A novel method of reconstructing planar flow field from given distribution of single velocity component: comparison to conventional divergence-free approach

Measurements of a single flow velocity component are still prevalent due to their reasonable costs and some difficulties in multiple-component measurements. If the transverse component can be obtained additionally by a numerical technique, qualitative features of the flow will be understood more effectively. In this context, methods based on the 2-dimensonal divergence-free assumption have been widely used for problems in which a single velocity component is measured over a planar domain. In this study, the authors proposed a method of approximating the second planar velocity component by minimising an objective function expressed with divergence and vorticity so that the mass transport in the out-of-plane direction could be taken into consideration. The present method was tested with numerically produced 3-dimensional flows in a hexahedral chamber and a flow around a bluff body measured by particle image velocimetry. There was a tendency that the present method calculated the second velocity component with smaller errors than existing divergence-free approaches. It was also shown that the present method had a high capability to locate strong suction and generation caused by the mass transport in the out-of-plane direction. The present method is deemed promising for many one-component flow measurements in engineering and medicine.