Visual hull based 3D reconstruction of shocks in under-expanded supersonic bevelled jets

Three-dimensional shock structures produced by Mach 1.45 supersonic bevelled jets were digitally reconstructed based on schlieren photography and a voxel-based visual hull technique. By taking advantage of the strong edge features commonly found in schlieren images of shock waves, the proposed technique demonstrates the possibility of performing shock wave reconstruction in supersonic jet applications without prior knowledge of the global density or velocity field. Semi-synthetic camera parameters were introduced as a method to circumvent camera calibration issues faced in the reconstruction procedure. This is key to achieving accurate and high-resolution reconstructed shock waves for both axisymmetric and asymmetric test cases with an average of 2.5% error when validated against raw schlieren images. When applied to bevelled jets with non-uniform nozzle exit geometries, an additional assumption was made to address the problem of schlieren line-of-sight blockage by the non-conventional nozzle, and reconstruction errors were found to be larger near regions of poorer shock wave contrast. Current results indicate that the technique is robust and fast during image calibration and processing, with accuracy of reconstructed shock waves in both conventional and non-conventional nozzles strongly dependent on shock wave contrast. Compared to existing techniques that can be used to reconstruct 3D shock structures, the proposed technique has the advantage of being totally non-intrusive as compared to point or particle-based measurements, requires significantly less computation than tomographic methods, offers high resolution reconstruction even with limited camera resolution and projected schlieren views, and is easy and cost effective to implement.