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HIGH-FIDELITY NUMERICAL MODELING OF SPARKPLUG EROSION WITH VIZSPARK(Published June 4, 2020)

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HIGH-FIDELITY NUMERICAL MODELING OF SPARK PLUG EROSION WITH VIZSPARK

Overview
Spark-plug erosion is critical in determining the overall efficiency of a spark ignition engine. Over its lifetime,a spark plug is subject to millions of firings. Each spark event results in material erosion due to several mechanisms such as melting, vaporization, sputtering, and oxidation. With electrode wear, the inter-electrode spacingincreases and a larger voltage difference is required to initiate the spark. The probability of engine misfire also
increases with electrode erosion. Once a critical gap is reached, the energy in the ignition coil is no longer
sufficient to cause a spark breakdown and the spark plug must be replaced. Due to the long relevant timescales
over which erosion occurs and the difficulty of analyzing the spark plug environment during operation, determining spark plug lifetime requires time consuming and expensive field testing. A numerical model capable ofmodeling electrode erosion and deformation would be a useful alternative to supplement the design and fieldtesting of spark plugs. VizSpark is a thermal plasma simulator capable of coupling arc physics with electrodeerosion and deformation. The model includes the capability of coupling high fidelity arc physics with a modelthat can dynamically alter the electrode geometry of an electrode. The erosion mechanism is modeled using aphenomenological model based on energy delivered to the electrode from the arc. The electrode erosion model
is validated against experimental results and a 3D electrode erosion in stationary and cross-flow conditions isperformed as a demonstration.

ObjectiveThe objective of this work is to demonstrate a model capable of coupling arc physics, erosion physics, andelectrode deformation as a fully coupled modeling approach. A phenomenological model capable of modeling
electrode erosion that is suitable for a plasma fluid model is presented along with validation. A demonstrationof how the model can be used to predict lifetime using a realistic 3D spark plug model in cross-flow conditions
is demonstrated.

Erosion Model Validation Simulation Setup
The erosion model is based on previous work described in the literature [1] and quantifies the electrode erosion
as a function of the incident energy flux to the electrode through a proportionality factor called the K-factor.

Figure 1: Domain and mesh for the pin to plane arc simulation. The mesh consists of 9,664 cells. The anode (topelectrode) is conical in shape with base diameter of 0.6 mm, and the cathode (bottom electrode) is cylindrical(diameter 1 mm).

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HIGH-FIDELITY NUMERICAL MODELING OF SPARK PLUG EROSION WITH VIZSPARK

Figure 2: Domain and mesh for the pin to plane arc simulation. The mesh consists of 9,664 cells. The anode (topelectrode) is conical in shape with base diameter of 0.6 mm, and the cathode (bottom electrode) is cylindrical(diameter 1 mm).

Figure 3: Domain (left) and numerical mesh (fight) for 3-D sparkplug with constant current power source andgrounded L-jacket. The boundary where inflow is applied is shown with red arrows. The numerical meshconsisting of 328,287 cells split amongst 40 computing processors.
This K-factor is calibrated against experiments from Refs. 1 and 2 for tungsten (W), iridium (Ir), nickel (Ni),platinum (Pt), tin (Sn) and silver (Ag). The inputs to the model are geometry, electrical parameters and thepredicted outputs are volume of eroded electrode and the total spark discharge energy. The ablation K-factor
for air from Ref. 2 is used in the our simulations which uses input electrical power (surface voltage times surfacecurrent) as the dependent energy.
The geometry and mesh shown in Figure 1 consists of an axisymmetric pin-to-plane spark plug, with acylindrical cathode (diameter 1 mm), and a conical anode (max diameter 0.6 mm). The mesh consists ofvariable sized triangles across the entire domain. At the cathode boundary, a fixed current profile is appliedwith a peak amplitude of 0.9 A that decreases linearly to 0 over 1.1 milliseconds (see Figure 2). The anodeboundary is treated as electrically ground. For the outer boundaries, a symmetry condition is applied such that
there are no far-field gradients for flow or electric field variables.

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HIGH-FIDELITY NUMERICAL MODELING OF SPARK PLUG EROSION WITH VIZSPARK

Figure 4: Time transients of the arc channel and electrodes for the sparkplug in 8 m/s crossflow at start of eachsimulated pulse (10 pulses total).

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HIGH-FIDELITY NUMERICAL MODELING OF SPARK PLUG EROSION WITH VIZSPARK

3-D Spark Plug Erosion
Spark erosion occurs over many millions of spark events. Simulating millions of sparking events at high fidelity
is numerically infeasible. We assume the approximation that the erosion that occurs over long-time scales andmillions of firings can be approximately captured with only a few high-fidelity simulations and a multiplier on
the rate of ablation at the arc root surface. A typical spark duration for a car ignition system is of the orderof 1 millisecond and for inductive ignition systems the current profile will often have a sawtooth waveform. [3]In this work the electrical input boundary condition is specified as a sequence of 100 microsecond sawtooth
current wave form pulses with an initial peak of 50 mA which then decrease linearly to zero as in.
A numerical mesh consisting of 328,287 tetrahedral cells is imposed on the problem domain and shown in
Figure 3. A domain decomposition approach is utilized, where the numerical mesh is split equally amongst
multiple processors and solved in parallel to reduce the computational solve time.
For both flow and no-flow simulations, 10 numerical pulses of 0.1 milliseconds are applied. Each pulse
consists of applying an input current with peak current of 50 mA which then decreases linearly to zero (sawtoothpulsing).
The rate at which ablation takes place along the electrode surface can be accelerated beyond the timescaleof the arc event by applying a multiplicative factor to the surface erosion rate calculated by the surface erosion
model. We apply an erosion multiplicative factor of 106 such that each simulated pulse removes the mass thatapproximately 106 real sparking events would remove.
Each simulated pulse is separated by 20 microseconds of zero-current off time. During the pulse off-time,
the arc channel quenches such that each new pulse is applied to a cool arc channel and ensuring that eachsimulated spark is independent of the prior simulated arc.

8 m/s Crossflow
The results for the simulation with an 8 m/s cross-flow are presented first. Figure 4 presents time snapshots of
the arc temperature and the electrode surface topology at the end of each simulated pulse. One can see the arc
stretch due to the cross-flow in each of the images and the steady removal of cells on the powered cathode as
the simulation evolves with time.
Figure 5 presents the current applied and voltage measured at the base (bottom side) of the powered electrodeas function of pulse. The current was applied in a series of saw-tooth pulses and the voltage on the electrodeis obtained self-consistently by the solver. Observe that initially, there is a high voltage spike at the start ofeach current pulse indicating gas breakdown. Note also, the increase in voltage as the arc stretches with thecross-flow during each pulse. Furthermore, as the electrode surface erodes and the gap distance increases, thearc voltages required to maintain the arc change. In general, the voltages increase as the surface erodes.

No-Crossflow
The same simulation configuration is repeated with no-crossflow to determine the impact of flow on spark lifetime.
The voltage and current transients as a function of individual pulses are shown in Figure 5. The same sawtooth current profile that was used for the cross-flow case is used as a boundary condition input to the cathode.
The voltage profile displays voltage peaks during breakdown and a slow increase in the voltage. Compared

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HIGH-FIDELITY NUMERICAL MODELING OF SPARK PLUG EROSION WITH VIZSPARKFigure 5: Electric current (top) and voltage (bottom) transients as function of applied pulse for the simulation
with cross-flow.

Figure 6: Erosion profiles for sparkplug cathode after 10 simulated pulses for the case with 8 m/s crossflow(left) and case with no cross- flow (right).
to the case with cross-flow (Figure 5), the peak voltages are lower and the magnitude of voltage increase overeach pulse duration is lower. The lower voltages indicate that the spark channel resistance in the no-flow caseis lower compared to the cross-flow case. This makes sense intuitively as the channel length and hence channelresistance is lower when there is now cross-flow compared to the case when there is cross-flow and arc stretch.
The erosion profile of the powered electrode (cathode) for the case with and without cross-flow are comparedin Figure 6. The cross-flow case shows preferential wear on the downwind side of the electrode.
The eroded mass of the powered electrode (cathode) for 8 m/s cross-flow and stationary flow comparedin Figure 7. Two trends are noticeable: the first is that during breakdown at the start of each pulse there ismore mass removal then during the arc phase. The second is that the net eroded mass is higher for the case ofcross-flow. The observation of increased material erosion for the case of cross-flow can be explained throughthe following argument: the supplied current for both simulations is the same yet cross-flow stretches the arc.
The arc channel can be thought of as a resistive element, hence a longer stretched arc will have more electricalresistance then a non-stretched arc. More energy is required to maintain a stretched arc compared to a stationary
arc and because electrode erosion is a function of electrical energy deposition, more energy is transferred to theelectrodes which leads to more erosion.

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HIGH-FIDELITY NUMERICAL MODELING OF SPARK PLUG EROSION WITH VIZSPARK

Figure 7: Eroded electrode (cathode) mass as a function of simulated pulses. The eroded mass for stationary
flow is shown with the dashed line (blue). Eroded mass for the cross-flow case is shown with the solid line(red).

References[1] L. A, F. Soldera, and F. Mucklich Zeitschrift fur Metallkunde, vol. 95, no. 2, pp. 102–108, 2004.
[2] F. A. Soldera, F. T. Mucklich, K. Hrastnik, and T. Kaiser, “Description of the discharge process in spark

plugs and its correlation with the electrode erosion patterns,” IEEE Transactions on Vehicular Technology,
vol. 53, pp. 1257–1265, July 2004.
[3] T. Shiraishi, A. Teraji, and Y. Moriyoshi, “The effects of ignition environment and discharge waveformcharacteristics on spark channel formation and relationship between the discharge parameters and the egr
combustion limit,” SAE Int. J. Engines, vol. 9, pp. 171–178, 09 2015.

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