Experimental Study of Turbulence under Planar Straining and Destraining and Elimination of Peak locking Error in PIV Analysis Using the Correlation Mapping Method

J. Chen
PhD Thesis, The Johns Hopkins University
December 2004
Baltimore MD

ABSTRACT: In part I, the response of turbulence subjected to planar straining and de-straining is studied experimentally, and the impact of the applied distortions on the energy transfer across different length scales is quantified. The data are obtained using Planar Particle Image Velocimetry (PIV) in a water tank, in which high Reynolds number turbulence with very low mean velocity is generated by an array of spinning grids. Planar straining and de-straining mean flows are produced by pushing and pulling a rectangular piston towards, and away from, the bottom wall of the tank. The data are processed to yield the time evolution of Reynolds stresses, anisotropy tensors, turbulent kinetic energy production, and mean subgrid-scale (SGS) dissipation rate at various scales. During straining, the production rises rapidly. After the relaxation period the small-scale SGS stresses recover to isotropy, but the Reynolds stresses still display significant anisotropy. Thus, when destraining is applied, a strong negative production (mean backscatter) is observed where turbulence fluctuations return kinetic energy to the mean flow. The SGS dissipation displays similar behavior at large filter scales, but the mean backscatter gradually disappears with decreasing filter-scales. Energy spectra are compared to predictions of Rapid Distortion Theory (RDT). Good agreement is found for the initial response but, as expected for the time-scale ratios of the experiment, turbulence relaxation causes discrepancies between measurements and RDT at later times. A priori tests are performed on several SGS models: Smagorinsky, standard dynamic, and scale-dependent Smagorinsky models, as well as the non-linear mixed model, whose model coefficients are determined in dynamic and scale-dependent dynamic approaches. Compared with both dynamic models, the Smagorinsky model is more robust than expected when applied to the present test conditionIn part II, a new PIV cross-correlation analysis algorithm is introduced. The Peak-locking effect causes mean bias in most of the existing cross-correlation based algorithms for PIV data analysis. This phenomenon is inherent to the smooth curve fitting through discrete correlation values, which are used to obtain the sub-pixel part of the displacement. Almost all of the existing effective methods to solve this problem require iterations. In this thesis we introduce a new technique for obtaining sub-pixel accuracy, which bypasses the sub-pixel curve fitting, and thus eliminates the peak-locking effect, but does not require iterations. The principles of the "Correlation Mapping Method" are based on the following logic: If one uses a bi-cubic interpolation to express the second image based on the first one and the unknown displacement, the correlation between them becomes a polynomial of the displacement, whose coefficients depend on the first image. Matching this polynomial with the measured correlation provides an equation for the displacement for each point of the correlation map. A least square fit for the displacements calculated for the correlation values in the vicinity of the correlation peak (e.g. 5*5 points) provides an estimate for the particle displacement, including its sub-pixel part. This method is tested using synthetic and experimental data. The peak locking bias essentially disappears in all cases, and even the "random" error seems to be smaller than the results obtained using sub-pixel curve fit to the discrete correlation values. The proposed method also combines the Correlation Mapping Method with corrections for particle image distortion to further reduce the uncertainty in PIV data analysis. Typically three iterations achieve converged results.

The new technique described in part II was developed using Mathlab, thus is quite time consuming. It was not yet implemented during the analysis of PIV data in part I of the present study.

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