How to Analyze 2-D Schlieren Photographs to Obtain the Density Gradient Structure of 3-D Flow Fields

A technique is outlined by which density gradients visible in two- dimensional schlieren photographs can be analyzed to obtain the density gradient structure (i.e., the shape and location of density gradients such as shock waves and vortices) of three-dimensional flow fields. Practical application of the technique relies on obtaining a series of schlieren photographs of the flow field from different viewing orientations. The analysis is specialized to the case of a right-circular cone at angle of attack. Results are presented which show the shape and location of the bow shock of a 5 deg half-angle right- circular cone at a nominal Mach number of 5.0, a nominal free-stream Reynolds number per foot of 4,800,000 and angles of attack equal to 15 and 40 deg.