Alteration of the Tip Vortex Structure of a Hovering Rotor
Using Oscillatory Jet Excitation
Zhijian Liu*
Lakshmi N. Sankar†
School of Aerospace Engineering
Georgia Institute of Technology, Atlanta, GA 30332-0150
Ahmed A. Hassan‡
The Boeing Co., Mesa, AZ
ABSTRACT
The aerodynamic characteristics of a rotor in hover,
equipped with a synthetic jet slot on the upper surface are
studied. A three-dimensional unsteady flow solver is used,
which employs a Navier-Stokes analysis to model the
boundary layers and the wake, and a potential flow algorithm
to model the far field effects. The magnitude of the synthetic
jet velocity varied between 5% and 10% of the tip speed. The
frequencies varied between 5 per rev and 30 per rev. It was
found that synthetic jets are effective “spoilers” that would
reduce sectional lift distribution, tip vortex strength, total
thrust, and torque. The jets were not as effective at very high
(30 per rev) operating frequencies. A quantitative
comparison between the synthetic jet concept, and other
competing tip vortex alteration concepts such as steady jets
and spoilers, is given.
INTRODUCTION
The wake shed by a helicopter rotor, particularly in
the tip region, plays a dominant role in the aerodynamic and
aeroacoustic characteristics of the rotor. The outer part of the
rotor wake rolls into a strong tip vortex structure and
influences the inflow through the rotor, which in return
affects the radial variation of the rotor loads. Strong
aerodynamic interactions between the rotor and the vortex
can occur during descent, as the vortices are pushed up
against the rotor. This phenomenon is called blade-vortex
interaction (BVI), and can lead to vibratory loads and
generation of noise. Preliminary numerical studies by Lee
and Smith [1] have shown that tip vortices associated with a
larger core size have a less detrimental effect on the
aerodynamic loads on a rotor blade during BVI. Therefore,
if one can alter the vortex core size or its strength using a
passive or an active flow control mechanism, then both the
BVI noise and vibratory air loads can be reduced.
Steady blowing have been used in numerous
investigations as an effective active flow control mechanism
for modifying the lift, drag and stall characteristics of airfoils
and wings [2,3]. Steady jets have also been utilized for
altering the structure of the leading edge vortex on a delta
wing [4], and on rotors [5,6]. Guy et. al [4] applied periodic
blowing and suction at the leading edge of a delta wing to
control vortex breakdown. Hassan et. al [5] numerically
investigated the effects of steady surface blowing on the BVI
characteristics of a five-bladed MD-900 rotor.
They
concluded that a steady normal jet can be used to alleviate
BVI noise while suction would have a detrimental effect. In
an experimental study, Gowanlock and Matthewson [6]
demonstrated the potential benefits of using a steady jet as a
means for the active control of the rotor tip vortex strength.
Specifically, they demonstrated the effects of the jet on
dispersing the vorticity present in the blade tip vortex wake.
An accurate numerical scheme that captures the tip
vortex structure without false numerical diffusion is essential
to a systematic study of various tip vortex alteration
concepts. Melander and Hussian [7] demonstrated the
importance of accurately modeling the vortex core. They
indicated that the position of the vortex filaments relative to
the rotor depends significantly on the vortex self-induction,
which in turn, is related to the internal core dynamics,
particularly the vortex core size.
Navier-Stokes flow solvers for rotorcraft have been
shown to yield good blade surface pressures and spanwise
load distributions. Strawn and Barth [8], Srinivasan and
McCroskey [9], Srinivasan et. al [10], Srinivasan and Baeder
[11], Srinivasan et al. [12], Duque [13], and Duque and
Srinivasan [14] have studied rotors in hover and in forward
flight. In all these studies, the rotor wake was captured from
first principles. Hariharan and Sankar [15,16] used spatially
higher order methods to solve the flow field over a rotor in
hover from first principles. Ahmad and Duque [17] analyzed
the AH-1G two-bladed rotor in forward flight using
structured embedded grids. A structured/unstructured grid
approach was used by Duque [18] to model a rotor in hover.
All of the above studies for modeling the tip vortex
of a rotor have been more qualitative than quantitative.
Certain global characteristics such as the tip vortex
trajectory, contraction and descent rates have been captured
well [10]. Accurate quantitative prediction of the vortex core
structure is still lagging. Nevertheless, these first principles
based methods can at least be used to qualitatively assess the
*
Graduate Research Assistant
Regents' Professor, Associate Fellow AIAA
‡
Associate Technical Fellow, Associate Fellow AIAA
Copyright © 2000 by the American Institute of Aeronautics
and Astronautics Inc. All rights reserved.
†
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effects of a control device (jets, slats, flaps, spoliers, etc.) on
the tip vortex structure, and the blade airloads.
SCOPE OF THE PRESENT WORK
The present work addresses the alteration of the
blade tip vortex wake using oscillatory (i.e., jets that alternate
between blowing and suction) jets. The present numerical
scheme is an extension of an earlier fifth-order accurate finite
volume scheme developed by Hariharan for accurately
capturing the vortex wake from fixed and rotary wings [18].
WHY USE AN OSCILLATORY JET?
In an earlier investigation [19], results from
simulations of a rotor utilizing steady blowing near the tip
and a rotor equipped with a trailing edge spoiler were
compared. In these studies, it was shown that upper surface
blowing can be used to emulate the beneficial effects of a
spoiler (reduction in tip vortex strength, increase in core size)
without the attendant drag and power penalty. It was also
demonstrated that when blowing is applied on the lower
surface of the blade, the jet acts like a vortex flap, increasing
the blade loads and the tip vortex strength.
The use of steady jets on rotors, however, is not
practical for a number of reasons. Compressed air must be
available from the engine, or a separate electrically operated
compressor. A sealed duct system must also be installed
within the rotor blade and the shaft for delivering the
compressed air from the compressor to the rotating blades.
Electrically or pneumatically controlled valves must be
installed to control the blowing. These devices will add
considerable cost, complexity, and weight to the rotor
system.
A technology that does not rely on the supply of
compressed air is the zero-net-mass jet (or synthetic jet)
concept. As shown in Figure 1, a synthetic jet consists of a
small cavity directly mounted on the skin of the rotor blade,
with a flexible diaphragm lining the bottom surface of the
cavity. The diaphragm can be pushed up or down using
electromechanical or piezoelectric actuators. The cavity
draws air directly from the boundary layer when the
diaphragm deflects downwards increasing the cavity volume.
The cavity squirts the air out in the form of a jet when the
diaphragm moves up. If the diaphragm moves up and down
at a sufficiently high frequency, a series of ring vortices will
be generated which will move up and away from the balde
surface. These ring vortices will induce a steady jet-like flow
far away from the cavity. A complex boundary layer, ring
vortex interaction is present, and is worthy of an
investigation in itself.
In this work, the details of the synthetic jet
generation process were not simulated. Rather, the normal
velocity boundary condition was modified to represent a
sinusoidal variation of the normal velocity, as shown in
figure 2. In the present analysis, the location of the jets, the
normal velocity magnitude, and the frequency can all be
independently changed.
Consider the situation where the synthetic jet is
placed on the blade upper surface. The upward directed jet
will act as a spoiler, disrupting the flow over the boundary
layer. The circulation over the affected areas and the
sectional lift will decrease. A schematic of the resulting nearwake, and the expected radial variation of the bound
circulation are shown in figures 4 and 5.
The overall effect of the synthetic jet on the upper
surface (or a steady jet, for that matter) is to decrease the
total lift generated by the rotor, and the peak bound
circulation. Since the peak bound circulation determines the
tip vortex strength, the tip vortex strength will decrease as
well. Thus, synthetic jets mounted on the blade upper surface
are an effective means of reducing the tip vortex strength for
brief periods of time, in a controlled manner. Although the
present simulations are for a rotor in hover, the synthetic jet
concept is more useful in forward flight. It can be used to
reduce the vibratory airloads, redistribute the spanwise
loading, and mitigate the adverse aerodynamic and
aeroacoustic effects of blade-vortex interactions.
MATHEMATICAL FORMULATION
The mathematical and numerical formulation has
been extensively documented in Refs. [15,18]. Here, only
the essential details of the formulation are given.
The three dimensional, unsteady, compressible
Navier-Stokes equations are solved using a finite volume
approach. The fluxes crossing the finite volume cell faces are
computed using Roe’s approximate Riemann solver [20].
The flux requires flow information on the left and right sides
of each of the six cell faces. In this work, this information is
obtained using a fifth-order ENO scheme, developed by
Harten and Chakravarthy [21, 22].
The temporal derivatives are modeled using either a
two-point or a three-point backward scheme, making the
scheme either first, or second order in time. The viscous
terms are computed with a second-order accurate scheme.
The effects of turbulence are simulated using the algebraic
Baldwin-Lomax turbulence model.
In the solver used in this study, the Navier-Stokes
equations are solved only in regions close to the rotor blade
and in the near wake. Away from the rotor, a more efficient
potential flow method with a Lagrangean modeling of the tip
vortices is used. This hybrid Navier-Stokes-potential flow
solver is computationally more efficient than the full NavierStokes approach, and has been extensively validated for
rotors in hover [23].
RESULTS AND DISCUSSION
Clean Rotor (Baseline case):
We first discuss the performance of a hovering
rotor. These calculations are for a hovering rotor tested by
McAlister [24]. The rotor has a rectangular planform and an
aspect ratio of 6.0. The rotor operated at 1100 rpm
(corresponding to a tip Mach number of 0.388). The flow
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regions above and below the rotor disk are divided into two
grid blocks, each of size 152X43X40. For rotors in hover, the
flow field is periodic from blade to blade. Thus, only a
portion of the rotor disk needs to be modeled.
For the baseline rotor case, the computed CT was
0.00483 and the power coefficient CQ was 0.000491. These
results are in excellent agreement with measured data (CT =
0.0050; CQ = 0.00050). The clean rotor serves as a baseline
against which other concepts can be compared.
Additional code validations have also been done,
such as the comparison of the axial and tangential velocities
with measured data. These results are presented in Reference
25.
Synthetic Jet Configuration:
We next discuss the modification of the tip vortex
structure through the use of synthetic jets for the rotor
configuration discussed above. In the calculations presented
here, the slot spanned the region 68%R to 94%R, over the
last 12.5% chord, as shown in figure 3. The slot location was
chosen to facilitate comparisons with a steady jet case given
in a previous work [19], and with a spoiler configuration
given in Russell et al [25]. Two synthetic jet velocity
amplitudes, equal to 5% and 10% of the tip speed R , were
considered. The frequency was systematically varied from 5
per revolution to 30 per revolution.
Table I shows the thrust and torque characteristics
of the various combinations considered: baseline rotor, rotor
equipped with a spoiler, rotor with a steady jet, and rotor
equipped with a synthetic jet device, for various frequencies
and amplitudes. From this table, it is clear that jets operating
at the 10-per-rev frequency were more effective in changing
the rotor thrust and the peak bound circulation, than those
operating at the 30-per-rev frequency. For this reason, all the
results presented below are for the 10-per-rev case.
Table I also shows that steady jets and spoilers are
perhaps more effective in altering the rotor thrust, and the tip
vortex strength. There are distinct disadvantages with these
concepts, however. Spoilers are draggy, and consume large
amounts of power. Steady jets require a compressed air
supply and are not practical, as discussed earlier.
Rotor Loads:
Figure 6 shows the radial distribution of the timeaveraged bound circulation for the baseline rotor, a rotor
equipped with a steady jet, and a rotor with a synthetic jet.
The computed breaks in the bound circulation at the inboard
edge of the jet (station A) and outbound edge of the jet
(station B) are clearly seen. The 10% synthetic jet produced
more pronounced variations in the bound circulation. The
steady jet produces even larger variations. All these devices
produce a net loss in thrust. The induced velocity through the
rotor is reduced as a result of the weaker tip vortices and
reduced thrust. Thus, the induced torque and the overall
torque are also reduced, as seen in Table I.
Figure 7 shows the temporal variation of the bound
circulation, at point A (just inboard of the synthetic jet slot),
and point B (just outboard of the jet slot), for the 5% jet case.
The peak bound circulation is also shown. A net reduction in
the tip vortex strength (also seen in the previous figure) is
evident, when steady jets and synthetic jet devices are
employed. The vortices shed at station A and station B are
much weaker in strength, and will tend to cancel each other
out when they merge in the far wake. It can therefore be
argued that only the tip vortex will survive in the far field. Its
time-averaged strength was found to be approximately 86%
of that of the clean rotor for both the 5% and 10% jet cases.
Associated with the bound circulation reduction are
a reduction in the thrust coefficient CT, and the torque
coefficient CQ, as seen in figures 8 and 9, respectively. These
fluctuate with time as expected, due to the unsteady effects
of the synthetic jet. When the synthetic jet peak velocity was
5% of the tip speed, there was a 9% loss in CT and 16%
reduction in CQ. For the 10% synthetic jet case, the
corresponding reduction in CT and CQ are 17% and 21%
respectively.
In light of these results, it is clear that synthetic jets
can be used to alter the rotor thrust, hence the strength of the
blade tip vortex wake without undue penalties to rotor
power. If synthetic jets are placed on the lower surface of the
blade, they would act as vortex flaps, and one would expect
an increase in the rotor mean thrust and an increase in mean
torque. A combination of synthetic jets placed on the upper
and rotor surface should prove to be quite effective in
reducing vibratory loads, and alleviating BVI phenomena.
CONCLUDING REMARKS
The effect of synthetic jet devices on the hover
performance characteristics of a rotor has been investigated.
It has been demonstrated that that these devices behave like
spoilers when they are deployed on the upper surface,
reducing the overall thrust, and the tip vortex strength.
Although these synthetic devices are less effective than
spoilers or steady jets in altering the tip vortex strength, they
have a lower power penalty. They are also likely to be
lighter, less expensive, and easier to install and operate.
This work is preliminary in nature and limited in
scope, because only a single rotor configuration in hover has
been considered. Nevertheless, additional studies of this
promising technology are warranted for rotors in hover and
forward flight.
ACKNOWLEDGEMENTS
This work was supported by the National Rotorcraft
Technology Center (NRTC). Dr. Yung Yu was the technical
monitor.
REFERENCES
1.
2.
Lee, D.J. and Smith, C.A., “Effect of Core Distortion
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Rediniotis, O.K., Ko, J. and Yue, X., “Synthetic Jets,
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flow Control”, AIAA Paper 99-1000, 1998.
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American Institute of Aeronautics and Astronautics
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Periodic Blowing and Suction”, AIAA Paper 99-0132.
Hassan, A.A. Straub, F.K., and Charles, B.D., “Effects
of Surface Blowing/suction on the Aerodynamics of
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Numerical Simulation”, Proceedings of the AHS
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5, May 1993.
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McCroskey, W.J., "Flowfield analysis of modern
helicopter rotors in hover by Navier-Stokes method",
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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.
Ahmad, J. and Duque, E. P. N., " Helicopter Rotor
Blade Computation in Unsteady Flows using Moving
Embedded Grids, " AIAA Paper 94-1922, June 1994.
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Grid solver for Helicopter Rotor Flows, " 50th Annual
AHS Forum, June 1994.
Liu, Z., Sankar, L. N., Hassan, A. A., "Alterations of
the Tip Vortex Structure of a Hovering Rotor
blowing," AIAA Paper 99-0906.
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Chakravarthy, C.R., “Some Aspects of Essentially
Nonoscillatory (ENO) Formulations for the Euler
Equations,” NASA CR-4285, May 1990.
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Torok, M. S., “ Navier-Stokes/Full Potential/FreeWake Method for Rotor Flows,” Journal of Aircraft,
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J.C., “3-D Wake Measurements Near a Hovering
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"Alterations of the Tip Vortex Structure from a
Hovering Rotor using Passive Tip Devices,"
Proceedings of the AHS Forum, April 29-May 1,
1997, pp. 755-774.
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CT
CQ
Figure
of Merit
McAlister, Experiment
0.005
0.0005
0.5
Clean Rotor, Present
Simulation, Coarse Grid
Clean Rotor, Present
Simulation, fine Grid
Rotor with Spoiler
0.0052
0.00046
0.5764
0.00483
0.000491
0.48342
0.00266
0.000966
0.10042
0.00367
0.000307
0.51209
0.00366
0.000309
0.50670
0.00572
0.00417
0.000586
0.000389
0.52201
0.48949
0.00424
0.000391
0.49929
0.00444
0.000418
0.50048
Upper Surface Steady jetCoarse Grid
Upper Surface Steady JetFine Grid
Lower Surface Steady Jet
Synthetic Jet with a
velocity equal to 10% of
tip speed; 10 per rev
Synthetic Jet with a
velocity equal to 5% of
tip speed; 5 per rev
Synthetic Jet with a
velocity equal to 5% of
tip speed; 30 per rev
Table I. Comparison of Thrust, Torque and Figure of Merit for the
Various Tip Vortex Alteration Concepts Studied
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Blade surface
Flexible surface (pliable diaphragm)
Figure 1 Synthetic Jet Actuator
Vn = A sin(t)
Blade surface
Flexible surface (pliable diaphragm)
Figure 2 A Simple Model of the Synthetic Jet Actuator Used in the Present Study
Jet slot covers the last 13%
of chord
68% R
Figure 3. Placement of the Synthetic Jet Slot on the Upper Surface
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94% R
Jet, acts like a weak
spoiler.
B
C
Tip vortex is shed.
Vortex III
A
Bound circulation
grows from root to
station A
Circulation
rebuilds. Vortex
II
A weak vortex is shed as rotor
loses bound circulation. Vortex I
Single vortex with large core.
Figure 4 Schematic of the Effect of Synthetic Jets on the Rotor Wake
Bound
circulation
Station A
Station B
Station C
r/R
Figure 5 Expected Variations in Bound Circulation
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0.08
0.06
steady jet
clean rotor
5% pulse jet
10% pulse jet
Circulation
0.04
0.02
0
Station B
Station A
-0.02
-0.04
-0.06
0
0.2
0.4
0.6
0.8
1
r/R
Fig 6 Time-Averaged Bound Circulation Distribution over the Blade
0.07
0.06
Trailing Vortex Strength
0.05
0.04
station A--pulse jet
station B--pulse jet
station C--pulse jet
station A--steady jet
station B--steady jet
station C--steady jet
tip vortex--clean rotor
0.03
0.02
0.01
0
0
10
20
30
40
50
60
-0.01
-0.02
t
Wt
Fig 7 Temporal Variation of Bound Circulation at a number of Radial locations;
Jet Speed: 5% of Tip Speed; 10 per Rev.
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70
5.10E-03
Clean Rotor
4.90E-03
4.70E-03
CT
4.50E-03
4.30E-03
Average for 5% Synthetic Jet
4.10E-03
3.90E-03
5% Synthetic Jet, 10 per Rev
3.70E-03
3.50E-03
0
100
200
t
300
400
500
600
Figure 8 Variation of Thrust Coefficient with Time
5.50E-04
Clean Rotor
5.00E-04
CQ
4.50E-04
4.00E-04
3.50E-04
Average for 5% Synthetic Jet
5% Synthetic Jet, 10 per Rev
3.00E-04
0
100
200
t 300
400
Figure 9 Variation of Torque Coefficient with Time
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500
600