PIV Investigation Of Space-time Correlation Model In Shear Turbulence

Correlation function which is a fundamental statistical tool in turbulence researches and necessary part of turbulent statistical theories and models has important theoretical and practical significance. Space-time correlation includes complete temporal and spatial information of coherent structure. It receives inadequate intention due to its complication which make it impossible to collect enough data in experiments. But researchers encount the difficulty of transformation between spatial and temporal dimensions. A canonical solution is Taylor frozen hypothesis which connects the temporal and spatial dimensions by a linear relationship. Taylor hypothesis is easily applicable for the simple transformation but inaccurate for representing the real relationship between temporal and spatial scales and total features of temporal-spatial motions in turbulence. The validity of Taylor hypothesis builts on the basement that the aspects of the flow satisfy several prerequisites, otherwise the application brings evident errors. A new model for space-time correlation – elliptic approximation(EA) hypothesis is proposed recently. EA expands space-time correlation on Taylor series from the 1st order to the 2nd order, combining with Kraichnan’s “random sweeping hypothesis”. EA considers the variation of space-time correlation influenced by distortions of coherent motions through a new parameter, sweep velocity.EA hypothesis has been verified in a few kinds of experimental and simulated flows whose dataset have the quality of simple homogeneous turbulence or quasi-isotropic turbulent Rayleigh-Benard convection. The present work is the first experimental validation and applicable extension in a real inhomogeneous anisotropic turbulent boundary layer(TBL) over a flat wall. Next the work explores the limitations of the new hypothesis in TBL over a wavy wall. The final aim is to study the crucial parameters in the model for a comprehensive understanding. All the work is combined with the analyses of representive coherent structures, especially as to the core issues of convection, distortion and attenuation which have a influence on correlations. The datasets consist of full-component velocity fields of TBL over a flat wall acquired by tomographic PIV and planar velocity fileds of TBL over a wavy wall acquired by 2D PIV.The analysis of TBL over a flat wall indicates that cane vortices, arch vortices and hairpin vortices, as dominate coherent structures in the flow, induce the adjacent fluid to form large-scale streamwise correlated streaks, and the latter changes the environment around the coherent structures in turn. The interactions between them participate the dynamic development of turbulence, and thus have an impact on the correlation function. The 2nd space-time correlation of streamwise velocity fluctuation has a distribution coincident with the prediction of EA, which means that EA is valid in such shear turbulence. The iso-correlation contours show the same 2 features as EA that all the curves share an identical inclination angle and aspect ratio. EA not only includes the convection of coherent structures, but also captures the de-correlation process in the flow in contrast to Taylor hypothesis. It’s more appropriated for EA to describe coherent motions in shear turbulence because of solving the “non-closure” problem of space-time correlation. There are 3 special nature of TBL over a wavy wall: periodicity, adverse pressure gradient(APG) and shear layer. The space-time correlation in the flow is different from the former flow over a flat wall, that in the near-wall region the distributions of space-time correlation are no longer elliptical but the deviation vanishes far away from the wavy wall. It’s believed that the APG in the near-wall region undermines the validity of EA. The results reveal the limitations of EA that some quantities in turbulence, like pressure fluctuation that has a distinct quality from velocity fluctuation, are not suitable for modeling by EA.Convection velocity stands for the convection motion of coherent structures in the flow. The first analysis based on the traditional Fourier decomposition(FD) reveals that the convection velocity has a more prominent spanwise scale than streamwise scale, which only exists in the near-wall region. Proper orthogonal decomposition(POD) which is next employed in analysis of scale-dependence is adaptive, energy-optimal and more in accordance with the physical quality of turbulence. POD separates the scales of flow according to their contributions of turbulent kinetic energy. The scenarios of TBL revealed by POD scale-separation are consistent with the multi-scale coherent structures model for TBL proposed by Elsinga. The results of POD are quite different from the results of FD, that the large-scale velocity fields consist of large-scale coherent structures and induced streaks, moves slower as the entirety than coherent structures in the small-scale velocity fields. Sweep velocity measurements the degree of distortion and attenuation of coherent structures produced by the induction of large-scale energy-containing eddies and the effect of mean shear. Sweep velocity is determined mainly by Taylor micro-scale, mean shear and velocity fluctuation in shear turbulence. With increasing modes in the POD reconstruction, Taylor micro-scale decreases, the reduced distortion from mean shear is more significant than the increased distortion from enhanced velocity fluctuation. The total distortion is eventually cut down which means sweep velocity becomes smaller along with more POD scales. The variation of sweep velocity implies the change of de-correlation process, thereby the decay of space-time correlation in shear turbulence.