Flame transfer functions and interference analysis under nanosecond repetitively pulsed discharge actuation

We present a numerical investigation of how nanosecond repetitively pulsed discharges (NRPDs) modify the linear response of a laminar stagnation flame. We focus on two main discharge parameters, pulse energy deposition E p and pulse repetition frequency (PRF). Compared to the non-actuated flame, NRPDs shift the flame upstream toward the fresh gases, increase the mean and local heat release rate (HRR), enrich the radical pool, and modify the local velocity field. The global response is built from contributions arising from different parts of the flame, and plasma actuation redistributes these contributions along the flame front. We identify the local flame regions that interfere constructively or destructively as a function of the NRPD parameters. These results show that variations of E p or PRF affect flame dynamics differently at different frequencies, highlighting that NRPDs require well-tuned parameters for successful mitigation of unstable flames. Novelty and significance statement: NRPDs can be used to alter the thermoacoustic stability of combustors, but the effect of actuation parameters on the linear flame response remains poorly quantified. To the best of our knowledge, this is the first systematic numerical study in which both pulse energy deposition E p and PRF are varied, and FTFs are computed. The results show that NRPDs modify gain and phase mainly through changes in the mean flame shape and position, which affect the effective time delays and the balance between constructive and destructive contributions. NRPD actuation therefore offers a promising route for thermoacoustic control, but it requires a sound understanding of how the NRPD parameters affect the flame response.