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

TL;DR

This paper presents a novel tomographic background-oriented schlieren technique for visualizing and reconstructing the density fields of overexpanded supersonic jets, enabling detailed flow analysis with sparse camera setups.

Contribution

It introduces a new TBOS method combined with tomographic reconstruction to visualize 3D density fields of supersonic jets using minimal camera resources.

Findings

Successfully visualized overexpanded jet density fields.

Reconstructed 3D density distributions from sparse camera data.

Extracted flow features like shock spacing.

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{\deg} 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.