Quantitative Flow Fields Visualization Based on Deflectometry

We propose a method for quantitatively visualizing two-dimensional flow fields based on deflectometry. In this method, from the perspective of inverse Hartmann testing, the light rays emitted from the camera travel to the screen after being perturbed by the shock-wave flow field. After obtaining the coordinates of the point source using phase information, we can calculate the deflection angle of the light ray and subsequently determine the distribution of the density field. We provide a detailed description of the principles behind Density Field Measurement Deflectometry (DFMD). In the experiment, we first validated the effectiveness of this method by measuring the refractive index distribution of a GRIN lens. Subsequently, we measured a wedge-shaped model in supersonic wind tunnels, further demonstrating the effectiveness and accuracy of the deflectometry technique in quantitative flow visualization.We compared the experimental results obtained using our proposed method with theoretical results, and the deviation between the two was approximately 2‰. This method offers the advantages of rapid measurement, a straightforward setup, and cost-effectiveness. It introduces a novel approach to measuring the density field of shock-wave flow fields.