Optical Density Measurements and Analysis for Single-Mode Initial-Condition Buoyancy-Driven Mixing

Abstract

The Texas A&M water channel experiment is modified to examine the effect of single-mode initial conditions on the development of buoyancy-driven mixing (Rayleigh-Taylor) with small density differences (low-Atwood number). Two separated stratified streams of ~5°C difference are convected and unified at the end of a splitter plate outfitted with a servo-controlled flapper. The top (cold) stream is dyed with Nigrosine and density is measured optically through the Beer-Lambert law. Quantification of the subtle differences between different initial conditions required the optical measurement uncertainties to be significantly reduced. Modifications include a near-uniform backlighting provided through quality, repeatable, professional studio flashes impinging on a white-diffusive surface. Also, a black, absorptive shroud isolates the experiment and the optical path from reflections. Furthermore, only the red channel is used in the Nikon D90 CCD camera where Nigrosine optical scatterring is lower. This new optical setup results in less than 1% uncertainty in density measurements, and 2.5% uncertainty in convective velocity. With the Atwood uncertainty reduced to 4% using a densitometer, the overall mixing height and time uncertainty was reduced to 5% and 3.5%, respectively. Initial single-mode wavelengths of 2, 3, 4, 6, and 8 cm were examined as well as the baseline case where no perturbations were imposed. All non-baseline cases commence with a constant velocity that then slows, eventually approaching the baseline case. Larger wavelengths grow faster, as well as homogenize the flow at a faster rate. The mixing width growth rates were shown to be dependent on initial conditions, slightly outside of experimental uncertainty.