Numerical study of the effect of passive rotor-tip devices on tip vortexes.

1. Alterations of the Tip Vortex Structure from a Hovering Rotor
using Passive Tip Devices
Justin W. Russell, Graduate Research Assistant
Lakshmi N. Sankar, Regents’ Professor
School of Aerospace Engineering
Georgia Institute of Technology, Atlanta, GA 30332-0150
Chee Tung, Research Scientist
Army Aeroflightdynamics Directorate
NASA Ames Research Center, Moffett Field, CA 94035
Michael T. Patterson, Sales Analyst
Silicon Graphics/Cray Research, Inc.
Peachtree City, GA 30269
ABSTRACT
Numerical studies of the tip vortex structure
from a hovering rotor with and without various
spoilers are presented. A general multizone
unsteady three-dimensional Navier-Stokes solver is
developed to determine the flowfield. A scheme
which is fifth-order accurate in space and first order
accurate in time is used to improve the capturing of
the tip vortex. Velocity data from the core of the
vortex is studied at various planes behind the blade
trailing edge. Computations of this velocity data for
a clean rotor are first compared with experimental
results obtained for the same rotor test case. Three
different trailing edge spoiler configurations are then
investigated to see if the tip vortex structure can be
favorably altered.
INTRODUCTION
With greater emphasis today being placed on
noise reduction both for civil and military rotorcraft,
studies of the tip vortices produced by rotors become
more and more important. This is because a
substantial component of the noise generated by a
rotor is due to Blade-Vortex Interaction (BVI),
which is the effect of the tip vortex created by
previously _____________________
Presented at the American Helicopter Society 53rd Annual Forum,
Virginia Beach, Virginia, April 29 - May 1, 1997. Copyright ©
1997 by the American Helicopter Society, Inc. All rights reserved
passing blades on a given blade. Preliminary
numerical studies by Lee and Smith [1] have shown
that vortices with larger core sizes have a less
detrimental effect on the lift of a blade during BVI.
Hence, if the tip vortex can be somehow altered so
that its core size is substantially increased, then both
the BVI noise and the vibratory airloads can be
reduced.
Early studies by Tangler [2] aimed at
reducing “blade slap” have shown that passive
devices such as a stub/subwing mounted at the rotor
tip can be used to improve slap signature with no
noticeable difference in performance of the rotor
between the stub/subwing and the square tip. Berry
and Mineck [3] have tested a rotor with a
stub/subwing and a winglet, but found a higher
torque requirement for one test case in hover and
therefore had eliminated these concepts from further
testing. More recently, Smith and Sigl [4] have
shown that devices such as a stub/subwing can
diffuse the tip vortex by as much at 47% with a 9%
decrease in drag, and that the NASA star tip device
can diffuse the tip vortex by 100% with a 67%
increase in drag. Green and Duan [5] have also
tested a ducted tip for hydrofoils which has shown to
make the vortex core size larger. These results offer
motivation that a passive device, if properly
designed, can be used produce significant increases
in vortex core size (thus reducing BVI) with minimal
or no loss in rotor performance.
To properly study the variety of devices
suggested for tip vortex alteration, an accurate
solution method is needed which can capture the
characteristics of the vortex core. The importance of

2. modeling the core correctly can be seen in a
theoretical study by Melander and Hussian [6] which
shows that the vortex core size has a direct effect on
the position of vortex filaments (which also affects
BVI) and the dynamics of three dimensional vortical
flows in general. In recent years, Navier-Stokes flow
solvers for rotorcraft have proven to yield generally
good blade pressure and load distributions. Strawn
and Barth [7], Srinivasan and McCroskey [8],
Srinivasan et. al [9], Srinivasan and Baeder [10],
Srinivasan et al. [11], Duque [12], and Duque and
Srinivasan [13] solved hovering rotor flowfields by
capturing the rotor wake in an Eulerian fashion, and
from first principles. Hariharan and Sankar [14]
used higher-order methods to solve the flowfield of a
rotor in hover from first principles. Ahmad and
Duque [15] analyzed the AH-1G two bladed rotor in
forward flight mode using structured embedded
grids. In addition, a structured/unstructured grid
approach was attempted by Duque [16] to solve
hovering rotors. An excellent survey of state of the
art in Euler and Navier-Stokes calculations for rotor
flows is given by Srinivasan and Sankar [17]. More
recently, Sheffer et al. [18] have even coupled a
Navier-Stokes solver to a structural code so that
aeroelastic effects can be accounted for in the
computations. In addition, Wake and Baeder [19]
have shown fair correlation of performance data with
experiment for such complex configurations as the
Black Hawk rotor in hover. They conclude that
higher-order schemes are necessary to improve the
capturing of the tip vortex. That is, until now, most
studies of the tip vortex of a rotor have been more
qualitative than quantitative. Certain global
characteristics such as the tip vortex trajectory,
contraction, and descent have been captured.
However, the details of the flow within the core of
the vortex have not been resolved. This knowledge
is essential to understanding how to alter the tip
vortex by active (e.g., blowing) and/or passive (e.g.,
spoilers, stub/subwings, winglets) means.
The present work addresses the aspect of tip
vortex modeling (i.e., the details of the velocity field
within the core), as well as the study of tip vortex
alteration by passive devices. A recent survey by Yu
[20] offers insight into the types of tip alterations
that have been tested to reduce BVI noise. However,
he notes that only acoustic measurements are taken
in these experiments with the tip devices. That is,
the physics of the flowfield due to these devices is
not well understood. The present work involving the
tip vortex modeling is an extension of the studies by
Hariharan where the details of the tip vortex from a
fixed wing were modeled [21]. In the case of rotors,
the problem is made more complex by the fact that
the vortex structure significantly influences the blade
loading and vice versa. For more insight into the
recent advances in modeling of rotor wakes, the
reader is referred to a survey paper by McCroskey
[22]. The present calculations for a clean rotor are
compared with experiments by McAlister et al. [23]
to show the effectiveness of the numerical scheme in
capturing the dynamics and size of the vortex core.
With this established, passive tip devices such as
spoilers are then investigated to show their benefits
and/or detriments to the rotor and their effects on
near-wake characteristics.
A Mathematical Criterion for Vortex Stability
To study of the effects of passive devices, it is
first important to understand that the goal of the
passive device is to diffuse or destabilize the tip
vortex. Early theoretical studies on columnar
vortices by Leibovich and Stewartson [24, 25] have
shown that a sufficient condition for vortical flow to
be unstable is:
V
d
dr
d
dr
d
dr
dW
dr
Ω Ω Γ
+














<
2
0 (1)
where, W(r) is the axial velocity component, V(r) is
the azimuthal velocity component, r is the radial
distance from the vortex axis, Ω is the angular
velocity V/r, and Γ is the circulation rV. The
justification in considering this model for stability
criterion is that it is formulated using a vortex model
which represents the behavior of a trailing line
vortex downstream of a wing tip. Note that this
equation is derived in a cylindrical coordinate system
with r = 0 being the vortex center (where V = 0).
Hence, V(r) can also be thought of as the tangential
velocity. This notational convention is described in
more detail in Figure 1. From this, the following
relations can be derived:
d
dr
r
dV
dr
V
Γ
= + (2)
d
dr r
dV
dr
V
r
Ω
= −
1
2
(3)
If we define the vortex core as that region between
the vortex center r = 0 and the radial location where
dV/dr = 0 (again, see Figure 1), we see from

3. equation (2) above that dΓ/dr must be positive in the
core region. Therefore, the only way to force the
vortex to become unstable is to force dΩ/dr to be
negative at a point where dΓ/dr is small and dW/dr is
large, specifically,
d
dr
d
dr
dW
dr
Γ Ω
<






2
. From
equation (3) above, for dΩ/dr to be negative requires
dV/dr be small where r is small, that is,
dV
dr
V
r
< .
From equation (2), this would also tend to lead to a
small value of dΓ/dr. Note also, that dW/dr tends to
be large when r is small. Hence, physically we seek
to diffuse the core region of the vortex which results
in a small dV/dr where r is small. This is consistent
with the studies previously discussed. Note that in
McAlister’s defining work, the symbols Vz and Vx
are used to represent V and W (with Vz = |V| and Vx
= W), respectively. This notation is also used in the
present work.
The passive tip devices tested will seek to
diffuse the vortex core, and consequently reduce the
induced velocity due to the tip vortex. This will have
a beneficial effect on BVI. Even if equation (1) can
not be satisfied, it still offers guidelines for which
trends we desire in the near wake of the rotor. That
is that we seek to “fatten” the tip vortex, which has
previously been shown to lead to favorable BVI
characteristics. The devices considered in the
present work include three different trailing edge
spoiler configurations. The high-order accurate
numerical solution procedure described below will be
suitable for examining these vortex destabilization
concepts patterned after the above criterion.
MATHEMATICAL FORMULATION
The mathematical and numerical formulation
behind the present approach has been extensively
documented in Reference [21]. For brevity, only the
general characteristics of the formulation are
described here.
This numerical scheme solves the three
dimensional, unsteady, compressible Navier-Stokes
equations. The inviscid and viscous flux terms are
computed using a cell-vertex finite volume
formulation. The inviscid fluxes at the cell faces are
computed using Roe’s approximate Riemann solver
[26]. This solver requires flow information on the
left and right sides of a cell face for each coordinate
direction. In this work, this information is obtained
using a fifth-order essentially-non-oscillatory (ENO)
scheme developed by Harten and Chakravarthy [27,
28].
The solution is advanced in time using an
implicit three-factor diagonal alternating-direction-
implicit (ADI) scheme due to Pulliam and Chaussee
[29]. This makes the procedure first order accurate
in time. In addition, implicit fourth-order artificial
dissipation using a spectral radius scaling factor is
used to improve the temporal stability characteristics
of the scheme.
NUMERICAL MODELING
For all of the simulations described below, the
full Navier-Stokes equations are solved in a time-
accurate fashion using the algebraic Baldwin-Lomax
turbulence model. The complexity of the
configuration requires that the flowfield be divided
into zones or blocks, as will be discussed later. Data
is passed between zonal interfaces to ensure fifth-
order spatial accuracy throughout the interior of the
computational domain. Note, however, that the
scheme drops to first-order accurate near solid
surfaces and farfield boundaries. Only one blade of
the multi-bladed rotor is solved in hover, with a
periodic boundary condition used at the azimuthal
boundaries.
Boundary Conditions
All of the farfield boundaries are
approximated by a first-order extrapolation. No
mass-sink boundary condition is used at the lower
boundary to help develop the inflow. This is because
such an ad-hoc treatment may alter the velocities in
the vortex core which would diminish the fact that
the vortex is captured from first principles. Two-
point averages of the flow properties are used at the
zonal interfaces. A simple periodic condition is also
used at the azimuthal boundaries simulating the
existence of other blades. A no-slip boundary
condition is used at all solid surfaces. At these
surfaces, density is extrapolated to second-order and
pressure to first-order. For the blunt ends of the
blade, special zones called “cap” grids are used as
shown in Figure 2. These cap grids contain singular
faces at the leading edge and trailing edge of their
airfoil shape. Here, two-point averages are used just
as is done at the leading and trailing edge of the
blade surface (due to the H-grid topology).

4. COMPUTATIONAL MODIFICATIONS
The numerical simulations presented in this
paper are performed by a computer program named
"GTrot3d". GTrot3d is written in FORTRAN 77
and has undergone development at Georgia Tech for
many years.
Most of computations presented in this paper
were performed on a Cray Research J-916, Cray's
entry-level parallel/vector supercomputer. Initial
tests of the computer program indicated that
GTrot3d achieved acceptable vector performance on
the J-916, but that the program did not parallelize
well. The computational requirements of the
solutions demanded performance improvements: a
360 degree revolution of the two-bladed rotor was
estimated to require 2000 cpu hours on a Cray J-
916, using a 1.2 million point grid.
Modifications to GTrot3d improved the
program's performance characteristics. The
modified program was estimated to require 400 cpu
hours to complete a 360 degree revolution of the
rotor. Implementation of a three-factor ADI scheme
(from two-factor scheme) improved numerical
stability and allowed the time-step size to be
doubled, thereby reducing cpu time further, to under
200 cpu hours. Parallelization on eight cpu's was
successful: each of the solutions presented in this
paper required just 29 elapsed hours per 360 degree
revolution to compute. Lastly, the parallelization
improvements required an increase in total memory
requirements, with the largest of the solutions
requiring 800 megabytes of memory. For this
reason, the original serial version with the updated
three-factor scheme is still available.
CONFIGURATIONS CONSIDERED
Clean Rotor
The reference rotor is modeled after that
described in Reference [23]. The grid used for the
model consists of 1,210,330 grid points and has an
H-H-O topology. The grid is divided into 6 zones
with the first two zones forming the H-H-O topology
and encompassing a majority of the computational
domain. These two zones allow the root and tip
airfoil geometries to extend to the farfield boundaries
which minimizes grid “kinks” (a source of
numerical error) in the radial direction. For
reference, these zones are depicted in Figure 3.
In most three dimensional simulations for
rotors in both hover and forward flight, the grid in
the rotor root and tip regions is simply “pinched off”,
which physically represents a wedge-shaped end to
the rotor root and tip. However, in this simulation
we seek to more accurately model the rotor tip
geometry and capture the tip vortex. Hence, the
rotor root and tip regions are “capped” with two-
zone H-H grids that are in the shape of airfoils of the
region from which they extend. Again, these cap
grids are shown graphically in Figure 2. Note that
each zonal interface matches grid point for grid
point so as to avoid the use of an interpolation
scheme.
Rotor with Trailing Edge Spoiler
In order to make a just comparison between
the clean rotor results and the results for the rotor
with a spoiler, the exact same grid is used in the
spoiler simulations. The only difference between the
two grids is that the upper and lower H-H-O zones
are split vertically at the trailing edge. This yields a
total of 8 zones. A schematic diagram of this
configuration is shown in Figure 4.
To model the three spoilers, a solid surface
boundary condition is applied at the trailing edge
zonal interfaces over a range of specified grid points.
This yields a spoiler model which is grid-aligned
(nearly parallel to the axis of rotation) and of zero
thickness. A graphical representation of the trailing-
edge spoiler is given in Figure 5.
Three different spoiler sizes are tested, with
the dimensions and locations as shown below in
Table 1.
Table 1. Dimensions for the Three Spoilers
Spoiler
Number
Height
(%chord)
Width
(% radius)
Location
(% radius)
1 .039 .058 .875 - .933
2 .050 .088 .856 - .944
3 .084 .133 .835 - .968
These dimensions are approximate since the spoiler
is actually grid-aligned. The width corresponds to
the spanwise dimension and the height is that
dimension normal to the flow direction both on the
upper and the lower side of the rotor.
RESULTS AND DISCUSSION
Clean Rotor

5. Results for the clean rotor are first presented
to validate the numerical procedure for predicting
the characteristics of the vortex core. Results are
presented at various instances in time, with the
solution starting from a zero-flow initial condition.
The measurement plane is explained in detail in
Reference [23]. The reader should think of the x-
component as the chordwise or axial component
(positive towards the blade), the y-component as the
radial component (positive inboard), and the z-
component as the normal component (positive
upward.
Figure 6 compares the three velocity
components in the core of the tip vortex with the
experimental data given in Reference [23]. At this
point in time, the blade has traveled only one half of
a revolution. The usefulness of this figure is to show
that the general characteristics of the tip vortex in
the x and z directions can be captured with little
computational effort. However, the peak of y-
component is not captured at all. This make sense,
since the inboard component is greatly dependent on
the wake contraction and the effects of the vortex
wake from below. In contrast, the x-component is
strongly dependent on the wake viscous effects, and
the z-component largely dependent on the lift.
Notice that the z-component is overpredicted at the
peaks. This is due to the fact that the inflow has yet
to develop, which leads to higher lift and
consequently higher shed circulation. However, also
notice that the thickness of the core and velocity
slope are captured well. For visualization purposes,
Figure 7 gives a particle trace in a blade-fixed frame
of reference after one half of a revolution, which
shows the evolution of the tip vortex and its relative
path. In addition, Figure 8 show the velocity vectors
in the measurement plane. In this figure, the tip
vortex has a well-behaved and expected form.
It was expected that simply running the
simulation further would improve the results. This
was not exactly the case. When beginning from a
zero-flow condition, the blade initially sheds a
starting tip vortex in the plane of rotation. Hence,
once the two-bladed rotor travels one half of a
revolution, the second blade hits this starting vortex
which causes a large decrease in the lift of the rotor,
as seen in Figure 7. Consequently, the shed tip
vortex becomes weaker, and the predictions worsen.
This is evident in Figure 9 which shows the z-
velocity component after one full revolution. This
weakening occurs during the second half-revolution
and is evidenced by the very low peak velocity values
in Figure 9. Eventually the inflow reestablishes as
the vortices shed by the previous blade are pushed
below the blade and the lift recovers. In addition,
the wake begins to contract (though rather slowly).
Velocities through the vortex core are
presented after one and a half revolutions in Figure
10. The magnitude of the peaks for the x and z-
components of velocity are predicted well. The y-
component is still well underpredicted, but there
appears to be some inboard velocity forming
compared to the solution after only one half of a
revolution, which is encouraging. Also notice that
the vortex thickness is overpredicted. This is due to
the fact that the vortex has moved inboard (due to
the contraction effects of the vortex below) where
fewer grid points exist. This, in effect, “smears” the
vortex causing a fatter x-velocity distribution and an
underpredicted slope in the z-component velocity
distribution. A calculation with radially
redistributed points is now in progress to improve
these results. The fact that the axial and normal
velocity components are captured well within one
half of a rotor revolution, however, allows us to
study the destabilizing effects on the tip vortex due
to a trailing edge spoiler. Finally, the computed
thrust and inviscid torque coefficients after one and
one half revolutions are CT = 0.00448 and CQ =
0.000300 which are lower than McAlister’s values of
CT = 0.0051 and CQ = 0.00052. Of course the
computed torque will be improved once the viscous
contributions are added. In addition, improvements
to the results will be made if the solution is advanced
further to a steady-state condition
Spoiler Results
As previously stated, the most important
components of velocity through the core of the
vortex (as far as stability of the vortex is concerned)
are the axial (x) and normal or tangential (z)
components. Hence, since the goal is to destabilize
and diffuse the tip vortex, we will focus only on
these components in the vortex core. Figure 11
shows comparisons of the velocity components for
the 3 spoiler configurations with the clean rotor
solutions after one half of a revolution. In addition,
Figure 12 shows the velocity vector profiles in the
measurement plane at this same instant in time.
Recall that the first half of a revolution seems to
yield good qualitative and fairly good quantitative
results with regards to the x and z-components of
velocity through the core. Referring to Figure 11, it
is evident from the normal velocity distributions that
the presence of the spoiler does indeed decrease
dV/dr (i.e., the slope of the normal velocity
distribution in the vortex core) which is desirable.

6. Furthermore, dV/dr decreases in the core region as
the spoiler size increases. Hence, with these results,
it is seen that a larger spoiler (as much as excess
power would allow) is more beneficial in
destabilizing the vortex. This can also be seen in
Figure 12, where the velocity vectors show that the
overall organization of the tip vortex degrades as
spoiler size increases. Finally, referring to the axial
velocity distribution in Figure 11, it is evident that
dW/dr remains relatively large with all spoiler
configurations present. This implies that with a
spoiler present, the most relevant aspect of the vortex
core with regards to the stability of the vortex is the
normal (or tangential) velocity distribution.
The velocity distributions for the rotor/spoiler
configurations after one and a half revolutions are
shown in Figure 13. For comparison purposes, the
clean rotor results are also plotted. Notice that the
larger the spoiler the less the normal or tangential
velocity changes in the core, as was seen in the first
half revolution. Here, however, the spoiler shows an
even more pronounced effect on the slope of the
normal velocity through the core. Again, according
to equation (1), this has a destabilizing effect on the
vortex, which is what we are seeking. Note also that
the axial velocity maintains a relatively large slope
near the vortex core, with the larger spoiler having a
greater “smearing” effect on the distribution.
Overall, the effects of the different spoilers
can be seen in Figure 14, which shows the lift
coefficient distribution variations for the rotor with
the spoilers. Again, the clean rotor results are
plotted for comparison. As expected, the presence of
the spoiler causes a decrease in lift in the vicinity of
its location. Since lift is proportional to the bound
circulation on the rotor blade, conservation of
vorticity requires that trailing vorticity must be shed
due to the radial change in lift. At the inboard
station where the lift first drops due to the presence
of the spoiler, it is expected that a significant amount
of vorticity will be shed forming a vortex which
rotates in the same direction as the tip vortex. Also,
outboard of the spoiler where the blade experiences a
sharp increase in lift, a counter-rotating vortex is
expected to be shed. A schematic diagram of this is
shown in Figure 15.
These effects do indeed occur and can be seen
in Figure 16, which shows the velocity vectors in a
radial plane approximately 0.5 chordlengths behind
the blade trailing edge. For the largest spoiler (#3),
all three vortices can be seen, with the two due to the
spoiler being smaller and weaker than the tip vortex.
As for spoiler #2, only the counter-rotating vortex
appears. This is likely due to the fact that for spoiler
#2, the inboard drop in lift is much less drastic than
that for the larger spoiler #3. Hence, the inboard
shed vorticity is spread out over a much greater
range, and is consumed by the dominating tip vortex
and/or the outboard spoiler vortex. Further
downstream, these vortices tend to interact and
diffuse the tip vortex to various degrees. This can be
seen in Figure 17, where the velocity vectors are
shown in the measurement plane 3 chordlengths
down stream of the blade trailing edge for spoilers
#2 and #3. Notice here the distorted tip vortex,
especially for spoiler #3, where the rotation is spread
out over a large number of grid points.
These vortex formations are also depicted
graphically in Figure 18, which shows the vorticity
magnitude contours at various azimuthal locations
behind and in front of the blade. In this figure, the
inboard vorticity shed from the spoiler is clearly
visible in the near wake, but becomes consumed and
distorts the tip vortex. Further downstream (i.e., in
front of the blade), the vorticity is much more spread
out than is normally seen with a clean rotor blade.
The overall effect of this tip vortex alteration is also
seen in the particle traces shown in Figure 19 for
both spoiler configurations. Comparing these traces
with that shown in Figure 7 for the clean rotor, it is
obvious the destabilizing effect the spoilers have on
the tip vortex. From these figures, it is seen that
increasing the spoiler size has the effect of
“unwinding” the tip vortex. This “unwinding” or
diffusion of the tip vortex is what is desired in order
to improve the BVI characteristics of the blade.
Finally, the computed thrust coefficients for
the two largest spoilers are CT = 0.00445 (spoiler #2)
and CT = 0.00403 (spoiler #3). As expected, the
trends show that the thrust decreases as the spoiler
size increases and that the spoiler causes and overall
decrease in thrust compared to the clean rotor
calculation. The torque requirements are yet to be
computed.
CONCLUSIONS
1. A high-order spatial accuracy scheme appears to
be capable of capturing the rotor tip vortex, provided
enough grid points remain distributed through the
vortex core.
2. Many revolutions are potentially needed to allow
the rotor wake to develop and to accurately capture
the rotor tip vortex with respect to all three
coordinate velocity distributions (especially the
inboard direction).

7. 3. Reasonable qualitative and quantitative results
about the vortex core in the normal and axial
directions can be captured within one half of a rotor
revolution. This can lead to less computational
effort if only general effects on the vortex due to
some rotor modification (i.e., implementation of a
passive tip device) is desired.
4. A trailing edge spoiler yields a beneficial effect
with regards to destabilization and/or diffusion of a
rotor tip vortex in hover, which leads to better BVI
characteristics for the blade. The larger the spoiler,
the more destabilizing to the tip vortex. In other
words, a larger spoiler causes greater diffusion of the
tip vortex.
5. Further studies are needed to determine the
performance degradation (power penalty) resulting
from the use spoilers, as well as to determine an
“ideal” spoiler for a given rotor configuration and
flight condition (i.e., the spoiler yielding the most
destabilizing effects for the least amount of
performance penalty).
ACKNOWLEDGMENTS
The first two authors acknowledge the
support of the National Rotorcraft Technology
Center (NTRC) for this project, as part of the
Georgia Tech Rotorcraft Center of Excellence.
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Rotorcraft Acoustics and Rotor Fluid dynamics,
Philadelphia, PA, October 1991.
12. Duque, E.P.N., " A Numerical Analysis of the
British Experimental Rotor Program Blade,"
American Helicopter Society 45th Annual Forum,
Boston, MA, May 1989.
13. Duque, E.P.N. and Srinivasan, G.R., "
Numerical Simulation of a Hovering Rotor using
Embedded Grids,” American Helicopter Society 48th
Annual Forum, Washington, DC, June 1992.
14. Hariharan, N. and Sankar, L.N., "Higher Order
Numerical Simulation of Rotor Flow Field," AHS
Forum and Technology Display, Washington, DC,
May 1994.
15. Ahmad, J. and Duque, E.P.N., " Helicopter
Rotor Blade Computation in Unsteady Flows using
Moving Embedded Grids," AIAA Paper 94-1922,
June 1994.

8. 16. Duque, E.P., "A Structured/Unstructured
Embedded Grid solver for Helicopter Rotor Flows,"
American Helicopter Society 50th Annual Forum,
June 1994.
17. Srinivasan, G.R. and Sankar, L.N., “Status of
Euler and Navier-Stokes CFD Methods for
Helicopter Applications,” American Helicopter
Northeast Region Aeromechanics Specialist
Meeting, Bridgeport, CT, October 1995.
18. Sheffer, S.G., Alonso, J.J., Martinelli, L. and
Jameson, A., “Time-Accurate Simulation of
Helicopter Rotor Flows Including Aeroelastic
Effects,” AIAA Paper 97-0399.
19. Wake, B.E. and Baeder, J.D., “Evaluation of a
Navier-Stokes Analysis Method for Hover
Performance Prediction,” Journal of the American
Helicopter Society, Vol. 41, (1), January 1996.
20. Yu, Y.H., “Rotor Blade-Vortex Interaction
Noise: Generating Mechanisms and its Control
Concepts,” American Helicopter Northeast Region
Aeromechanics Specialist Meeting, Bridgeport, CT,
October 1995.
21. Hariharan, N., ”High Order Simulation of
Unsteady Compressible Flows Over Interacting
Bodies with Overset Grids,” Ph.D. Thesis, Georgia
Institute of Technology, Atlanta, GA, August 1995.
22. McCroskey, W.J., “Wake Vortex System of
Helicopters,” AIAA Paper 95-0530, January 1995.
23. McAlister, K.W., Schuler, C.A., Branum, L.,
and Wu, J.C., “3-D Wake Measurements Near a
Hovering Rotor for Determining Profile and Induced
Drag,” NASA Technical Paper 3577, August 1995.
24. Leibovich, S. and Stewartson, K., “A sufficient
condition for the stability of columnar vortices,”
Journal of Fluid Mechanics, Vol. 126, July 1982.
25. Stewartson, K. and Leibovich, S., “On the
stability of a columnar vortex to disturbances with
large azimuthal wavenumber: the lower neutral
points,” Journal of Fluid Mechanics, Vol. 178,
August 1986.
26. Roe, P.L., “Approximate Riemann Solvers,
Parametric Vectors, and Difference Schemes,”
Journal of Computational Physics, Vol. 39, 1981.
27. Chakravarthy, C.R., “Some Aspects of
Essentially Nonoscillatory (ENO) Formulations for
the Euler Equations,” NASA CR 4285, May 1990.
28. Harten, A. and Chakravarthy, C.R., “Multi-
Dimensional ENO Schemes for General
Geometries,” NASA CR 187637, September 1991.
29. Pulliam, T. H. and Chaussee, D.S., “A Diagonal
Form of an Implicit Approximation -Factorization
Algorithm,” Journal of Computational Physics, Vol.
39, 1981.

9. Figure 1: Schematic Diagram Showing the
Notation used for the Study of a Columnar Vortex.
Figure 2: Airfoil-Shaped H-H Cap Grids.
Figure 3: The Two Largest Zones of the H-H-O Grid
used in the Numerical Simulation.
Figure 4: Schematic Diagram of Grid
Configuration for Simulations of a Rotor with a
Trailing-Edge Spoiler.
Figure 5: Graphical Representation of a Trailing-
Edge Spoiler.

10. Comparison of X-velocity Component
with Experiment
0
2
4
6
8
10
12
14
16
-70 -50 -30 -10 10 30 50 70
y (mm)
Vx(m/s)
Vx 293Deg Rev1
Experiment
Comparison of Y-velocity Component
with Experiment
0
5
1 0
1 5
2 0
2 5
-70 -50 -30 -10 1 0 3 0 5 0 7 0
y (mm)
Vy(m/s)
Vy 293Deg Rev1
Experiment
Comparison of Z-velocity Component
with Experiment
-22
-18
-14
-10
-6
-2
2
6
10
14
18
22
-70 -50 -30 -10 10 30 50 70
y (mm)
Vz(m/s)
Vz 293Deg Rev1
Experiment
Figure 6: Comparison of Core Velocity Component Magnitudes with Experiment for a Clean Rotor; 3
Chordlengths Downstream of the Blade Trailing Edge after One Half of a Revolution.

11. Particle Trajectory for Previous Blade
Figure 7: Particle Trace (Evolution of the Tip
Vortex) after One Half of a Revolution.
Figure 8: Velocity Vectors Showing the Tip Vortex
after One Half of a Revolution; 3 Chordlengths
Downstream of the Blade Trailing Edge.
Comparison of Z-velocity Component
with Experiment
-22
-18
-14
-10
-6
-2
2
6
10
14
18
22
-70 -50 -30 -10 10 30 50 70
y (mm)
Vz(m/s)
Vz 80Deg Rev1
Experiment
Figure 9: Normal Velocity through the Core of the
Tip Vortex; 3 Chordlengths Downstream of the
Blade Trailing Edge after Approximately One Full
Revolution .

12. Comparison of X-velocity Component
with Experiment
0
2
4
6
8
1 0
1 2
1 4
-70 -50 -30 -10 1 0 3 0 5 0 7 0
y (mm)
Vx(m/s)
Vx 284Deg Rev2
Experiment
Comparison of Y-velocity Component
with Experiment
0
5
10
15
20
25
-70 -50 -30 -10 10 30 50 70
y (mm)
Vy(m/s)
Vy 284Deg Rev2
Experiment
Comparison of Z-velocity Component
with Experiment
-22
-18
-14
-10
-6
-2
2
6
10
14
18
22
-70 -50 -30 -10 10 30 50 70
y (mm)
Vz(m/s)
Vz 284Deg Rev2
Experiment
Figure 10: Comparison of Core Velocities 3 Chordlengths Downstream of the Blade Trailing Edge after 1.5
Revolutions.

13. Comparison of X-velocity Component
with and without Spoilers
-3
2
7
12
17
22
27
-70 -50 -30 -10 10 30 50 70
y (mm)
Vx(m/s)
Spoiler #2 293Deg Rev1
Clean Rotor 293Deg Rev1
Spoiler #1 293Deg Rev1
Spoiler #3 293Deg Rev1
Comparison of Z-velocity Component
with and without Spoilers
-22
-18
-14
-10
-6
-2
2
6
10
14
18
22
-70 -50 -30 -10 10 30 50 70
y (mm)
Vz(m/s)
Spoiler #2 293Deg Rev1
Clean Rotor 293Deg Rev1
Spoiler #1 293Deg Rev1
Spoiler #3 293Deg Rev1
Figure 11: Comparison of the Core Velocity Distributions 3 Chordlengths Downstream of the Blade Trailing
Edge

14. Small Spoiler: organized vortex still evident
Medium Spoiler: vortex is diffused, still visible
Large Spoiler: vortex is highly diffused, weak
Figure 12: Velocity Vectors in the Measurement Plane (Top to Bottom, Spoilers 1-3)

15. Comparison of X-velocity Component
with and without Spoilers
-3
2
7
12
17
22
27
-70 -50 -30 -10 10 30 50 70
y (mm)
Vx(m/s)
Clean Rotor 284Deg Rev2
Spoiler #3 284Deg Rev2
Spoiler #2 284deg Rev2
Comparison of Z-velocity Component
with and without Spoilers
-22
-18
-14
-10
-6
-2
2
6
10
14
18
22
-70 -50 -30 -10 10 30 50 70
y (mm)
Vz(m/s)
Clean Rotor 284Deg Rev2
Spoiler #3 284Deg Rev2
Spoiler #2 284Deg Rev2
Figure 13: Comparison of Velocity Distributions for the Rotor with and without a Trailing Edge spoilers 3
Chordlengths Downstream of the Blade Trailing Edge after One and a Half Revolutions

16. Cl Distribution
(Nondimensionalized by Tip Radius)
284Deg Rev2
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6
r/R
Cl
Clean Rotor
Spoiler #2
Spoiler #3
Figure 14: Variation in Cl Distribution for the Rotor Blade with and without Various Spoiler Configurations.
Figure 15: Schematic Diagram of Expected Vortex Shedding Due to the Presence of the Spoiler

17. Medium Spoiler: Two counter-rotating structure clearly seen
Large Spoiler: Three Vortical Structures seen; inboard spoiler structure very weak.
Figure 16: Velocity Vectors in the Near Wake of the Rotor with Two Different Spoilers Showing Counter and/or
Co-Rotating Vortex Formations. Spoiler #2 is above and Spoiler #3 is below.

18. Medium Spoiler: Tip vortex diffused, but still visible. Counter-rotating vortex still clearly visible
Large Spoiler: Tip vortex highly diffused, barely visible. Counter-rotating vortex still barely visible.
Figure 17: Velocity Vectors in the Measurement Plane 3 Chordlengths Downstream of the blade Trailing Edge for
Rotor With Two Different Spoiler Configurations Showing the Effects of The Merging Vortices. Spoiler #2 is
above and Spoiler #3 below.

19. Figure 18: Vorticity Magnitude Contours around the Azimuth for the Hovering Rotor with Various Spoiler
Configurations Showing Tip Vortex Breakdown.

20. Medium Spoiler: Particles traverse along large spiral trajectories.
Large Spoiler: Spiral nature is destroyed. Large lateral motion seen.
Figure 19: Particle Traces Around the Azimuth for the Rotor with Various Trailing Edge Spoilers