A new method for density gradient measurements in compressible flows

We suggest the use of a new method, moire deflectometry, for analysis of density gradients in compressible flows. This method, which is simpler to apply than schlieren and does not need precalibration, is capable of providing a fully quantitative diagnosis and map of the density gradient field. We demonstrate the method by a quantitative example of a two-dimensional diamond airfoil in a supersonic wind tunnel and compare it with other diagnostic methods widely used today. HE analysis of density distribution in compressible flows is of major importance in aerodynamics. Among the known methods for density measurements three are com- monly used: interferometry, schlieren, and shadowgraphy. Each method is sensitive to a different density derivative. The readings in interferometr y are proportional to the density, those in schlieren to the density gradients, and those in shadowgraphy to the Laplacian of the density. Although the most quantitative method is interferometry, it is only seldom applied. This is due to the severe mechanical stability requirements, about A/10, which dictate the use of either very heavy equipment to carry the optical components or short laser pulses. The most popular method is schlieren photography, which is a rather simple real-time method, and is more sensitive than shadowgraphy. The purpose of this paper is to demonstrate a new method, moire deflectometry, which was suggested recently,1 for the analysis and mapping of density gradient fields in supersonic wind tunnels. The method, which is based on moire effect, is capable of measuring the deflection of rays of a collimated light beam. The optical system consists of a collimated light source, of the type used in schlieren photography, and two gratings, Gj and G2, as shown schematically in Fig. 1. The moire pattern may be observed on a mat screen, S, attached to the grating G2. The two gratings, G, and G2, are oriented at an angle 6 to each other, so that the resultant moire pattern consists of straight fringes separated by a distance Pr given by2