Improved quantitative visualization of hypervelocity flow through wavefront estimation based on shadow casting of sinusoidal gratings

Abstract

A simple noninterferometric optical probe is developed to estimate wavefront distortion suffered by a plane wave in its passage through density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a continuous-tone sinusoidal grating. Through a geometrical optics, eikonal approximation to the distorted wavefront, a bilinear approximation to it is related to the location-dependent shift (distortion) suffered by the grating, which can be read out space-continuously from the projected grating image. The processing of the grating shadow is done through an efficient Fourier fringe analysis scheme, either with a windowed or global Fourier transform (WFT and FT). For comparison, wavefront slopes are also estimated from shadows of random-dot patterns, processed through cross correlation. The measured slopes are suitably unwrapped by using a discrete cosine transform (DCT)-based phase unwrapping procedure, and also through iterative procedures. The unwrapped phase information is used in an iterative scheme, for a full quantitative recovery of density distribution in the shock around the model, through refraction tomographic inversion. Hypersonic flow field parameters around a missile-shaped body at a free-stream Mach number of ∼8 measured using this technique are compared with the numerically estimated values. It is shown that, while processing a wavefront with small space-bandwidth product (SBP) the FT inversion gave accurate results with computational efficiency; computation-intensive WFT was needed for similar results when dealing with larger SBP wavefronts.

Time-resolved quantitative visualization of complex flow field emitted from an open ended shock tube using a wavefront measuring camera

“…Under geometrical optics, the casted shadow of the mask on the sensor plane is the eikonal approximation of the captured light wavefront through the mask pattern and thus any variation of the captured wavefront would displace the casted pattern from its original position when illuminated by a plane wave. The observed phenomenon is similar to the shadow-casting process, which has been reported before [21,22].…”

“…Many optical techniques such as schlieren, shadowgraph, holographic interferometry, particle image velocimetry (PIV), background oriented schlieren (BOS) [17][18][19][20], shadow-casting [21,22], laser induced fluorescence (LIF) [17,18] are extensively used in flow visualization in supersonic and hypersonic regimes in shock tunnels and wind tunnels. Among these, schlieren and shadowgraph schemes provide 2D projected qualitative images of the 3D domain, represented in intensity scale.…”