A new 2D analysis of light for computing the Mach number distribution in a flow field from Schlieren images taken across the shock wave and expansion zone is proposed and verified by a 2D numerical computation Specially, inserting experimental measuring sensors inside shock wave zone and associated flow field is difficult. Across the shock wave, the pressure and density of the fluid change at extremely high rates, which affect the light refraction. The intensity of the Schlieren light is a function of the medium density, which is a function of the light ray path position. The contrast of each pixel is determined by analyzing the image. The equations of Schlieren intensity light are derivated to be a function of Mach number. These functions are applied on an image of shockwave around hemisphere-cylinder at M=1.96.
To verify the results two-dimensional Navier-Stokes equations and conservation of energy equation are used to model the flow field and determine Mach number distribution around a hemisphere-cylinder of the supersonic flow, shock waves and associated flow field at the same previous conditions. The governing equations are discretized on a structured grid using an upwind difference scheme. The computational and experimental results show that there is a good matching in the iso-contour of the Mach number with difference less than 3%. The new proposed technique successfully represents the upstream region, the shock wave region, the subsonic region and the expansion fan region. This difference may be due to the noise in the image. This noise can be eliminated if Schlieren light received directly on a CCD camera. The results show that this analysis can be applied for both bright and dark regions of the Schlieren image with correcting the phase shift in the dark area. This optical technique has the advantages of optical measurements. This optical technique has all the advantages of optical measurements as does not disturb the flow and the high sensitivity to capture rapid variation.