In recent experiments on a two-bladed rotor in low axial
climb it was observed that vortices shed from each of the
blades interacted significantly at approximately one rotor
radius below the rotor disk plane. This phenomenon was
verified by numerical solutions of the rotor wake for the
same experimental conditions. In this paper we consider the
case of three and four blades in hover. A lifting line is
used to model each blade and a fully unsteady computation of
the motion of each tip-vortex is carried out using a highly
accurate Adams-Moulton method to advance the vortices. The
vortex-vortex interaction is particularly complicated and
several vortices are observed to become locally intertwined.
It is suggested that this kind of behavior can be explained
on the basis of classical vortex dynamics. Conditions under
which the motion of the vortices is steady are also
examined.
[FG.02] Nonlinear Instability of A Counter-Rotating Vortex Pair
Z. C. Zheng (University of South Alabama)
Long-wavelength and short-wavelength instability in vortex
system is of interest to both basic turbulence theory and
practical applications. A counter-rotating vortex pair is a
prototype of complex coherent structures in turbulence and a
model for aircraft trailing vortices. In current study, a
three-dimensional vortex method with Rosenhead core
structure is used to investigate nonlinear instability of a
parallel, counter-rotating vortex pair. The method has been
tested to simulate Crow type instability and the results
showed good agreement with the linear instability analysis.
The nonlinear simulations are initialized with disturbances
in several modes, as well as disturbances induced by
secondary vortical structures such as vortex rings. Both
symmetric and anti-symmetric disturbances are studied.
Temporal evolution of the energy spectra is then obtained to
relate energy transfer between different disturbance modes,
which can be used to elucidate the nonlinear mechanisms of
instability.
[FG.03] Experiments on 2- and 3-D Vortex Interaction
Jamey Jacob (University of Kentucky)
The interaction of multiple vortices is investigated in 2-
and 3-D experimentally. Wing semi-spans are used to generate
multiple wing-tip trailing vortices in a tow tank for the
3-D investigation while pitching wings are used to generate
vortices in a vertical soap film tunnel for the 2-D
investigation. In both experiments, the motion of the
vortices is observed while PIV is used to extract the
velocity fields. In particular, the merger dynamics of a
pair of co-rotating vortices with Re_\Gamma on the order
of 10^3 - 10^5 is investigated. The differences between
the 2- and 3-D cases are analyzed with emphasis on the
details of the merger physics. Comparisons are made with
computational analyses and the application of 2-D
simulations to study 3-D vortex behavior is discussed.
[FG.04] Wing Shaping to Suppress Vortex Breakdowns
Sutthiphong Srigrarom, Mitsuru Kurosaka (University of Washington)
Recently, we proposed
what we call the self induction mechanism of vortex
breakdown by considering the transient stage leading to the
formation of the vortex breakdown. Self induction in the
shear layers spiralling around the vortex core causes the
pile up of vorticity, which in turn induces backflow and
radial enlargement of stream surfaces. The mechanism hinges
on the straight trajectory of the vortex core associated
with the straight leading edges of a delta wing. If this
hypothesis is indeed correct, one may be able to suppress
the vortex breakdown by forcing the path of the core to
deviate from a straight line. Here we present results for
two means of perturbing the vortex path. Spanwise
perturbation is imparted by shaping the wing planform by
changing from a straight to a wavy shape; perturbation
normal to the wing surface is imparted by wing surface
shaping or installing bulges. Both are found to suppress
vortex breakdown.
[FG.05] Stereo DPIV Study of Velocity and Vorticity Distribution of Nonslender Delta Wings
Michael OL, Morteza Gharib (GALCIT, Caltech)
A delta wing with 65 degree sweep was tested at Re of
O(10^4) (based on root chord) in a water tunnel. In
contrast to most recent studies, angles of attack were kept
sufficiently low that the leading edge vortex (LEV)
breakdown lies downstream of the trailing edge. LEV core
trajectory and breakdown location were verified by dye
injection. Upstream of the breakdown, 3-component velocity
data were taken in crossflow planar cuts. Velocity data were
taken with a version of Stereo Digital PIV, based on the
Scheimpflug condition. Measures were taken to avoid problems
encountered at the water-air interface at the test section
walls. Results are in approximate conformity with the
well-known conical flow structure of slender delta wings.
Measurements were also made in the near wake, where
vorticity due to the LEV (associated with the “vortical
lift”) could be compared to that of the wingtip vorticies
(“potential lift”). Future studies are aimed at comparison
of the vortical and potential lift contributions of wings
with less sweep, where slender wing assumptions are less
appropriate, and theoretical models break down.
[FG.06] Equilibrium State of Trailing Vortices: Statistical Mechanics Approach
O.A. Likhachev (University of Arizona)
The equilibrium statistical mechanics of a system composed of a large number
of 2D point vortices is employed to describe the vortex system shed from
aircraft wings. According to this theory, these higher energy states of the
vortex
system can only be achieved by segregating the point vortices of like kind
into
two clusters that descend with a constant velocity. The equilibrium
statistics of
this vortex system is worked out to give the distribution of vortices in the
clusters.
The solution is given in terms of the integral constraints for each cluster:
total
circulation, center of inertia and kinetic energy. The negative
non-dimensional
inverse temperature of the system and the length scale related to angular
momentum
of a single trailing vortex are obtained versus initial interaction energy
of the vortex
system. Comparison of the theoretical results with available experimental
data
shows good agreement between the calculated tangential velocity distribution
in
the trailing vortex and the data. The flow characteristics for three
different wing
loads are also compared to emphasize the effect of the initial circulation
distribution
along a lifting wing on the vorticity distribution in the equilibrium
trailing vortices.
[FG.07] Downstream Thermal Evolution of Vortex Cores
A. Gómez-Barea, M.A. Herrada, M. Pérez-Saborid, A. Barrero (Escuela Superior de Ingenieros, Universidad de Sevilla, Spain)
The downstream evolution of the total temperature field in
a quasi-incompressible axisymmetric vortex core has been
computed. Starting at an initial station (z=0) with
velocity profiles of the Burgers type and given temperature
distributions, the numerical results of the evolution show
that, according to experimental results, the total
temperature in the near-axis region decreases substantially
due to the work done by pressure and viscous forces together
with the effect of both convection and conduction of heat.
Depending on the values of the parameters characterizing the
initial profiles and on the value of the Prandtl number, the
vortex either breaks down or eventually reaches a
self-similar regime. The results obtained shed light on the
basic physics involved in the thermal separation phenomenon
which appears inside Ranque-Hilsch vortex tubes.
[FG.08] Merging of co-rotating trailing vortices
C. Cerretelli (Cornell University), T. Leweke (Universites Aix-Marseille, France), C.H.K. Williamson (Cornell University)
The merging of co-rotating vortices is an important physical phenomenon in aerodynamics as well as in fundamental turbulent flows. Merging plays a role in the aerodynamics of airplane wing wakes, where it can accelerate the development of the Crow instability (Crouch 1997). Although vortex merger has been extensively studied, most numerical investigations concern the case of the two dimensional inviscid interactions. On the other hand, the dynamics of three dimensional viscous vortices, which spin around each other in an helical path, is not yet fully understood, and this is the focus of the present experimental investigation. Previous work by Chen, Jacob and Savas (1999) shows that merging of co-rotating vortices, from a flapped wing, occurs at approximately 0.8 of an orbit period after formation, independently of the circulation Reynolds number Re_\Gamma. In the present work, merging is studied by using a biplane wing system, as well as the DPIV technique. In our investigation, we find that the time taken for merging, measured in orbit periods, is a function not only of the experimental geometry, but is also a function of the circulation Reynolds number.
[FG.09] Analysis of the radar cross-section (RCS) of aircraft vortices
Karim Shariff, Alan Wray (NASA Ames)
Radar has been proposed as one way to track wake vortices to reduce aircraft spacing. Radar echoes from aircraft wakes are usually interpreted qualitatively using Tatarski's theory of scattering by isotropic atmospheric turbulence. The present work predicts RCS by (1) Keeping the weak scattering approximation but dropping the assumptions of a far-field and a uniform incident wave, neither of which is generally valid for a coherent wake (2) Considering three simple mechanisms for the structure and magnitude of refractive index variations: (i) Radial density gradient in each vortex (ii) Adiabatic transport of atmospheric fluid in the oval surrounding the vortices (iii) 3D fluctuations in the vortex cores. For mechanism (ii) the predictions agree with available data. However, the predictions have a cut-off away from normal incidence which is not present in the measurements due possibly to 3D fluctuations in the oval. The reflectivity of mechanism (i) is comparable but cuts-off at frequencies lower than those considered in the experiment. Finally, we suggest that hot engine exhaust could increase RCS by 40 db and reveal vortex circulation, provided its mixing is prevented in the laminar vortices.