Accurate measurement of nonlinear liquid sloshing

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.