Accurate Measurement of Nonlinear Liquid Sloshing

Abstract

The accurate measurement of nonlinear liquid sloshing in a liquid-filled spacecraft is of importance for precise flight control. In this paper, a novel noncontact method combining the fringe transmission technique with the liquidlevel reflection technique has been developed to accurately evaluate such behavior. To do this, a printed fringe pattern was first placed underneath a transparent test tank with fabricated calibration tails on the wall and, when viewed from above with a high-speed camera, a series of distorted transmission-fringe images with reflected images of the liquid level at different times during the sloshing process were achieved. Combing the quantitative relationship between the shape of the liquid surface and the distortion of the transmission fringes, as well as considering the height curves of the liquid level, the three-dimensional dynamic deformation field could be calculated using multidirectional Newton iterative algorithms. Both the dynamic deformation field of the liquid surface and the residual liquid volume in the tank could be accurately measured at the same time. An experimental verification was carried out, and the results obtained demonstrated the feasibility and reliability of this new method.Superscripts i, j = index of coordinates in x and y directions n = number of scattered points

3D shape measurement of complex transparent liquid surfaces using monoscopic deformed fringe transmissometry

“…Figure 1(a) shows the propagation of light on liquid surface. The carrier pattern such as lattices [22], fringes [23], speckles [21,24,25], grids [20], or dots [18], is placed at the bottom of the liquid for the measurement. First, the light of the carrier pattern is emitted from the bottom of the liquid and refracts as it passes through the surface of the liquid, and then travels straight up until captured by the optical camera.…”

“…The height of each point in the curve is related to the change of height with its' neighbor point in the same curve. According to Snell's law, the triangular relationship [23] in ∆A′N i A and ∆N i P i N i−1 , the three equations can be derived as:…”

“…However, they have a limited measurements range and only suitable for small deformations. Liu et al [20][21][22][23][24][25] proposed a fringe transmission technique for measuring the deformation of large liquid surface by analyzing the in-plane deformation of transmission fringe patterns. This set of techniques have advantages of non-contact and full-field measurements, and the experimental set-up is very simple and easy to operate.…”

Probing Micro-Newton Forces on Solid/Liquid/Gas Interfaces Using Transmission Phase Shift

“…Liquid/gas interfaces are found throughout nature and play important roles in almost all scientific fields from chemistry, , physics to biology and engineering . Floating versus sinking of solids on a liquid/gas interface has not only been driven by countless technological applications such as flotation, , self-assembly, − encapsulation, liquid sloshing, , or for the air–liquid interface cell culture but also is a matter of dead or alive for water-walking insects that live on the water surface. , These raise the natural question, When can an object float? The more specific question is, Why small objects that are denser than the liquid can still float?…”