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This article analyses numerically the simultaneous influence of the compression rate, fuel nature and the advanced injection of fuel on maximum cylinder pressure during the combustion phrase with the help of the Python Spyder calculation code.
Indeed, several authors have shown that the combustion of biofuels
which
make it possible to compensate for fossil and exhaustible resources, presents a cylinder pressure higher by about 3.5% compared to that of conventional diesel D100. This increase in pressure can be reduced by
the
means of control
ling
parameters making it possible to preserve the life of the engine and also reduce nitrogen oxides (NO_{x}) and particular matter (PM). This article has two objectives which are: putting in place a numerical tool for the evaluation and simulation of thermal engines and the influence of control parameters on cylinder pressure. The single zone 0D combustion model which considers only the physical phenomena and considers the mixed fuel as a perfect gas is used. The fuel used is the Neem biofuel produced by Doctor Merlin Ayissi of the University of Douala and the D100 diesel fuel. The results are obtained from three fuel injection angles of 20°, 13° and 10°
before the TDC (Top Dead Centre) and three values of the engine compression rates of 15, 20 and 25. The delay in combustion is characteristic of the fuel used as illustrated by the
cetane
number. The results show that the cylinder pressure increases with
increasing compression rate and a very high advanced injection. It also shows that the pressure is high when diesel D100 is used instead of D100 biodiesel
.

The engine sector for many years has been faced with the problems of fuel (fossil source which is exhaustible and also fluctuating prices) and pollution. With the objective of finding new fuels capable of replacing the existing sources, many researchers over the years have been pushed to the use of biofuels. The major problem of biofuels is generally the high pressure encountered during their combustion inside the cylinder. Almost all studies show an increase in NO_{x} (nitrogen oxides) in post-combustion gases when biodiesels are used pure whatever the raw material [_{x} is very often due to the temperatures generated by the combustion of biodiesels. Heywood [_{x}) but the cylinder temperatures remain high. The burned gas recirculation (EGR) device makes it possible to reduce the cylinder pressure (temperatures) and consequently the NO_{x} [_{x} reduction. The addition of several fuels has been experimented by researchers to improve the performance of biodiesel [_{x} in the engine.

The single zone 0D model combustion model based on the first law of thermodynamics for a closed system is considered. Assumptions made are [

• A homogenous fuel mixture considered a perfect gas

• Chemical equilibrium is attained during the combustion phase

• The initial combustion pressure is taken after compression

• Evolution of specific volume is a function of the crank angle

• The engine geometry is not considered

• The Woschni model of heat loss is considered

• The double phase Wiebe controls the fuel mass evolution

The auto inflammation delay is given by the Hardenberg and Hase [

Q − W = U (1)

Considering the gas mixture as a perfect gas, hence, the relation [

P V = m R T (2)

With differential form:

V d P + P d V = m R d T (3)

The internal energy of the perfect gas is a function of its temperature with differential form:

d U = d ( m C v T ) implying d U = m C v d T + m T d C v giving

R C v ( d U − m T d C v ) = m R d T (4)

Equations (3) and (4) give:

V d P + P d V = R C v ( d U − m T d C v ) (5)

Using equation (3) gives:

V d P + P d V = R C v ( d U − m T d C v ) (6)

In Equation (6) d U = C v R ( V d P + P d V ) − m T d C v and using the first principle applied to a closed system the following is obtained:

d Q n e t − d Q p − P d V = C v R ( V d P + P d V ) − m T d C v (7)

The classical hypothesis that the combustion chamber contains a homogenous mixture of a perfect gas at thermodynamic equilibrium is considered. When the valves are closed (i.e. compression and expansion phases) the speed at which the net heat is released equals energy flux liberated from burning the fuel after subtracting thermal loses. Dividing Equation (7) by d θ : gives [

d Q n e t d θ − d Q p d θ − P d V d θ = C v R ( V d P d θ + P d V d θ ) − m T d C v d θ (8)

On the other hand: R C v = γ − 1 and C v = R γ − 1 differentiating with respect to θ gives:

d C v d θ = − R ( γ − 1 ) 2 d γ d θ where Equation (8) becomes:

d Q n e t d θ − d Q p d θ − P d V d θ = C v R ( V d P d θ + P d V d θ ) + m R T ( γ − 1 ) 2 d γ d θ

making d P d θ the subject gives [

d P d θ = γ − 1 V ( d Q n e t d θ − d Q p d θ ) − γ P V d V d θ − P γ − 1 d γ d θ (9)

The combustion chamber volume, V, is given by Equation (10) below which is a function of the engine geometric parameters [

V ( θ ) = π D 2 S 8 ( 1 − cos ( θ ) + λ − λ 2 − sin 2 ( θ ) + 2 C R − 1 ) (10)

The differential form of the volume is given by Equation (11) below:

d V ( θ ) d θ = π D 2 S 8 ( 1 − cos θ λ 2 − sin 2 θ ) sin θ (11)

The parameters λ , D, S, θ and CR in Equations (10) and (11) are respectively ratio of crank radius to Connecting rod length, cylinder bore, stroke, crank angle and compression rate. On the other hand, γ is a function of temperature as given by the equation [

γ = 1.458 − 1.628 × 10 − 4 T + 4.139 × 10 − 8 T 2 (12)

The term Q p characterising heat loss can be modeled by the formula:

d Q p d θ = h c A ( θ ) ( T − T p ) 1 ω With ω = 2 π N where N is the rotational speed of

the engine and h c the coefficient of heat transferred by convection given by the Woschni model below as a function of the characteristic engine geometry.

h c = 3.26 D − 0.2 × P 0.8 × T − 0.55 × W 0.8 with W as the piston speed expressed as:

W ( θ ) = 2.28 U ¯ p + C 1 × V d × T a P a × V a ( P ( θ ) − P m ) (13)

During the compression phase, C 1 = 0 while during the combustion and expansion phases:

C 1 = 0.00324 also U ¯ p = N × S 30 . The coefficient C 1 depends on the phase

taking place in a diesel engine. The exchanged area A ( θ ) is given by the equation below:

A ( θ ) = ( π × D 2 2 ) + π × D × L 2 ( λ + 1 − cos θ − λ 2 − sin 2 ( θ ) ) (14)

Q n e t represents the heat liberated during the combustion phase and can be modelled by the double phase Wiebe function, which describes the mass fraction of the fuel burnt during the combustion phase. This is written as [

x b = 1 − exp [ − a ( θ − θ 0 Δ θ ) m + 1 ] (15)

d x b d θ = 1 Δ θ a v ( m v + 1 ) ( θ − θ 0 Δ θ ) m v exp ( − a v ( θ − θ 0 Δ θ ) m v + 1 )

d Q n e t d θ = 1 Δ θ m i n j ⋅ P C I a v ( m v + 1 ) ( θ − θ 0 Δ θ ) m v exp ( − a v ( θ − θ 0 Δ θ ) m v + 1 ) (16)

x b = 1 − exp ( − a v ( θ − θ 0 Δ θ ) m v + 1 ) (17)

The indices a v et m v are the Wiebe function parameters.

a) Engine characteristics

TheLISTER-PETTER-01005299-TS1 Series engine with characteristics listed below is simulated. (

b) Fuel characteristics (

c) Wiebe parameters and heat loses

The model used is a simple phase Wiebe equation, the form factor m v = 0.7 and a v = 5 [

LISTER-PETTER-01005299-TS1 Série | |
---|---|

General Information | 1 Cylinder with natural suction |

Technical details | 4 stroke direct injection |

Cooling system: air cooled | |

Injection pressure (Bar) | 250 |

Bore and Stroke (mm) | 95.3/88.9 |

Connecting rod length (mm) | 165.3 |

Cylinder capacity (cm^{3}) | 630 |

Compression ratio | 15 - 20 - 25 |

fuel injection timing BTDC | 13˚ - 15˚ - 20˚ |

Nominal power | 4.5 KW à 1500 trs/min |

Valve diameters Adm./Ech. (mm) | 42/35 |

Max lift of the valves (mm) | 10.61 |

Number of valves | 2 |

AOA/AOE | 36˚V/76˚V before BTDC |

RFA/RFE | 69˚V/32˚V after TDC |

Fuel Properties | Biofuel (Neem, B100) | Diesel (D100) |
---|---|---|

Density (Kg/m^{3}) | 883.3 | 830 |

Cetane Number | 56 | 39 |

Calorific Value MJ/kg | 37.54 | 42.82 |

%C | 0.7791 | 86 |

%H | 0.1266 | 14 |

%O | 0.111 | Not defined |

The numerical results are obtained by resolving the system of first order differential equations of temperature and cylinder pressure as a function of crank angle in Python. The pressure curves are illustrated in Figures 1-3 below.

The results above analyse the simultaneous influence of fuel nature, compression rate and advanced injection of fuel on peak cylinder pressure.

The Neem B100 and diesel D100 were used with injection advance crank angles of 13˚, 15˚ and 20˚ before TDC and compression ratios of 15, 20 and 25. The injection advance is a determining factor for the peak pressure. The injection advance of the fuel could help predict the quantity of fuel burnt before the TDC (using the Wiebe function) the earlier the fuel is injected, the more the pressure peak approaches the TDC. Attaining peak pressure near the TDC should be avoided because it has an enormous influence on the engine performance parameters and engine components [

The graphs have the same shape when varying the compression ratio in each case. It is seen that the higher the compression ratio the more the maximum pressure is elevated; this means that the initial combustion pressure which

represent the end of the compression phase depends on the compression ratio in the cylinder.

The peak pressure when using the Neem biofuel is more important than that from conventional diesel D100 (C_{10}_{.}_{65}H_{20.8}) due to the presence of oxygen in the chemical composition of the biofuel. This means the combustion of B100 (C_{22.36}H_{43}_{.}_{64}O_{2}) occurs under good conditions as compared to conventional diesel D100. This same remark was made by L. Tabaret [

The validation of the model is based on the experimental carried out by Dr. Ayissi Merlin [

In this article, it was a question of show that the problem of high temperature or high pressure encountered during the combustion of biofuels in diesel engines can be mitigated by the injection advance and the compression ratio of the engine. Equally, it was a question of showing that the emission of pollutants due to the combustion of fossil fuels can be satisfied by the use of biofuels. This study showed that the combustion of biodiesel takes place in better combustion than that of conventional diesel. Indeed, the Neem biodiesel presented a more important peak than the conventional diesel D100. In order to reduce the emission of NO_{x} and particulate matter (PM), we will use the present model to reduce the quantities of NO_{x} that strongly depends on the temperature.

We particularly thank the G.C.C team for always encouraging us in combustion and simulation aspects. We equally thank our team members in the Energy, Electric and Electronic Systems of the University of Yaoundé 1 for welcoming and assisting us in our research.

The authors declare no conflicts of interest regarding the publication of this paper.

Legue, D.R.K., Obounou, M., Henri, E.F., Ayissi, Z.M., Babikir, M.H. and Ehawe, I. (2019) Numerical Analysis of the Compression Ratio’s Influence, the Nature of the Fuel and the Injection Feed on the Cylinder Pressure. Energy and Power Engineering, 11, 249-258. https://doi.org/10.4236/epe.2019.116016

θ : cranck angle (˚CA)

Δ θ : total combustion duration (˚CA)

θ 0 : Start of combustion (˚CA)

X: burnt mass fraction

W: Work done (KJ)

U: Internal energy

CR: Compression ratio

c v : Specific heat at constant volume

h c : heat transfer coefficient (W∙m^{−2}∙K^{−1})

M: Masse (Kg)

R: Gas constant

Q : Heat transfer (KJ)

V: Volume (m^{3})

P: Pressure (Bar)

T: Temperature (K)

A ( θ ) : Area exposed to heat transfer (m2)

D : Cylinder bore (m)

S: Stroke (m)

N: rotational speed of the engine

ω : Angular velocity (rad/s)

U ¯ p : Mean piston speed

BTDC: Before Top Dead Centre