Large-Eddy Simulation of wind turbines wakes including geometrical effects

doi:10.1016/j.compfluid.2018.03.015

Computers & Fluids

Volume 173, 15 September 2018, Pages 133-139

https://doi.org/10.1016/j.compfluid.2018.03.015 Get rights and content

Highlights

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Large-Eddy Simulation strategy of wind turbine wakes including geometrical details is proposed.
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The methodology is assessed on two different test cases and validated with experimental results.
•
The use of unstructured grids to take into account geometrical effects is proved.
•
High order numerical schemes demonstrated the improvements of the results.

Abstract

Accurate simulation of wind turbine wakes is critical for the optimization of turbine efficiency and prediction of fatigue loads. These wakes are three-dimensional, complex, unsteady and can evolve in geometrically complex environments. Modeling these flows calls thus for high-quality numerical methods that are able to capture and transport thin vortical structures on an unstructured grid. It is proposed here to assess the performances of a fourth-order finite-volume LES solver to perform massively parallel scale-resolving simulations of wind turbines wakes. In this framework, the actuator line method that takes the effect of the wind turbine blades on the flow into account is implemented. It is demonstrated that both near and far parts of the turbine wakes are accurately modeled as well as geometrical details. The methodology is assessed on two different test cases and validated with experimental results. It is demonstrated that the flow predictions are of equivalent quality on both structured and unstructured grids. The influence of the geometrical details (e.g. nacelle and tower) on the wake development as well as the influence of the discretization scheme are also investigated.

Introduction

Considering current energetic and environmental challenges, wind turbines constitute an interesting alternative source of energy. It is indeed a renewable source of energy that helps reducing greenhouse gas emissions, by replacing combustion systems such as gas turbines or coal furnaces. In order to provide a large amount of electric power and reduce costs, wind turbines are usually gathered in the same location called a windfarm. Maximizing the electrical power yielded by a windfarm is currently a key issue [1]. For that purpose, the placement of the wind turbines with respect to each other has to be optimized. As the topology of the turbulent vortical wakes emanating from the tip of the blades can have a significant impact on the performances and the mechanical fatigue of the wind turbines located downstream, it is important to provide realistic modeling of these wakes. The latter are vortical flows which are fully turbulent: their simulation thus requires high-quality numerics with both low dispersion and diffusion errors to be able to transport them on long distances without artificial distortion. The range of space and time scales of the turbulence is so wide in such configurations that a direct numerical simulation (DNS) is not affordable. This calls for Large-Eddy Simulation (LES) turbulence modeling. LES is indeed well adapted to this problem since the considered flows are 3D, complex and strongly unsteady. As fully-resolved LES including a moving mesh discretizing the rotor is still expensive, aerodynamics models are often used to represent the effect of the rotating blades on the flow. There are many studies in the literature that are devoted to wind turbine rotor modeling. Most common methods used to model the effect of the rotating blades on the flow are actuator disc and actuator line methods. Actuator disc methods have been extensively used by several authors and results agree fairly well with that of experiments. Actuator disk methods were used in early LES studies of wind turbines wakes (see [2], [3]) and are still used in the context of large-scale windfarms simulations. An original and computationally efficient approach was developed by Chatelain et al. (see [4], [5]) who coupled a vortex particle-mesh method with immersed lifting lines for the Large-Eddy Simulation of wind turbine wakes. This method was successfully applied to the study of large-scale aerodynamics and wake behavior of horizontal and vertical axis wind turbines. This method is very well suited for free wake unbounded problems, however, it does not allow for complex geometries. In the framework of Eulerian discretizations, the actuator line method [6] is currently the most advanced model for the rotating blade aerodynamics [7].

In this paper, we propose to demonstrate that a massively parallel high-order finite-volume unstructured flow solver with an actuator line model is able to provide accurate flow predictions of wind turbine wakes. We first investigate the suitability of using fully unstructured meshes to simulate wind turbine wake flows. To this aim, the wake of a generic wind turbine similar to the Tjaereborg wind turbine is simulated [8], [9].

The other test case considered here is the NTNU wind tunnel model [10]. There is a great amount of experimental data available on this benchmark, that will allow validating the proposed approach. In particular, the geometrical effect of the tower and nacelle on the wake will be taken into account and its influence will be demonstrated using wall-modeled LES.

Section snippets

Governing equations

The governing fluid dynamics equations are the Navier–Stokes equations for incompressible flow, supplemented by a subgrid-scale (SGS) model. The filtering operator, which consists in projecting a field on the LES grid, is written as $\tilde{•}$ . Using this notation, the evolution equations for the LES velocity field are formally written as: $\begin{matrix} \nabla \cdot \tilde{u} & = & 0, \end{matrix}$ $\begin{matrix} \frac{\partial \tilde{u}}{\partial t} + (\tilde{u} \cdot \nabla) \tilde{u} & = & - \nabla \tilde{P} + ν \nabla^{2} \tilde{u} + \nabla \cdot {\tilde{τ}}^{M} + f, \end{matrix}$ where $\tilde{P} = \frac{1}{ρ} \tilde{p}$ is the reduced pressure field, ν the kinematic viscosity, and ${\tilde{τ}}^{M}$ the modeled SGS stress tensor. The body

LES of a generic 30 m rotor horizontal axis wind turbine: structured vs. unstructured grid

The first case investigated to assess the proposed method is representative of the Tjaereborg [8], [9] wind turbine. It has a diameter $D = 2 R \approx 61$ m and the rotor blade profiles are modeled using NACA4418 airfoils as in [18], with a chord length decreasing linearly from hub to tip. The wind speed U_∞ and the rotational speed Ω are set so that the tip speed ratio $T S R = λ = \frac{Ω R}{U_{\infty}} = 7.07$ . The aim of this investigation is to validate the fact that the numerical method proposed for unstructured grids is able to

LES of a model wind turbine located in a wind tunnel

The test case investigated here was described in detail in the report by Krogstad et al. [10]. This report provides geometrical parameters, wind tunnel inlet condition and CAD files for the blades and nacelle. The main focus of the proposed blind test was on the wake development behind the turbine. We propose here to assess the validity of our method and highlight the effects of the geometrical details as well as the order of the numerical scheme.

Concluding remarks

This work demonstrates the ability to perform massively parallel scale-resolving simulations where both near and far turbine wakes, as well as geometrical details, are accurately modeled. Thanks to the use of unstructured grids, complex geometries can be handled. This was assessed by considering tower and nacelle effects on a well-known yet severe benchmark case.

These simulations can be further exploited to get more insights into wind turbine wakes and their interactions with complex

Acknowledgments

This work was granted access to the HPC resources from CINES (Centre Informatique National de lEnseignement Superieur), from IDRIS (Institut du Developpement et des Ressources en Informatique Scientifique) and from TGCC-CEA under the allocations x20172b6880 made by GENCI (Grand Equipement National de Calcul Intensif). It was also granted CPU time by CRIANN under the allocation 2012006. This work is co-financed by the European Union with the European regional development fund (ERDF, HN0002137)

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Large-Eddy Simulation of wind turbines wakes including geometrical effects

Highlights

Abstract

Introduction

Section snippets

Governing equations

LES of a generic 30 m rotor horizontal axis wind turbine: structured vs. unstructured grid

LES of a model wind turbine located in a wind tunnel

Concluding remarks

Acknowledgments

J Wind Eng Ind Aerodyn

Math Comp

Combust Flame

SIAM J Numer Anal

Status of wake and array loss research

Tech. Rep.

A comparison of actuator disk and actuator line wind turbine models and best practices for their use

AIAA Paper

Large eddy simulation of wind turbine wakes

Flow Turbul Combust

Investigation of the effect of inflow turbulence on vertical axis wind turbine wakes

J Phys Conf Ser

Numerical modeling of wind turbine wakes

J Fluids Eng

Modeling wind turbine wakes for wind farms

Altern Energy Shale Gas Encycl