Mathematical Simulation of Eccentricity in Spark Plug and its Effects on Combustion Parameters in Spark Ignition Engine

Mathematical Simulation of Eccentricity in

Spark Plug and its Effects on Combustion

Parameters in Spark Ignition Engine

1_{A.Y. Bokhary,} 1_{Abdullah Turki,} 1_{Nafis Ahmad and} 2_{A.H. Jefri}

1

Department of Mechanical Engineering, King Abdulaziz University, Jeddah, Saudi Arabia. 2

Department of Mechanical Engineering, Integral University, Lucknow, India.

ABSTRACT

Spark plug location on cylinder head of a spark ignition engine plays an important role on combustion characteristics. In this paper an attempt has been made to simulate the effect of eccentricity of spark plug on various combustion parameters such as the maximum temperature of the burned and unburned gas, maximum cylinder pressure and normalized flame front area and normalized flame front volume for different values of clearance height, spark advance and crank angle with the help of a two zone combustion model. The simulated results have been compared for a given value of eccentricity with Blizard and Keck [3] turbulent entrainment model and it shows reasonably good agreement.

Keywords: Eccentricity of spark plug, Clearance height, Angle of spark.

INTRODUCTION

the reaction mixture strength, temperature and pressure. The governing equations have been transformed into a moving coordinate system to take into account the piston motion. The model behaves in a satisfactory manner in response to changes in fuel type, equivalence ratio, ignition timing, compression ratio and engine speed. Brown and Fristorm [17] developed a two zone flame model of flame propagation, which allows computation of flame propagation velocity and average properties in the radical generation and fuel type attack region of the flame. The approach is computationally simpler than formal flame velocity calculations, however it provides only limited information since detailed structure information is sacrificed for computational simplicity. Razavi [18] developed a quasi-dimensional cycle simulation program using two zone burning model to examine the effect of eccentricity in spark plug position on combustion in spark ignition engine. The purpose of his study was to model the geometric interaction between the propagating flame and the general cylindrical combustion chamber. It was found that the combustion chamber geometry and the position of spark plug have a strong effect on the burning time duration. In the present work a quasi-dimensional simulation model is based upon Blizard and Keck [3] combustion model to analyze the effect of spark plug location with respect to axis of the cylinder. The spark plug location affects the flame-front area, length of flame travel and time required for the combustion process.

SIMULATION MODEL

In the present simulation a relatively simple case of particular interest in connection with automotive engines is considered. The geometry is shown in figure 1. The combustion chamber is a right circular cylinder of radius ‘R’ with variable height ‘h’. The spark plug is eccentric by a distance ‘RS’ from the cylinder axis. It is assumed that the flame spreads as a spherical wave from the point of ignition. Tables 1 and 2 give the engine data for generating the simulated results and experimental pressure crank angle diagram for validation.

Table - 1: Specifications of the Spark Ignition Engine for (Simulated results):

Parameters Specifications 'mm'

Bore 63.50

Stroke 76.20

Compression ratio 5 : 1

l / r ratio 4.00

Length of connecting rod 200.00

Crank radius 50.00

Clearance height 19.05

Port diameter 24.89

Valve lift 4.83

Table – 2: Specifications of the Engine for (Experimental results):

Parameters Specifications 'mm'

Bore 90

Stroke 74

Compression ratio 5 : 1-19:1

Capacity 470 cc

ENGINE GEOMETRY

MODEL FORMULATION

The aerodynamic effects due to swirl and non-uniform combustion of unburned gas ahead of the flame front are neglected. The variable height ‘h’ is given by the relation,

h = ho + 1/2. S. (1 - Cos) -- (1)

Under these conditions the flame front area is given by the geometry of the flame as shown in the figure (1). Af = 2 . R F .0hd z -- (2)

The volume enclosed by flame front is given by

Vf =0h (r2+R2- R S . R . S i n) d z -- (3)

Where from the geometry,

C o s= ( R S2+ r2- R2) / 2 . R S . r -- (4) C o s= ( R S2+ R2- r2) / 2 . R S . R -- (5) r2 = R F2- z2 -- (6)

The above equations are solved by improved Euler’s method.

Normalized flame front area is given by

af = Af/ 2R2 -- (7)

Normalized volume enclosed by flame front is given by

vf = Vf /R2h -- (8)

The equation for v f can be approximated as

vf = ( 1 - y- 1) / ( 1 - y1- 1) -- (9)

Where

y = ( V / Vi) ( P / Pi) 1 / -- (10)

Where y1 is the value of y for x = 1 i.e. for fully burned mixture is given by

Where,

= (u-b) / (b- 1 ) -- (12)

b1= bi ( h1/ hi) (i- 1 ) -- (13)

It is further assumed that the compression of unburned gas is isentropic.

The unburned gas temperature is determined by the equation,

Tu = Tu o ( C R )(u – 1 ) -- (14)

Where,

C R = ( ho + S ) / ho -- (15)

The burned gas temperature is determined by the equation

Tb = [50000(1-)+{8.0+0.5(-1)}Tu]/{12.8+4.5(-1)} -- (16)

Non-dimensional flame radius is given by the equation

BRF= [-s-d{1-e- (-s ) /d}]/b -- (17)

b is an apparent burning angle given by

b= (. R / Ue) ( 1 - y1- 1) / l n y1 -- (18)

Ue is the turbulent entrainment velocity given by

Ue = 0 . 2 8 Ui -- (19)

Ui is inlet gas speed given by

Ui= (v. N . S . D2) / ( 2 . Dp. V L ) -- (20)

Where,

b = bi ( h / hi) (- 1 ) -- (21)

Where

bi = hf/ ( Cv u . Ti) -- (22)

d is an induction angle given by

d= 1 5 / 2 (le/ Ul) { (+) / ( bs-) } l n y 1 -- (23)

le is the eddy radius given by

le = 0 . 1 7 ( hs/ hi) . V L -- (24)

Laminar flame velocity Ul is given by

Ul = Uo. (R Ro). e {(EA/ 2R) (1/Tbo- 1/Tb)} -- (25)

Where hs/hi is reciprocal of the compression ratio at ignition.

Pressure of the gas is given by the equation

P = Pi . y 

u ( Vi/ V ) 

u -- (26)

The fraction of mass burned ‘x’ is calculated from the relation

x = { ( 1 +) ( y- 1 ) - ( y- 1- 1 ) } / ( b -. y- 1) -- (27)

RESULTS AND DISCUSSIONS

A parametric study of combustion in spark ignition engine has been carried out with the help of the graphs generated by taking into account the effect of different engine operating parameters as well as eccentricity in spark plug.

flame zone. The spark plug location in the centre gives approximately twice the flame surface area of the side plug geometry at a given flame radius and burns about twice as fast. The maximum cylinder pressure is high at smaller values of clearance height because of higher values of compression ratio.

Fig. 5 shows the variation of normalized maximum flame front area with respect to eccentricity of spark plug for different values of clearance height at the same angle of spark. It is evident from the figure that the normalized maximum flame front area decreases with an increase in eccentricity of spark plug. It may be due to the reason that the quenching of the flame takes place with cylinder walls. The value of normalized maximum flame front area is more at higher values of clearance height because of lower compression ratios.

Fig. 8 shows the variation of normalized maximum volume of the flame with respect to eccentricity in spark plug for different values of spark angle at constant engine speed of 2000 RPM. The figure shows that the value of the normalized maximum volume of the flame becomes almost constant for higher angles of spark i.e. 38 and 30 deg. BTDC. But the value of the normalized maximum volume of the flame decreases slightly at higher values of eccentricity of spark plug for smaller angle of spark i.e. 20 deg. BTDC, whereas the normalized maximum volume of the flame decreases appreciably with increase in the eccentricity of spark plug at spark angle of 10 deg. BTDC.

Fig. 10 shows the variation of normalized volume enclosed by flame front with respect to crank angle at different values of eccentricity in spark plug at the same angle of spark and engine speed. It can be observed from the figure that the normalized volume enclosed by flame front increases with an increase in crank angle and after a certain period it shows a constant trend for all. It can also be noticed from the figure that for higher values of eccentricities, the normalized volume enclosed by the flame front for different values of eccentricity approximately follow the similar trend.

Crank angle (Degrees)

-200 -150 -100 -50 0 50 100 150 200

Cy li n der Pr ess ur e ( b ar ) -10 0 10 20 30 40 50 60 Theo. Pressure Expt. Pressure

N = 2000 RPM CR = 8:1

Fig. 12 shows the comparison between experimental and theoretical pressure crank angle diagram

CONCLUSIONS

The following conclusions can be drawn for the cylindrical combustion chamber in which flame propagation occurs roughly spherically:

1. By increasing the percentage in eccentricity in spark plug, the temperatures of unburned and burned gas, maximum cylinder pressure, flame front area and flame front volume will decrease.

2. A validation has been made for normalized flame front volume for reference [3]. The comparison shows good agreement between the two results.

3. A pressure crank angle diagram is also generated and validated with the simulated results. The simulated results still need to be experimentally validated for different values of eccentricities, so that it can be used as a tool for engine design.

NOMENCLATURE

D Diameter of cylindrical vessel h Variable height of the vessel ho Clearance height

S Stroke length

R Radius of cylinder RS Eccentricity of spark plug

 Crank angle relative to TDC

TDC Top dead center

ANGS Angle of spark BTDC Before top dead centre Ti Temperature at end of

compression

Pi Pressure at end of compression

Vi Initial volume of mixture

Cvu Constant Volume Specific heat of

unburned gases

CR Compression ratio

CRS Compression ratio at spark

Tuo Temperature of unburned gas

before compression

 Equivalence ratio (fuel-air) Tb Temperature of burned gas

Ul Laminar burning velocity

le Eddy radius

VL Valve lift

Tu Temperature of unburned gas

BRF= RF/R Non dimensional Flame radius Ue Entrainment velocity

Ui Inlet gas speed

RF Flame front radius Af Flame front area

Vf Volume enclosed by flame front

BH Normalized height i.e. h/R

, Arc angles made by flame front RPM Revolution per minute

 Mole fraction of burned gas recycled

s Spark angle

v Volumetric efficiency

N Engine speed

 Angular velocity L Turbulent integral scale

u Density of unburned gas

mb Mass burned

Sl Laminar flame speed

St Turbulent flame speed

 Normalized chemical reaction time

RRo Density ratio

EA Apparent activation energy

Dp Port diameter

b Apparent burning angle

d Induction angle

i Inlet conditions

b Non-dimensional quantity y Non-dimensional quantity TDC Top dead centre

af Normalized flame front Area Dp Port diameter

vf Normalized volume enclosed by VL Valve lift

flame front l Connecting rod length

r Crank radius

REFERENCES

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published in Fire and Materials Volume 2, Issue 3 pp 117 – 121, September 2004.