Density Field Reconstruction of an Overexpanded Supersonic Jet using Tomographic Background-Oriented Schlieren

Abstract

A Tomographic Background-Oriented Schlieren (TBOS) technique is developed to aid in the visualization of compressible flows. An experimental setup was devised around a sub-scale rocket nozzle, in which four cameras were set up in a circular configuration with 30° angular spacing in azimuth. Measurements were taken of the overexpanded supersonic jet plume at various nozzle pressure ratios (NPR), corresponding to different flow regimes during the start-up and shut-down of rocket nozzles. Measurements were also performed for different camera parameters using different exposure times and f-stops in order to study the effect of measurement accuracy. Density gradients and subsequently two-dimensional line-of-sight integrated density fields for each of the camera projections are recovered from the index of refraction field by solving a Poisson equation. The results of this stage are then used to reconstruct two-dimensional slices of the (time-averaged) density field using a tomographic reconstruction algorithm employing the filtered back-projection and the simultaneous algebraic reconstruction technique. By stacking these two-dimensional slices, the (quasi-) three-dimensional density field is obtained. The accuracy of the implemented method with a relatively low number of sparse cameras is briefly assessed and basic flow features are extracted such as the shock spacing in the overexpanded jet plume.