This work addresses the question of the validity of self-similar formulations in describing the structures of methane/air laminar counterflow diffusion flames subjected to incident sub-breakdown DC electric fields. The electric field is induced by two flat porous electrodes located on the oxidizer and fuel sides of the burner and arranged parallel to the mixing layer. Both experiments and numerical simulations of this configuration in recent work suggest the presence of a strong coupling effect between the aerothermochemical and electric fields whereby the velocity field is significantly modified by the momentum carried by a bi-directional ionic wind directed axially outwards from the diffusion flame. However, as shown in this study, such strong coupling is incompatible with standard self-similar formulations of the problem. An a-priori analysis of the steady axisymmetric numerical simulations results in Di Renzo et al. (2018) , which employ multi-component transport and detailed chemical kinetics, is presented in this study in order to address the suitability of self-similar descriptions in the present configuration. It is shown that, while self-similarity is preserved in unelectrified conditions along radial distances similar to one orifice radius, it breaks down profusely in electrified conditions as the applied voltage increases and nears saturation conditions, where the electric force field becomes two-dimensional and non-conservative in the close vicinity of the burner axis. As a result, for the purposes of self-similarity, increasing electrification counteracts the slenderness of the counterflow burner and decreases its effective aspect ratio. Counterflow burners should therefore be extra slender if preservation of self-similar conditions is sought under incident electric fields.
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