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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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References

Landgrebe, A. J., 1972, “The Wake Geometry of a Hovering Helicopter Rotor and Its Influence on Rotor Performance,” J. Am. Helicopter Soc., 17(4), pp. 3–15. [CrossRef]
Devenport, W. J., Rife, M. C., Liapis, S. I., and Follin, G. J., 1996, “The Structure and Development of a Wing-Tip Vortex,” J. Fluid Mech., 312, pp. 67–106. [CrossRef]
Leishman, J. G., 1998, “Measurements of the Aperiodic Wake of a Hovering Rotor,” Experiments Fluids, 25(4), pp. 352–361. [CrossRef]
Bhagwat, M. J. and Ramasamy, M., 2012, “Effect of tip vortex aperiodicity on measurement uncertainty,” Experiments Fluids, 53, pp. 1191–1202. [CrossRef]
Richard, H., Bosbach, J., Henning, A., Raffel, M., and van der Wall, B., 2006, “2c and 3c PIV Measurements on a Rotor in Hover Condition,” 13th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, June 26–29.
van der Wall, B. G., and Richard, H., 2006, “Analysis Methodology for 3c-PIV Data of Rotary Wing Vortices,” Experiments Fluids, 40(5), pp. 798–812. [CrossRef]
Kindler, K., Mulleners, K., Richard, H., van der Wall, B. G., and Raffel, M., 2011, “Aperiodicity in the Near Field of Full-Scale Rotor Blade Tip Vortices,” Experiments Fluids, 50(6), pp. 1601–1610. [CrossRef]
Mula, S., Stephenson, J., Tinney, C., and Sirohi, J., 2011, “Vortex Jitter in Hover,” AHS Southwest Region Technical Specialists's Meeting, Fort Worth, TX, February 23–25.
Bagai, A., and Leishman, J. G., 1995, “Rotor Free-Wake Modeling Using a Pseudo-Implicit Technique-Including Comparisons With Experimental Data,” J. Am. Helicopter Soc., 40(3), pp. 29–41. [CrossRef]
Bhagwat, M. J., and Leishman, J. G., 2001, “Stability, Consistency and Convergence of Time-Marching Free-Vortex Rotor Wake Algorithms,” J. Am. Helicopter Soc., 46(1), pp. 59–71. [CrossRef]
Bhagwat, M. J., and Leishman, J. G., 2003, “Rotor Aerodynamics During Maneuvering Flight Using a Time-Accurate Free-Vortex Wake,” J. Am. Helicopter Soc., 48(3), pp. 143–158. [CrossRef]
Ramasamy, M., and Leishman, J. G., 2003, “The Interdependence of Straining and Viscous Diffusion Effects on Vorticity in Rotor Flow Fields,” American Helicopter Society 59th Annual National Forum, Phoenix, AZ, May 6–8.
Bhagwat, M. J., and Leishman, J. G., 2002, “Generalized Viscous Vortex Core Models for Application to Free-Vortex Wake and Aeroacoustic Calculations,” Proceedings of the 58th Annual Forum of the American Helicopter Society International, Montréal, Canada.
Young, L. A., 2003, “Vortex Core Size in the Rotor Near-Wake,” NASA Technical Report TM-2003-212275.
Brand, A., Dreier, M., Kisor, R., and Wood, T., 2011, “The Nature of the Vortex Ring State,” J. Am. Helicopter Soc., 56(2), p. 22001. [CrossRef]
McCroskey, W. J., 1995, “Vortex Wakes of Rotorcraft,” 33th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 9–12, Paper No. AIAA 95-0530.
Mula, S., Stephenson, J., Tinney, C., and Sirohi, J., 2012, “Dynamical and Evolutionary Characteristics of the Tip Vortex From a Four Bladed Rotor in Hover,” American Helicopter Society 68th Annual Forum, Fort Worth, TX, May 1–3.
Squire, H. B., 1965, “The Growth of a Vortex in Turbulent Flow,” Aeronaut. Qtr., 16, pp. 302–306.
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Figures

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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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