Tip Vortex Formation and Evolution to the Near Wake of a Rotor in ...

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$(Performance \226 Class 1 Airplane Motions)$

espectively. Thompson also observed secondaryfeatures in the circumferential velocity profiles for earlywake ages. These were not understood at the time; atpresent we postulate that these are a manifestation of therollup of discrete vortical filaments during the formationof the tip vortex. However, Thompson’s flowvisualization and measurements showed that the tipvortex of a rotor does persist with much of its initialstrength for large vortex ages.Brand et al [5,6] and Liou et al [7-9] examined vortextrajectories and dynamics of the two-bladed rotor usedin the present paper, in forward flight in the same windtunnel. They showed, again, that vortex trajectoriesrepeated with precise periodicity, provided wakeimpingement on the tunnel floor, and wakerecirculation, were prevented by going to sufficientlyhigh advance ratio (>0.06 in this experimentalconfiguration). Again, the vortex was seen to maintainmuch of its initial strength for vortex ages over 400degrees, which was the limit of their interest becausethey were studying rotor vortex/airframe interaction.Komerath et al [10] extended the single-bladed rotorwith a double-swept blade tip in the 9-foot hover facilityat Georgia Tech to study effects at high pitch angles.During their experiments, they observed that at certainconditions, the tip vortices impinged on the edge of thewake inductor and recirculated in the facility: this wasassociated with the development of severe aperiodicjitter of the vortex trajectories.Funk et al [11] conducted extensive measurements ofthe flowfield between the 2-bladed rotor and a wing inthe John Harper wind tunnel. Although vortextrajectories were substantially altered by winginteraction, the results on periodic repeatability ofvortex locations, and persistence of vortices to largeages, both remained unchanged.Carradonna et al [12,13] visualized the wake of a 2-bladed rotor in axial climb in the 30’x30’ SettlingChamber of the 7’x 10’ wind tunnel at Ames ResearchCenter. Again they found that when wake recirculationwas prevented, the vortex trajectories repeated quiteperfectly from cycle to cycle of blade motion, even asthe climb velocity was brought towards zero. Vortexcores were discernible by the seed particle patterns forseveral turns of the vortex, until merger betweenvortices smeared the patterns. From the above, it is quiteclear that the tip vortex of a rotor persists over longvortex ages. Also, aperiodic “jitter” of vortices is not abasic fluid mechanical feature of rotor wakes, providedrecirculation is avoided.McAlister [14-15] studied the velocity field in the nearwake of a two-bladed rotor in hover using a 3-component laser velocimeter. The test conditions were aC t of 0.005 at 1100 and 550 RPM. He found that threechords downstream of the blade the vortex meander wasless than one core diameter. The meander increased byan order of magnitude by the time vortex reached 180°of vortex age. He also noted that changing the rotationalspeed did not have an effect on the core diameter, thegeneral appearance of the trailing vortex, or themagnitude of the velocity components relative to thetip-speed.In the late 1990s, measurements were reported byLeishman et al [16] using a single-bladed rotor in ahover facility, using a 3-component laser velocimeter.These measurements indicated rapid “diffusion” of thetip vortices within the first 90 degrees of vortex age.Substantial aperiodicity was observed. Thesephenomena were attributed to turbulence in the core,and the rapid smearing of the vortex velocity profiledata was described as turbulent diffusion [16]. Howeverthe data acquisition procedures used had taken noaccount of aperiodicity, raising the possibility thatvortex profile data, averaged over several cycles, hadbecome severely smeared by cycle-to-cycle uncertaintyin vortex position. Conlisk et al [17] showed byanalytical arguments based on orders of magnitude thatturbulent diffusion was not a plausible explanation forvortex decay of the rate reported in Ref. [16].Mahalingam et al [18-20] conducted measurements onthe advancing blade side (ABS) of the two-bladed rotorused in this paper, in low-speed forward flight. Heshowed by flow visualization and LDV measurementsthat the rotor flow field was periodic to better than 1° ofrotor azimuth at an advance ratios 0.1. Havingestablished periodicity to ensure the quality of the data,he studied the near-blade flowfield as well as the nearwake. In these measurements, he observed strongspanwise velocities directed towards the blade-tip onboth the suction and pressure sides of the blade. Thevelocities approached 40% of the tip-speed on thepressure side. Spanwise flow on the suction side wasmuch lower. Mahalingam also observed secondaryeffects in the circumferential velocity profiles duringformation. He showed that the turbulence level insidethe core was lower than that in the freestream, as mightbe expected in a region of favorable pressure gradient.Both the vortex strength and the axial velocity in thecore were shown to persist out to more than 500 degreesof vortex age.II.2 Previous Work on Seed Particle InertiaAs previously mentioned, velocity measurementtechniques that rely on seed particles carried by a fluidCopyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001
are subject to errors due to finite particle inertia. In thecase of laser velocimetry, the experimenter faces adilemma: light scattering from particles smaller than 1micron is generally difficult to capture accurately in thebackscatter mode (light captured at the same lens whichis used to transmit the laser beams) over the largedistances used for laser velocimetry in rotor facilities.Particles larger than one micron are believed toexperience substantial centrifugal drift with respect tothe flow in the core of a tip vortex. Thompson et al[3,4]dealt with this problem by developing an Off-AxisScatter Receiver [4]. This device could be alignedremotely to stay focused on the measurement volume asit was traversed across a large facility, and capturescattering from sub-micron particles. This is howeverless convenient than using a backscatter LV system, andis difficult when the rotor is near other objects whichblock the line of sight.It is therefore necessary to use larger particles, andquantify the error due to particle spinout. Dring et al[21] has examined the trajectories of particles in turbinecascades. He concluded that the Stokes number (St) hadthe greatest influence on particle behavior. Furthermore,he determined that particles with St ≤ 0.1 would veryclosely follow the streamlines and particles with St > 10would be centrifuged across streamlines. In anotherstudy, Dring [22] integrated the equations of motion forparticles in several flows to provide guidance on LVseed particle size selection. The flows included a turbinecascade, a step deceleration and exponential andsinusoidal accelerations. He determined that the Stokesnumber required to achieve 1% accuracy depended onthe type of flow. In a turbine cascade, he found that aStokes number of less than 0.01 was required, but in asinusoidal flow 0.14 was tolerable.Dring, et al [23] and Kriebel [24] examined the behaviorof particles in centrifugal particle separators. In theseflows, the gas experiences solid body rotation. This isanalogous to vortex core velocity profiles, except thatthe strong axial velocity is absent. Dring’s analysisassumed that the particle and gas velocity were equal.He also used several drag models instead of assumingthat Stokes relation holds. Dring [23] asserts: “axialvelocities do not alter the solution so long as theparticle and fluid axial velocities are equal andconstant.” Kriebel’s study did not place anyassumptions on the particle and fluid velocity. However,he used Stokes relation to estimate drag acting on theparticle. Comparison with experimental data is alsoprovided. Neither of these analyses is valid in thepotential velocity region outside the vortex core.Leishman [25] calculated the behavior of seed particlesin a “desingularized” vortex. His study used particlesranging from 0.5 to 2.0 µm and a vortex circulation of5.6 m 2 s -1 . Inside the vortex core, he predicted velocityerrors as high as 10% and 25% for the tangential andradial velocities, respectively, for the 2 µm particle. Thesmaller particles resulted in lower errors. His study alsoexamined particle count distribution. The highestparticle distributions occurred at r/R c of 1.7 for the0.5µm particles, 2.6 for the 1.0µm particles and 3.8 forthe 2.0µm particles. Although intended for rotor tipvortex applications, this work did not consider theeffects of the strong axial velocity in the core. It shouldbe noted here that the vortex strengths used byLeishman [25] are almost 5 times those encountered inthe present rotor flowfield.The previous work on seed particle inertia has beenfocused on 2-dimensional models of vortices. In therotor tip vortex core, as shown by Refs. [3-14], there is avery substantial axial velocity. The resulting sink-likeeffects on the flowfield should cause an inward-directedradial fluid velocity, which should considerably inhibitthe drift of particles out of the middle of the core, wherethe centrifugal acceleration is much lower than at thecore edge. Considering experimental results obtained atthe present authors’ laboratory with cleanly-periodic,well-resolve vortices, it is evident that the estimates ofseed-particle inertia error cited, for example, in [25]convey an overconservative picture. This issue needs tobe considered, and upper bounds are sought for thesetypes of errors.III. Issues and objectives of present workIn the present work, the flowfield near the blade tip ismeasured, to examine the development of the tip vortex.These measurements are then related to measurementsof the vortex in the wake. Mineral oil seeding is used.The dynamics of the seed particles are examined in thecontext of velocity field error, and the observedevacuation of particles from the vortex core as vortexage increases. Issues are:1.What are observed differences of rotor tip vortexcores from fixed-wing vortex cores?2. What is the nature of the nascent core?3. How does the vortex circulation change as the vortexdevelops over the blade tip?4. Are the predictions of error due to particle spin-outvalid for rotor tip vortices?5. Why does the vortex core become clear of seedparticles further downstream?6. What are the implications for the evolution of thevortex further downstream in the wake?The objective of the paper is to resolve thecontradictions seen in the literature regarding the aboveissues. It is noted that the results given here are limitedto the incompressible flow regime. The blade used has aCopyright © American Helicopter Society. Presented at the 57 th AHS Forum, June 2001
Page 1: Tip Vortex Formation and Evolution
Page 5 and 6: V. Formulation of the Seed Particle
Page 7 and 8: VI.4 Wake Evolution to 540 degreesD
Page 11 and 12: VI. 8 Accuracy of the SimulationThe

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