Scale-free scalar imaging velocimetry: Towards a general technique for four-dimensional velocity field measurements in turbulent flows

The inability to measure the three-dimensional velocity field and the nine-component velocity gradient field is one of the greatest obstacles blocking the experimental study of turbulent flows. Scalar imaging velocimetry (SIV) overcomes this obstacle by measuring all three velocity and all nine velocity gradient components in four-dimensional spatio-temporal volumes. Relying on four-dimensional turbulent scalar field measurements, this technique determines the velocity field by inverting the scalar transport equation from measured scalar field data. Previous work has shown that SIV yields accurate results if the scalar fields are fully resolved; however, this limits the technique to small volume sizes and low Reynolds number turbulent flows for which the smallest length scales can be resolved. Presented here are results on the extension of SIV to “scale-free SIV” which would eliminate these restrictions. In scale-free SIV, there is a convolution of the scalar and velocity terms in the scalar transport equation. This presents problems in solving the variational equations for the velocity field that are similar to subgrid scale modeling in large eddy simulations (LES). Several methods to address this issue are examined using synthetic scalar field data. Then results are presented for scale-free SIV applied to laser induced fluorescence data from a turbulent jet. Results indicate that if a suitably accurate subgrid scale model is developed, scale-free SIV may become an accurate measurement technique yielding accurate velocity and velocity gradient fields.