**3.2. Calculation of period t2**

General form of equation that determines the injection time, after adding the coefficient of

1 2

æ ö × ×× + × ç ÷

è ø <sup>=</sup> -× × <sup>ò</sup> (3)

(4)

*<sup>c</sup> sS S*

*D*

( )

*<sup>s</sup> <sup>t</sup> ds V VC d*

2 2

( ) 0.667

<sup>15</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>60</sup> <sup>90</sup> <sup>100</sup> <sup>120</sup> <sup>140</sup> <sup>160</sup> <sup>175</sup>

**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]

**Angle of fuel injection before** 

**TDC [<sup>o</sup> ]**

1 4 1.16 <sup>24</sup> 0.42 1 0.15Re Re 1 4.25 10 Re *CD* - =+ +

0-0,001 0,001-0,002 0,002-0,003 0,003-0,004 0,004-0,005 0,005-0,006 0,006-0,007

+ ×

800 1500 3000 5000 7000

**Crankshaft speed [rpm]**

0 0 10

turbulence dependent on a path, can be stated as:

94 Advances in Internal Combustion Engines and Fuel Technologies

*s* − distance traveled by the fuel stream,[m]

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

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

0 0,001 0,002 0,003 0,004 0,005 0,006 0,007

**Time t1**  [s]

*d*<sup>0</sup> − diameter of fuel injection nozzle,[m]

where:

*S*1, *S*<sup>2</sup> − constants

*inj*

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)*.

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

Velocity of the fuel stream just before its impact on the piston head surface is:

$$V\_{S1} = \frac{R\_w \left(1 + \frac{\lambda}{2} \sin \left(\alpha - \alpha t\_1\right)^2 - \cos \left(\alpha - \alpha t\_1\right)\right)}{t\_1} \tag{5}$$

800 1500 3000 5000 7000

g

(10)

)) (9)

**Crankshaft speed [rpm]**

<sup>15</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>60</sup> <sup>90</sup> <sup>100</sup> <sup>120</sup> <sup>140</sup> <sup>160</sup> <sup>175</sup>

**Figure 10.** The time which the fuel stream takes to go from the moment of entry into the curvature of the piston head to the moment when it passes the half-length of the recess, depending on the crank angle and the rotational speed of

Time 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 (*Fig.11)*.

Velocity of the fuel stream in the piston head with regard to resistance of the piston head

*CD*<sup>2</sup> − resistance coefficient with regard to friction of the fuel stream against the piston head,

<sup>3</sup> *S t s r* = ×a

*V VC VC C V S SD SDD T* 3 12 123 = × -× × + ( cos(

The way of the jet on the curvature in the piston surface is calculated:

0-0,001 0,001-0,002 0,002-0,003 0,003-0,004 0,004-0,005 0,005-0,006 0,006-0,007

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

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

97

**Angle of fuel injection before** 

**TDC [<sup>o</sup> ]**

0 0,001 0,002 0,003 0,004 0,005 0,006 0,007

the engine, at constant injection pressure 5 [MPa]

*CD*<sup>3</sup> − resistance coefficient of the air.

**3.3. Calculation of period t3**

surface and the air is:

where:

**Time t1**  [s]

where:

 $R\_W$  - сrank  $\text{arm}\_! [\mathfrak{m}]$ 


Subsequently the initial diameter of the injected fuel jet at contacting the piston is calculated. The assumed angle of jet dispersion is*β* =12<sup>0</sup> , the obtuse angle of the piston head curvature *<sup>α</sup><sup>t</sup>* =120<sup>0</sup> and radius of the piston head curvature*r* =25 *mm* .

The way of the injected fuel jet in time t1 equals:

$$s\_1 = \frac{R\_w \left(1 + \frac{\lambda}{2} \sin \left(a - \alpha t\_1\right)^2 - \cos \left(a - \alpha t\_1\right)\right)}{\cos \left(\gamma\right)}\tag{6}$$

the radius along which the fuel jet flows along the curvature in the piston head is calculated and equals:

$$r\_S = r - \frac{1}{3}d\_S \rightarrow d\_S = 2s\_1 \cdot \tan\left(\frac{\beta}{2}\right) \rightarrow s\_2 = r\_S \cdot a\_t \tag{7}$$

Assuming that flow velocity of the fuel stream along the piston recess is constant, time t2 can be calculated from the following equation:

$$t\_2 = \frac{s\_2}{Vs\_2} \tag{8}$$

Calculation results of time t2 are shown in *Fig.10*.

**Figure 10.** The time which the fuel stream takes to go from the moment of entry into the curvature of the piston head to the moment when it passes the half-length of the recess, depending on the crank angle and the rotational speed of the engine, at constant injection pressure 5 [MPa]
