Coherent structures and energy transfer in decelerated turbulent boundary layers

Abstract

This thesis aims to expand our knowledge about turbulent boundary layers (TBLs) developing under adverse pressure gradients (APG). The main focus of this thesis is coherent structures and energy transfer mechanisms in APG TBLs with small and large velocity defects. For this, two novel non-equilibrium APG TBL direct numerical simulation databases are generated. The first database is a non-equilibrium APG TBL with $Re_\theta$ reaching 8000 and a shape factor spanning between approximately $1.4$ and $3.2$. It is the main database utilized throughout the thesis. The second database has identical domain and boundary conditions to the first one. The difference between them is that turbulence in the inner layer of the second database is artificially eliminated. This second database is generated to examine the effect of the inner layer on the outer layer turbulence. For comparison purposes, a channel flow case, two zero pressure gradient (ZPG) TBLs and two homogeneous shear turbulence (HST) databases from the literature are employed. The energy-carrying and –transferring structures are examined using the spectral distributions and two-point correlations. The analysis reveals that energy-carrying structures in small defect APG TBLs and canonical flows have similar spatial and spectral features. In the large defect case, turbulence in the inner layer, which is the dominant region in canonical flows and small defect APG TBLs, loses its importance and outer-layer turbulence becomes dominant. The inner peak in the $\langle u^2\rangle$ spectra does not exist in the large-defect case. Moreover, two-point correlations show that the spatial organization becomes different in the large-defect case as well. Regarding the energy-transferring structures, production, pressure-strain and dissipation structures behave in a similar fashion to the energy-carrying structures. The spectral distributions show that the canonical flows and small defect APG TBLs behave very similarly. The shape of the spectra is qualitatively similar in both cases. In the large defect case, the wall-normal distributions of production and pressure-strain become different since the outer layer becomes dominant. However, the shape of 2D spectra and the aspect ratio of structures are alike in all cases. The production and pressure-strain structures are analyzed in more detail using the relative size and wall-normal positions with respect to each other and energetic structures using spectral distributions. The results show that production and pressure-strain spectra have similar features in both the inner and outer layers regardless of the velocity defect, despite the differences in energetic structures. In the inner layer, the results suggest that the near-wall cycle or another mechanism with similar spectral features exists in large defect APG. As for the outer layer, an interesting result is that in large-defect APG TBLs it acts more like a free shear layer than in small-defect APG TBLs or canonical flows. Besides that, production and inter-component energy transfer mechanisms are similar in all cases regardless of velocity defect. No inflection point instability in the outer layer of the large-defect APG TBLs was detected. The effect of the near-wall region on the outer-layer layer structures is examined through Reynolds-shear-stress carrying structures' spatial features by detecting individual structures using spatio-temporal volumetric data. The results show that the outer layer is not significantly affected by the inner-layer turbulent activity. The structures' spatial features mostly depend on the mean shear. The aspect ratio of Reynolds-shear-stress carrying structures remains almost identical in the outer layer when the inner-layer turbulence is eliminated. Moreover, the aspect ratio follows a similar trend in both outer layers of APG TBLs and HSTs when the structures' size is normalized with the Corrsin length scale. The overall conclusion is that energy transfer mechanisms remain the same within one layer regardless of the velocity defect. The reason why the wall-normal distribution of energy and energy transfer dramatically changes in the large defect case is probably the change in the mean shear profile due to the increasing velocity defect.