Startseite Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
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Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes

  • Sebastian Różowicz EMAIL logo
Veröffentlicht/Copyright: 20. März 2018
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Open Physics
Aus der Zeitschrift Open Physics Band 16 Heft 1

Abstract

The paper presents the results of analytical and experimental studies concerning the influence of different kinds of fuel additives on the quality of the spark discharge for different configurations of the ignition system. The wear of the spark plug electrode and the value of spark discharge were determined for various impurities and configurations of the air-fuel mixture.

Keywords: ignition system; spark plugs; fuel mixture impurities; microstructure; laser welding; refractory materials
PACS: 07.05.Bx; 07.05.Tp; 01.50.Pa; 02.60.Cb

1 Introduction

The dynamic development of the automotive industry in recent decades has been linked to the continuous improvement of the components of internal combustion engines. Consequently, increased reliability and better environmental performance have been achieved. One of the components that considerably influenced those two factors is the ignition system [1, 2, 5, 9, 11, 12, 13, 14]. The purpose of the ignition system is to provide the electrical spark to ignite air fuel mixture in the cylinder at the appropriate time and with the required spark discharge energy [1, 3, 4, 6]. It is vital that the electrical charge provided by the ignition system to the plug be of high frequency, high stability and sufficient duration. All the properties of the spark discharge significantly affect the quality of the combustion process of the fuel-air mixture in the engine cylinder, and therefore the toxicity of the exhaust gas. In addition, to prevent the detonation in the fuel, additives are usually used. Some fuel (mixture) combustion products may accumulate on the power supply components (plug insulators) or in the combustion chamber of the engine, thereby reducing emission or hindering the ignition of the mixture, which results in the increased toxicity of the exhaust gas. The increased degradation of the ignition system components (the spark plug) affects the spark energy value and leads to the increased wear of the spark plug electrode. The use of worn spark plug in the increased temperature of the combustion chamber can result in uneven engine operation, loss of power and increased fuel consumption. The dynamics of the phenomena in the ignition system together with the influence of external factors make the analysis a difficult research problem. Many scientists around the world carry out research into optimum operation of ignition system. However, the results of the simulation tests differ from those obtained experimentally.

In the paper an attempt is made to analyse the operation of the ignition system by means of digital simulation and subsequent verification of the results obtained on a real object. Both the spark energy value for different levels of impurities in the air-fuel mixture and the wear of the plug electrode were determined.

2 Toxic components in the exhaust gases

In the exhaust gas the level of CO, CmHn, NOx and soot levels in diesel engines should be subject to control. Carbon monoxide and hydrocarbons are produced as a result of the incomplete combustion process, where CO depends on the coefficient λ. Nitrogen oxides are the natural chemical products of the combustion reaction. The effect of the composition of the mixture on the toxic constituents of the exhaust gas is shown in Figure 1.

Figure 1 The content of toxic components in the exhaust gas as a function of the composition of the mixture [8]
Figure 1

The content of toxic components in the exhaust gas as a function of the composition of the mixture [8]

There are several ways to reduce the toxicity of exhaust by acting on the composition of the mixture. One of the methods is to feed the engine with a lean mixture (λ = 1,2 ÷ 1,3). This reduces the content of nitrogen oxides NOx, but then at the same time the level of hydrocarbons CmHn raises. Requirements for the precise dosage of fuel are very high, because the mix is depleted to the flammable limit. This method of NOx reduction has proved to be unfavorable, since the engine develops lower power, while wear of spark plugs and simultaneously fuel consumption are increased. When the engine power supply is rich (λ = 0.7 − 0.55), the content of NOx is also relatively low. The increased emission of CmHn and CO can be reduced by using an afterburner in the exhaust system. The disadvantage of this solution is the increased fuel consumption, up to 30%. The study showed that the best settlement is to feed the engine with stoichiometric mixture (λ = 1). On the other hand, when it is fed with the rich mixture, low presence of CO and NOx is reduced to free N2. Then the afterburner does not cause reduction of nitrogen oxides, because the excess oxygen, and too small amount of CO prevent the reduction of NOx to N2 [8, 11, 12, 13, 14, 15].

3 Model of the ignition system

Ignition systems accumulating energy in inductance are more commonly used than those accumulating energy in capacitance [1, 2, 3]. In Figure 2a diagram of ignition system used to build a mathematical model is shown.

Figure 2 Model of the ignition system for the simulation studies. Ub – battery voltage, R1 – resistance of the ignition coil primary winding, L1 – inductance of the ignition coil primary winding, L2 – inductance of the ignition coil secondary winding, R2 – resistance of the ignition coil secondary winding, R4 – resistance representing the losses in the coil core, R3 – radioelectrical interference resistance, R45 – flow resistance of the spark plug, Rls – discharge resistance, C2 – self-capacity of the coil, C45 – selfcapacity of the spark plug, M – coupling [1, 2]
Figure 2

Model of the ignition system for the simulation studies. Ub – battery voltage, R1 – resistance of the ignition coil primary winding, L1 – inductance of the ignition coil primary winding, L2 – inductance of the ignition coil secondary winding, R2 – resistance of the ignition coil secondary winding, R4 – resistance representing the losses in the coil core, R3 – radioelectrical interference resistance, R45 – flow resistance of the spark plug, Rls – discharge resistance, C2 – self-capacity of the coil, C45 – selfcapacity of the spark plug, M – coupling [1, 2]

The equivalent circuit of the ignition system presented in Figure 2 is described by equations (1) for two states of the control block.

UB−i1R1−L1di1dt+Mdi2dt=0,L2di2dt−Mdi1dt+i2R2+i3R3+uC45=0,uC2=L2di2dt−Mdi1dt+i2R2,uC2=iR4R4,i3=i2+iR4+iC2i3=iR45+iC45,uC45=iR45R45iC2=C2duC2dt,iC45=C45duC45dt(1)

By introducing state variables: x1= i1, x2= i2, x3= uC2, x4= uC45 to the equation (1):

UB−x1R1−L1dx1dt+Mdx2dt=0,L2dx2dt−Mdx1dt+x2R2+R3x4R45+R3C45dx4dt+x4=0,x3=L2dx2dt−Mdx1dt+x2R2x4R45+C45dx4dt=x2+x3R4+C2dx3dt(2)

Transforming the system of equations (2), we obtain:

dx1dt=A1x1+B1x2+C1x3+D1UBdx2dt=A2x1+B2x2+C2x3+D2UBdx3dt=A3x1+B3x2+C3x3+E3x3+D3UBdx4dt=A4x1+B4x2+C4x3+E4x4+D4UB(3)

where the parameters are determined using the following relationships:

A1=R1M2L2−L1,B1=MR2L2M2L2−L1,C1=−ML2M2L2−L1,D1=−1M2L2−L1,A2=−MR1L1L2−M2L1,B2=−R2L2−M2L1,C2=1L2−M2L1,D2=ML1L2−M2L1,A3=C45A4C2,B3=C45B4C2−1C2,C3=C45C4C2−1C2,D3=C45C2D4UB,E3=1C2R45+C45E4C2,A4=MA12R3C45−L2A22R3C45,B4=MB12R3C45−L2B22R3C45+R22R3C45,C4=MC12R3C45−L2C22R3C45,D4=−L2D22R3C45,E4=−R32R3C45R45+12R3C45(4)

The solution to Equation (3) has the form:

x=x1x2x3x4,A=A1B1C10A2B2C20A3B3C3E3A4B4C4E4,B=UBD1D2D3D4(5)

At the first switch-on, the initial conditions are zero and Eq. (5) assumes the form:

ddtx=Ax+B,x=eAtx0+∫0teA(t−τ)Bdτ,x=∫0teA(t−τ)Bdτ(6)

The solution of equations for the control block (Figure 2) in the open state was obtained by using the state variable method.

The next stage of the calculation (7) refers to the operation of the system with the closed-loop control block where the initial conditions, i.e., the final conditions of the previous state (1), have to be calculated from the control block formula in the contact state for the time equal to the time of contact.

UB−i3R1−L1di3dt+Mdi2dt−L2di2dt+Mdi3dt−i3R3−uC45=0,uC2=L2di2dt−Mdi3dt+i2R2,uC2=iR4R4,i3=i2+iR4+iC2,i3=iR45+iC45,uC45=iR45R45,iC2=C2duC2dt,iC45=C45duC45dt(7)

In this case, the unknowns are: i2, i3, iR4, iC2, iR45, iC45, uC2, and uC45.

By introducing state variables: x1 = i2, x2 = i3, x3 = uC2, x4 = uC45 to the equation (7):

UB−x2(R1+R3)+(M−L1)dx2dt+(M−L2)dx1dt−x4=0x3=L2dx1dt−Mdx2dt+x1R2→dx2dt=L2Mdx1dt+x1R2M−1Mx3x2=x1+x3R4+C2x3dt→C2x3dt=−x1+x2−x3R4x2=x4R45+C45dx4dt→C45dx4dt=x2−x4R45(8)

Transforming the system of equations (8), we obtain:

dx1dt=a1x1+b1x2+c1x3+d1x4+e1UBdx2dt=a2x1+b2x2+c2x3+d2x4+e2UBdx3dt=a3x1+b3x2+c3x3dx4dt=b4x2+d4x4(9)

For the system of equations (9) the parameters a1 … d4 are defined by the relationships:

a1=−R2(M−L1)[L2(M−L1)+M(M−L2)],b1=M(R1+R3)[L2(M−L1)+M(M−L2)],c1=(M−L1)[L2(M−L1)+M(M−L2)],d1=M[L2(M−L1)+M(M−L2)],e1=−d1,a2=a1L2+R2M,b2=b1L2M,c2=c1L2−1Md2=d1L2M,e2=−e1L2Ma3=−1C2,b3=1C2,c3=−1C2R4,b4=1C45,d4=−1C45R45(10)

The solution to Equation (9) has the form:

x=x1x2x3x4,A=a1b1c1d1a2b2c2d2a3b3c300b40d4,B=UBe1e200(11)

Eq. (9) assumes the form:

ddtx=Ax+B,x=eAtx0+∫0teA(t−τ)Bdτ(12)

x0 – initial conditions, or final conditions from the previous state, to be calculated from the formulae for the control block in the contact state for the time equal to the time of contact [2].

The time t will be counted from the moment the block is no longer in the contact state.

The results of the computer simulation shown in Figure 3 show the difference in the voltage waveforms u1(t) and u2(t). It is evident that the response of u2(t) (the output voltage to the new spark plug) is different from the response of the spark plug working for 40 hours with contaminated fuel.

Figure 3 Secondary voltage for new spark plug u1(t) and voltage u2(t) for spark plug after 30 hours of working with contaminated fuel
Figure 3

Secondary voltage for new spark plug u1(t) and voltage u2(t) for spark plug after 30 hours of working with contaminated fuel

It is worth getting to know even the outline of the waveforms that arise as a result of the load of the ignition wire by components such as the spark plug. We often see the effects of reflections on the ends of cables and multiple overlapping of the reflected waves. It can be assumed that such a match will have a significant impact on the spark discharge and consequently the energy, the reliability of the ignition or, of such importance in the present day, the toxicity of exhaust gases. In summary, it seems that the more appropriate model of the ignition system should be the model (being developed by the authors of this paper), which takes into account, in addition, the shape of the spark plug electrodes and the description of the ignition cable as a distributed system.

4 Results of studies

4.1 The effect of fuel impurities on the wear of spark plug electrodes

In both types of ignition systems, one-electrode NGK spark plugs were used. The tests were carried out at combustion temperature of the fuel-air mixture of 500° C. First assessment of the spark plug wear was made after 10 hours of service (Figure 4a, 4b), and the next after 30 hours (Figure 4c, 4d). In all experiments the air-fuel mixture containing impurities was used.

Figure 4 The image of the gap between electrodes
Figure 4

The image of the gap between electrodes

The analysis of the wear of emission surfaces of electrodes was conducted using HIROX KH-8700 electron scanning microscope.

4.2 Determination of spark discharge energy for different types of electrodes

For an 30 hour operation of spark plugs at 500°C for spark plugs NGK discharge energy for capacitor discharge system, calculated on the basis of the results presented in Figure 5a and 5b, amounts to 32.6 mJ.

Figure 5 (a) Current for 10 hour and 30 hour operation of spark plugs at 500°C; (b) Voltage for 10 hour and 30 hour operation of spark plugs at 500°C Calculated energy is: E = 32.6 mJ
Figure 5

(a) Current for 10 hour and 30 hour operation of spark plugs at 500°C; (b) Voltage for 10 hour and 30 hour operation of spark plugs at 500°C Calculated energy is: E = 32.6 mJ

5 Conclusion

Very good results in NOx reduction can be achieved by using spark plugs with increased hardness of the electrodes by surfacing. As it is shown by simulated studies, (Figure 5a and 5b), the most advantageous fuel-air mixture for the internal combustion engine is a stoichiometric mixture (λ = 1).

The results of the study indicate that the energy of the spark discharge after 30 hours of operation has decreased by about 10% compared to the initial state.

References

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Received: 2017-10-31
Accepted: 2017-11-30
Published Online: 2018-03-20

© 2018 Sebastian Różowicz, published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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https://doi.org/10.1515/phys-2018-0011
Schlagwörter für diesen Artikel
ignition system; spark plugs; fuel mixture impurities; microstructure; laser welding; refractory materials
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  9. Constructing analytic solutions on the Tricomi equation
  10. Feynman diagrams and rooted maps
  11. New type of chaos synchronization in discrete-time systems: the F-M synchronization
  12. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus
  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
  16. Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
  17. Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction
  18. A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis
  19. Dynamics of a dry-rebounding drop: observations, simulations, and modeling
  20. Modeling the initial mechanical response and yielding behavior of gelled crude oil
  21. Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation
  22. Solitary wave solutions of two KdV-type equations
  23. Applying industrial tomography to control and optimization flow systems
  24. Reconstructing time series into a complex network to assess the evolution dynamics of the correlations among energy prices
  25. An optimal solution for software testing case generation based on particle swarm optimization
  26. Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation
  27. Alternative methods for solving nonlinear two-point boundary value problems
  28. Global model simulation of OH production in pulsed-DC atmospheric pressure helium-air plasma jets
  29. Experimental investigation on optical vortex tweezers for microbubble trapping
  30. Joint measurements of optical parameters by irradiance scintillation and angle-of-arrival fluctuations
  31. M-polynomials and topological indices of hex-derived networks
  32. Generalized convergence analysis of the fractional order systems
  33. Porous flow characteristics of solution-gas drive in tight oil reservoirs
  34. Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method
  35. A Note on Koide’s Doubly Special Parametrization of Quark Masses
  36. On right-angled spherical Artin monoid of type Dn
  37. Gas flow regimes judgement in nanoporous media by digital core analysis
  38. 4 + n-dimensional water and waves on four and eleven-dimensional manifolds
  39. Stabilization and Analytic Approximate Solutions of an Optimal Control Problem
  40. On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy
  41. New prediction method for transient productivity of fractured five-spot patterns in low permeability reservoirs at high water cut stages
  42. The collinear equilibrium points in the restricted three body problem with triaxial primaries
  43. Detection of the damage threshold of fused silica components and morphologies of repaired damage sites based on the beam deflection method
  44. On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem
  45. Ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons
  46. Analysis of projectile motion in view of conformable derivative
  47. Computing multiple ABC index and multiple GA index of some grid graphs
  48. Terahertz pulse imaging: A novel denoising method by combing the ant colony algorithm with the compressive sensing
  49. Characteristics of microscopic pore-throat structure of tight oil reservoirs in Sichuan Basin measured by rate-controlled mercury injection
  50. An activity window model for social interaction structure on Twitter
  51. Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method
  52. On the zagreb polynomials of benzenoid systems
  53. Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance
  54. The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method
  55. Quantifying the global solar radiation received in Pietermaritzburg, KwaZulu-Natal to motivate the consumption of solar technologies
  56. Sturm-Liouville difference equations having Bessel and hydrogen atom potential type
  57. Study on the response characteristics of oil wells after deep profile control in low permeability fractured reservoirs
  58. Depiction and analysis of a modified theta shaped double negative metamaterial for satellite application
  59. An attempt to geometrize electromagnetism
  60. Structure of traveling wave solutions for some nonlinear models via modified mathematical method
  61. Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation
  62. Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations
  63. Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel
  64. Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials
  65. Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity
  66. Rank correlation between centrality metrics in complex networks: an empirical study
  67. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  68. Modeling of electric and heat processes in spot resistance welding of cross-wire steel bars
  69. Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure
  70. Design optimization of an axial-field eddy-current magnetic coupling based on magneto-thermal analytical model
  71. Thermal constitutive matrix applied to asynchronous electrical machine using the cell method
  72. Temperature distribution around thin electroconductive layers created on composite textile substrates
  73. Model of the multipolar engine with decreased cogging torque by asymmetrical distribution of the magnets
  74. Analysis of spatial thermal field in a magnetic bearing
  75. Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
  76. Assessment of short/long term electric field strength measurements for a pilot district
  77. Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence
  78. Magnetic transmission gear finite element simulation with iron pole hysteresis
  79. Pulsed excitation terahertz tomography – multiparametric approach
  80. Low and high frequency model of three phase transformer by frequency response analysis measurement
  81. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion
  82. Optimal design of a for middle-low-speed maglev trains
  83. Eddy current modeling in linear and nonlinear multifilamentary composite materials
  84. The visual attention saliency map for movie retrospection
  85. AC/DC current ratio in a current superimposition variable flux reluctance machine
  86. Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method
  87. Cogging force reduction in linear tubular flux switching permanent-magnet machines
  88. Modeling hysteresis curves of La(FeCoSi)13 compound near the transition point with the GRUCAD model
  89. Electro-magneto-hydrodynamic lubrication
  90. 3-D Electromagnetic field analysis of wireless power transfer system using K computer
  91. Simplified simulation technique of rotating, induction heated, calender rolls for study of temperature field control
  92. Design, fabrication and testing of electroadhesive interdigital electrodes
  93. A method to reduce partial discharges in motor windings fed by PWM inverter
  94. Reluctance network lumped mechanical & thermal models for the modeling and predesign of concentrated flux synchronous machine
  95. Special Issue Applications of Nonlinear Dynamics
  96. Study on dynamic characteristics of silo-stock-foundation interaction system under seismic load
  97. Microblog topic evolution computing based on LDA algorithm
  98. Modeling the creep damage effect on the creep crack growth behavior of rotor steel
  99. Neighborhood condition for all fractional (g, f, n′, m)-critical deleted graphs
  100. Chinese open information extraction based on DBMCSS in the field of national information resources
  101. 10.1515/phys-2018-0079
  102. CPW-fed circularly-polarized antenna array with high front-to-back ratio and low-profile
  103. Intelligent Monitoring Network Construction based on the utilization of the Internet of things (IoT) in the Metallurgical Coking Process
  104. Temperature detection technology of power equipment based on Fiber Bragg Grating
  105. Research on a rotational speed control strategy of the mandrel in a rotary steering system
  106. Dynamic load balancing algorithm for large data flow in distributed complex networks
  107. Super-structured photonic crystal fiber Bragg grating biosensor image model based on sparse matrix
  108. Fractal-based techniques for physiological time series: An updated approach
  109. Analysis of the Imaging Characteristics of the KB and KBA X-ray Microscopes at Non-coaxial Grazing Incidence
  110. Application of modified culture Kalman filter in bearing fault diagnosis
  111. Exact solutions and conservation laws for the modified equal width-Burgers equation
  112. On topological properties of block shift and hierarchical hypercube networks
  113. Elastic properties and plane acoustic velocity of cubic Sr2CaMoO6 and Sr2CaWO6 from first-principles calculations
  114. A note on the transmission feasibility problem in networks
  115. Ontology learning algorithm using weak functions
  116. Diagnosis of the power frequency vacuum arc shape based on 2D-PIV
  117. Parametric simulation analysis and reliability of escalator truss
  118. A new algorithm for real economy benefit evaluation based on big data analysis
  119. Synergy analysis of agricultural economic cycle fluctuation based on ant colony algorithm
  120. Multi-level encryption algorithm for user-related information across social networks
  121. Multi-target tracking algorithm in intelligent transportation based on wireless sensor network
  122. Fast recognition method of moving video images based on BP neural networks
  123. Compressed sensing image restoration algorithm based on improved SURF operator
  124. Design of load optimal control algorithm for smart grid based on demand response in different scenarios
  125. Face recognition method based on GA-BP neural network algorithm
  126. Optimal path selection algorithm for mobile beacons in sensor network under non-dense distribution
  127. Localization and recognition algorithm for fuzzy anomaly data in big data networks
  128. Urban road traffic flow control under incidental congestion as a function of accident duration
  129. Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm
  130. Feasibility simulation of aseismic structure design for long-span bridges
  131. Construction of renewable energy supply chain model based on LCA
  132. The tribological properties study of carbon fabric/ epoxy composites reinforced by nano-TiO2 and MWNTs
  133. A text-Image feature mapping algorithm based on transfer learning
  134. Fast recognition algorithm for static traffic sign information
  135. Topical Issue: Clean Energy: Materials, Processes and Energy Generation
  136. An investigation of the melting process of RT-35 filled circular thermal energy storage system
  137. Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions
  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
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Heruntergeladen am 22.10.2025 von https://www.degruyterbrill.com/document/doi/10.1515/phys-2018-0011/html
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