Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2105.12059

A vortex sheet based analytical model of the curled wake behind yawed wind turbines

Majid Bastankhah·Carl R. Shapiro·Sina Shamsoddin·Dennice F. Gayme·Charles Meneveau
View original source ↗Read source document ↗Export metadata ↓

Abstract

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Majid Bastankhah, Carl R. Shapiro, Sina Shamsoddin, Dennice F. Gayme, Charles Meneveau. 2021-09-30. A vortex sheet based analytical model of the curled wake behind yawed wind turbines. https://doi.org/10.1017/jfm.2021.1010

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reynolds-number regimes of corrugation-induced lift enhancement in two-dimensional dragonfly-like wings

Corrugated wing structures commonly observed in insect wings can enhance aerodynamic performance at low Reynolds numbers ($Re \simeq O(10^3)$). However, their effectiveness strongly depends on the Reynolds number, and the corresponding operating range remains unclear. Direct numerical simulations of an impulsively started corrugated wing are performed over a wide range of Reynolds numbers ($100 \leq Re \leq 4000$) to identify the conditions under which corrugation is beneficial. Three Reynolds-number regimes are identified within the examined parameter sets. No characteristic lift-enhancement mechanism is observed for $100 \leq Re < 1000$. For $1000 \leq Re \leq 4000$, lift enhancement is associated with alternating vortices formed within the V-shaped region of the corrugated wing, which generate low-pressure regions near the wing surface. Above $Re=2000$, the collapse and confinement of a secondary vortex within the V-shaped region emerge as an additional dominant mechanism, further enhancing the lift. An analysis based on a local Reynolds number organizes the onset conditions of these mechanisms and provides a useful local measure for characterizing the onset of vortex detachment from the corrugation. Furthermore, long-time simulations confirm that the observed vortex dynamics persist well beyond the initial transient response following an impulsive start. These results elucidate Reynolds-number-dependent lift-enhancement mechanisms and define aerodynamic conditions under which corrugated wings provide an advantage.

physics.flu-dyn↗
arXiv2026

PhysMiner: An Agentic AI Framework for Automated Flow Component Analysis

Uncovering the physical mechanisms of turbulent flows remains a fundamental challenge in fluid mechanics. In particular, conventional velocity-gradient analysis methods suffer from shear contamination, which hinders accurate identification of the dominant physical mechanisms. This study presents PhysMiner, an automated framework integrating the triple decomposition method of the velocity gradient tensor with large language model-driven reasoning for turbulence-physics discovery. The triple decomposition module automatically decomposes flow fields into rigid rotation, pure shearing, and normal straining components, enabling statistical analysis, contour visualization, vortex-line extraction, and threshold-insensitive vortex identification while eliminating shear contamination. These automated capabilities are validated across five benchmarks, ranging from canonical configurations to complex engineering flows. A discover-physics agent combines flow statistics, spatial structures, and literature-derived knowledge to perform pattern recognition and physical inference, while a review Agent iteratively validates physical consistency to ensure reliable conclusions. A continuously evolving Triple Decomposition Library accumulates statistical knowledge from successfully analyzed flows, enabling cross-case comparison and progressive enhancement of inductive capability. The complete PhysMiner pipeline is validated end-to-end on the periodic hill flow, where the framework autonomously generates turbulence modeling recommendations and derives an improved subgrid-scale model with superior Reynolds-stress predictions. PhysMiner is open to the public and establishes a foundation for long-term collaborative advancement in automated turbulence-physics discovery.

physics.flu-dyn↗
arXiv2026

Lattice Boltzmann Methods for Navier-Stokes Equations in General Orthogonal Coordinates for Efficient Flow Simulations using Nonuniform Clustered Grids

Resolving multiscale fluid flows or boundary layers effectively requires the use of nonuniform meshes with local grid clustering. The standard lattice Boltzmann method (LBM), a kinetic theory-based approach for computational fluid dynamics, however, is restricted to the use of uniform Cartesian grids. We present new and improved formulations of the LBM that accommodate continuously varying spatial grids via coordinate transformations to simulate the Navier-Stokes equations (NSE) in the general orthogonal coordinates (GOC). They are constructed using a Chapman-Enskog analysis to specify the equilibrium moments of the distribution functions and the geometric force terms used in the collision step to be dependent on the local metric factors and their spatial derivatives, along with the density, momentum and their fluxes, and some correction terms related to the normal velocity gradients so as to accurately represent the NSE in the GOC. The resulting GOC-LBM importantly maintains the simplicity of the collide-and-stream approach and is Galilean invariant that is free of the cubic velocity artifacts. Our GOC-LBM is general and modular in that it can be used with any collision model with appropriate modifications to the equilibria and forcing terms. We present its implementation details for a variety of collision models while the central moments-based model using multiple relaxation times was found to be the most robust in practical implementations. We validate the GOC-LBM through numerical simulations for various benchmark flow problems. Moreover, we demonstrate significant computational advantages of our approach for a case study on simulating boundary layer flows efficiently that involves coupling the GOC-LBM for the NSE with a new GOC-LB scheme for solving the magnetic induction equation for magnetohydrodynamics (MHD), and for another case study involving orthogonal curvilinear grids.

physics.flu-dyn↗