Evaluation of the shadowgraph method for the convective flow in a side-heated cavity

Abstract

The shadowgraph method is used to visualize the convective flow in a water-filled square cavity, which is differentially heated and cooled from the opposing vertical sidewalls. Since in this system a quantitative recovery of the temperature field from the observed shadowgraph images is not possible, we apply a somewhat reverse procedure. The numerical solution of the cavity flow yields the field of the refractive index. By numerically integrating the path of light through this field, artificial shadowgraph images are constructed. This makes a comparison of the numerical and the experimental temperature fields possible and also leads to a clearer interpretation of the shadowgraph images and a better understanding of the way in which certain features are generated. The procedure is not restricted to the cavity flow, but can be applied whenever the field of the refractive index is available.

Imaging techniques for mapping solution parameters, growth rate, and surface features during the growth of crystals from solution

“…Under the assumption that the light rays undergo only infinitesimal deviations inside the inhomogeneous field, and between the exit face and the screen, it can be shown, under linear approximation, that the governing equation for the shadowgraph process is [46,445]:…”

“…In particular, the research groups led by Merzkirch, Mayinger, Goldstein, and Settles exploited the use of optical techniques, primarily shadowgrapy, for heat and mass transfer studies [169,303,316,455]. Several other research groups working in the field of thermal sciences have also used it for studies on transport phenomena [302,395,445]. However, this technique has not been widely used for crystal growth studies.…”

Comparison of interferometry, schlieren and shadowgraph for visualizing convection around a KDP crystal

“…Shadowgraph analysis requires tracing the path of individual rays through the aqueous solution. When subjected to linearizing approximations that include small displacement of the light ray, a second-order partial differential equation can be derived for the refractive index field with respect to the intensity contrast in the shadowgraph image [18]. With D as the distance of the screen from the optical window on the beaker and D as the Laplacian operator in the x2y plane, this equation is…”

Development and application of color schlieren technique for investigation of three-dimensional concentration field

“…Literature on the application of refractive index-based imaging techniques reveals that interferometry and schlieren techniques have primarily been employed to image the salt concentration distribution during the crystal growth process [4,[11][12][13][14][15][16]. Several researchers have developed and applied microscopic interferometric and schlieren techniques to resolve the salt concentration gradients within this region.…”