MAV Propulsion System Using the Coanda Effect

AIAA 2009-4809
45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
2 - 5 August 2009, Denver, Colorado
MAV propulsion system using the Coandǎ effect
M.J.T. Schroijen,∗ M.J.L. van Tooren
†
Delft University of Technology,
Faculty of Aerospace Engineering,
Department of Aerospace Design Integration and Operations,
P.O.Box 5058 2600 GB, Delft, The Netherlands
In an effort to to fill the micro aerial vehicle (MAV) performance gap between efficient
cruise (fixed wing) and hover (rotary), a Coandǎ type propulsive platform is proposed. A
jet, deflected by a curved surface is used for hover, while the curved surface can also be
used as a wing for efficient cruise. The principles allowing the attachment of the flow are
not clear and therefore efficient sizing of the surface and jet is difficult. For this purpose
design rules are proposed and validated by Reynolds averaged Navier-Stokes and latticeBoltzmann models.
The efficiency of converting the jet into thrust was in the order of 60 to 80 percent with
respect to the predicted ideal thrust for the tested configurations. The correspondence in
predicted and calculated pressure coefficient for circular surfaces was adequate, with the
exception of the expansion of the jet and the stagnation point at separation. Measurements
are, therefore, still needed for further validation of the computations.
I.
Introduction
For Micro Aerial Vehicles (MAV), meaning with dimensions smaller than 70 cm, several propulsive
concepts exist: fixed, rotary and flapping wing. Fixed wing aircraft are most efficient on long range missions.
Getting to an observation area is therefore not a problem, however, they lack the capability to hover, making
observation of a single spot more complex. Rotary wings on the other hand have the opposite problem. The
third category, flapping wing aircraft, are currently limited to small sizes and employ a complex system of
moving parts.
Efficient flight over long distances, hover capability and a limited number of moving parts might be achieved
by the propulsion system proposed by Coandǎ. His vision was an aircraft based on different flying principles:
“These airplanes we have today are no more than a perfection of a toy made for children to
play with. My opinion is we should search for a completely different flying machine, based on
other flying principles. I consider the aircraft of the future, that which will take-off vertically, fly
as usual and land vertically. This flying machine should have no parts in movement.”
His proposal was to use the Coandǎ effect to provide vertical thrust and hover capability. This thrust should
be produced by a jet of air being curved by a surface (Coandǎ effect) from horizontal downward. The surface
used for curving the flow could then also be used to fly horizontally like a normal aircraft. MAV’s of this
type already exist,1, 5 however little is known about the principles and the performance of this system. The
intent is therefore to design and build a demonstrator model to show the capabilities of this propulsion
system. To be able to design such a novel propulsion system the performance has to be quantified. To
quantify this performance the efficiency of the concept and required lift in hover are investigated by means
of mathematical models.
The goal of this paper is to investigate the principles and design rules used to achieve the performance
required for the demonstrator MAV. The focus will be on the hover performance, as the lift requirements
∗ Ph.D.
Student, [email protected]
[email protected]
† Professor,
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American
Institute
of Aeronautics
and Astronautics
Copyright © 2009 by M.J.T. Schroijen. Published by the American
Institute
of Aeronautics
and Astronautics,
Inc., with permission.
will probably determine the sizing of the on-board power. No attempt has been made as yet to evaluate the
transition phase between hover and cruise.
The opportunities of the Coandǎ propulsion concept for a MAV are investigated in the next section. This
is done by investigating the requirements of MAVs, in particular lift and power. Momentum evaluations are
elaborated with Euler, RANS and lattice-Boltzmann models. These results are compared to a preliminary
wind tunnel test to investigate the validity of these models. Finally conclusions are drawn about the models
and recommendations are given for future work.
II.
Coandǎ MAV demonstrator
Current MAVs perform several functions, but are mainly used for observation tasks. Most of them
therefore consist of a platform carrying a payload. This payload usually consists of sensors for the observation
task and is (ideally) interchangeable so the MAV is able to fulfil various different missions.2 The platform has
the task of transporting this payload to the desired location and stay there for the needed observation time
as efficiently as possible. The choice and performance of the propulsion system is a key factor in unmanned
aerial vehicle (UAV) and MAV design.7 A general mission of a MAV can schematically be represented by
the phases shown in Figure 1.
Pre launch
check
/ Launch
_
/
_
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Fly toward
/ Observe
/ Fly back target area
target
to base
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
/ Land
Figure 1. General mission profile of a MAV.
Two important flight phases can be identified; a (long distance) flight phase to and from the target area and
an observation flight phase (Figure 2). The take-off and landing phase are not included as most MAVs are
launched, either by hand or external system. The platform options currently employed are the fixed wing
aircraft and the rotary wing aircraft. Both are efficient in one of these flight phases. The fixed wing MAV
Perform mission
SSS
m
m
SSS
mmm
SSS
m
m
m
SSS
m
m
SS)
mv mm
Perform flight
Perform Navigation
Perform Observation
OOO
OOO
OOO
OOO
'
Hover
Cruise
Observation flight
Figure 2. Functional breakdown focussing on the MAV platform.
usually lacks the capability to hover, making the observation task more difficult. The rotary wing MAVs, on
the other hand, are usually less efficient in forward flight. Flapping wing aircraft are a positioned in between
with respect to performance, however, are complex due to the large number of moving parts. This is shown
schematically in Figure 3. The expected efficiency in both flight phases of the Coandǎ plane is also shown.
Coandǎ propulsion system The Coandǎ propulsion system might be able to provide both an efficient
cruise phase as well as hover capability. This propulsion system uses a “jet” of air which is deflected downward
using a curved surface. In this way lift is generated to hover. This curved surface is used as a regular wing
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Fixed wing
Cruise efficiency
Coanda
Flapping wing
Rotary wing
Hover/ observation efficiency
(b) Proposed test model to determine the lift capability
and installed power needed for a Coandǎ type MAV.
(a) Expected efficiencies in both flight phases of a general
MAV mission.
Figure 3. Coandǎ type MAV.
in horizontal flight. The performance in hover should be at least equal to that of a helicopter and in forward
flight at least equal to a fixed wing aircraft. The propulsion system proposed for the MAV consists of an
engine which accelerates air into a tube with a slot at the side where air can be expelled and blown over the
wing (Figure 3). The air is deflected by the curved wing, creating lift even during hover. In hover the tube is
closed on one side. In forward flight the end of the tube can be opened providing a thrust in flight direction.
The diminished air flow over the wing, and with it the diminished lift, is compensated by “normal” fixed
wing lift.
III.
Performance of the propulsion concept in hover
For a better understanding of the sizing of the Coandǎ MAV and required power several conceptual tools
were created. First a two dimensional momentum analysis was performed in order to identify the design
parameters. This analysis also proved to be a useful tool for a better understanding of the principles behind
the technology. The simple model was extended by a two dimensional Euler model which was compared to
a wind tunnel test.
Performance analysis
u
h
w
V
α
Figure 4. Schematic of the control surface used.
The proposed Coandǎ propulsion system mainly operates by deflecting the impulse of ingested flow
downward over a curved surface. This deflection results in a lower static pressure over the upper side
resulting in a force perpendicular to this surface based on the change of momentum of the flow. As an initial
sizing the momentum equations are used while assuming that the initial jet flow can be created (e.g. rocket,
jet engine or propeller). The force on a control volume of fluid can be written,3
Z
Z
d
Ff =
(mV) = (ρV · ds) V + pds
(1)
dt
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rewriting for the control volume shown in Figure 4 and using continuity of mass,
"
#
"
# ! Z
u
u
Ff = −ρuh
−
+ pds.
0
−v
in
(2)
out
Furthermore assuming a frictionless flow and subsequently a uniform outflow separating at the sharp edge
of the curve and perpendicular to the control surface. This allows the assumption that the force on the fluid
is only caused by the pressure on the curved section of the wall as the outside of the jet has a pressure equal
to the static pressure. The pressure integral is therefore included in the fluid force term,
#
"
#!
"
h
sin
α
1
.
(3)
Ff = −ρhu2in
−
w − cos α
0
The jet velocity is assumed to be uniform uin = Vj resulting in an equation for the lift (y-direction), solely
dependent on the outflow angle, jet velocity and dimensions of the jet slot,
L=ρ
h2 2
V cos α.
w j
(4)
For a given lift the jet slot height, w is assumed to increase due to viscous effects, in particular boundary layer
formation and subsequent non-uniform velocity profile at the outflow of the control volume. Furthermore,
the flow may separate before the end of the curve, reducing the deflection angle of the flow and subsequently
the produced lift. To account for these effects an efficiency parameter is introduced,
Lact = ηT Lid
(5)
This factor ηT is most likely a function of the geometry of the surface and can be regarded a measure for
the efficiency of converting the jet mass flow into lift by the surface.
Power needed in hover The previous paragraph indicated the maximum amount of lift that could be
produced by a certain jet and flow deflection. The minimum power needed to produce this lift is compared
to for example the power required for a similar helicopter configuration. The power needed to create the
velocity at the jet outlet is approximated by the momentum of the flow times jet velocity,
Pr =
1
ρAVj3
2
(6)
The assumption has been made that the fluid could be accelerated without energy losses and is therefore a
minimum value. The weight of the vehicle is W in Newton and using the previously derived relation for the
lift, then gives for hover,
W =
hlρVj2 cos α
L
=
ηT
ηT
(7)
which results in a minimum power requirement of
1
Pr =
2
s
ηT3 W 3
,
ρhl cos3 α
(8)
indicating that the power needed for hover decreases with increasing area of outflow (mass flow). For the
Coandǎ plane this means increasing the height or length of the mass flow injector. Comparing to the power
required by a helicopter to hover
s
Pr =
W3
2ρπR2
(9)
indicates that the minimum power (ηT = 1) to produce a certain lift for a given mass flow is twice the power
needed for a helicopter. The comparison does, however, not include the method of creating the jet of the
Coandǎ plane.
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Euler model
To achieve a better understanding of the pressures on the curved surface, a 2D Euler model has been created
and compared to wind tunnel test results. The Coandǎ effect is assumed to be caused by viscous effects
between the jet and wall flow. The jet flow “drags along” the flow attached to the surface creating a mass
deficiency and subsequently a pressure decrease and the flow curves towards the surface. Assuming a nonviscous flow, therefore requires prescribing that the flow attaches to the surface.3 The momentum equation
in polar coordinates and radial direction is given by,
∂ur
∂ur
uθ ∂ur
u2
∂p
+ ur
+
− θ =− .
(10)
ρ
∂t
∂r
r ∂θ
r
∂r
∂
∂
Furthermore, assuming steady flow ∂t
= 0 about a circular arc ∂θ
, ur = 0 with a constant angular
velocity uθ = Vj gives
u2
∂p
(11)
−ρ θ =− .
r
∂r
Integrating this equation from R to R + h while assuming the pressure of the outer boundary of the jet to
be equal to the static pressure, gives the pressure at the boundary. The velocity of the jet is used to make
the pressure coefficient dimensionless,
cp
=
−2 ln
R+h
R
(12)
For a constant curvature and ideal (frictionless, incompressible) flow the pressure coefficient is constant along
the surface and only dependent on the radius of curvature and height of the jet velocity.
(a) TecQuipment AF10 Airflow bench
(b) Test Section
Figure 5. Preliminary test setup.
Comparison with preliminary measurements The preliminary test was performed in a TecQuipment
AF10 Airflow Bench (Figure 5), a simple wind tunnel at the Delft University of Technology. The wind
tunnel produces a uniform laminar flow of 34 meters per second through a nozzle of 0.10m by 0.05m (w × h).
The test section, shown in Figure 5, consisted of a circular curved plate of radius 0.31m with two squared
side plates. The side plates act as end plates to be able to assume a two dimensional flow. Furthermore,
the measurements were corrected for gravity as the used test section was mounted vertical. The pressure
coefficient calculated by the Euler approximation was found to be −0.299 (R = 0.31, h = 0.05).
The results of both the Euler approximation and the tests are shown in Figure 6 and show that in contrast
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0.1
Measurements
Euler
0.05
0
Cp
−0.05
−0.1
−0.15
−0.2
−0.25
−0.3
0
0.05
0.1
0.15
0.2
0.25
0.3
x [m]
Figure 6. Test results of the preliminary test.
with the Euler simulation the pressure coefficient is not constant over the surface. In the first region of the
curve the pressure coefficient decreases rapidly due to the settling of the flow. After this initial phase the
pressure coefficient is reasonably constant. The maximum pressure coefficient is about half the value of the
Euler approximation which is probably due to formation of a boundary layer. For the jet height radius ratio
h
= 0.16 the thrust efficiency therefore equals 0.5 for the two dimensional case.
of R
Viscous fluid models
h
R
3/2R
R
Figure 7. Dimension of the jet nozzle and quarter circle and ellipse used for the RANS and LB model.
To investigate the difference between the experiments and the Euler model further viscous effects are
to be included. Therefore, a Reynolds average Navier-Stokes (RANS) model as well as a lattice-Bolzmann
model were created. For the RANS model a quarter cylinder and ellipse were modeled as shown in Figure
7. The semimajor axis to semiminor axis ratio for the ellipse was chosen to be 3/2.
Reynolds averaged Navier-Stokes model Two models, one circle and one ellipse, were created and
evaluated by the Fluent® flow solver.4 The jet velocity per radius (Vj /R) was varied between 0.5 and
50, resulting in Reynolds variation of 2000 to 200000, based on R and Vj . These various jet velocities gave
marginally different flow fields. Velocity magnitude contours are given in Figure 8 for the circle configuration
and in Figure 9. The average jet velocity seems to remain higher for larger initial velocities before separating
at the sharp edge. This is the case for both the circle configuration as well as the ellipse, showing that
both configurations are potential candidates for the Coandǎ design. This can be seen as well in Table 1
where the non-dimensional forces show an increase with jet velocity. Changing from a circular curve to a
ellipse increases the efficiency, which implies that reducing curvature benefits the efficiency of converting
thrust into lift. Increasing the jet height and therefore the mass flow decreases the efficiency, probably as
due to boundary layer formation the curvature of each subsequent radial position decreases. The pressure
distributions shown in Figure 10, show that the trend of the measurement described in the previous section
is resembled by the RANS results for the circular section: the circular pressure distributions show a large
adverse pressure gradient towards the lower stagnation point, resulting in a deceleration of the flow and
subsequent decrease in lift. Using the Euler formula for the pressure coefficient for this configuration, a
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(a) Vj /R = 5
(b) Vj /R = 50
Figure 8. RANS velocity magnitude contours (m/s) for the circle configuration.
pressure coefficient of −0.15 (h/R = 0.075) is obtained which is also found from the RANS model, except
from the initial flow settling and the final stagnation point.
Table 1. Non dimensional force per unit of length for various jet velocities. The values in bracket denote the
thrust efficiency ηT .
h/R
Circular
Ellipse
0.075
0.150
0.075
0.150
Vj /R
0.5
0.018(0.60)
5
0.020(0.67)
0.043(0.72)
0.022(0.73)
0.039(0.65)
25
0.024(0.80)
0.040(0.67)
50
0.023(0.77)
0.043(0.72)
0.024(0.80)
0.043(0.71)
Lattice-Boltzmann model The jet flow was also modeled by an in-house created lattice-Boltzmann
model (LBM). The discrete lattice-Boltzmann equation is solved by the Bhatnagar-Gross-Krook approximation,6
fa (x, t) − faeq (x, t)
fa (x + ea ∆t, t + ∆t) = fa (x, t) −
(13)
τ
which consists of a streaming and a collision (most right) term. The distribution function f eq is defined as
!
2
2
9
e
u̇
3
u
e
u̇
a
a
−
(14)
faeq (x) = wa ρ(x) 1 + 3 2 +
c
2
c2
2 c2
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(a) Vj /R = 5
(b) Vj /R = 50
Figure 9. RANS velocity magnitude contours (m/s) for the ellipse configuration.
0.15
Circular, V/R 5
Circular, V/R 50
Ellipse, V/R 5
Ellipse, V/R 25
Ellipse, V/R 50
0.1
Cp [−]
0.05
0
−0.05
−0.1
−0.15
−0.2
0
0.5
1
1.5
y/R [−]
Figure 10. Pressure coefficient distributions, non-dimensionalized by the jet velocity.
and the relaxation factor dependent on the kinematic viscosity. For the chosen D2Q9 scheme, shown in
Figure 11, the weight factors wa are shown in Table 2
The computation was performed on a grid of 1000 by 1000 nodes. For the stability of the computation
this grid limited allowable computation to Reynolds numbers of 2000 and the subsequent inflow velocity for
the configuration of interest to 0.1 meters per second, which is much lower than needed for the generation of
sufficient lift. The main reason of the creation of the model was, however, the investigation and understanding
of the interaction of the jet and the curved wing surface, which is represented by the model.
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2
5
3
0
1
7
4
6
8
Figure 11. Schematized principle of the D2Q9 lattice-Boltzmann grid.
Table 2. Node weight values.
Node
wa
ex
ey
0
4/9
0
0
1
1/9
1
0
2
1/9
0
1
3
1/9
-1
0
4
1/9
0
-1
(a) 30000 steps
5
1/36
1
1
6
1/36
-1
1
7
1/36
-1
-1
8
1/36
1
-1
(b) 60000 steps
Figure 12. Flow pattern as calculated with the lattice-Boltzmann model, showing the velocity magnitude
Comparison Both simulations show a similar flow pattern in which the flow is attached to the surface,
meaning a jet with limited variation in thickness. Due to the limitation of the LBM to a Reynolds number of
2000 the jet velocity was limited to values lower than necessary for lift and modeling of realistic flow patterns
was therefore impossible. However, the RANS model showed that increasing the jet velocity shows marginal
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variation in flow patterns. The stagnation point, located at the end of the curve, considerably decelerates
the flow, creating a possibility for further increasing the obtained lift. This potential is limited, however, as
the pressure forces have a limited contribution to the vertical force. This therefore creates the ideal position
for control surfaces for lateral control.
IV.
Conclusion
The Coandǎ propulsion concept is intended to fill the efficiency gap between the rotary wing and fixed
wing micro aerial vehicles (MAV). It should have the capability to hover efficiently as well as cruise efficiently.
This puts the concept in direct competition with the flapping wing MAVs, however the Coandǎ propulsion
concept could benefit from the reduced number of moving parts.
Calculations and a preliminary wind tunnel test have been performed in order the gain a better understanding of the Coandǎ effect. The preliminary wind tunnel test and Euler computation showed a difference in
pressure coefficient of a factor 2, which is probably caused by viscous effects, like boundary layer formation
and separation. This was also shown by the RANS model. Which showed a similar flow pattern as the
lattice-Boltzmann model. The latter was limited to a Reynolds number of 2000 for calculation time reasons.
The results of the RANS model are therefore assumed to be a good representation of reality.
The main design parameters investigated for the Coandǎ platform were the nozzle height, the factor semimajor axis to semiminor axis and jet velocity. Increasing nozzle height appeared to have a decreasing effect
on the efficiency, whereas increasing the factor semimajor axis to semiminor axis and jet velocity had an
efficiency increasing effect.
The Coandǎ propulsion platform is therefore a feasible option considering lift and power in hover, as long
as the necessary jet can be produced.
References
1 http://www.gfsprojects.co.uk .
2 http://www.uavnet.com.
3 J.D.
Anderson, Jr. Fundamentals of aerodynamics. McGraw Hill, second edition, 1991.
Fluent Inc.
5 J.N. Audin. http://jnaudin.free.fr.
6 M.C. Sukop and D.T. Thorne. Lattice-Boltzmann modeling. Springer Berlin, 2007.
7 S. Tsach, J. Chemla, and D. Penn. UAV systems development in IAI past, present and future. Report AIAA 2003-6535,
American Institute of Aeronautics and Astronautics, 2003.
4 ANSYS,
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