BOS for Internal Flows: Part 2 - Challenges for Boundary Conditions

The Background Oriented Schlieren (BOS) method can be used to experimentally characterize optical density (OD) fields.  The line-of-sight (LOS) integrated OD gradient field is measured determining the displacement vectors of a reference background pattern.  The LOS integrated OD field is then computed by solving a Poisson equation.  This method is readily applied to open flows, where the image displacement vectors are solely caused by density gradients in the flow, and quiescent boundary conditions are practical.  For internal flows, viewing windows complicate the relationship between the image displacement field and the fluid gradient field and other bounding surfaces have unique boundary conditions.  In this work, we discuss the challenges associated with the latter by using an analytical Green’s function approach.