Title: Filtered lifting line theory and application to the actuator line model

Abstract

Lifting line theory describes the cumulative effect of shed vorticity from finite span lifting surfaces. In this work, the theory is reformulated to improve the accuracy of the actuator line model (ALM). This model is a computational tool used to represent lifting surfaces, such as wind-turbine blades in computational fluid dynamics. In ALM, blade segments are represented by means of a Gaussian body force distribution with a prescribed kernel size. Prior analysis has shown that a representation of the blade using an optimal kernel width$$\unicode[STIX]{x1D716}^{opt}$$of approximately one quarter of the chord size results in accurate predictions of the velocity field and loads along the blades. Also, simulations have shown that use of the optimal kernel size yields accurate representation of the tip-vortex size and the associated downwash resulting in accurate predictions of the tip losses. In this work, we address the issue of how to represent the effects of finite span wings and tip vortices when using Gaussian body forces with a kernel size larger than the optimal value. This question is relevant in the context of coarse-scale large-eddy simulations that cannot afford the fine resolutions required to resolve the optimal kernel size. For this purpose, we present a filtered lifting line theory for a Gaussian force distribution. Based on the streamwise component of the vorticity transport equation, we develop an analytical model for the induced velocity resulting from the spanwise changes in lift force for an arbitrary kernel scale. The results are used to derive a subfilter-scale velocity model that is used to correct the velocity along the blade when using kernel sizes larger than$$\unicode[STIX]{x1D716}^{opt}$$. Tests are performed in large-eddy simulation of flow over fixed wings with constant and elliptic chord distributions using various kernel sizes. Results show that by using the proposed subfilter velocity model, kernel-size independent predictions of lift coefficient and total lift forces agree with those obtained with the optimal kernel size.

Authors:

Martínez-Tossas, Luis A.  ^[1];

• Search DOE PAGES for author "Martínez-Tossas, Luis A."
• Search DOE PAGES for ORCID "0000-0003-2353-4999"

Meneveau, Charles  ^[2]

• Search DOE PAGES for author "Meneveau, Charles"
• Search DOE PAGES for ORCID "0000-0001-6947-3605"

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+ Show Author Affiliations

1. National Renewable Energy Lab. (NREL), Golden, CO (United States); Johns Hopkins Univ., Baltimore, MD (United States)
2. Johns Hopkins Univ., Baltimore, MD (United States)

Publication Date:

Wed Jan 23 00:00:00 EST 2019

Research Org.:

National Renewable Energy Laboratory (NREL), Golden, CO (United States)

Sponsoring Org.:

USDOE Office of Energy Efficiency and Renewable Energy (EERE), Wind and Water Technologies Office (EE-4W)

OSTI Identifier:

1492502

Report Number(s):

NREL/JA-5000-72646
Journal ID: ISSN 0022-1120

Grant/Contract Number:  

AC36-08GO28308

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Fluid Mechanics

Additional Journal Information:

Journal Volume: 863; Journal ID: ISSN 0022-1120

Publisher:

Cambridge University Press

Country of Publication:

United States

Language:

English

Subject:

17 WIND ENERGY; actuator line model; wind energy; computational fluid dynamics; large-eddy simulation; drag