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Research Papers: Multiphase Flows

Measurements of Loading and Tip Vortex Due to High-Reynolds Number Flow Over a Rigid Lifting Surface

[+] Author and Article Information
Michael H. Krane, Richard S. Meyer, Matthew J. Weldon, Brian Elbing, David W. DeVilbiss

Applied Research Laboratory,
Penn State University,
State College, PA 16804

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 25, 2013; final manuscript received February 1, 2015; published online March 19, 2015. Assoc. Editor: Peter Vorobieff.

J. Fluids Eng 137(7), 071301 (Jul 01, 2015) (9 pages) Paper No: FE-13-1340; doi: 10.1115/1.4029723 History: Received May 25, 2013; Revised February 01, 2015; Online March 19, 2015

An experimental study of high-Reynolds number flow over a rigid hydrofoil (David Taylor model basin (DTMB) modified NACA66-009, rectangular planform, aspect ratio (AR = 4, square tip) is presented. The measurements were performed in the Garfield Thomas Water Tunnel at Applied Research Laboratory (ARL) Penn State. Load measurements were performed at ReC = 1.5 × 106 and 2.4 × 106, for angles of attack between −8 deg and +8 deg. Measurements of three components of velocity were performed using stereo particle image velocimetry (SPIV) on a cross-flow plane to resolve the tip vortex flow 0.42 chord lengths downstream of the trailing edge, for four angles of attack ranging from 0.5 deg to 3.5 deg. Nondimensional tip vortex circulation varied weakly with angle of attack. Vortex location in the plane of measurement, relative to the trailing edge, was unchanged for the ranges studied, though the vortex core grew in size with angle of attack. These results are consistent with the finding that the net lift force acts between 45% and 46% span, measured from the root, in that any angle of attack variations in tip vortex strength or radius result in minimal changes in spanwise loading distribution.

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Figures

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Fig. 1

Installation of the hydrofoil (fin) in the Garfield Thomas Water Tunnel test section (1219 mm diameter). (a) Cutaway shows flat wall liner and windows offering optical access. Coordinate axes are also shown. (b) Detail of hydrofoil installation, showing load cell and location of SPIV measurement plane.

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Fig. 2

SPIV setup used to characterize the tip vortex flow

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Fig. 3

Angle-of-attack variation of the load coefficients for rigid fin, ◇—lift coefficient, CL; ◻—drag coefficient, CD; Δ—pitch moment about 1/4-chord, CMZ; o—roll moment, CMX; empty symbols: ReC = 1.5 × 106, and solid symbols: ReC = 2.4 × 106

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Fig. 4

Variation of spanwise lift point of application ZL/b with angle of attack, empty symbols—ReC = 1.5 × 106, filled symbols—2.4 × 106. Dashed lines indicate vertical and horizontal asymptotes: vertical asymptote is at α = −2.67 deg, the zero-lift angle of attack, at which ZL/b is singular. Horizontal asymptotes are located at approximately ZL/b = 0.45 and 0.47, for ReC = 2.4 × 106 and 1.5 × 106, respectively.

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Fig. 5

Tip vortex flow on cross-flow plane, 0.42 c downstream of hydrofoil trailing edge, viewed from upstream. (a) α = 0.5 deg, (b) α = 2.5 deg, (c) α = 3.0 deg, and (d) α = 3.5 deg. Left column: velocity vectors superimposed on shading indicating axial velocity component. Right column: velocity vectors superimposed on shading indicating axial vorticity. Dark line denotes location of hydrofoil trailing edge, located below Y/c = 0 for α > 0 deg. Tip/trailing edge corner is located at Y/c = 0, Z/c = 2 for α = 0 deg.

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Fig. 6

Scatter plots showing profiles of velocity and vorticity in the tip vortex flow at 0.42 c downstream of the trailing edge (for the lifting surface at zero angle of attack). Each grouping of three plots corresponds to a particular angle of attack, and shows (1) transverse velocity profiles Uy/U versus (ZZv)/c (*) and −Uz/U versus (Y − Yv)/c (o); (2) axial of velocity velocity Ux/U versus (Z − Zv)/c (Δ); and (3) axial vorticity ωx rc2/Γ versus both (Z − Zv)/c (o) and (Y − Yv)/c (*). (a) α = 0.5 deg, (b) α = 2.5 deg, (c) α = 3.0 deg, and (d) α = 3.5 deg.

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Fig. 7

Estimation of tip vortex circulation, α = 3.5 deg. Plot shows estimated circulation versus length of side of square integration path around the tip vortex center. When tip vortex is contained, estimated circulation increases with contour size, because of axial vorticity in wing wake, though at a slower rate than when the contour does not fully contain the vortex. The location of slope change is taken to indicate the tip vortex circulation, as well as vortex core size.

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Fig. 8

Tip vortex behavior, deduced from SPIV measurements shown in Fig. 5. (a) vortex circulation normalized by average wing circulation and (b) vortex core size, normalized by chord length. Small variations in tip vortex strength (relative to wing circulation) and location suggest that the effect of tip flow on lift distribution depends weakly on angle of attack.

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