Abstract Quantitative schlieren imaging is a flow measurement technique that is capable of measuring density fields throughout refractive flowfields. The technique was applied here to measure the density field surrounding supersonic conical projectiles in free flight. Shock waves attached to a supersonic conical projectile offer a simple geometry with the well-established Taylor-Maccoll analytical flow solution to which these experimental measurements were compared. The schlieren images recorded a projection of the index of refraction field surrounding the 10° half-angle cones which was converted to density first through an Abel inversion and then the Gladstone-Dale law. Three Abel inversion methods — two-point, three-point, and ARAP — were applied to deconvolute the three-dimensional flow within the constrained axisymmetric flow field. The resulting reconstructed density profiles were compared to the Taylor-Maccoll solution, parameterized by cone geometry and Mach number. The experimental density fields demonstrated strong agreement with the theoretical profiles. Experimental consistency was confirmed across various projectile speeds, demonstrating quantitative schlieren's capability to accurately reconstruct the density of the flow field, even within the resolution constraints imposed by high-speed imaging. An assessment of experimental uncertainties in the density reconstruction was performed.
Morrow et al. (Fri,) studied this question.