Reconstruction of the Unsteady Supersonic Flow around a Spike Using the Colored Background Oriented Schlieren Technique

Abstract

In this paper, the improved Background Oriented Schlieren technique called CBOS (Colored Background Oriented Schlieren) is described and used to reconstruct the density fields of three-dimensional flows. The Background Oriented Schlieren technique (BOS) allows the measurement of the light deflection caused by density gradients in a compressible flow. For this purpose the distortion of the image of a background pattern observed through the flow is used. In order to increase the performance of the conventional Background Oriented Schlieren technique, the monochromatic background is replaced by a colored dot pattern. The different colors are treated separately using suitable correlation algorithms. Therefore, the precision and the spatial resolution can be highly increased. Furthermore a special arrangement of the different colored dot patterns in the background allows astigmatism in the region with high density gradients to be overcome. For the first time an algebraic reconstruction technique (ART) is then used to reconstruct the density field of unsteady flows around a spike-tipped model from CBOS measurements. The obtained images reveal the interaction between the free-stream flow and the high-pressure region in front of the model, which leads to large-scale instabilities in the flow.In this case, assuming that the flow is axially symmetrical, every projection perpendicular to the symmetry axis should look the same. Earlier studies by Ota et al. [14] showed that good reconstruction data can be obtained from 36 projection angles ranging from 0˚ to 175˚ with intervals of 5˚. This configuration leads to an underestimation for the density of about 7% even in regions with high gradients. For the reconstruction of the flow field 152  240  240 voxels are used, which corresponds to a

Background-oriented schlieren (BOS) techniques

“…5) by a shift of one of the base color patterns. Details of this procedure are described by Leopold et al (2014).…”

Background-oriented Schlieren technique with vector tomography for measurement of axisymmetric pressure fields of laser-induced underwater shock waves

“…In CT, reconstruction is performed from the divergence of the projected field [34,35,37,38,26]. In this paper, we use the analytical method of filter back-projection (FBP) [64,65] for CT, following Hayasaka [26].…”

“…In conventional 3D reconstruction, instead of the vector field of apparent displacement w, reconstruction is performed on a scalar field, namely, the divergence ∇ • w of w [34,35]. Existing BOS techniques use 3D reconstruction methods, such as filtered back-projection (FBP) [34,36,37] and the algebraic reconstruction technique (ART) [35,38,31], which are types of computed tomography (CT). The BOS technique with computed tomography is hereinafter referred to as CT-BOS.…”

The Quantitative Density Measurement of Unsteady Flow around the Projectile

“…Ota et al also aimed the three-dimensional density measurements by using CGBOS technique. The previous reports have focused on the reconstruction of steady flow, reproducible unsteady flow or axially-symmetrical unsteady flow in the wind tunnel test because the flow field was measured with one camera from one direction and multi-projections of flow were obtained with repetition of many blow-downs [9] [10] or one projection under axially-symmetric condition [11]. However, the unsteady phenomena should be measured simultaneously from multi-projection angles because the "real" phenomena would never happen again.…”