Multiphysics Modeling of Spark Discharges in High Crossflow Ignition Environments

In SI engines, the initial stages of flame kernel formation play an important role in determining the overall thermal efficiency and in reducing the cycle-to-cycle variability. Introducing a cross-flow within the spark gap has shown to reduce the combustion fluctuations by shortening this initial ignition period and activating a larger volume of the fuel-air mixture. This work presents a computational study of spark discharges in high cross-flow ignition environments using a high-fidelity, multi-physics equilibrium plasma solver. The numerical framework is designed to simultaneously model chemically reacting fluid flow coupled with electromagnetics, surface ablation physics and external circuit dynamics in a fully coupled manner. The spark channel is simulated in a constant volume combustion chamber under different operating conditions and cross flow velocities. The simulation model is validated by comparing several key parameters associated with the discharge such as the breakdown voltage, dwell current, restrike timing, and spark stretch against experimental measurements.

High-Fidelity Energy Deposition Ignition Model Coupled With Flame Propagation Models at Engine-Like Flow Conditions

With the heightened pressure on car manufacturers to increase the efficiency and reduce the carbon emissions of their fleets, more challenging engine operation has become a viable option. Highly dilute, boosted, and stratified charge, among others, promise engine efficiency gains and emissions reductions. At such demanding engine conditions, the spark-ignition process is a key factor for the flame initiation propagation and the combustion event. From a computational standpoint, there exists multiple spark-ignition models that perform well under conventional conditions but are not truly predictive under strenuous engine operation modes, where the underlying physics needs to be expanded. In this paper, a hybrid Lagrangian-Eulerian spark-ignition (LESI) model is coupled with different turbulence models, grid sizes, and combustion models. The ignition model, previously developed, relies on coupling Eulerian energy deposition with a Lagrangian particle evolution of the spark channel, at every time-step. The spark channel is attached to the electrodes and allowed to elongate at a speed derived from the flow velocity. The LESI model is used to simulate spark ignition in a non-quiescent crossflow environment at engine-like conditions, using CONVERGE commercial CFD solver. The results highlight the consistency, robustness, and versatility of the model in a range of engine-like setups, from typical with RANS and a larger grid size to high fidelity with LES and a finer grid size. The flame kernel growth is then evaluated against schlieren images from an optical constant volume ignition chamber with a focus on the performance of flame propagation models, such as G-equation and thickened flame model, versus the baseline well-stirred reactor model. Finally, future development details are discussed.

THERMAL RADIATION IN SPARK DISCHARGE

The work is devoted to numerical study on thermal radiation in spark discharge. The influence of radiative thermal conductivity on the expansion of the spark channel has been established. The study of the effect of value of the capacitance of the discharge capacitor on the energy emitted by the discharge has been carried out. The change in the thermodynamic state of the gas in the spark channel is considered taking into account following factors: change in the capacitance of the discharge capacitor, the length of the discharge gap and the initial gas pressure. The influence of the initial gas pressure and the gap length on the parameters of thermal radiation of a gas under conditions of a constant breakdown voltage supplied to the spark gap is investigated.

Numerical simulation of gap length influence on energy deposition in spark discharge

The aim of the work is to study the influence of the length of the spark gap on energy input into the discharge channel during its gas-dynamic expansion. Methodology. The research is carried out by numerical modeling of the process of spark discharge development at variable values of the discharge gap length and at invariable other discharge conditions. The length of the gap was set in the range from 1 mm to 20 mm. The study was conducted using a numerical model of spark development, which takes into account the processes of nonstationary gas-dynamic expansion of the spark channel, the transient process in the electric circuit, nonequilibrium chemical processes, gas ionization, heat transfer and electrons thermal conductivity. The simulation was performed in atmospheric pressure nitrogen. The calculation was performed for various parameters of the RLC circuit, such as capacitance, inductance, resistance and voltage across the capacitor. Results. The study evaluates the influence of the spark length on the discharge current, the resistance of the spark channel, the energy deposited in the spark channel, and the distribution of thermodynamic parameters of the gas during the development of the spark discharge. It is confirmed that increasing the length of the gap increases the resistance of the spark. The deviation from the linear relationship between the deposited energy or the radiated energy and the length of the spark gap is estimated. Scientific novelty. A linear relationship between the gap length and the deposited energy is revealed when the total energy is above tens of Joules. Deviations from the linear dependence were detected in the discharge circuit when the total energy is below one of Joules. Practical value. The research results allow predicting the effect of the spark gap length on the energy input into the discharge channel under conditions of a slight change in the discharge current. In the conditions of essential change of amplitude of discharge current it is expedient to apply numerical researches for specification of changes in the energy deposited into a spark discharge.

EXPERIMENTAL AND NUMERICAL STUDIES OF PRESSURE AND GAP LENGTH EFFECTS ON ENERGY DEPOSITION IN SPARK DISCHARGE

A study of the influence of the discharge gap length and the initial gas pressure on the energy deposition into the discharge channel was done. The study was conducted at the same total discharge energy. It is experimentally shown that the connection of the voltage probe to the discharge circuit significantly affects the discharge current. The determination of the energy deposited into the spark channel is based on the results of numerical simulation of the spark channel development. Experimentally measured discharge currents at different pressures and the gap length were used as initial data for the calculation. Based on the obtained results, it is determined which of the factors (the initial pressure or the gap length) has the strongest influence on the energy input into the spark channel.

Considerations on Spark- Gap Channel Radius and Electrical Conductivity

A simple phenomenological model is established to determine the temporal evolution of spark gap channel radius and electrical conductivity during the resistive phase period. The present determination is based on the Braginskii’s equation for the channel radius which includes the electrical conductivity of the discharge channel as a constant quantity. In the present model, however, the electrical conductivity is regarded as a time varyingquantity. Basing on this, a mathematical formulation for the channel radius as a function of time was derived, and this has made possible the derivation of an explicit expression for the conductivity as a function of time as well. Taking the temporal average of the electrical conductivity offers an alternative mathematical formulation for the instantaneous radius based on a steady conductivity value that can be determined according to some experimental parameters. It has been verified that both of the channel radius formulations mentioned above lead to similar results for the temporal evolution. The obtained results of the channel radius were used to determine the instantaneous inductance of the spark channel. The present model was used to examine the role of gas pressure and gap width on the temporal evolutions of the channel radius, conductivity, and inductance in nanosecond spark gaps.

COMPARISON OF SPARK CHANNEL EXPANSION IN HYDROGEN, OXYGEN AND NITROGEN

The results of the spark channel expansion simulation in various gases such as hydrogen, oxygen and nitrogen have been presented. Difference in thermodynamic properties of the various gases has been taken into account. Influence of a type of gas on the discharge current, the spark resistance, the energy deposited in the spark and the spark gas-dynamic expansion has been found out. Influence of initial species concentration in mixture of nitrogen, hydrogen and oxygen on detonation initiation by spark discharge has been discussed.