Spatial resolution enhancement/smoothing of stereo-particle-image-velocimetry data using proper-orthogonal-decomposition-based and Kriging interpolation methods

Methods for data reconstruction and spatial enhancement of experimental data for a transitional boundary layer with laminar separation bubble are investigated. Particularly, proper orthogonal decomposition (POD) is applied to direct numerical simulation (DNS) data to extract the DNS-based POD modes, which are projected onto the experimental data (via a least-squares procedure) in order to obtain model coefficients. These model coefficients are then used to reconstruct, "interpolate," and smooth the experimental data based on the DNS modes. In addition, in order to compare and assess the effectiveness of the present DNS-based procedure, Kriging interpolation is performed on the experimental (as well as numerical) data. These procedures are applied to time periodic (experimental) instantaneous spanwise vorticity (ω_z) at a constant spanwise location. We have demonstrated that particle-image-velocimetry (PIV)-based POD modes can be smoothed by Kriging interpolation, thus a noise-free reconstruction of PIV data can be achieved. It is also found that for very low resolution experimental data, DNS-based interpolation is superior over Kriging interpolation. On the other hand, Kriging interpolation based on the Gaussian correlation model works very well for sufficiently high resolution experimental data. The correlation parameter can be used to control the degree of smoothness in the data reconstruction. Both procedures effectively eliminate the unwanted noise in the experimental data. One important difference between the two procedures is that, with quite some confidence, the DNS-based procedure can also be used for "extrapolation" since the model coefficients do not depend on spatial variation. In fact, we show that near-wall spanwise vorticity, which is not available from experimental data, can be recovered faithfully. Moreover, the enhancement (interpolation and smoothing) of full three-dimensional PIV data has been performed by Kriging interpolation employing a Gaussian correlation model.