Time-averaged three-dimensional density and temperature field measurement of a turbulent heated jet using background-oriented schlieren

Three-dimensional time-averaged density and temperature fields of a heated air jet from a circular 10 mm diameter nozzle are reconstructed using tomographic background-oriented schlieren. A hybrid filtered back-projection–algebraic reconstruction (FBP-ART) technique reconstructs the refractive index gradient field in the flow. The number of ART iterations is varied to observe the effect on reconstruction artefacts. The largest improvement is observed after 1 ART iteration with filtering of the initial FBP solution. Subsequently, the gradient field is used to form a Poisson equation solved in a quasi-3D manner using successive over-relaxation. Convergence of the refractive index field is studied with iteration number and the effect this has on the temperature and density profiles, after applying the Gladstone-Dale relation and ideal gas law. The quasi-3D solution parallelises well, and converges rapidly.