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Numerical simulations of axisymmetric nanosecond pulsed discharges at atmospheric pressure and temperature are performed with a novel fully implicit time integration approach. The plasma fluid equations with a drift-diffusion model and local-field approximation are made dimensionless and solved using a preconditioned Jacobian Free Newton-Krylov method. A simplified kinetics model is employed, including electrons, one positive ion, and one negative ion. The chemical processes of ionization, attachment, detachment, and recombination are considered along with photoionization. The newly developed fully-implicit integration scheme with physics-based preconditioning allows for the efficient simulations capable of describing the cathode sheath over time-scales of O(10 us). The implicit solver overcomes the limiting time scales related to electron drift, diffusion, dielectric relaxation, and ionization. 

A robust and efficient framework for simulating NSPD in multiple dimensions is developed. The reactive Navier-Stokes equations are extended to include a drift-diffusion plasma-fluid model with a local field approximation (LFA) in a finite-volume solver, which uses an adaptive mesh refinement (AMR) strategy to address the wide separation of length scales in the problem. A two-way coupling strategy is used whereby the plasma-fluid model and reactive Navier-Stokes equations are integrated simultaneously. The oxidation of ethylene/air mixtures mediated by NSPD is simulated in a pin-to-pin configuration. All phases of the plasma discharge are simulated explicitly (including streamer ignition, propagation, and connection, as well as the subsequent spark phase), along with the evolution of the plasma during the inter-pulse period. Temporally and spatially-resolved results are presented, with an emphasis on the analysis of heating and energy deposition, as well as of the evolution of the concentration of active particles generated during the NSPD and their influence on ignition. 

The burning rate in a spherically turbulent premixed flame is explored using direct numerical simulations, and a model of ordinary differential equations is proposed. The numerical dataset, from a previous work, is obtained from direct numerical simulations of confined spherical flames in isotropic turbulence over a range of Reynolds numbers. We begin the derivation of the model with an equation for the burning rate for the domain under consideration, and using a thin flame assumption and a two-fluid approach, we find the normalized turbulent burning rate to be controlled by the increase in flame surface area due to turbulent wrinkling, and correction factor which is observed to be consistently less than unity. A Reynolds scaling hypothesis for the flame turbulent wrinkling from a previous work using the same numerical dataset is used to model the term controlling the increase in flame surface area. The correction factor is hypothesized to reflect flame stretch effects, and hence this factor is modeled using Markstein theory applied to global averaged quantities. The ordinary differential equations are rewritten to reflect easily observable quantities such as the chamber pressure and mean flame radius, and then expressed in dimensionless form to assess dependence on various dimensionless parameters. The model predictions are found to be in good agreement with the numerical data within expected variances. Additionally, Markstein theory is found to be sufficient in describing the effects of flame stretch in the turbulent premixed flames under consideration.