K. P. J. Reddy

Quantitative estimation of density variation in high-speed flows through inversion of the measured wavefront distortion

Abstract. A simple method employing an optical probe is presented to measure 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 random dot pattern. Local slopes of the distorted wavefront are obtained from shifts of the dots in the pattern. Local shifts in the dots are accurately measured by cross-correlating local shifted shadows with the corresponding unshifted originals. The measured slopes are suitably unwrapped by using a discrete cosine transform 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 5.8 measured using this technique are compared with the numerically estimated values.

Quantitative Visualization of High Speed Flow through Optical Tomography

The preferred tool for studying hypersonic flow dynamics is that the technique which uses the noninvasive, light-based flow visualization techniques. Various strategies leading to qualitative as well as quantitative flow visualization such as Shadowgraphy, Schlieren imaging, background oriented Schlieren (BOS), interferometry and laser induced fluorescence(LIF) etc. are reported in literature [1, 2]. Shadowgraphy and Schlieren techniques can give only qualitative information about the flow. Though the Interferometry and LIF can provide quantitative information of the hypersonic flows, the techniques are rather complicated to be used in bigger hypersonic facilities and also require expensive instrumentation such as lasers, CCDs etc. Notwithstanding the above, quantitative information of density gradient around an object facing high-speed flow is an extremely important parameter for studying shock generation and its propagation, which is also important in designing future hypersonic space vehicles.

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

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.

Orthogonal Projection Based Computationally Efficient Algorithm for Deflection Tomography in High Speed Flow Studies

Optical computed tomography is extensively used for quantitative flow visualization studies [1, 2]. Based on detection methodology it is classified as phase and deflection tomography. Here, we are considering deflection tomography method.

Tomographic Visualization of the Hypersonic Flow Field over a Waverider

Waveriders are geometric configurations proposed for hypersonic flight, which benefit from the lift generated by the shock wave [1]. They are designed to achieve not only high lift-to-drag ratios but also fore-body shock compression which is essential for the intakes of hypersonic propulsion systems. Typically a conically derived waverider has its upper surface parallel to the freestream offering no obstruction to the flow, while the lower surface obstructs the flow and results in a shock, resulting in the required lift production. The lower surface is tailored in such a way that the shock is attached to the edges so as to avoid spillage from the bottom to top surfaces [2]. Clearly the flow field over a waverider is three-dimensional. While much of experimental studies on waverider are performed in hypersonic wind tunnels, shock tunnel experiments are required in order that the high-flow total enthalpies of the hypersonic flow are also simulated along with Mach numbers. There are few shock tunnel measurements on waverider reported in the literature [3, 4], and there is an acute lack of three-dimensional visualization of the flow field over waverider. It is with this backdrop that the present shock tunnel experiments are initiated to study the flow field around a generic waverider.

Improved Flow Visualization for Fast Recovery of Flow Gradients in Shadow-Casting Technique

Nonintrusive optical schemes are preferred for quantitative flow diagnostics. Shadow-casting scheme is one of the flow diagnostic techniques in which the projected shadow of a random-dot pattern mask reveals the flow information under the observation of the interrogating beam. Any variation in the flow field is seen as a change in position of the casted shadows of the mask which are calculated by cross-correlation scheme. The main downfall of such data processing schemes is the time requirement to process information, which has been targeted in this manuscript. The random-dot pattern mask is replaced with a 2D cosine grid, and Fourier data processing scheme is introduced to reveal orthogonal gradients of the flow field. A preliminary demonstration of the technique has been performed in hypersonic shock tunnel (HST2) facility using a hemispherically shaped test model placed in the flow field at Mach 8.83. Significant improvement in processing speed is observed while dealing with such data for recovering orthogonal flow gradients. The calculated slopes are further used in tomographic reconstruction for quantitative analysis of the flow around the test model.

Handheld Wavefront Measuring Camera for Quantitative Flow Visualization

In this manuscript a handheld camera is proposed that is built around a modified CMOS image sensor chip. The camera can detect both light amplitude and variation of light phase quantitatively. The refractive material of interest is interrogated by passing light through it, and the exit light from the test object is captured by the proposed camera. The variation in amplitude and phase of the exiting light wavefront from the phase object is determined quantitatively by the proposed camera. The camera is used to analyze strong refractive elements such as a sculpture and a lens made of transparent acrylic and BK7 materials, respectively. Notwithstanding to these materials the camera is also used in moderate refractive materials such as high-speed gas flow experiments that include a supersonic jet emanating from a convergent-divergent nozzle and flow field around a hemispheric shaped model placed in hypersonic flow. In all the experiments the proposed camera shows good agreement with the actual values.

Aberration correction for transport of intensity phase imaging

Transport of intensity phase imaging suffers from phase aberration due to presence of noise in experimental data and aberration induced by optical system. This induced low frequency aberration corrupts the original phase and makes it difficult to use for any further quantitative processing. In this paper an aberration correction scheme is proposed. A polynomial model is used to represent the low frequency induced aberrations, and further subtracted from the corrupted phase for correcting the phase profile. The proposed scheme is implemented on experimental data obtained from a static microstructure phase object, of 100 nanometer height. The results obtained from the proposed scheme shows a good agreement with the actual known values.