Research Papers: Flows in Complex Systems

Vortex Ring Model of Tip Vortex Aperiodicity in a Hovering Helicopter Rotor

[+] Author and Article Information
Anand Karpatne

Department of Aerospace
and Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: anand.karpatne@utexas.edu

Jayant Sirohi

Assistant Professor
Department of Aerospace
and Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: jayant.sirohi@utexas.edu

Swathi Mula

Department of Aerospace
and Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: swathimula.ae@utexas.edu

Charles Tinney

Assistant Professor
Department of Aerospace
and Engineering Mechanics,
University of Texas,
Austin, TX 78712
e-mail: cetinney@utexas.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 20, 2013; final manuscript received February 5, 2014; published online May 6, 2014. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(7), 071104 (May 06, 2014) (9 pages) Paper No: FE-13-1384; doi: 10.1115/1.4026859 History: Received June 20, 2013; Revised February 05, 2014

The wandering motion of tip vortices trailed from a hovering helicopter rotor is described. This aperiodicity is known to cause errors in the determination of vortex properties that are crucial inputs for refined aerodynamic analyses of helicopter rotors. Measurements of blade tip vortices up to 260 deg vortex age using stereo particle-image velocimetry (PIV) indicate that this aperiodicity is anisotropic. We describe an analytical model that captures this anisotropic behavior. The analysis approximates the helical wake as a series of vortex rings that are allowed to interact with each other. The vorticity in the rings is a function of the blade loading. Vortex core growth is modeled by accounting for vortex filament strain and by using an empirical model for viscous diffusion. The sensitivity of the analysis to the choice of initial vortex core radius, viscosity parameter, time step, and number of rings shed is explored. Analytical predictions of the orientation of anisotropy correlated with experimental measurements within 10%. The analysis can be used as a computationally inexpensive method to generate probability distribution functions for vortex core positions that can then be used to correct for aperiodicity in measurements.

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Fig. 1

Oblique view of vortex rings convecting downstream

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Fig. 2

Top view of vortex ring geometry showing two vortex rings. Element ds on ring 1 induces a velocity on ring 2.

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Fig. 3

Analytical predictions of tip vortex core positions normalized by rotor diameter D at a blade loading Ct/σ = 0.042. Model parameters: number of vortex rings emitted = 120, rotational speed = 1520 rpm, δ = 4, initial core radius = 0.0081 m (0.14c).

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Fig. 4

Rotor test stand with 1 m diameter, four-bladed, articulated rotor [8]

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Fig. 5

Schematic illustrating the 95% confidence intervals for tip vortex core positions at various vortex ages ζ (ranging from 100 deg to 170 deg). Each dot indicates instantaneous tip vortex core position at a particular vortex age.

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Fig. 6

Baseline case: mean slipstream boundary (axial (z/R) and radial (r/R)) as a function of vortex age, averaged over 1000 emitted rings

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Fig. 7

Baseline case: thrust produced by the rotor as a function of vortex age, as predicted by the VREM. Thrust was computed until 1000 rings were emitted from the rotor blade. The thrust estimated from BEMT is shown as a dotted line.

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Fig. 8

Baseline case: spanwise loading predicted by the VREM and BEMT after 1000 vortex rings are emitted

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Fig. 9

Effect of initial tip vortex core radius on mean slipstream boundary. The baseline value of r* = 0.14c is based on experimental measurements.

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Fig. 10

Difference in the predicted thrust from baseline for various values of initial tip vortex core radius. The baseline thrust is calculated for rcore = 0.14c.

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Fig. 11

Variation of the mean slipstream boundary for various values of time step

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Fig. 12

Difference in the predicted thrust coefficient from baseline (Δt = 0.0099 s) for various values of time step

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Fig. 13

Effect of the number of emitted rings on the slipstream boundary

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Fig. 14

Correlation between orientation of vortex aperiodicity predicted by VREM and measured by experiment, at 0 deg, 180 deg, and 270 deg vortex ages)

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Fig. 15

Comparison between measured and predicted vortex core positions (250 samples) for vortex age of 90 deg. The dots represent instantaneous tip vortex positions at this vortex age. The arrow indicates the preferred direction of aperiodicity (major axis of the ellipse).

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Fig. 16

Vortex aperiodicity predicted by the VREM at a vortex age of 90 deg for different values of blade loadings (Ct/σ = 0.0187, 0.042, 0.0561, and 0.0704). Each dot represents an instantaneous tip vortex position.

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Fig. 17

Variation in rotor thrust as a function of vortex age for different values of blade loading



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