Characteristics-based measurements of supersonic flows from schlieren images

Abstract

A novel method is presented to measure Mach number and flow angle from schlieren images of two-dimensional supersonic flows. A line detection technique is used to extract characteristic lines from schlieren images to measure the velocity direction and the Mach number at the intersection of characteristic curves. The proposed technique is independent of fluid thermodynamics and applies to dilute gas flows and non-ideal compressible flows. The velocity magnitude and fluid thermodynamics are retrieved from the fluid thermodynamic model, assuming constant total enthalpy and entropy. Mach number measurements are also obtained at solid walls by integrating the compatibility equation along the characteristic lines, using the measurements within the flowfield as initial conditions. Results are presented for two exemplary cases: an asymmetric converging–diverging nozzle and the supersonic flow around a diamond-shaped airfoil. Measured values of the Mach number and the flow angle agree with numerical predictions and indirect Mach number measurements based on pressure measurements. The reconstructed pressure and velocity magnitude values agree fairly well with available measurements and simulations in the dilute gas and in the non-ideal regimes.