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Research Papers: Flows in Complex Systems

# 2D Numerical Simulations of Blade-Vortex Interaction in a Darrieus Turbine

[+] Author and Article Information
E. Amet

Laboratoire des Ecoulements Géophysiques Industriels (LEGI), Grenoble 38041, France

T. Maître

Institut National Polytechnique de Grenoble (INPG), Grenoble 38031,France

C. Pellone, J.-L. Achard

Centre National de la Recherche Scientifique (CNRS), Grenoble 38042, France

J. Fluids Eng 131(11), 111103 (Oct 21, 2009) (15 pages) doi:10.1115/1.4000258 History: Received July 02, 2008; Revised August 31, 2009; Published October 21, 2009

## Abstract

The aim of this work is to provide a detailed two-dimensional numerical analysis of the physical phenomena occurring during dynamic stall of a Darrieus wind turbine. The flow is particularly complex because as the turbine rotates, the incidence angle and the blade Reynolds number vary, causing unsteady effects in the flow field. At low tip speed ratio, a deep dynamic stall occurs on blades, leading to large hysteresis lift and drag loops (primary effects). On the other hand, high tip speed ratio corresponds to attached boundary layers on blades (secondary effects). The optimal efficiency occurs in the middle range of the tip speed ratio where primary and secondary effects cohabit. To prove the capacity of the modeling to handle the physics in the whole range of operating condition, it is chosen to consider two tip speed ratios ($λ=2$ and $λ=7$), the first in the primary effect region and the second in the secondary effect region. The numerical analysis is performed with an explicit, compressible RANS $k-ω$ code TURBFLOW , in a multiblock structured mesh configuration. The time step and grid refinement sensitivities are examined. Results are compared qualitatively with the visualization of the vortex shedding of Brochier (1986, “Water channel experiments of dynamic stall on Darrieus wind turbine blades,” J. Propul. Power, 2(5), pp. 445–449). Hysteresis lift and drag curves are compared with the data of Laneville and Vitecoq (1986, “Dynamic stall: the case of the vertical axis wind turbine,” Prog. Aerosp. Sci., 32, pp. 523–573).

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## Figures

Figure 1

Typical Darrieus rotor performance CP as a function of the tip speed ratio (7)

Figure 2

Forces and velocities in a Darrieus turbine (20)

Figure 3

Tip speed ratio effect on α(θ) curves; curvature parameter effect on F∗(α)

Figure 4

Velocities and forces acting on a blade and their conventional positive directions

Figure 5

Overview of the grid mesh N1

Figure 6

Computed vortices trajectories for λ=2, using Q criterion, nondimensionalized by (C/(ΩR))2

Figure 7

Vorticity vector isocontours and relative streamlines

Figure 8

Lift coefficient for one revolution, λ=2

Figure 9

Drag coefficient for one revolution, λ=2

Figure 10

Vorticity vector for λ=7 (black color-counterclock rotating)

Figure 11

Computed lift coefficient for one revolution, λ=7

Figure 12

Computed drag coefficient for one revolution, λ=7

Figure 13

Isovalues of axial velocity ratio UX/U∞ for θ=0 deg, λ=2

Figure 14

Isovalues of axial velocity ratio UX/U∞ for θ=0 deg, λ=7

Figure 15

Rotor drag coefficient

Figure 16

Influence of inner-iterations on the lift coefficient at the beginning of the dynamic stall

Figure 17

Residuals of ρE for three time steps and various inner-iterations

Figure 18

Lift coefficients for the three meshes

Figure 19

Drag coefficients for the three meshes

Figure 20

Vorticity isocontours and relative streamlines for the three meshes and three azimuthal angles; numbers 1 to 3 refer to positions indicated on Figs.  1819

Figure 21

Computed lift coefficient, λ=2

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