Quantitative analysis of high speed flows is always an interesting field of study owing to recent developments in supersonic space vehicles. In this context optical techniques such as Interferometry, BOS, Shadow-casting [1] are commonly used for investigating the flow. In the above mentioned optical techniques light is used as an interrogating tool. The phase of light wavefront, coming out of the flow changes and this change in phase carries information of the flow phenomenon. The change in the out coming wavefront can be seen as displaced fringe pattern in Interferometry and displacement of dots in BOS and Shadow-casting.The prime requirement in Interferometry is the laser along with dedicated optical components to perform Interferometry experiments. However a random pattern and white light source is sufficient to provide flow information with the help of BOS and Shadow-casting schemes, making BOS and Shadow-casting favorable over Interferometry.
For complete recovery of flow information especially the density distribution around a model placed in the highspeed flow, the displacements of dots need to measure accurately. In this context, for calculating displacements of dot, cross-correlation algorithm is usually used. Images are compared (one during the flow and another one as the reference) in a sub-window at a time and the whole image is scanned in raster scan fashion for full recovery of displacements. This raster scanning scheme for full recovery of displacements is a slow time consuming process.
Recently Akatsuka et al. [2] and Hatanaka et al. [3] suggested using sinusoidal pattern for faster computation of displacements. But the sinusoidal pattern can provide displacement information only in orthogonal directions of the pattern that further needs to line integrate for full recovery of 2d phase. Since the flow field is noisier the line integration generates streaking effect in recovered phase information. The situation becomes worse with an object placed in the flow field which is a common scenario in shock tunnel facility.
In our study a new multiplexed pattern is used and the data is processed such that it can give both horizontal and vertical gradients of the flow field. Further the wavefront is computed from these calculated gradients (equivalently from slopes). Fourier domain processing is utilized for faster and efficient calculation of slopes and then the phase from the calculated slopes. Preliminary demonstration of the technique has been performed in hypersonic shock tunnel (HST2) facility in our laboratory using a hemispheric test model in the flow field at Mach 8.83. It shows a good agreement with the CFD simulation for the same experimental conditions. It is observed that the processing time for an 18mega pixel image when used with random dot pattern takes few hours whereas the multiplexed pattern with the adopted Fourier domain analysis takes only 30secs. The computed gradients for the experimental data are shown in the Figure1 which resembles the vertical and horizontal knife edge Schlieren images. The calculated slopes are further used in tomographic reconstruction for quantitative analysis of the flow around the test model.
The detailed analysis of the proposed scheme will be discussed in the full length paper.
[1] Biswajit Medhi, G.M. Hegde, K.P.J. Reddy, D. Roy, and R.M. Vasu, “Quantitative visualization of high speed flow through optical tomography” 28th International Symposium on Shock Waves (ISSW28), Manchester, 17-22, July, 2011.
[2] Akatsuka J., Nagai S., and Honami S.: Improved flow visualization methods based on thebackground oriented Schlieren technique, Trans Jpn. Soc. Mech. Eng.Ser B 77 (784) 2391-2400, (2011)
[3]Hatanaka K. and SaitoT.: Background oriented schlieren method usingmulti-scale periodic pattern, 29th International Symposium on Shock Waves (ISSW29), Wisconsin, USA, 2013
