Modified Application of Algebraic Reconstruction Technique to Near-Field Background-Oriented Schlieren Images for Three-Dimensional Flows

A novel approach which leverages the model surface itself as the background pattern in the background-oriented Schlieren technique is applied to a hypersonic wind tunnel test. The ordinary background-oriented Schlieren approach assumes that the distance between the background pattern and the area of interest is constant. However, this is not generally true when the model surface is used as the background pattern. A new mathematical formulation of an algebraic reconstruction technique used in computerized tomography (CT) is therefore used to account for the varying distance. Another practical problem is the fact that only a very small displacement due to refraction can be expected due to the short distance between the point of refraction and the background plane. To solve this problem practically and to confirm the overall validity of the mathematical formulation, the approach has been applied to the visualization of the shock structures formed around a cylinder perpendicular to a sharp-nosed flat plate in a hypersonic flow of Mach 7. The CT reconstruction using the sand-blasted model surface as the background pattern and accounting for the varying distance shows clear shock structures even in regions close to the flat plate surface, demonstrating the effectiveness of the new concept.