A Single-Camera Synthetic Schlieren Method for Measuring Two-Dimensional Liquid Surfaces

Abstract

A single-camera synthetic Schlieren method is introduced here to measure two-dimensional topography and depth of dynamic free liquid surfaces. The method is simple and easy to implement. Because of light refraction (following Snell’s law), markers on a flat bottom which are seen through the surfaces of a transparent liquid are virtually displaced. This leads to a governing equation that the liquid surface depth (and its topography) is associated with the marker displacement. In the equation, the refractive index of the liquid (e.g. water) can be obtained by a refractometer (or from a technical reference), and the displacements of the markers can be obtained by a cross-correlation method which is usually used in particle image velocimetry. In the equation, the only unknown, the depth of the surface, can be obtained by solving the governing equation with boundary conditions. Unlike free-surface synthetic Schlieren (FS-SS) of Moisy et al. (Exp. Fluids, 1021, 46, 2009), our method does not require a reference depth (which is obtained before or after experiments), so that flows with temporally evolving depth can be measured. Experiments of liquid ripples and dam-break flows were performed to test the method. The results agree well with those obtained with FS-SS and visualization measurements.