**3.1. Calculation of period t1**

**3. Calculation of periods of phases of fuel injection in the spark –**

Carried out calculations aim at determination of durations of particular phases of injected fuel stream in the Mitsubishi GDI engine during work on the stratified mixture, including resistances prevalent inside the cylinder [8]. The mathematical model was elaborated by use

The phases of injected fuel stream during work on the stratified charge are shown in *Fig.6*.

For the calculation model, the total time needed to cross a distance from injection moment to

**1.** Period t1 – from the fuel injection moment to contact of the stream with the piston head,

**2.** Period t2 – from the moment of entry into curvature of the piston head to the half-length of the curvature, including frictional resistance between the fuel stream and the piston head

**3.** Period t3 – from the half-length of the piston head curvature to the moment when the fuel stream exits the head, including both frictional and air resistances for the evaporating fuel

**4.** Period t4 – from exit the curvature of the piston head to the moment when the fuel

the sparking plug points reaching was divided into four stages, namely:

**Ignition engine with direct fuel injection during work on the**

**heterogeneous mixture**

92 Advances in Internal Combustion Engines and Fuel Technologies

of *Mathcad Professional.*

**Figure 6.** The phases of injected fuel stream

including air resistance

stream reaches the sparking plug points.

Time t1, from the fuel injection moment to contact of the stream with the piston head, includ‐ ing air resistance (*Fig.7)*.

α0 – the moment of the beginning injection of the fuel stream

**Figure 7.** First sector i.e. contact of fuel mixture with the bowl of the piston

General form of equation that determines the injection time, after adding the coefficient of turbulence dependent on a path, can be stated as:

$$t\_{inj} = \int \frac{2 \cdot \sqrt{2 \cdot s} \cdot \left(\mathcal{S}\_1 + \mathcal{S}\_2 \cdot \frac{c}{s}\right)}{\left(V\_0 - V\_0 \cdot \mathcal{C}\_{D1}\right) \cdot d\_0} ds\tag{3}$$

**3.2. Calculation of period t2**

**Figure 9.** Second section determined with angle α<sup>2</sup>

Time t2 , from the moment of entry into curvature of the piston head to the half-length of the curvature, including frictional resistance between the fuel stream and the piston head (*Fig.9)*.

Stratified Charge Combustion in a Spark-Ignition Engine With Direct Injection System

http://dx.doi.org/10.5772/53971

95

where:

*S*1, *S*<sup>2</sup> − constants


*CD*<sup>1</sup> − air resistance in sector 1, is determined by :

$$\mathcal{C}\_{D1} = \frac{24}{\text{Re}} \Big( 1 + 0.15 \,\text{Re}^{0.667} \right) + \frac{0.42}{1 + 4.25 \cdot 10^4 \,\text{Re}^{-1.16}} \tag{4}$$

Calculation results of time t1 are shown in *Fig.8*.

**Figure 8.** The time which the fuel stream takes to go from the moment of injection to its contact with the piston head, depending on the crank angle and the rotational speed of the engine, at constant injection pressure 5 [MPa]
