II. Literature Study of Hub Drag Reduction Concepts
A number of approaches for reducing hub drag have been studied by researchers. Passive concepts, active
control concepts, and biologically inspired concepts have been studied.
A. Passive Concepts
Stroub et al2 have conducted experiments to study the effects of fairing, camber, lower surface curvature, and
relative size of the hub on hub drag. These investigators also examined the effects of gap and hub fairing inclination
on drag. In a follow-on study, Stroub3 investigated the use of a large circular fairing on drag reduction. Larry Young
et al4 have examined hub-fairing camber, hub-fairing thickness ratio, hub-fairing surface curvature, hub-fairing
height with respect to the fuselage, inclusion of blade shanks in the hub fairings, hub- and pylon-fairing gaps, pylon-
fairing cross-sectional geometry, pylon-fairing thickness ratio and camber.
Other passive approaches in use include rounding sharp corners, sealing the gaps, use of strakes, and add-on
flow vanes.5-9
These concepts have been extensively studied in the context of automotive and truck aerodynamics.
These concepts are extensively used in industry and found to be helpful in hub drag reduction. Although these
methods have the advantage of being simple, one of their major drawbacks is that they are optimized for a single
design condition.
B. Biologically Inspired Concepts
It is known that aquatic animals are superior to technologies developed by aeronautical engineers in a number of
ways. Dolphins can achieve speed in excess of 10 m/s, while fish can accelerate at rates in excess of 50 m/sec2. A
variety of physical mechanisms contribute to this superior performance. The addition of long polymer chains is
known to reduce viscous drag. The mucus secreted over a fish surface is considered to contribute to the drag
reduction. Sharks and other mammals have riblets on their skin which are known to act as fences that break up
spanwise vortices, reduce skin friction, and decrease momentum loss. Compliant skins, essentially an elastic skin on
top of the underlying dermis are considered effective in damping out instabilities that cause transition to turbulence.
Constructive interference of vortices from the caudal fins of fish has been postulated as enhancing the propulsive
efficiency. Finally leading edge bumps were found to behave like strakes on aircraft and may create vorticity that
constructively interferes with stall and associated drag. For related work the reader is referred to Refs. 10-18.
C. Active Techniques
Active drag reduction concepts attempt to alter the wall shear layer behavior, and have been used in a number of
ways. Coanda jets keep the boundary layer attached to a highly curved surface and may be used to increase lift and
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decrease drag. Figure 1 from Ref. 19 indicates how the trailing edge vortex shedding characteristics of a bluff body
may be modified with blowing. Suction is often used for removal of low velocity reversed flow regions. Blowing
may be used to energize the boundary layer. Blowing and circulation control require an external supply of
compressed air, while suction requires a pump that will remove the low velocity flow and discharge it elsewhere in
the flow. These concepts are thus difficult to employ in the hub region, particularly over rotating components (blade
shank, pitch link, etc).
Zero mass jets (also known as synthetic jets or pulsed jets) have been proposed as an alternative and successfully
used in literature to overcome these requirements. They draw in a low-momentum mass of fluid and expel an equal
mass of high-momentum fluid. This periodic excitation can be achieved with relatively small piezoelectric plates or
electromechanical piston arrangements in cavities located just beneath the body surface. Due to the suction and
blowing, a pair of counter rotating vortices is created which induce a jet like flow away from the surface. This
region is called the synthetic jet. One of the main advantages of synthetic jets is that it does not require complex
ducting systems. Power required to drive these devices is lower compared to the steady blowing or suction.
A very rich body of literature exists in the area of flow control, and even a cursory discussion of these concepts
is not attempted here. Some applications for synthetic jets include improved heat transfer, jet vectoring, enhancing
mixing, and controlling a turbulent boundary layer for drag reduction. This concept has been used for the
modification of the aerodynamic characteristics of bluff bodies,20-22
control of lift and drag on airfoils23-27
, reduction
of skin friction of a flat-plate boundary layer28
, mixing in circular jets29
, and control of internal flow separation30
.
The reader is referred to Ref. 31-38 for additional representative examples.
III. Motivation for the Present Study
The present study aims to investigate the physical mechanisms behind drag reduction for configurations
representative of helicopter components. The first is a NACA 0036 airfoil, representative of shrouds that are placed
around bluff configurations (rotor shaft, blade root shank, etc). The second is a hump shape representative of a pylon.
There are a number of possible causes for drag reduction – energization of boundary layer through momentum
addition (which would cause an increase in the momentum and energy thickness), removal of mass through suction
(which will decrease the displacement thickness and momentum thickness), enhanced turbulence levels causing
improved mixing between the outer layer and the low momentum fluid within the separation bubble, and
manipulation of boundary layer instabilities to promote turbulence and mixing. All these mechanisms, in addition to
reducing the separated flow region, will improve pressure recovery and reduce pressure drag.
The reduction in drag and savings in power (roughly proportional to D times ∞V , where D is the drag and ∞V is
the vehicle forward speed) should be balanced against the power required to operate the active flow control devices.
The power consumption is of the order of ( Jm& times 2
JV times 1/ (2η) whereηis constant that accounts for losses
in the device operation). A secondary objective of this study is to identify the power requirements of these concepts
and determine which of these concepts are most beneficial from a power savings point of view.
IV. Numerical Formulation
The present studies were done using the public domain solver CFL3D39
and using an in-house solver
GENCAS.40-41
Both are multi-zone analyses which solve two- and three-dimensional, time-dependent, Reynolds-
averaged compressible Navier-Stokes equations with an upwind finite-volume formulation. These formulations
employ local time step scaling, grid sequencing, and in the case of CFL3D a multi-grid smoothing algorithm, to
accelerate convergence to steady state.
These analyses output grid and solution files in a standard PLOT3D format which can be read into several post-
processors. The solution file could contain either the primitive variables or the turbulent Reynolds stresses
depending on an input parameter. There are options to output turbulent viscosity as a ‘function’ file which may also
be read into post-processing software. For the present study, the results are post-processed using a commercial flow
visualization software called FieldView. The computational surface is then visualized and several flow field
variables are compared and analyzed. In the case of unsteady flows (e.g. synthetic jets), several sets of solution files
are saved at different phases of cycle. These are processed to obtain a ‘movie’ file to visualize the flow for a whole
synthetic jet cycle.
Displacement, momentum, and energy thickness of the boundary layer before and after the actuation may be
obtained using stand-alone post processing analyses or using Excel. Because these are integral quantities, they may
only be used to monitor the global changes to the boundary layer characteristics, but not the detailed physical
mechanisms underlying these changes. For this reason, these parameters are not discussed in this study.
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As stated earlier, another important quantity to monitor is the power expended by the active flow control devices.
If the power saved is less than the power expended on the device, active flow control would not be an attractive
prospect. The ratio of the power saved by the device to the power used is studied. The power used by the device (Pj)
can be written as
2
2
1JJj VmP &
η= (1)
where η is the efficiency of the device (nominally assumed to be 0.8 in this study), Jm& is the mass flow rate into or
from the active flow control device and JV is the jet velocity. In the case of the synthetic jet devices JV is the root
mean square velocity and Jm& is given by
JJJJ VAm ρ=& (2)
where Jρ is the density of the jet and JA is the area of cross section of the jet slot. In the present two-dimensional
case it is the width or height of the slot per unit span.
The power saved by the device (Ps) may be written as
dos CVcVP ∆= ∞∞∞ .2
1 2ρ (3)
where ∞ρ is the freestream density and ∞V is the freestream velocity. Also, c is the chord and doC∆ is the reduction
in total drag due to active flow control. For the configurations considered here, doC∆ is predominantly due to
pressure recovery affected by the reduction in separation. The ratio of Ps to Pj indicates whether using active flow
control is suitable for any given case. The higher the ratio, the smaller the amount of power required to drive the
flow control device and hence more attractive for commercial use.
In practical applications, other factors enter into the acceptance of these devices. These include the ease with
which these devices may be incorporated in existing and new configurations, their robustness in harsh environments,
and manufacturability. A system of systems approach is needed for designing these devices, where aerodynamic
analyses such as those attempted here form a single but important component.
V. Results
Two cases of separation control have been studied. The first case is that of flow past a thick NACA 0036 airfoil
whose shape is similar to the shroud surrounding a helicopter rotor hub and the second is that of flow over a hump.
This hump is a bluff body reminiscent of a backward facing step. Further description of these cases and the results
obtained are described below. Whenever possible, the computational results obtained have been compared to
experiment.
A. Flow past a NACA 0036 airfoil Two sets of experimental data are available for this case. Initial detailed experiments were conducted in the
NASA Ames Fluid Mechanics Laboratory 32inch-x-4ft wind tunnel. Description of this facility and the measured
results can be found in Ref. 42. Follow on experiments were conducted in the California Polytechnical State
University (San Luis Obispo) 3ft-x-4ft low-speed wind tunnel with the same two dimensional NACA 0036
separation control model of previous experiments. Further details of this experiment can be found in Ref. 43. Both
these experiments showed that there is significant reduction in pressure drag of the airfoil due to the use of synthetic
jets. There has been some CFD effort done in parallel with these experiments by the same researchers and their
associates. 42,44
All present computations are two-dimensional and are done at a freestream Mach number of 0.1352
(approximately twice that of experiment) and a Reynolds number of 0.9 million. A grid sensitivity study was done
for a subset of the cases reported here and is documented elsewhere.45
The results shown here were done on a
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257x129 point C grid shown in Fig. 2. Several turbulence models (Spalart-Allmaras-Detached Eddy Simulation:
SADES, k-ε, and k-w-SST) were used and the results were insensitive to the turbulence model employed for the
prediction of surface pressures and for the drag reduction attributable to the pressure recovery.45
In this work, results
from the k-ω SST turbulence model simulations are used, because of the documented ability of this model to better
resolve turbulent separated flow compared to the other models.
For the baseline no flow control case, computations were performed for α = 0o, 5
o and 10
o. Figure 3 shows the
comparison of Cp distributions for one case, α = 0o, between experimental and computational data
42-44 and the
present CFD simulations. Separation occurs around 82% chord and the Cp distribution flattens out in this region
indicating a loss of pressure recovery, and an attendant rise in pressure drag. The measurements had a slight
asymmetry between the upper and lower surfaces even at zero angle of attack for this symmetric configuration, and
is likely attributable to the installation of the devices on the baseline configuration. The results show a good
comparison between the present CFD results and experiment except in the region of separation. However, it can be
seen that the difference between CFD and experiment is of the order of the difference between the two experiments.
The computed and measured lift (Cl) and (pressure) drag (Cd) coefficients are shown in Figs. 4(a) and 4(b)
respectively. There are considerable differences between the two sets of experiments. Because the forces were
extracted by integrating the surface pressures from sparsely placed pressure taps, these measurements should be
viewed as qualitative rather than quantitative indicators of the pressure drag. The trend of the Cl and Cd curves from
the present study matches well with experiment by Martin et al. The negative lift curve slope at low angles of attack
is an anomaly typical of this particular airfoil. Early CFD results using FLUENT42
were not able to capture this key
behavior, but were later captured by Arad et al44
and the present simulations also capture this anomaly. As the airfoil
is pitched up from α = 0o to α = 5
o the separation on the upper surface increases rapidly which limits the flow
acceleration. On the lower surface, the separation is suppressed and the flow experiences higher acceleration. As α
increases further, suction begins to develop on the upper surface, decreasing the negative lift, and ultimately giving
rise to positive lift.
Given the differences between the experiments, the asymmetry of the flow even at zero angle of attack, and the
sparse placement of the pressure ports in the experiments, it was decided to quantify all the changes to the drag (∆Cd)
relative to the baseline CFD based Cd. To reduce the number of parameters that were changed, the angle of attack
was held fixed at α = 0o.
The NACA 0036 airfoil used has a chord of 2 ft. A 0.06 inch wide slot was simulated at 65% chord in
accordance with the location of the slot in the experiments. Steady blowing, steady suction, and synthetic jet
computations were all performed at this angle of attack. The synthetic jet device was found to be most effective in
terms of drag reduction, and had the lower power required among competing concepts. For brevity, the steady
blowing and suction cases are not reported here. Computations were done for mean momentum coefficient (Cµ)
values of 0.001, 0.0023, 0.004, and 0.0086. The last three values have been chosen to match the mean Cµ of
experiment for the synthetic jet case.
As seen Fig. 5(a), a steady reduction in (time-averaged) pressure drag is achieved as Cµ is increased. Flow
visualization studies indicate that the trailing edge separation is reduced and eventually eliminated. The pressure
drag even for the smallest Cµ simulated is less than that in the baseline case. On the other hand, as shown in Fig.
5(b), the (time-averaged) skin friction drag increases with Cµ as the shear layer reattaches to the solid surface.
However, the time-averaged total drag coefficient in the case of the synthetic jet case is still less than the baseline
value. For a mean Cµ = 0.004, for zero degree angle of attack, experiment shows a pressure drag of approximately
0.026 for the synthetic jet case, which is within 5% of the CFD result. Also, for this Cµ there is a 19% decrease in
drag compared to the baseline CFD case.
Now, the flow field is examined to study the mechanism behind this drag reduction. A comparison of the Mach
number contours, in Fig. 6, shows that with increase in mean Cµ the low Mach number region progressively
decreases. This indicates that the momentum of the flow is increased from the baseline case due to the synthetic jet.
Higher Cµ causes a greater increase in momentum of the flow.
In order to analyze the effect of synthetic jet on turbulence quantities in the flow, comparison of non-dimensional
turbulent kinetic energy (k), and non-dimensional turbulent eddy viscosity (µT/µ∞) with the baseline CFD results
were made. Figure 7 shows the k contours for the baseline case and for the synthetic jet cases with a mean Cµ of
0.004 and 0.0086. It is seen that the k decreases with increase in Cµ, with an attendant reduction in the turbulent
eddy viscosity levels as shown in Fig. 8. This is to be expected since the eddy viscosity is proportional to k2. Note
that the separation is almost fully eliminated for Cµ = 0.0086, while the eddy viscosity levels are much lower than in
the baseline case. It thus appears that the reduction in the separation region and the attendant improvement in
pressure recovery is not attributable to increased turbulence levels at least at this angle of attack. Examination of the
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flow field revealed that some of the low momentum fluid within the separated region is removed by the device
during the suction portion of the synthetic jet cycle. This is followed by injection of high velocity flow into the
boundary layer causing energization during the blowing portion of the cycle. The overall effect is to replace the low
velocity reversed flow in the separated region with high velocity higher Mach number flow by the synthetic jet
device.
In order to assess if the synthetic jet concept is viable option for commercial rotorcraft, the ratio of the power
saved due to synthetic jet devices to the power used by AFC is calculated for each Cµ. As expected, the power saved
by the device decreases with increase in Cµ, as shown in Fig. 9. It should be noted that this decrease is not linear.
The efficiency of the device η (viewed as the ratio of power of synthetic jet to the electrical power supplied to the
device) is assumed to be 0.8. At low Cµ the power saved by the jet is a much higher fraction of the power consumed;
hence it is advisable to use jets at low Cµ, which also reduce the drag considerably, compared to their higher Cµ
counterparts. As Cµ increases the disadvantage due to the increase in power consumed outweighs its usefulness in
drag reduction.
B. Flow over a hump model
A second case representative of the region aft of pylons on helicopters is the ‘Flow over a Hump Model’ case. A
CFD validation workshop on synthetic jets and turbulent separation control (CFDVAL2004)46,47
was held in March
2004 in Williamsburg, VA. The purpose of this workshop was to assess the current capabilities of different classes
of turbulent flow solution methodologies to predict flow fields induced by synthetic jets and separation control. This
configuration is one of the three cases documented in this workshop. As a result, a large body of detailed simulations
is available for this configuration, in addition to test data.
In the test case and the present study both, the freestream Mach number was 0.1 and the Reynolds number based
on the 420 mm chord of the hump was 0.936 Million. The grid, shown in Fig. 10, is non-dimensionalized with
respect to the chord and extends up to 6.39 chords upstream and approximately 4 chord lengths downstream of the
hump. The grid used in the present study is the ‘Structured 2D Grid #5’, obtained from the NASA website46
. The top
wall of the geometry has been adjusted to approximately account for side plate blockage found in the experiment.
The hump surface has a synthetic jet unit (cavity) attached to it at 65% chord. This slot has an opening (vertical) of
0.00187c. Both the external flow and the flow within the cavity were modeled. As in the NACA 0036 case, the k-ω-
SST turbulence model was used.
First, the baseline case was modeled with the bottom wall of the cavity closed so that no air flows through it.
Figure 11 shows comparisons between computed and measured surface pressure distribution (Cp) over the hump.
Good agreement is seen between the measurements and the predictions. Separation was found to start around 0.6545
chord in CFD against 0.66-0.67 chord of experiment. The reattachment point predicted by CFD is around 1.24 chord
which is much further than 1.11 chord predicted by experiment. Most CFD data documented at the Williamsburg
Workshop had a similar discrepancy. This may be due to the low levels of turbulent viscosity predicted by the CFD
turbulence model in the separation region as shown by the non-dimensionalized Reynolds shear stress ''vu , in Fig.
12. Although the qualitative behavior of the Reynolds shear stress is good with experiment, the magnitude is
underpredicted.
Next, active flow control was simulated. Steady suction and synthetic jet concepts were explored. For the steady
suction case, mass was removed at the bottom of the cavity at a rate of 0.01518 kg/s out of the domain. The Cp
distribution for this CFD case again is in reasonable agreement with experiment everywhere except the separated
region, as shown in Fig. 13. Figure 14 shows the Reynolds stress variation across separated flow region at three x/c
locations. As in the baseline case, the computed Reynolds stress levels were lower than those measured. This
influenced the prediction of pressure recovery and the reattachment point, both. For this case the separation occurs at
x/c = 0.6618 in CFD while experiment predicts a separation between x/c = 0.675 and 0.685. The reattachment point
predicted by CFD is at x/c = 1.19 which is further downstream of that predicted by experiment, x/c = 0.94. Note that
the Reynolds shear stress values are lower in the steady suction case compared to the no flow control case,
indicating that for this case the decrease in separation is due to the removal of the low momentum fluid due to
suction.
Finally, the synthetic (oscillatory) jet case was simulated in CFL3D by imposing a sinusoidal velocity boundary
condition at the bottom wall of the cavity. This jet has a frequency of 138.5 Hz and a peak velocity of 26-27 m/s.
Further details of the CFD setup can be found in the paper by Rumsey48
. As shown in Fig. 15, the Cp distribution
agrees very well with experiment up to the slot location, but as in the previous cases, the agreement is not good in
the separated flow region. The reattachment takes place earlier than that predicted in the no control or even the
steady suction case showing a decrease in the separation region, an improvement in pressure recovery compared to
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the baseline case, and an attendant decrease in the drag. As in the case of the NACA 0036 case studied earlier, this
could be because of a dual mechanism taking place in the case of the synthetic jet compared to the suction case.
Both concepts remove the low momentum fluid due to suction. Only the synthetic jet subsequently adds high
momentum fluid into the flow.
A comparison of the Reynolds shear stress with experiment at a phase of 260o of the synthetic jet cycle is shown
in Fig. 16. Although the instantaneous values of Reynolds shear stress for this particular phase are greater than the
corresponding parts in the suction and baseline cases, the time averaged values are smaller as shown in Fig. 17. This
is consistent with the findings from the NACA0036 case described previously. To confirm the conjecture that the
increase in momentum of the flow due to the jet is a probable cause for drag reduction, comparison of Mach number
contours are shown in Fig. 18. The higher Mach numbers with the synthetic jet device are in support of this
conjecture.
The pressure distribution over the hump shape has been integrated, from x/c = -0.5 to x/c = 1.5, to extract the
pressure drag forces. Because this is not a finite geometry (as in the case of airfoils) absolute drag values are not as
interesting as the trends themselves. The bar graph in Fig. 19 shows the comparison of pressure drag between the
baseline, suction and synthetic jet cases. The pressure drag coefficient has been non-dimensionalized with the
baseline pressure drag. Hence the graph shows the decrease in pressure drag due to active flow control for the hump
case. It can be seen that there is a decrease of around 11% and 14% in drag from the baseline to the suction and
synthetic jet cases respectively. While the decrease from the suction case to the synthetic jet case is only around 3%,
it should be noted that the mean Cµ in the synthetic jet case shown is slightly less than that for the suction case. In
addition, the energy required to drive the piezoelectric actuator in the former case is much lower than in the latter
case, making the use of synthetic jet devices more advantageous.
Now, the amount of power consumed by the two active flow control cases is examined. The ratio of power saved
by the steady suction jet to the power consumed by it is 25.0 whereas that for the synthetic jet is 37.0. Note that
efficiency has been assumed to be 0.8 for comparisons. In other words, with a small 2% to 3% expenditure in power,
substantial savings in the power consumption associated with drag may be achieved. While both approaches were
successful, the increased reduction in drag, the lower power required, and the elimination of suction pumps, make
synthetic jets a more attractive drag reduction device compared to steady blowing jets for this configuration.
VI. Conclusions and Recommendations
Two cases of separation control have been studied. One is of flow past a thick NACA 0036 airfoil whose shape
is similar to that of a helicopter rotor hub and the second is that of flow over a hump model which is a bluff body
reminiscent of region aft of a pylon. For the NACA 0036 case baseline and synthetic jet simulations have been
performed and compared to experiments wherever possible. Synthetic jet was simulated at four different momentum
coefficient values. The drag reduction increases with increased Cµ. However the energy consumption by the jet
increases drastically with the increase in Cµ, and lower Cµ values were found to be more attractive.
Next, the flow over a hump model was simulated. In this case steady suction and synthetic jet were simulated,
and drag reduction was observed. It was noticed that the power consumed by the synthetic jet is less compared to the
suction case although the reduction in drag is more in case of the synthetic jet. Hence it is concluded that synthetic
jets are more effective in drag reduction compared to steady jets.
In the airfoil as well as hump case the flow field along with turbulent quantities was examined. From this it was
concluded that the main reason for reduction in drag is the removal the low momentum fluid by the jet during the
suction portion of the cycle, followed by energization of the flow during the blowing phase. Contrary to expectations,
this reduction in the extent of separation could not be traced to improved mixing due to turbulent eddies as measured
by the Reynolds stress and turbulent kinetic energy levels.
Even the most sophisticated turbulence model used in this study was unable to accurately model the eddy
viscosity levels within the separated region. Other researchers who have studied these configurations have reported
similar difficulties, even with LES and DNS models. There is thus a need to develop new turbulent models which
would correctly predict the turbulent viscosity observed in experiment.
Acknowledgments
This project was funded by the U. S. Army under the Vertical Lift Research Center of Excellence (VLRCOE)
program managed by the National Rotorcraft Technology Center, Aviation and Missile Research, Development and
Engineering Center under Cooperative Agreement W911W6-06-2-0004 between Georgia Institute of Technology
and the U. S. Army Aviation Applied Technology Directorate. Dr. Michael Rutkowski is the technical monitor. The
authors would like to acknowledge that this research and development was accomplished with the support and
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guidance of the NRTC. The views and conclusions contained in this document are those of the authors and should
not be interpreted as representing the official policies, either expressed or implied, of the Aviation and Missile
Research, Development and Engineering Center or the U.S. Government.
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