NUMERICAL SIMULATIONS OF THE RESTRICTED NONLINEAR SYSTEM

large eddy simulation;restricted nonlinear system;reduced-order modeling;wind farms;Mechanical Engineering

Bretheim, Joel UMeneveau, Charles V. ;

Johns Hopkins University

关键词: large eddy simulation;    restricted nonlinear system;    reduced-order modeling;    wind farms;    Mechanical Engineering;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/59172/BRETHEIM-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 摘 要 】

The restricted nonlinear (RNL) model is a simplified model for wall-boundedturbulence derived directly from the Navier-Stokes equations by restricting the nonlinear interaction between non-zero streamwise Fourier modes. The model is motivated by the prevalence of streamwise coherent structures in wall-bounded turbulent flows. In the last several decades, these flow structures have motivated many analytical, experimental, and numerical investigations to better understand the role they play in the dynamics of wall-bounded turbulence. The simplified nature of the RNL system offers a new, more tractable approach to understanding, for example, the connection between streamwise coherent structures and the momentum transfer mechanisms of wall-bounded turbulence.Numerical simulations of wall-bounded turbulence using the RNL modelhave been shown to generate realistic mean velocity profiles in canonicalwall-bounded flows at low Reynolds numbers. Initial simulations at higherReynolds numbers produced less accurate results, and while a logarithmic region had been observed, its von Kármán constant is not consistent with the standard logarithmic law. In direct numerical simulations (DNS) of ahalf-channel flow, we demonstrate in the first part of this work that limitingiithe streamwise-varying wavenumber support of RNL turbulence (producinga system which we term the ;;band-limited’ RNL model) to one or a fewempirically determined modes improves its predictions considerably. In particular, the mean velocity profiles obtained with the band-limited RNLmodel follow standard logarithmic behavior for a range of moderate Reynolds numbers. Despite the more tractable nature of the RNL system, DNS of higher Reynolds number RNL flows are still limited by the demanding cross-plane resolution requirements for full resolution of the viscous terms.In the second part of this work we extend the RNL model to arbitrarily high Reynolds numbers by developing a RNL large eddy simulation (LES) framework along with a method to systematically identify an appropriate streamwise wavenumber support based on spectral properties of wall-bounded turbulence. This method leads to a band-limited RNL-LES system that is successful in reproducing some of the most important statistical features cap-tured in previous low to moderate Reynolds number simulations, e.g., themean velocity and second-order moment profiles. As in the low to moderate Reynolds number DNS setting, the RNL-LES framework offers a new approach to understanding the connection between coherent structures and the momentum transfer mechanisms of wall-bounded turbulence, but at arbitrarily high Reynolds numbers. Additionally, we demonstrate a new numericalapproach to solving the RNL-LES equations that exploits the properties of the system to achieve significant computational speedups relative to traditionalLES.In the third and final part of this work, we introduce a new approach toiiithe reduced-order modeling of wind farms based on the RNL-LES framework. The low computational cost nature of the RNL-LES framework makes it a potentially attractive candidate for a reduced-order approach to studying wind farm behavior over a range of conditions. To enable this, we use an appropriately altered version of the actuator disk turbine model to evaluate the ability of the RNL-LES framework to simulate very large wind farms in the fully-developed regime through comparisons with standard LES of wind farms under a variety of conditions. Then, the low computational cost of theRNL-LES approach is exploited to conduct a large parametric study of several vertically-staggered wind farm configurations in order to assess the impact of vertical staggering on wind farm power production.