**2. Theoretical analysis of pressure and temperature of the combustion process of stratified charge in a direct injected four stroke engine**

#### **2.1. Scheme of charge propagation**

Using the CAD program a mode of charge stratification of ultra – lean combustion was ela‐ borated based on considering the shape of the concave bowl of the piston and injection cas‐ tor angle presented in Fig.1.

The small spheric bowl in the piston shown in Fig.1 works as a chamber and is located on the side of the inlet channel. The geometry of the bowl in the piston bottom is designed in such a way that the fuel sprayed from the injector falling on the concavity is directed under the ignition plug. High pressure of the injected fuel is thought to prevent formation of a fuel film on the piston bottom during refraction and supply of an adequate rich dose of fuel un‐ der the ignition plug.

An adequate gap between the injector and the ignition plug is necessary to accelerate the evaporation and diffusion of the sprayed fuel in order to make the too rich mixtures leaner around the ignition plug (λ < 0.5) which may delay the ignition. In accordance with it, the beginning initiation of injection should occur earlier and earlier with the increase in the rota‐ tional speed.

γ - angle of injector position

The improvement of the above mentioned parameters was possible owing to the implemen‐ tation of the system of laminar lean fuel-air mixture combustion in the range of partial load and low to medium rotational speeds of the engine. The laminar load was created by the

The injected fuel spout, with the proper angle of the crankshaft revolution during the com‐ pression stroke rebounces from the piston head and is directed towards the spark plug elec‐ trodes. The rapid development of internal combustion engines with direct petrol injection caused the introduction into batch production of the Renault concern IDE engines, Toyota's D4, Volkswagen group's FSI, PSA group's HPI, Ford's SCI, Mercedes' CGI, and the JTS unit

In 2004 the first turbocharged engines with indirect petrol injection were introduced in Audi vehicles, and in 2006 Mercedes presented CLS 350 CGI model, in the engine of which the laminar load is created by the spray-guided injection. At present piezoelectric injectors are used in most direct injection systems, which characterize with considerably larger fuel dos‐ age accuracy than the hitherto used electromagnetic injectors. This type of fuel supply sys‐ tem shows that the gasoline engine with direct petrol injection, apart from the benefits resulting from the combustion of lean mixtures, has numerous other virtues, compared to

**•** increase power compared with other spark ignition engines with multiple-point fuel in‐

The aim of engine constructors is essentially to increase the overall efficiency, not merely one of the partial efficiencies of which it constitutes, therefore the profound analysis of the

**2. Theoretical analysis of pressure and temperature of the combustion**

Using the CAD program a mode of charge stratification of ultra – lean combustion was ela‐ borated based on considering the shape of the concave bowl of the piston and injection cas‐

The small spheric bowl in the piston shown in Fig.1 works as a chamber and is located on the side of the inlet channel. The geometry of the bowl in the piston bottom is designed in such a way that the fuel sprayed from the injector falling on the concavity is directed under the ignition plug. High pressure of the injected fuel is thought to prevent formation of a fuel film on the piston bottom during refraction and supply of an adequate rich dose of fuel un‐

**process of stratified charge in a direct injected four stroke engine**

wall-guided fuel injection.

used by Alfa Romeo.

jection.

the conventional fuel supply systems, namely:

86 Advances in Internal Combustion Engines and Fuel Technologies

**2.1. Scheme of charge propagation**

tor angle presented in Fig.1.

der the ignition plug.

**•** fuel consumption comparable with other self-ignition engines,

above mentioned factors deciding of its real value is understandable.

**Figure 1.** Variation of fuel mixture in combustion chamber.

As a result, the point the fuel impinges the concavity in the piston differs at different velocities.

The geometry of the concavity and the angle of injection were designed so that the behav‐ iour of the fuel after injection would not be sensitive to the moment and place of injection.

#### **2.2. Thermodynamics method of comparative cycle on the basis of heat amount introduced into the cycle**

The following assumptions were adopted for calculations:


Basic equation of heat balance used for calculations takes this form:

$$\mathbf{C}\_{v1} \cdot T\_2 + \frac{\boldsymbol{\xi} \cdot \mathcal{W}\_u}{L\_p \cdot (1 + \boldsymbol{\gamma})} = \mu\_r \cdot \mathbf{C}\_{v2} \cdot T\_m \tag{1}$$

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

ence to the indicated pressure in a Gasoline Direct .

Two mathematical models were elaborated by use of which the required values of pressures and temperatures were calculated for both algorithms for the same data in order to compare the obtained results. The mathematical model was elaborated by use of *Mathcad Professional.*

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89

**2.4. Comparison of pressure and temperature calculated by use of the thermodynamics**

A comparison of traces of temperature changes for these methods was given in *Fig.5*.

**Figure 2.** Traces of pressure changes in the cylinder for various coefficient of air excess λ obtained by use of the ther‐

For either of these models calculation of pressures for charges of different coefficient of air excess λ were performed in order to calculate a substitute coefficient of air excess λz; these are presented in *Fig.2* and *Fig.3* respectively. Subsequently, in *Fig.4* pressure traces for the two methods were presented respectively; moreover a comparison of indicated pressures calculated by use of the thermodynamic method and Vibe's method was given with refer‐

**and vibe's method with reference to real indicated pressure in a GDI**

*θ* − angle of combustion start,[m]

*φ<sup>Z</sup>* − total angle of combustion,[m]

*m*− Vibe's exponent, (m=3.5).

modynamic method

where:

*CV* <sup>1</sup> −specific heat of agent at constant volume in the initial point of combustion process,[kJ/ kgK]

*CV* <sup>2</sup> −specific heat of agent at constant volume in the end of combustion process, [kJ/kgK]

*T*<sup>2</sup> −charge temperature at the beginning of the combustion process, [K]

*L <sup>p</sup>* −actual mass demand of air for combustion of 1 kg of fuel, [kmol/kg]

*γ* −coefficient of pollution of the fresh charge with rests of exhaust gases,

*Tm* −maximal temperature of the cycle, [K]

#### **2.3. Method of comparative cycle calculation on the basis of combustion process determined by vibe's function**

Analysis of pressures and temperatures was carried out using the known Vibe's function de‐ termining participation of burnt fuel in the cylinder.

Vibe's combustion function:

$$\chi\left(\alpha\right) = 1 - e^{-6.908 \cdot \left(\frac{\alpha - \theta}{\varphi\_z}\right)^{m+1}}\tag{2}$$

where:

*x* − the distance of the piston from the TDC,[m]

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

*θ* − angle of combustion start,[m]

**4.** For a spark ignition engine heat is supplied at a constant volume, however, the possibil‐

**5.** The rest of exhaust gasses (mass, temperature and pressure) left from the former work

**7.** For calculations purposes a substitutive calculation coefficient of air excess was adopted corresponding to the charge stratification in such a way that combustion of a stratified charge gives maximal pressure and temperature of combustion which is equal to the

ity of incomplete and non – total combustion is taken into account.

pressure and temperature of a homogeneous charge combustion.

*p*

*L* x

*T*<sup>2</sup> −charge temperature at the beginning of the combustion process, [K]

*L <sup>p</sup>* −actual mass demand of air for combustion of 1 kg of fuel, [kmol/kg]

*γ* −coefficient of pollution of the fresh charge with rests of exhaust gases,

( )

a

1

*<sup>z</sup> x e*

**2.3. Method of comparative cycle calculation on the basis of combustion process**

Analysis of pressures and temperatures was carried out using the known Vibe's function de‐

6.908

a q

<sup>+</sup> æ ö - - ×ç ÷ ç ÷

j 1

è ø = - (2)

*m*

*Tm* −maximal temperature of the cycle, [K]

termining participation of burnt fuel in the cylinder.

*x* − the distance of the piston from the TDC,[m]

**determined by vibe's function**

Vibe's combustion function:

where:

Basic equation of heat balance used for calculations takes this form:

**6.** Heat exchanged between the factor and walls of the combustion is neglected.

( ) 1 2 <sup>2</sup> 1 *u v rv m*

g

*CV* <sup>1</sup> −specific heat of agent at constant volume in the initial point of combustion process,[kJ/

*CV* <sup>2</sup> −specific heat of agent at constant volume in the end of combustion process, [kJ/kgK]

*<sup>W</sup> C T C T*

<sup>×</sup> ×+ =× ×

m

× + (1)

cycle are considered.

88 Advances in Internal Combustion Engines and Fuel Technologies

where:

kgK]

*φ<sup>Z</sup>* − total angle of combustion,[m]

*m*− Vibe's exponent, (m=3.5).

Two mathematical models were elaborated by use of which the required values of pressures and temperatures were calculated for both algorithms for the same data in order to compare the obtained results. The mathematical model was elaborated by use of *Mathcad Professional.*

## **2.4. Comparison of pressure and temperature calculated by use of the thermodynamics and vibe's method with reference to real indicated pressure in a GDI**

For either of these models calculation of pressures for charges of different coefficient of air excess λ were performed in order to calculate a substitute coefficient of air excess λz; these are presented in *Fig.2* and *Fig.3* respectively. Subsequently, in *Fig.4* pressure traces for the two methods were presented respectively; moreover a comparison of indicated pressures calculated by use of the thermodynamic method and Vibe's method was given with refer‐ ence to the indicated pressure in a Gasoline Direct .

A comparison of traces of temperature changes for these methods was given in *Fig.5*.

**Figure 2.** Traces of pressure changes in the cylinder for various coefficient of air excess λ obtained by use of the ther‐ modynamic method

For determination of the decrease in fuel consumption a comparison of maximal values of combustion pressures of a homogeneous and stratified charge was made.

Stratification of the charge was chosen in such a way that 5 zones of different coefficients of air excess λ occurred, this was shown in *Fig. 1*.

At the assumption of equal volumes of charges of λ = 0.9 and λ = 1.9 a subsidiary calculation coefficient of air excess λz = 1.113. Combustion of such a stratified charge gives maximal combustion pressure and temperature equal to the pressure and temperature of a homoge‐ neous charge of λ = 1.

**Figure 4.** Diagrams of pressures obtained by use of two methods for a substitutive coefficient of air excess λ<sup>z</sup> =1.113 and a comparison of indicated pressures calculated by use of the thermodynamic and Vibe's method with indicated

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91

**Figure 5.** Diagrams of temperature obtained by use of two methods for a substitutive coefficient of air excess λz =1.113

pressure in a gasoline direct injection engine

**Figure 3.** Traces of pressure changes in the cylinder for various coefficient of air excess λ obtained by use of method with use of Vibe's combustion function

Stratified Charge Combustion in a Spark-Ignition Engine With Direct Injection System http://dx.doi.org/10.5772/53971 91

For determination of the decrease in fuel consumption a comparison of maximal values of

Stratification of the charge was chosen in such a way that 5 zones of different coefficients of

At the assumption of equal volumes of charges of λ = 0.9 and λ = 1.9 a subsidiary calculation coefficient of air excess λz = 1.113. Combustion of such a stratified charge gives maximal combustion pressure and temperature equal to the pressure and temperature of a homoge‐

**Figure 3.** Traces of pressure changes in the cylinder for various coefficient of air excess λ obtained by use of method

combustion pressures of a homogeneous and stratified charge was made.

air excess λ occurred, this was shown in *Fig. 1*.

90 Advances in Internal Combustion Engines and Fuel Technologies

neous charge of λ = 1.

with use of Vibe's combustion function

**Figure 4.** Diagrams of pressures obtained by use of two methods for a substitutive coefficient of air excess λ<sup>z</sup> =1.113 and a comparison of indicated pressures calculated by use of the thermodynamic and Vibe's method with indicated pressure in a gasoline direct injection engine

**Figure 5.** Diagrams of temperature obtained by use of two methods for a substitutive coefficient of air excess λz =1.113
