**3.3. Calculation of period t3**

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 surface and the air is:

$$V\_{S3} = \left(V\_{S1} \cdot \mathbb{C}\_{D2} - V\_{S1} \cdot \mathbb{C}\_{D2} \cdot \mathbb{C}\_{D3} + V\_T \cos(\gamma)\right) \tag{9}$$

where:

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

1

*S*

96 Advances in Internal Combustion Engines and Fuel Technologies

*λ* − crank radius to connecting-rod length ratio

The assumed angle of jet dispersion is*β* =12<sup>0</sup>

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

1

*s*

be calculated from the following equation:

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

*α* − actual angle of revolution of the crankshaft,[deg]

*V*

where:

*RW* − crank arm,[m]

*t*<sup>1</sup> − time in sector 1

*<sup>α</sup><sup>t</sup>* =120<sup>0</sup>

and equals:

*ω* − angular velocity,[rad/s]

2 *<sup>w</sup>*

and radius of the piston head curvature*r* =25 *mm* .

2

<sup>1</sup> 2 tan 3 2 *S SS S t rr d d s sr*

=- ® = × ® = × ç ÷

l

l

( ) ( ) <sup>2</sup> 1 1

 aw

è ø <sup>=</sup> (5)

, the obtuse angle of the piston head curvature

1

Subsequently the initial diameter of the injected fuel jet at contacting the piston is calculated.

( ) ( )

1 1

 aw

è ø <sup>=</sup> (6)

a

è ø (7)

*Vs* <sup>=</sup> (8)

( )

g

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

Assuming that flow velocity of the fuel stream along the piston recess is constant, time t2 can

2

2 *s*

2

*t*

1 2

b

æ ö

1 sin cos

aw

cos

*R tt <sup>w</sup>*

2

æ ö ç ÷ + -- -

æ ö ç ÷ + -- -

*t*

1 sin cos

aw

*R tt*

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

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

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

$$s\_3 = r\_S \cdot \alpha\_t \tag{10}$$

**Figure 11.** Third section determined with angle α<sup>3</sup>

For time t3 calculations are made from the value of the angle *α<sup>t</sup>* =60<sup>0</sup> till *α<sup>t</sup>* =120<sup>0</sup> .

Assuming that the flow velocity of the fuel stream along the piston recess is constant and equal *VS* 3, time t3 can be calculated according to:

$$t\_3 = \frac{s\_3}{V\_{S3}}\tag{11}$$

Calculation results of time t3 are shown in *Fig.12*.

0-0,0005 0,0005-0,001 0,001-0,0015 0,0015-0,002 0,002-0,0025 0,0025-0,003 0,003-0,0035

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

**Figure 12.** The time which the fuel stream takes to go from the moment when it passes the half-length of the recess to the moment when it exits the piston head, depending on the crank angle and the rotational speed of the engine, at

Time t4, from exit the curvature of the piston head to the moment when the fuel stream

It is assumed that sparking plug is situated centrally in the cylinder axis, in the top of the combustion chamber. Furthermore, a distance between the piston top and the head LS is:

2

 n

n

( ) <sup>123</sup>

æ ö

Distance that the piston has to go from the start of the third sector to the GMP:

<sup>2</sup> *<sup>w</sup> x R*

naw

<sup>4</sup> 1 sin cos

l

800 1000 1500 2000 3000 4000 5000 6000 7000 8000 15 20 30 40 60 90 100 120 140 160 175 0

constant injection pressure 5 [MPa]

**3.4. Calculation of period t4**

reaches the sparking plug points (*Fig.13)*.

**Crankshaft speed [rpm]** 

0,0005

**Angle of fuel injection before TDC** 

5 *<sup>S</sup> L mm* = é ù ë û (12)

=+ - ç ÷ è ø (13)

=- -- *ttt* (14)

0,001

0,0015

**Time t3** 

0,002

0,0025

0,003

0,0035

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

99

Calculation results of time t3 are shown in *Fig.12*.

**Figure 12.** The time which the fuel stream takes to go from the moment when it passes the half-length of the recess to the moment when it exits the piston head, depending on the crank angle and the rotational speed of the engine, at constant injection pressure 5 [MPa]

#### **3.4. Calculation of period t4**

**Figure 11.** Third section determined with angle α<sup>3</sup>

98 Advances in Internal Combustion Engines and Fuel Technologies

equal *VS* 3, time t3 can be calculated according to:

For time t3 calculations are made from the value of the angle *α<sup>t</sup>* =60<sup>0</sup>

Assuming that the flow velocity of the fuel stream along the piston recess is constant and

3

*S*3 *s*

3

*t*

till *α<sup>t</sup>* =120<sup>0</sup>

*<sup>V</sup>* <sup>=</sup> (11)

.

Time t4, from exit the curvature of the piston head to the moment when the fuel stream reaches the sparking plug points (*Fig.13)*.

It is assumed that sparking plug is situated centrally in the cylinder axis, in the top of the combustion chamber. Furthermore, a distance between the piston top and the head LS is:

$$L\_S = \mathbb{E}\left[\begin{array}{c}mm\end{array}\right] \tag{12}$$

Distance that the piston has to go from the start of the third sector to the GMP:

$$\mathbf{x}\_4 = \mathbf{R}\_w \left( 1 + \frac{\lambda}{2} \sin \nu^2 - \cos \nu \right) \tag{13}$$

$$\nu = \alpha - \alpha \left(t\_1 - t\_2 - t\_3\right) \tag{14}$$

**Figure 13.** The fourth sector – fuel mixture reaches the electrodes of the spark plug; it is determined with angle α<sup>4</sup>

Distance that the fuel stream has to go from the start of the third sector to the sparking plug:

$$s\_4 = \mathbf{x}\_4 + L\_S \tag{15}$$

Assuming that the fuel stream goes through distance s3 with mean velocity we obtain:

<sup>2</sup> <sup>3</sup> *t t*

*LS*

<sup>3</sup> *CD*<sup>4</sup> ime t4

 <sup>n</sup>cos<sup>2</sup>

 sin <sup>2</sup>

4

3

<sup>4</sup> *VS VS <sup>s</sup> <sup>t</sup>*

nt of the air for ti

e shown in *Fig.1*

0.001 0.001-0.

4

*14*.

s to go from the *s*<sup>4</sup> *x*<sup>4</sup> oes through dist

*t*

go from the start

 

1 *Rw* <sup>1</sup> *t*

*CD*<sup>4</sup> −resistance coefficient of the air for time t4

stance coefficien

ults of time t4 are

he fuel stream g

e fuel stream has

e piston has to g

4 *x* 

D

istance that the

Distance that the

Assuming that th

*CD*<sup>4</sup> resis

Calculation resu

D

A

C

**F**

**Fig.14.** The ti piston angle a

**An inje**

gine, at constant injection pressure 5 [MPa]

**3.5. Calculation of total time t5**

reaches the sparking plug:

**ngle of fuel ction before TDC**

me which the fu head to the mo and the rotationa

The results of time t5 are shown in the *Fig.15*.

15

fuel stream takes oment when it r al speed of the e

800 1000

s to go from the reaches sparking ngine, at constan

**Figure 14.** The time which the fuel stream takes to go from the moment of exit the curvature of the piston head to the moment when it reaches sparking plug point, depending on the crank angle and the rotational speed of the en‐

The total time - which the fuel stream takes to go from the injection to the moment when it

<sup>1500</sup> <sup>2000</sup> <sup>3000</sup> <sup>40</sup>

**Cra**

e moment of ex g plug point, de nt injection pres

xit the curvature epending on the sure 5 [MPa]

 of the e crank

0 0.001 0.002 0.003 0.004 0.005

0 8000

**m]**

<sup>51234</sup> *t tttt* =+++ (17)

0.006

**Time**

**e t4**

0.007

0.008

<sup>000</sup> <sup>5000</sup> <sup>6000</sup> <sup>7000</sup>

**ankshaft speed [rpm**

Calculation results of time t4 are shown in *Fig.14*.

0-0

4

start of the third

of the third secto

  or to the GMP:

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

d sector to the sp

ean velocity we o

003 0.003-0.00

*S SD* 3 34 *s*

tance s3 with me

.002 0.002-0.0

*V VC* <sup>=</sup> - × (16)

 obtain:

04

parking plug:

(14)

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

(15)

(16)

101

 (17)

Assuming that the fuel stream goes through distance s3 with mean velocity we obtain: 4 *x* sin <sup>2</sup> 1 *Rw* <sup>n</sup>cos <sup>2</sup> <sup>2</sup> <sup>3</sup> *t t* (14)

tance s3 with me

1

oes through dist

e shown in *Fig.1*

*14*.

3

$$t\_4 = \frac{s\_4}{V\_{S3} - V\_{S3} \cdot \mathcal{C}\_{D4}}\tag{16}$$

obtain:

(15)

 (17) ean velocity we o

*CD*<sup>4</sup> −resistance coefficient of the air for time t4 he fuel stream g 4 <sup>4</sup> *VS VS <sup>s</sup> <sup>t</sup>* <sup>3</sup> *CD*<sup>4</sup>

ults of time t4 are

e fuel stream has

D

istance that the

Distance that the

Assuming that th

Calculation resu

D

A

C

Calculation results of time t4 are shown in *Fig.14*. *CD*<sup>4</sup> resis stance coefficien nt of the air for ti ime t4

 *t*

**F Fig.14.** The ti piston angle a me which the fu head to the mo and the rotationa fuel stream takes oment when it r al speed of the e s to go from the reaches sparking ngine, at constan e moment of ex g plug point, de nt injection pres xit the curvature epending on the sure 5 [MPa] of the e crank **Figure 14.** The time which the fuel stream takes to go from the moment of exit the curvature of the piston head to the moment when it reaches sparking plug point, depending on the crank angle and the rotational speed of the en‐ gine, at constant injection pressure 5 [MPa]

#### **3.5. Calculation of total time t5**

**Figure 13.** The fourth sector – fuel mixture reaches the electrodes of the spark plug; it is determined with angle α<sup>4</sup>

100 Advances in Internal Combustion Engines and Fuel Technologies

Distance that the fuel stream has to go from the start of the third sector to the sparking plug:

4 4 *<sup>S</sup> sxL* = + (15)

The total time - which the fuel stream takes to go from the injection to the moment when it reaches the sparking plug:

$$t\_5 = t\_1 + t\_2 + t\_3 + t\_4 \tag{17}$$

The results of time t5 are shown in the *Fig.15*.

**4. Modelling of injection process in gasoline direct injection engine by**

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

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

103

In up-to-date combustion engines the fuel is injected directly into the cylinder, where the load has a raised temperature. The evaporation is better than at the injection into the inflow duct. With regard to a very short time lapse between the start of injection and the ignition during the mixture stratification in recent gasoline engines with direct fuel injection into the cylinder the presentation of a precise mathematical model describing evaporation of fuel

During fuel injection disintegration of drops, falling into smaller and smaller ones, takes place. They are subjected to aerodynamic forces which are the direct cause of their disin‐ tegration. The presentation of a precise mathematical model of the process of drop move‐ ment, disintegration, and evaporation is, so far, not possible. However, a number of models based upon aero- and thermodynamic laws and experimental investigations have already been built. As a rule, reciprocal collision of drops is not considered. In some models only one kind of drop contact with the wall (rebouncing or spilling) is assumed. The best known, at present, models of fuel evaporation are the models given by Spald‐ ing [6] and included in the module GENTRA in the programme *Phoenics* of the firm

Mathematical models considered in these programmes are more suitable for numerical sim‐ ulation of the fuel injection process in gasoline engines. Apart from it, the mathematical

In program *KIVA 3V* make use of complicated mathematical models describing the behav‐ iour of the fuel injected into the engine cylinder, and so: shaping of the fluid jet (Reitz model [5]), fuel drops breakup (TAB - Taylor Analogy of Breakup procedure [3]), evaporation of fuel drops (Spalding model [6]), resistance and movement forces (Amsden model [2]), tur‐

The program for computer modelling and simulation of combustion engine *KIVA 3V* pos‐ sesses a large, developed, graphic interface which may additionally consider the inflow and outflow system and create complicated curved surfaces describing, as in our case, the head of piston. For such a complicated system as the combustion chamber Mitsubishi GDI the commercial program *KIVA 3V* in the Laboratory Los Alamos describes fully the physical and thermodynamical processes inside the cylinder. In *Fig.17* shows a geometrical model of

In the case of an irregular combustion chamber calculation of the size of the contact surface of flame and cylinder walls and head can be performed applying division of the w hole sur‐ face above the piston into a number of elementary volumes. This method should be applied

model given by Hiroyasu [4] and the PICALO model should also be considered.

bulence of the charge in the combustion chamber (two - equation κ- ε model [8]).

a piston of a gasoline engine type 4G93GDI of the firm Mitsubishi.

**kiva 3v**

drops is necessary.

CHAM and programme *KIVA*.

**4.1. Geometry of the calculation model**

at irregular shapes of the combustion chamber.

**Figure 15.** The total time which the fuel stream takes to go from the injection to the moment when it reaches the sparking plug, depending on the crank angle and the rotational speed of the engine, at constant injection pressure 5 [MPa]

From the calculated values of the angle by which the crankshaft revolts during the jet travel the value of the advance angle of injection with consideration of the advance angle of igni‐ tion is calculated.

It has to be emphasized that the actual injection angle has to be increased by the ignition advance angle what is superposed and presented in *Fig. 16*.

**Figure 16.** The actual injection advance angle as a function of rpm for different values of injection pressure.
