Rainbow Schlieren Deflectometry for spherical fields: A new algorithm and numerical validation approach

Abstract

The authors present a new algorithm for analyzing ray deflection within spherical refractive index fields. The algorithm emanates from the well-known deconvolution algorithm for axisymmetric refractive index fields using the inverse Abel transformation and can be used for experimental Rainbow Schlieren Deflectometry (RSD) data. It was numerically validated by Computational Fluid Dynamics (CFD) calculations of free convection around an isothermal sphere and successive ray tracing through the determined temperature field. The algorithm determined radial temperature profiles and local Nusselt numbers from resulting deflection angles of the ray tracing simulations. An excellent agreement between original and reconstructed temperature field within the limits of assumptions was reached. This proves the usability of the algorithm for the experimental determination of spherical refractive index fields from future heat or mass transfer experiments.

Keywords:

• Algorithm validation
• free convection
• rainbow Schlieren deflectometry
• ray tracing
• spherical refractive index fields

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the German Research Foundation (DFG) under Grant number 423448517.