Flow physics and Stokes’ theorem in wind turbine aerodynamics

Schmitz, Sven; Chattot, Jean‐Jacques

doi:10.1016/j.compfluid.2007.03.009

Cited by 12 publications

(3 citation statements)

References 6 publications

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“…1, the methodology in this paper minimizes the Navier-Stokes (NS) zone to a few reference chord lengths surrounding the airfoil, the circulation of the airfoil is determined through numerical integrating along closed contour lines ABCDA enclosing the airfoil within the small NS zone. Schmitz and Chattot [4] have given a viscous lift theorem derived from a momentum balance and Stokes' theorem, which is a generalization of the classical Kutta-Zhukovsky lift theorem for the viscous near field for 2D attached and separated flow. The grids of NS zone around the wind turbine airfoil are shown in Fig.…”

Section: Numerical Methodologymentioning

confidence: 99%

Applications of a Coupled Methodology to the Wind Turbine Airfoils

Chen

Guo

2012

AMR

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In this study, a coupled methodology is proposed for the aerodynamic behavior of wind turbine airfoils. The idea is to combine a Navier-Stokes solver with a free vortex model. The zone for the calculation of CFD is confined to the surrounding of the airfoil, whilst the free vortex model accounts for the far field of the airfoil. The flow around the airfoil is assumed to be two-dimensional (2D) incompressible fully turbulent flow, which is modeled by two equation turbulence models. The computed aerodynamic coefficients are presented for two wind turbine airfoils and compared with wind tunnel data.

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Section: Numerical Methodologymentioning

confidence: 99%

Applications of a Coupled Methodology to the Wind Turbine Airfoils

Chen

Guo

2012

AMR

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“…The derivation leading to Equation (10), valid for 2D irrotational flows, is here assumed to apply in the case of the AS. Schmitz and Chattot [13] have studied this hypothesis using a coupled Navier-Stokes/vortex-panel solver for the study of wind turbine aerodynamics and have found that deviations from Equation (10) are to the order of a few percents, especially when the blade is experiencing stall. In practice, the evaluation of V av can be made on the wing or at some location upstream; Vortex methods [3] that are based on lifting lines usually estimate the wing bound circulation from Equation (10).…”

Section: Blade-element Analysismentioning

confidence: 99%

“…For example, for the element shown in Figure 5(a), the contribution of mass fluxes to the global balance of the CV centered around node 1 isṁ 1 −ṁ 3 , whereṁ 1 andṁ 3 are the mass fluxes across CS1 and CS3, respectively. Since the addition of all mass fluxes must be null for each CV in the solution domain, the algebraic decomposition of CS mass fluxes for every element, and then, their further assembly for each CV, yields a discretized set of equations relating pressures between nodes and their neighbors of the type described in Equation (13). In the algebraic decomposition process, pseudo-velocities and pressure coefficients, which are stored at the domain nodes, are linearly interpolated at the center of all CSs of a triangular element and are assumed to prevail over the CS, while discretization of pressure gradients is made assuming that pressure varies linearly over the triangular element.…”

Section: Presentation Of the Modelmentioning

confidence: 99%

Modeling of lifting‐device aerodynamics using the actuator surface concept

Watters

Masson

2009

Numerical Methods in Fluids

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The actuator surface (AS) concept and its implementation within a differential, Navier-Stokes control volume finite-element method (CVFEM) are presented in this article. Inspired by vortex and actuator disk methods, the AS concept consists of using porous surfaces carrying velocity and pressure discontinuities to model the action of lifting surfaces on the flow. The underlying principles and mathematics associated with AS are first reviewed, as well as their implementation in a CVFEM. Results are presented for idealized 2D cases with analytical solutions, as well as for the 3D cases of a finite wing and an experimental wind turbine. In the case of the finite wing, wake induction is well handled by the model with accurate predictions of induced angles and drag when compared with the Prandtl lifting line model. Comparisons with volume force approaches, often used to model the action of propellers or wind turbine blades in a simplified analysis, show that the AS concept has some interesting advantages in terms of accuracy and respect of flow physics. This new approach is easy and rapid to embed in most computational fluid dynamics (CFD) methods. It is applicable to a wide range of problems involving thin lifting devices like finite wings, propellers, helicopter or wind turbine blades. THE ACTUATOR SURFACE CONCEPT 1265 and force distributions acting within them is important issues that can strongly influence the flow solution. With regards to fans or propellers, the actuator disk concept introduced by Froude should also be included in this group of simplified models; however, the action of the modeled device is spread over a surface rather than a volume. Volume forces become surface forces and discontinuities occur at the actuator disk surface in flow properties like pressure and velocity (see for example [9]). Inspired by the actuator disk concept, this article proposes the use of a new type of singular surface, called an actuator surface (AS), to represent the action of any lifting surface within a differential Navier-Stokes, control volume (CV) finite-element-based method. An AS is simply a geometric surface carrying velocity and pressure discontinuities, as well as surface forces, which are all determined from the circulation along the lifting sections of the AS. Equivalently, an AS is a porous vortex sheet that represents the bound vorticity system of a lifting device. The flow induced by the AS is solved using a CFD method that has been adapted to account for the kinematic and dynamic influence of the AS. As for volume force approaches, the trailing system of vorticity is naturally modeled by the CFD method. To situate the AS approach, Figure 1 presents a possible classification of models for lifting-device aerodynamics by sketching different approaches to model e.g. a lifting wing. On the left part of the figure, vortex models regroup lifting-line, vortex-lattice and panel models. These models are based on distributions of vorticity singularities whose magnitudes are set either based on kinematic conditions (s...

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Application of the actuator surface concept to wind turbine rotor aerodynamics

2010

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The structure of blade tip vortices is recognized as a key issue in wind turbine aerodynamic modelling by many researchers in the field. In the search for an intermediate model between full Navier–Stokes and blade‐element momentum simulations, this article presents a method using rotating actuator surfaces to model wind turbine aerodynamics. An actuator surface is a simple planar surface, porous to the flow, which is characterized by velocity and pressure discontinuities, whose action on the flow is achieved through an attached system of forces. These discontinuities and forces are determined from blade‐element analysis and the Kutta–Joukowski relation. After implementing this concept in a three‐dimensional CFD (Computational Fluid Dynamics) method, results are produced for the experimental rotors of NREL and TUDelft. The method is validated against both experimental measurements and the predictions of three other numerical models for wind turbine aerodynamic analysis. Qualitative and quantitative comparisons show that the actuator surface concept agrees well with the other numerical models. In addition to rotor aerodynamic analysis, the actuator surface concept can be used in the study of wake aerodynamics, or as the Eulerian flow solver in hybrid methods. Copyright © 2009 John Wiley & Sons, Ltd.

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Flow physics and Stokes’ theorem in wind turbine aerodynamics

Cited by 12 publications

References 6 publications

Applications of a Coupled Methodology to the Wind Turbine Airfoils

Applications of a Coupled Methodology to the Wind Turbine Airfoils

Modeling of lifting‐device aerodynamics using the actuator surface concept

Application of the actuator surface concept to wind turbine rotor aerodynamics

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