Graduate Seminar in Fluid Mechanics
4:10 pm Presentation
“Turbulent Flow over Fractal Urban-Like Topography: Prognostic Roughness Model for Unresolved Generations”
Presented by XIAOWEI ZHU (Adviser: Prof. Zaki)
Urban-like topographies are composed of a wide spectrum of topographic elements, which results in a multiscale, fractal-like surface height distribution. Computational modeling of turbulent flows responding to fractal-like geometries poses unique challenges, especially when the number of self-similar generations renders a spectrum of the constituent wavelengths ﬁner than the computer mesh resolution. In the background of large-eddy simulation (LES), high-resolution multiscale topography needs to be spatially ﬁltered to obtain a resolved topography to be directly used in LES. The eﬀects of the subgrid-scale topography need to be modeled. Inspired by the self-similar nature of the topography, we modeled the effects of these truncated topographic modes based on the behaviors of the large-scale geometry. Firstly, the iterated function system (IFS) was used to construct urban-like, fractal geometries. And five fractal dimensions were used to investigate the parameterization of unresolved generations. Secondly, we quantiﬁed the momentum deficit associated with changing attributes (such as fractal dimension and generation), which enabled a posteriori deduction of roughness length parameters needed to model aerodynamic surface stress. We further showed that aerodynamic stress associated with the descendant, sub-generation elements can be parameterized, with only the first few generations resolved on the computational mesh. Finally, a logarithmic law-based roughness model was proposed for the unresolved, sub-generation topographic elements.