Streamwise Homogeneous Turbulent Boundary Layers

Citation

Ruan, Joseph Y. (2021) Streamwise Homogeneous Turbulent Boundary Layers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qjfk-5q05. https://resolver.caltech.edu/CaltechTHESIS:06062021-094519451

Abstract

Boundary layers are everywhere and computing direct numerical simulations (DNS) of them is crucial for drag reduction. However, traditional DNS of flat-plate boundary layers are prohibitively expensive. Due to the streamwise inhomogeneity of the boundary layer, simulations of spatially growing boundary layer simulations require long domains and long convergence times. Current methods to overcome streamwise inhomogeneity (and allow for shorter streamwise domains) either suffer from a lack of stationarity or have difficult numerical implementation. The goal of this thesis is to develop and validate a more efficient method for simulating boundary layers that will be both statistically stationary and streamwise homogeneous.

The current methodology is developed and validated for the flat plate, zero pressure gradient, incompressible boundary layer. The Navier-Stokes equations are rescaled by a boundary layer thickness to produce a new set of governing equations that resemble the original Navier-Stokes equations with additional source terms. Streamwise homogeneity and statistical stationarity are verified through non-periodic and periodic simulations, respectively. To test the accuracy of the methodology, a sweep of Reynolds number simulations is conducted in streamwise periodic domains for Re_δ^*=1460-5650. The global quantities show excellent agreement with established empirical values: the computed shape factor and skin friction coefficient for all cases are within 3% and 1% of empirical values, respectively. Furthermore, to obtain accurate two-point correlations, it is sufficient to have a computational domain of length 14δ₉₉ and width 5δ₉₉, thus, leading to large computational savings by one-to-two orders of magnitude. This translates into increasing the largest possible Reynolds number one could simulate by about a factor of 3.

Thanks to the streamwise homogeneous nature of the simulation results, it is now possible to apply cost-efficient data-driven techniques like spectral proper orthogonal decomposition (SPOD; Towne et al. 2018) to extract turbulent structures. Particular emphasis is place on identifying structures for waves in the inner and outer layers. To interpret these structures, 1D resolvent analysis (McKeon and Sharma 2010) is leveraged. The peak location for the extracted inner wave is captured by traditional resolvent analysis, assuming a parallel flow. However, the peak location for the extracted outer wave differs from that predicted by the classic 1D resolvent analysis by 20%. Recovering the peak location requires including in the resolvent operator the mean wall-normal velocity profile and the streamwise growth of the boundary layer.

This methodology has natural extensions to slowly growing boundary layer flows, including thermal boundary layers, rough wall boundary layers and mild pressure gradient flows.

Thesis Files