such as optimization methods, coupled with modern tools of numerical simulation, is today very effective to accomplish these tasks, especially in complex systems. Numerical procedures, in fact, may be used to generate a series of progressively improved solutions to the optimization problem, starting from an

The optimization problem here discussed is intended to the reduction of the fuel consumption of the considered single cylinder engine, through the more proper choice of the injection strategy under moderate load, moderate speed, lean mixture condition. The underlying design variables are identified in the time of spark ignition (SI) and in the start of the single injection event. More into detail, since both single and double injection strategies are considered, the variable is just the hereafter called SOI in the case of single injection, or the start of the first injection event, SOI1, and the dwell time between two successive pulses, dw, in the case injection is split in two parts. The choice of the range of variation of the samples, as well as of the step between successive samples, is a subjective matter, strongly affecting the efficiency and speed of the optimization procedure. Physical considerations are made in the assessment of the DOE space, as avoiding injection in the valves overlap period, or considering the existence of a MBT value corresponding to a given SI, which helps in

The objective function is chosen as the cycle area in the pressure-volume plane, relevant to the closed valves period. This function is to be maximised. As an example, Fig. 30 shows the

The algorithm chosen for the maximisation of the objective function, the Simplex, by Nelder & Mead, is an optimization algorithm seeking the vector of parameters corresponding to the global extreme (maximum or minimum) of any N-dimensional function F(x1, x2,..,xN) in the parameter space. This algorithm for non-linear optimization problems does not require

Two successive analyses are effected in the single injection case: the first consists in fixing the time of SI just at the found value of 680° and varying SOI in a pre-defined range, the second in assuming both SOI and SI as input variables for the optimization procedure. In both the situations the Simplex algorithm is used to search for the inputs maximizing the

derivates evaluations, so it is more robust than algorithms based on local gradients.

initial one. The process is terminated when some convergence criterion is satisfied.

Fig. 28. Injected and evaporated gasoline mass for Pinj=10 MPa and Pinj=20 MPa.

Results relevant to the 3D simulation of the moderate-load overall lean condition (A/F=17) at 5000 rpm are summarised in Fig. 29.

Fig. 29. Normalized mean indicated pressure in the closed valve period under moderateload as a function of SI.

Injection is realized in a single event, as characterized by an injection pressure equal to 6 MPa, hence by a duration, at the considered engine speed, of about 60°. SOI is fixed at 450° and SI is varied between 670° and 710°, step 5°. The value of SOI is assumed on the ground of the physical consideration that the injection has to fully exploit the motion of the air entering the cylinder, hence by accounting for the fact that the maximum intake valves lift occurs at 470°. The indicated mean pressure, relevant to the closed valves period and normalized with respect to its maximum value, is reported in Fig. 8 as a function of SI. The maximum value of the curve, hence the maximum brake torque (MBT), is attained in correspondence of SI at 680°, namely 40° before the top dead centre (BTDC). This situation is hereafter considered as a reference case to be used as a term of comparison for the following analysis (starting point).
