Fluid flow diagnostics using rainbow schlieren imaging and computer tomography.

Abstract

The deflections obtained from rainbow schlieren images were inverted using computer tomography. Tomography is a multi-angular technique which involves making M line of sight measurements (deflections) at N angles. These M x N measurements are used to reconstruct the original two-dimensional test object. Several tomographic reconstruction techniques are available. The theory of the convolution backprojection algorithm used in this work is presented.

Next, the technique was applied to investigate physical phenomena in an asymmetric 3-D field. The phenomenon chosen was the development of a laminar rectangular heated air jet. The rectangular jet had a cross-sectional area of 8.7mm by 3.9mm. The Reynolds number based on the width (smaller dimension) was 500. The jet exit temperature was 450 K. The temperature profiles along the minor and major planes of the rectangular jet were determined at various locations downstream of the jet. It was shown that the trend observed was consistent with published results on three dimensional jets. It was found that the spreading rate of the thermal shear layer of the jet in the plane of major axis was higher than that in the plane of the minor axis. This study shows that the quantitative schlieren measurement technique could be useful to gain understanding of the fluid/combustion dynamics.

Having demonstrated the technique, the round jet was tilted to provide a test field which was asymmetric. The jet exit was inclined by 30 degrees to the vertical axis, which created an asymmetric temperature field above the jet. This necessitated the use of computer tomography to reconstruct the three-dimensional temperature field. The jet Reynolds number was 380 and the jet I.D was 5.4mm. The measurements were determined by recording multi-angular views of the test field using the rainbow schlieren imaging technique. Thermocouple measurements were also made at two axial planes above the jet exit. Measurements by the two different techniques agreed with each other within the experimental errors.

Quantitative analysis of 3-D flow fields by rainbow schlieren deflectometry is presented. The method is based on the measurement of the deflection of collimated light rays due to the gradients in the refractive index of the test flow field. In this method, the schlieren apparatus is modified by replacing the knife edge with a computer-generated continuously-graded color (rainbow) filter. This modification results in the refractive index gradients appearing in the schlieren image as gradations in color rather than irradiance.

The rainbow schlieren technique was used to measure temperature in an axisymmetric heated air jet. The Reynolds number of the jet was 570 and the jet I.D. was 7.1mm. The heated axisymmetric jet was chosen to demonstrate the technique by comparing reconstructed temperatures with thermocouple probe measurements. Because of axisymmetry of the jet, only one view was required to reconstruct the temperature field using the rainbow schlieren technique. The temperature reconstructions of the jet at several axial locations above the jet were found to agree with the thermocouple measurements. This agreement demonstrated that the rainbow schlieren technique could be used for temperature measurements in test fields of various configurations.