Time-averaged density tomography of non-axisymmetric jets with a rotating nozzle and telecentric, single-camera BOS

Abstract

In this article, a method for density tomography using a telecentric BOS setup coupled with a motorized, rotating nozzle will be described. The telecentric optics allow for the disentanglement of the ray path integral and density gradient operators through Leibniz’s integral rule because the rays seen by a telecentric setup are parallel in the Schlieren domain. This enables the usage of a fast gradient inversion solver based on the rotating parallel ray integral method, previously developed by the author, to solve for the ray-integrated density fields in two dimensions for each view individually, producing a set of ray-integrated density measurements similar to a set of images captured by a regular absorption or emission-based computed tomography setup. By leveraging well-known computed tomography algorithms, such as the inverse Radon transform, a tomographic reconstruction of the average density field is quickly found only requiring a simple 2D camera calibration. A demonstration experiment setup is used to test the technique, where a low-speed hot jet produced by different nozzle shapes is measured. The 3D density fields are then converted to temperature fields and the temperatures are compared to a reference measurement with a thermocouple scanner. The strong agreement between the two measurements creates confidence that this technique can be deployed to produce quantitative measurements of the density fields in complex flows, which can be combined with 3D PIV measurements to obtain the four time-averaged thermodynamic fields in compressible jet flows.