Quantitative Rainbow Schlieren Deflectometry for Supersonic Binary Ideal Gas Mixing

Rainbow schlieren deflectometry (RSD) is used for visualizing density gradients in compressible flows, yet its application to supersonic binary-gas mixing remains limited due to simultaneous variations in pressure, temperature, and species concentration. This work presents a methodology for obtaining quantitative density fields of a helium jet issuing into quiescent air under highly underexpanded conditions using RSD. A three-region interpretation framework is introduced to isolate the relevant thermodynamic dependencies: a near-field unmixed pure-helium core, a shock-containing mixing region where both pressure and composition vary, and a far-field isobaric region dominated by shear layer mixing interactions. By combining RSD-derived refractive index distributions with nozzle exit pressure estimates, adiabatic mixing relations, and an appropriate equation of state, local gas properties are recovered across all flow regions. Experiments were conducted at stagnation pressures of 1000 kPa and 2000 kPa to assess the method’s fidelity across differing pressure ratios. The reconstructed density fields reveal the complete structure of underexpanded jets, including expansion fans, the Mach disk, barrel shock, and self-similar mixing downstream. Radial density profiles extracted at multiple axial stations show consistent trends with theoretical expectations and demonstrate the sensitivity of RSD to both compressible and diffusive processes. The results confirm that RSD, when paired with a physics-informed interpretation strategy, can serve as a quantitative diagnostic tool for supersonic multi-species flows. The approach provides a foundation for future non-intrusive measurements in high-pressure injection, multi-component mixing, and other applications where traditional schlieren techniques are limited.