Extended-resolution of a single-camera synthetic Schlieren method for measurement of free liquid surfaces

Abstract

In a synthetic Schlieren method of measuring the height of a dynamic free liquid surface, the smallest wavelength of the measured surface topography is determined by the spatial resolution of the displacement field of markers. Currently, a displacement vector is obtained for each interrogation window, including a few markers, with a cross-correlation algorithm. In this study, the measurement resolution is extended by obtaining the displacement of individual markers. This simple and rational change, however, brings technical difficulties in numerically solving the governing equation over spatially randomly distributed markers. For this, the governing equation, which associates the surface height to be measured with the virtual displacements of the markers, is solved by the finite-volume scheme for the unstructured meshes, where a marker locates at the center of each triangular mesh face. The present method is examined with the synthetic generated data, in laboratory experiments of a transparent solid carved with a sinusoidal surface, and in experiments of water ripples. The measurement uncertainty is discussed.