Quantitative analysis and validation

The Rayleigh-Bernard (R-B) experiment is conducted to demonstrate and quantitatively validate the data analysis procedure of the color schlieren technique. Figure 3 shows the transient sequence of color schlieren images of R-B convection. Initially, the beam is focused at the red region of the color filter, Figure 3(a), which is used as the reference image for subsequent calculations. After recording the base image, a temperature difference is applied between the top and bottom walls of the cavity by circulating cold and hot water in the respective tanks. Unstable density gradients are created in the fluid medium as the air near the top cold wall becomes denser compared to air near the lower hot wall, setting up convection currents across the cavity. The density gradients lead to a change in the index of refraction of the media and the light beam deflects from its original path. The deflected beam falls on various regions of the color filter depending on the strength of the refractive index gradient, creating a range of colors. Figure 3(f) shows the steady state convection pattern. Here, a large color variation is observed near the horizontal walls and no color variation is seen in the central region. This is due to high thermal gradients in the near wall region because of diffusion mode of heat transfer compared to the central region, where convection mode is predominant. The color change near the vertical sides is not very prominent because of the insulated boundary conditions. Thus, the color schlieren image clearly brings out the thermal boundary-layer type of the flow structure in the cavity with an overall circulation loop.

Figure 3: Transient evolution of the convective ield in an ir filled rectangular cavity with top surface temperature, and bottom surface temperature The corresponding Rayleigh number is Ra=48,000: (a) base image (t=0 h); (b) t=0.25 h; (c) t=0.5h; (d) t=1; (e) t=2h and (f) t=4h