Quantitative velocity measurement of high-temperature turbulent flows utilizing pseudo-schlieren imaging techniques

Accurate velocity measurement in high-temperature turbulent flows remains a significant challenge in aerospace engineering due to the limitations of intrusive probes and particle-seeding techniques. This study presents a non-intrusive velocity measurement method utilizing background-oriented schlieren (BOS) grounded in Fermat’s principle. Fermat’s principle is introduced to provide a physically consistent framework for describing light propagation in an inhomogeneous refractive-index field, supporting the subsequent pseudo-schlieren images generation and simulation process. A time-resolved series of pseudo-schlieren images was generated to record flow perturbations, and a hybrid algorithm combining optical flow and cross-correlation was employed to reconstruct the velocity vector fields. The method was validated using a controllable thermal turbulent jet generated by a heat gun, with operating temperatures ranging from 300 °C to 500 °C and flow velocities between 1.5 m s −1 and 3.0 m s −1 . Experimental results were quantitatively compared with high-precision Pitot tube measurements across multiple heights (2–6 mm) above the nozzle. The results demonstrate that the proposed method achieves high measurement fidelity, with relative velocity errors consistently maintained within 1.4% compared to the Pitot tube data. This study confirms the efficacy of Fermat-based BOS for quantitative diagnostics of complex thermal flows without the need for seeding particles or complex multi-camera setups.