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Research Papers

The Inverse Vortex Wake Model: A Measurement Analysis Tool

[+] Author and Article Information
Wouter Haans

Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlandsw.haans@lr.tudelft.nl

Gijs van Kuik, Gerard van Bussel

Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, The Netherlands

J. Sol. Energy Eng 130(3), 031009 (Jul 01, 2008) (14 pages) doi:10.1115/1.2931508 History: Received February 22, 2007; Revised October 30, 2007; Published July 01, 2008

To reduce the level of uncertainty associated with current rotor aerodynamics codes, improved understanding of rotor aerodynamics is required. Wind tunnel measurements on model rotors contribute to advancing our knowledge on rotor aerodynamics. The combined recording of blade loads and rotor wake is desired, because of the coupled blade and wake aerodynamics. In general, however, the small size of model rotors prohibits detailed blade load measurements; only the rotor wake is recorded. To estimate the experimental blade flow conditions, a measurement analysis tool is developed: the inverse vortex wake model. The rotor wake is approximated by a lifting line model, using rotor wake measurements to reconstruct the vortex wake. Conservation of circulation, combined with the Biot–Savart law, allows the induced velocity to be expressed in terms of the bound circulation. The unknown bound circulation can be solved for, since the velocity is known from rotor wake measurements. The inverse vortex wake model is subsequently applied to measurements on the near wake of a model rotor subject to both axial and yawed flow conditions, performed at a TUDelft open jet wind tunnel. The inverse vortex wake model estimates the unsteady experimental blade flow conditions and loads that otherwise would have remained obscured.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the model rotor in the wind tunnel. Both the global Cartesian coordinate system (xm,ym,zm) and the global cylindrical coordinate system (r,θ,z) are attached to the nonrotating model support. θb is the blade azimuth angle, Ψ is the yaw angle, with ym the yaw axis.

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Figure 2

Average location of the tip vortex centers in the horizontal (xm,zm)-plane from quantitative smoke visualization with the blade positioned at θb=90deg, hence intersecting the horizontal plane, for all three conditions. Tip vortex locations are expressed in the Cartesian (xm,zm)-coordinates of the rotor in axial flow.

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Figure 3

Hot-film measurement results at a plane z∕Rt=5.83×10−2 downstream for the Ψ=30deg flow condition with blade orientation θb=50deg. Viewpoint is upstream of the rotor, looking downstream, the blades rotate clockwise. Left plot: ⟨V⟩, with the contour indicating Vz∕(W0*cosΨ) and the vectors being the in-plane velocity (Vr,Vθ). Right plot: 1−sVeff.

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Figure 4

Schematic of the discretized blade circulation

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Figure 5

Schematic of the discretized wake circulation for the blade at θbk

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Figure 6

The vortex wake from a single rotor blade, for the axial flow condition with the blade at θb=90deg. Left plot: overview; right plot: detail of the very near wake and the near wake. Root vortex, tip vortex, and vortex sheet can be seen in the very near wake, with solid lines. The near wake, with dashed lines, and the far wake, with solid lines, only have a root and tip vortex. Rotor plane is located at z∕Rt=0, far wake extends up to z∕Rt=10.

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Figure 7

Tip vortices in the (xm,zm)-plane for the Ψ=30deg condition. Closed symbols, solid tip vortex line: measurements. Open symbols, dotted tip vortex lines: far-wake estimates. Far-wake assumption: the tip vortex convection velocity is uniform and constant throughout the far wake. Consequently, vortex line length dnw=dfw, wake skew angle χnw=χfw, wake twist angle βnw=βfw and zm-pitch pz,nw=pz,fw.

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Figure 8

Influence of the downstream extent of the far wake, expressed in zm∕Rt, on Γb∕(W0*Rt). Γb is assumed constant across the blade. First data point, at zm∕Rt=1.24, corresponds to a vortex wake without a far wake.

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Figure 9

The effect of rs∕Rt on the resulting Γb-distribution (left plot) and on RR (right plot)

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Figure 10

The effect of aroot on the resulting Γb-distribution (left plot) and on RR (right plot).

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Figure 11

⟨V⟩-distribution at a point fixed at (r∕Rt,θ,z∕Rt)=(0.4,90deg,1.50×10−1). Plotted are Vz∕W0*, Vθ∕W0*, and Vr∕W0* in the left, middle, and right plots, respectively.

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Figure 12

Schematic velocity and lift force decompositions on a blade section

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Figure 13

α versus r∕Rt derived with the inverse vortex wake model (open symbols), with and without the contribution of a′, compared with measurement estimates (filled symbols)

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Figure 14

Spanwise cl-distribution (left plot) and Fz- and Fθ-distribution (right plot, open and filled symbols, respectively). Both inverse vortex wake method results and results obtained by applying an airfoil model to the lifting line inflow conditions computed with the inverse vortex wake method are shown.

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Figure 15

Γb∕(W0*Rt)-distribution along the lifting line during a blade cycle for all three cases, plotted as a Γb∕(W0*Rt)-contour across the rotor plane. Viewpoint is upstream of the rotor; looking downstream, the blades rotate clockwise. The undisturbed velocity component parallel to the rotor plane, W0*sinΨ, is from left to right.

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Figure 16

1−Vz∕(W0*cosΨ)-distribution along the lifting line during a blade cycle for all three cases

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Figure 17

α-distribution along the lifting line during a blade cycle for all three cases

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Figure 18

cl-distribution along the lifting line during a blade cycle for all three cases

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Figure 19

Fz∕(ρW0*2Rt)-distribution along the lifting line during a blade cycle for all three cases

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