A ‘frozen electric-field’ approach to simulate repetitively pulsed nanosecond plasma discharges and ignition of hydrogen–air mixtures

High-fidelity modelling of nanosecond repetitively pulsed discharges (NRPDs) is burdened by the multiple time and length scales and large chemistry mechanisms involved, which prohibit detailed analyses and parametric studies. In the present work, we propose a ‘frozen electric-field’ modelling approach to expedite the NRPD simulations without adverse effects on the solution accuracy. First, a burst of nanosecond voltage pulses is simulated self-consistently until the discharge reaches a stationary state. The calculated spatial distributions and temporal evolution of the electric field, electron density and electron energy during the last pulse are then stored in a library and the electrical characteristics of subsequent pulses are frozen at these values. This strategy allows the timestep for numerical integration to be increased by four orders of magnitude (from 10−13 to 10−9 s), thereby significantly improving the computational efficiency of the process. Reduced calculations of a burst of 50 discharge pulses show good agreement with the predictions from a complete plasma model (electrical characteristics calculated during each pulse). The error in species densities is less than 20% at the centre of the discharge volume and about 30% near the boundaries. The deviations in temperature, however, are much lower, at 5% in the entire domain. The model predictions are in excellent agreement with measured ignition delay times and temperatures in H2–air mixtures subject to dielectric barrier NRPD over a pressure range of 54–144 Torr with equivalence ratios of 0.7–1.2. The OH density increases with pressure and triggers low-temperature fuel oxidation, which leads to rapid temperature rise and ignition. The ignition delay decreases by a factor of 2, with an increase in pressure from 54 to 144 Torr. In contrast, an increase in the H2–air equivalence ratio from 0.7 to 1.2 marginally decreases the ignition delay by about 20%. This behaviour is attributed to the insensitivity of OH production rates to the variation in the equivalence ratio.