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Title: A Solution Method for the Filtered Lifting Line Theory

Journal Article · · Journal of Fluids Engineering
DOI: https://doi.org/10.1115/1.4066296 · OSTI ID:2462703
 [1];  [2];  [3];  [1]
  1. National Renewable Energy Laboratory (NREL), Golden, CO (United States). National Wind Technology Center
  2. Delft Univ. of Technology (Netherlands)
  3. Univ. of Massachusetts, Amherst, MA (United States)
+ Show Author Affiliations

The filtered lifting line theory presents a continuous form of the inviscid momentum equations of flow over a lifting device, such as a wing or rotor blade, using body forces without mathematical singularities. This theory is also consistent with an actuator line representation of a lifting device. In this work, we present a reformulation of the equations in terms of the local flow angle along the line, which allows solving the stand-alone equations using multivariate root-finding algorithms. This approach can be used to obtain a fast, computationally inexpensive solution of the loading distribution along a wing without the need to perform computational fluid dynamic simulations. We study the requirements in terms of resolution in the spanwise direction and establish the criteria for spacing and minimum amount of points required along the blade to obtain converged solutions. The solutions are compared to results from large-eddy simulations, and we observed excellent agreement with less than a percent difference in quantities along the blade between the methods.

Research Organization:
National Renewable Energy Laboratory (NREL), Golden, CO (United States)
Sponsoring Organization:
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Wind Energy Technologies Office
Grant/Contract Number:
AC36-08GO28308
OSTI ID:
2462703
Report Number(s):
NREL/JA--5000-90389; MainId:92167; UUID:ca7cb896-361f-4a67-8219-12e007509859; MainAdminId:73225
Journal Information:
Journal of Fluids Engineering, Journal Name: Journal of Fluids Engineering Journal Issue: 1 Vol. 147; ISSN 0098-2202
Publisher:
ASMECopyright Statement
Country of Publication:
United States
Language:
English

References (16)

Mesh and load distribution requirements for actuator line CFD simulations journal August 2012
A simple solution method for the blade element momentum equations with guaranteed convergence: Guaranteed solution of the BEM equations journal June 2013
Large eddy simulations of the flow past wind turbines: actuator line and disk modeling: LES of the flow past wind turbines: actuator line and disk modeling journal April 2014
Optimal smoothing length scale for actuator line models of wind turbine blades based on Gaussian body force distribution: Wind energy, actuator line model journal January 2017
A new tip correction for actuator line computations journal February 2020
Generalized filtered lifting line theory for arbitrary chord lengths and application to wind turbine blades journal October 2023
A Comparative Study on Methods for Convergence Acceleration of Iterative Vector Sequences journal March 1996
Large-Eddy Simulation of a wind turbine using a Filtered Actuator Line Model journal March 2022
Filtered lifting line theory and application to the actuator line model journal January 2019
SciPy 1.0: fundamental algorithms for scientific computing in Python journal February 2020
Spectral residual method without gradient information for solving large-scale nonlinear systems of equations journal April 2006
A derivative-free nonmonotone line search and its application to the spectral residual method journal November 2008
Numerical Modeling of Wind Turbine Wakes journal May 2002
Lifting Line with Various Mollifications: Theory and Application to an Elliptical Wing journal January 2019
A Quasi-Vortex-Lattice Method in Thin Wing Theory journal September 1974
A vortex-based tip/smearing correction for the actuator line journal January 2019

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Related Subjects

17 WIND ENERGY
97 MATHEMATICS AND COMPUTING
actuators
algorithms
blades
computational fluid dynamics
flow (dynamics)
large eddy simulation
resolution (optics)
simulation
wings