An Ultrasonic Measurement Model to Predict a Reflected Signal from Non-Linear Burning Surface of Solid Propellants

While determination of the solid propellant burning rates by ultrasound, it has been reported that the frequent data scatters were caused by two major factors; 1) variation in the acoustical properties, and 2) non-linear burning of a solid propellant sample under investigation. This work is carried out for the purpose of investigating the effect of non-linear burning of solid propellant samples. Specifically, we propose an ultrasonic measurement model that can predict the reflections from solid propellant surfaces with non-linear burning by the combination of two ingredients; 1) a pulse-echo ultrasonic measurement model for a planar, circular reflector imbedded in the second medium in an immersion set-up, and 2) an efficient model of non-linear burning surfaces with a number of small, planar circles. Then, we demonstrate the capability of the proposed measurement model by simulation of the surface echo signals from four different burning surfaces that have been generated by the combination of two factors; the base shape (flat or paraboloidal) and the surface roughness (perfectly smooth or randomly rough). From the simulation presented here, we can confirm the fact that the non-linear burning of the propellant can cause the waveform change of the burning surface echo and the corresponding spectrum variation.