THEORETICAL MODELING OF ELECTRICALLY OPERATED AMMONIUM NITRATE PROPELLANT COMBUSTION

Certain propellants exhibit combustion zone properties that allow burn rate manipulation by application of a transverse electric field, perpendicular to the axis of flame propagation. In the configuration of interest, the solid propellant is dielectric, but its melt layer underneath the gaseous flame region is electrically conductive. The applied electric field imparts ohmic heating to the subsurface region adjacent to the flame. The advantages of ammonium nitrate (AN) propellants for this method of burn-rate control have been known for some time; a clear effect, on the order of 100% of normal burn-rate amplification, could be possible using moderate voltages. Whereas AN is dielectric in all its known solid phase variants, its melt phase is electrically conductive. The objective of this study is to provide a theory for this mode of electrically enhanced combustion. A quasi one-dimensional model of the solid/melt/gas combustion zone is derived at steady state. The resulting two-point boundary value formulation for the melt layer is based on variable electrical conductivity as a function of temperature. This leads to a unique Sturm-Liouville formulation for which eigenvalues and associated eigenfunctions are solved. The two parameters of physical significance are the Péclét number and the eigenvalue. The analysis herein offers physical insight into this electrically augmented combustion process at steady state, which explains the dependence of burn rate and apparent melt layer resistance upon the applied electrical voltage. These functional dependences are verified by correlating the available experimental results.