**5. The optimization problem**

200 Computational Simulations and Applications

450 500 550 600 650 700 750 Crank angle (°)

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)

670 680 690 700 710 SI (°)

Fig. 29. Normalized mean indicated pressure in the closed valve period under moderate-

injected pinj=10 MPa evaporated pinj=10 MPa injected pinj=20 MPa evaporated pinj=20 MPa

0.0E+000

at 5000 rpm are summarised in Fig. 29.

0.75

0.8

0.85

(IMEP/IMEPmax

load as a function of SI.

 )clos ed v alves

0.9

0.95

1

2.0E-005

4.0E-005

Liquid mass (kg)

6.0E-005

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

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 limiting the interval of variation of this last quantity.

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

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

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 mean indicated pressure in the closed valves period.

Numerical Modelling and Optimization of the

0.00E+000

with respect to the assumed starting point.

injection realized in one shot.

decrease equal to 2.6 % in the fuel consumption.

visible.

Fig. 32. Pressure cycles relevant to five different values of SOI.

1.00E+006

2.00E+006

Pressure (Pa)

3.00E+006

Mixture Formation Process by Multi-Hole Injectors in a GDI Engine 203

SOI = 445° SOI = 475° SOI = 485° SOI = 495° SOI = 535°

640 680 720 760 800 Crank angle (°)

The dramatic effect of a change in SOI on the in-cylinder pressure at moderate-load is visualized in Fig. 32, where five different cycles are plotted, chosen between those computed during the optimization procedure. All of them have the SI at the same crank angle, 680°. It is evident that injection has to be not so much delayed, and has to really exploit the motion of the air entering the cylinder, before the valves lift decreases too much. The optimal choice of the start of the injection event allows an increase of the 5.3% of the pressure cycle area

Results of the second optimization analysis relevant to the single injection case are reported in Figs. 33. It is evident that the couple of values of SOI and SI maximizing the engine performances is SOI at 475° and SI at 680°. The value of SOI coincides with the one found in the first optimization analysis, where the value of SI is considered as fixed. This last, on the other hand, is found equal to the value previously set on the ground of the parametric analysis. The gain in the pressure cycle area with respect to the starting point is clearly

Effects of splitting the injection in two successive events characterized by a same injected mass (50%+50%), is discussed by varying SI and the starts of both the first and the second injection event. More precisely, as previously said input variables are assumed as SI, SOI1, SOI of the first injection, and the dwell time between the two injection events. Fig. 34 represents the modeFRONTIER results, which show the optimal values being SOI1 at 450° and a dwell time equal to about 80°. The optimal spark advance remains at 680°, although the relevant graph is here not reported. Splitting injection in two events allows an increase of the work greater than the 8% with respect to the case assumed as starting point, with

The comparison between the in-cylinder pressure cycles found as optimal in the single injection case and in the double injection case is made in Fig. 35. The total injected mass is the same, namely 20 mg/str. The increase in the cycle area is well visible. It corresponds to a

The optimization of the time of SOI alone is effected in order to understand how the injection event has to be synchronized with the intake or the compression phase. The interval of explored crank angles starts at 445° and ends at 615°, thus covering situations where the injection is fully realized at open intake valves or completely during compression with closed valves. As previously said, the maximum intake valves lift is at 470°, whereas their closing angle occurs at 608°. The results of the optimization analysis lead to state that the maximum work, hence the minimum fuel consumption, is realized starting the injection at 475°. This can be deduced from Fig. 31, where the optimized variable is reported as a function of the SOI. The starting point is indicated, whereas the maximum increase in the optimised variable is evident at 475°.

Fig. 30. Flow chart of the optimization problem in the case mixture formation is realized through split injection.

Fig. 31. Normalized mean indicated pressure in the closed valve period for the first optimization problem as a function of SOI.

The optimization of the time of SOI alone is effected in order to understand how the injection event has to be synchronized with the intake or the compression phase. The interval of explored crank angles starts at 445° and ends at 615°, thus covering situations where the injection is fully realized at open intake valves or completely during compression with closed valves. As previously said, the maximum intake valves lift is at 470°, whereas their closing angle occurs at 608°. The results of the optimization analysis lead to state that the maximum work, hence the minimum fuel consumption, is realized starting the injection at 475°. This can be deduced from Fig. 31, where the optimized variable is reported as a function of the SOI. The starting point is indicated, whereas the maximum increase in the

Fig. 30. Flow chart of the optimization problem in the case mixture formation is realized

Starting point

440 480 520 560 600 640 SOI (°)

Fig. 31. Normalized mean indicated pressure in the closed valve period for the first

optimised variable is evident at 475°.

through split injection.

0.4

optimization problem as a function of SOI.

0.6

0.8

(IMEP/IMEPref)clos

 ed v alves 1

1.2

Fig. 32. Pressure cycles relevant to five different values of SOI.

The dramatic effect of a change in SOI on the in-cylinder pressure at moderate-load is visualized in Fig. 32, where five different cycles are plotted, chosen between those computed during the optimization procedure. All of them have the SI at the same crank angle, 680°. It is evident that injection has to be not so much delayed, and has to really exploit the motion of the air entering the cylinder, before the valves lift decreases too much. The optimal choice of the start of the injection event allows an increase of the 5.3% of the pressure cycle area with respect to the assumed starting point.

Results of the second optimization analysis relevant to the single injection case are reported in Figs. 33. It is evident that the couple of values of SOI and SI maximizing the engine performances is SOI at 475° and SI at 680°. The value of SOI coincides with the one found in the first optimization analysis, where the value of SI is considered as fixed. This last, on the other hand, is found equal to the value previously set on the ground of the parametric analysis. The gain in the pressure cycle area with respect to the starting point is clearly visible.

Effects of splitting the injection in two successive events characterized by a same injected mass (50%+50%), is discussed by varying SI and the starts of both the first and the second injection event. More precisely, as previously said input variables are assumed as SI, SOI1, SOI of the first injection, and the dwell time between the two injection events. Fig. 34 represents the modeFRONTIER results, which show the optimal values being SOI1 at 450° and a dwell time equal to about 80°. The optimal spark advance remains at 680°, although the relevant graph is here not reported. Splitting injection in two events allows an increase of the work greater than the 8% with respect to the case assumed as starting point, with injection realized in one shot.

The comparison between the in-cylinder pressure cycles found as optimal in the single injection case and in the double injection case is made in Fig. 35. The total injected mass is the same, namely 20 mg/str. The increase in the cycle area is well visible. It corresponds to a decrease equal to 2.6 % in the fuel consumption.

Numerical Modelling and Optimization of the

0.00E+000

crank angle of SI.

**6. Conclusion** 

in a GDI engine is presented.

1.00E+006

2.00E+006

Pressure (Pa)

3.00E+006

Mixture Formation Process by Multi-Hole Injectors in a GDI Engine 205

640 680 720 760 800 Crank angle (°)

Fig. 35. Optimal pressure cycles relevant to single injection and double injection.

Fig. 36. Equivalence ratio distribution on a plane passing through the spark location in the optimal single injection case (left) and in the optimal double injection case (right) at the

The double injection event, with the second pulse entirely realized during the compression stroke, gives rise to a more effective charge stratification around the spark plug. This implies a faster propagation of the flame front within the combustion chamber. The problem of the presence of a rich zone closest to the cylinder walls and opposite to the injector position is

The application of CFD techniques to the study and optimisation of the combustion process

A first part of the work is devoted to the numerical multidimensional modelling of the dynamics of sprays issuing from new-generation multi-hole injectors for GDI applications.

not avoided, but can be solved by possibly reducing the injection pressure.

optimal single SOI=475° optimal double SOI1=450° dwell=80°

Fig. 33. Results of the second optimization as a function of SOI (a) and SI (b).

The explanation of the better performances relevant to the double injection case is simply drawn on the ground of the work of Li *et al.* [Li *et al.*, 2007], and by looking at Fig. 36, where the equivalence ratio distribution on a plane passing through the spark plug, at the crank angle of SI, is visualized in the two cases of single and double injection. The spark is in central position on the engine head. The occurrence of a quite well stratified charge is evident, although a rich zone still appears close to the piston wall opposite to the injector location. This is represented as a red arrow in the figure.

Fig. 34. Optimal synchronization of two injection events w.r.t. SOI (a) and dwell time (b).

0.8

1

Fig. 34. Optimal synchronization of two injection events w.r.t. SOI (a) and dwell time (b).

1.02

1.04

1.06

(IMEP / IMEPref)closed valves

1.08

1.1

The explanation of the better performances relevant to the double injection case is simply drawn on the ground of the work of Li *et al.* [Li *et al.*, 2007], and by looking at Fig. 36, where the equivalence ratio distribution on a plane passing through the spark plug, at the crank angle of SI, is visualized in the two cases of single and double injection. The spark is in central position on the engine head. The occurrence of a quite well stratified charge is evident, although a rich zone still appears close to the piston wall opposite to the injector

0.85

0.9

0.95

(IMEP/IMEPref)closed valves

1

1.05

1.1

440 460 480 500 520 SOI (°)

20 40 60 80 100 120 Dwell (°)

660 670 680 690 700 SI (°)

location. This is represented as a red arrow in the figure.

440 445 450 455 460 465 SOI (°)

(a) (b)

 (a) (b) Fig. 33. Results of the second optimization as a function of SOI (a) and SI (b).

0.8

1

1.02

1.04

1.06

(IMEP / IMEPref)closed valves

1.08

1.1

0.85

0.9

0.95

(IMEP/IMEPref)closed valves

1

1.05

1.1

Fig. 35. Optimal pressure cycles relevant to single injection and double injection.

The double injection event, with the second pulse entirely realized during the compression stroke, gives rise to a more effective charge stratification around the spark plug. This implies a faster propagation of the flame front within the combustion chamber. The problem of the presence of a rich zone closest to the cylinder walls and opposite to the injector position is not avoided, but can be solved by possibly reducing the injection pressure.
