Numerical simulations of turbulent flow around a distributed
propeller wing
António Salreta
Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal
November 2016
Abstract: New advances in electric propulsion have been encouraging new studies in aeronautic propulsion.
A new field of study that shows great promise is distributed electric propulsion (DEP). The present work aims
to study the effects of changes of the propellers in a DEP aircraft. This study looks at the effects in lift and
drag coefficients of the aircraft and is divided in three parts: changes made to the geometry and power of
the propellers, changes made to the inflow velocity and changes in the number of propellers working. The
CFD program used for this work is STAR-CCM+, where RANS simulations were run using SST K-Omega
turbulence model. The mesh generation and mesh refinement are also included in this work, as well as the
creation of a performance curve for the propellers from the program JavaProp. Leading edge position
changes are not big enough to influence differences in lift and drag, while differences in diameters and power
lead to some interesting conclusions. Inflow velocity is a big influential factor for DEP aircrafts. Propellers
close to the tip of the wing show more influence on lift.
Keywords: Distributed electric propulsion, lift and drag coefficients, STAR-CCM+, RANS, SST K-Omega,
JavaProp
-----------
Introduction
Electric engines are a good
alternative to combustion engines. These
have many benefits including good
efficiency, low noise and high reliability.
However the most interesting characteristic
of electric engines is the possibility of
producing smaller engines and locating
them in strategic places of the airplane. This
way aircraft designers and engineers have
more design freedom, creating vastly
different designs without being restrained by
the weight and volume of the actual
combustion propellers. Some early concepts
of turboelectric distributed propulsion
vehicles with subsonic fixed wing show
promise for better efficiency and noise
reduction. N3-X is a NASA’s project that predicts the combination of a blended wing
body configuration and distributed
propulsion system produces a 70% fuel-burn
reduction relative to a B777-200LR
reference aircraft [1].
Distributed electric propulsion (DEP)
has shown great promise especially in light
weight aircrafts. In this design many small
propellers are distributed along the span of
the wing increasing dynamic pressure, and
facilitating of flight at lower velocities
excluding the need for multi-element high lift
devices. While being a promising design,
this brings higher structural complexity.
Variable pitch loading can be achieved by
controlling individual propellers, making it
easier to optimally match the needs of the
aircraft. It is also a redundant and robust
system that can be advantageous in case of
engine failure.
This work aims to study the
influence of inflow conditions as well as
parametric changes made to the electric
propellers for a DEP small man-controlled
airplane. This plane is entitled of Silent Air
Taxi (SAT).
Configuration Description
SAT’s configuration was inspired by
NASA’s SCEPTOR configuration, following
the same idea of distributed propellers. In
this case the airplane geometry is presented
in figure 1 and the configurations in table 1,
showing five smaller identical propellers
distributed along the span of the wing, and
one bigger propeller at the tip (this refers
only to one wing). The number of propellers
was already chosen and quantity of
propellers was not tested. The reason for the
location of the propellers in front of the
leading edge compared to locating them
behind the wing is for favourable pitching
moment, acoustic, cruise drag and structural
complexity [2].
Comparisons were made to Cirrus SR22, Cessna 172R and Tecnam P2006T airplanes because these represent the current state of the art for this class of aircraft and share a similar wing span (table 2). Propeller configurations are displayed in table 1. These propeller were chosen to have the same characteristics as pre-existing propellers. Simulations were done only to one wing taking advantage of symmetry and excluding the fuselage to be less computationally demanding. The geometry was tested without flap.
Figure 1 - SAT's geometry
Objectives
To study changes in lift a reference
configuration was chosen as the starting and
comparison point for the other simulations,
while the whole geometry remained
constant. Only numerical simulations were
done. Different speeds were tested, for
cruise at 110.6 m/s and take-off/landing
31.38 m/s. Parametric changes to the
propellers were made to the diameter,
distance to the leading edge and power of
the engine. These were tested for higher
velocity (110.61 m/s) to produce higher
differences. While to study the influences of
each inner propeller, the simulations were
made for an inflow velocity of 31.38 m/s. To
do these last simulations these propellers
were switched off one by one.
Mathematical models
RANS simulations were performed using the
commercial program STAR-CCM+. Both
mesh generation and simulations were
accomplished using this program. SST
(Menter) K-Omega was the turbulence
model because it behaves well in adverse
pressure gradient, and solves the flow inside
and outside the boundary layer with
relatively accuracy.
SST (Menter) K-Omega model is a hybrid of
two other models using K-Omega in the
inner boundary layer and K-Epsilon in the far
field. Using the following equation to
calculate the turbulent viscosity:
𝜇𝑡 = 𝜌𝑎1𝑘
𝑚𝑎𝑥(𝑎1𝜔,𝛺𝐹2) ( 1)
where 𝑎1 is a constant, Ω is the absolute value
of the vorticity, and 𝐹2 is a function that is one
for boundary-layer flows and zero for free
shear layers. 𝑘 and 𝜔 are calculated by two
transport equations. [3]
Wall laws for this wall treatment are chosen
automatically based on the behaviour of the
turbulence model. For this case, blended wall
laws are used, which include a buffer region
that smoothly blends the laminar and the
turbulent profiles together.
The axial force and normal force on a surface
are computed by the Star-CCM+ as:
𝑓 = ∑ (𝑓𝑆𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 + 𝑓𝑆
𝑆ℎ𝑒𝑎𝑟). 𝑛𝑓𝑓 ( 2)
𝑓𝑆𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = (𝑝𝑓 − 𝑝𝑟𝑒𝑓)𝑎𝑓 ( 3)
𝑓𝑆𝑆ℎ𝑒𝑎𝑟 = −𝑇𝑓𝑎𝑓 ( 4)
where 𝑓𝑆𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 and 𝑓𝑆
𝑆ℎ𝑒𝑎𝑟 are the pressure
and shear force vectors on the surface face S,
𝑛𝑓 is the direction defined by the user, 𝑎𝑓 the
face area vector, 𝑝𝑓 if the face static pressure,
Inner Tip
Number of Blades 5 3 Design RPM 4000 3000 Outer diameter 0.75 m 1.5 m Inner diameter 0.056 m 0.292 m Airspeed (m/s) 110.6 Power (kW) 20 50 Airfoil MH 114 13% Re =
500 000
Table 1 - Propellers' configurations
𝑝𝑟𝑒𝑓 is the reference pressure, and 𝑇𝑓 is the
stress tensor at face 𝑓.
Table 2 - Comparison of reference configuration with similar plane
Numerical approximations
Segregated flow model was chosen,
with second order convection and diffusion.
This solves the flow equations (one for each
component of velocity, and one for pressure)
in a segregated or uncoupled manner. The
linkage between the momentum and
continuity equations is achieved with a
predictor corrector approach. This model also
solves the total energy equation with the
temperature as the solved variable. Enthalpy
is then computed from temperature according
to the equation of state. In this case the
equation of state is given by the ideal gas
theory.
Propeller model
For simulating the propellers, a
virtual disk was used to induce force
distributions instead of resolving the
propellers blade geometry. This is a faster way
of simulating a large number of propellers. The
rotor is simulated through source terms in the
momentum equations. The method employs a
uniform volume force distribution over the
cylindrical virtual disk. The volume force
varies with the radial direction. The radial
distribution varies with the Goldstein optimum
and is given by: [4]
𝑓𝑏𝑥 = 𝐴𝑥𝑟∗√(1 − 𝑟∗) ( 5)
𝑓𝑏𝜃 = 𝐴𝜃 .𝑟∗√1−𝑟∗
𝑟∗(1−𝑟ℎ′)+𝑟ℎ
′ ( 6)
𝑟∗ =𝑟′−𝑟ℎ
′
1−𝑟ℎ′ ( 7)
𝑟ℎ′ =
𝑅𝐻
𝑅𝑃, and 𝑟′ =
𝑟
𝑅𝑃 ( 8)
where 𝐴𝑥 and 𝐴𝜃 are functions of the propeller
hub radius 𝑅𝐻 and tip radius 𝑅𝑃.
Outside STAR-CCM+, JavaPROP
[5] is used to obtain the propeller curve for
both types of propellers. In this program
equations based on the formulas of Adkins
and Liebeck’s work of “Design of Optimum
Propellers” are used to arrive to an optimum
solution.[6] It is based on the theory of optimum
propeller as developed by Betz, Prandtl and
Glauert. Only a small number of parameters
need to be specified. These are:
Number of blades, B
Axial velocity v of the flow (flight speed or boat speed),
Diameter D of the propeller,
Selected distribution of airfoil lift and drag coefficients Cl and Cd along the radius. In this case the distribution is not directly selected but an airfoil is selected at each station (or radius) with the angle of attack.
Desired thrust T or the available shaft power P
Density 𝜌 of the medium
The disk is applied directly to the
original mesh specifying the diameter,
thickness and orientation. The table from the
resulting performance curve consists of the
advance ratio, propeller efficiency, thrust
coefficient 𝐾𝑇, and torque coefficient 𝐾𝑄 given
as: [4][5]
𝐽 =𝑉∞
𝑛 𝐷𝑂 ( 9)
𝑃 = 𝑇 ∙𝑉∞
𝜂 ( 10)
𝐾𝑇 =𝑇
𝜌𝑛2𝐷𝑂4 ( 11)
𝐾𝑄 =𝑄
𝜌𝑛2𝐷𝑂5 ( 12)
Where 𝑉∞ is the flow velocity, 𝐷𝑂 is the
propeller diameter, and 𝑛 the rotation rate.
Since the operation point is given by
the thrust, the advance ratio is calculated by
solving the following equation numerically:
𝑓(𝐽) = 𝐾𝑇 − 𝐾𝑇′ ( 13)
𝐾𝑇′ =
𝐽2𝑇𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡
𝜌𝑖𝑛𝑓𝑙𝑜𝑤 𝑝𝑙𝑎𝑛𝑒𝑉∞2 𝐷0
2 ( 14)
Boundary Conditions
The flow inlet is made from a semi-
spherical surface where a velocity magnitude
and direction are defined. (figure 2) This way
the wing is maintained static, and the flow
direction is only controlled by the inlet and the
propellers. In contact with the wing hub a
symmetry plane is placed. The wing and
nacelles have a no-slip condition. And finally,
the rest of the surfaces (semi-cylindrical and
semi-circle) are considered as a pressure
outlet where the flow is extrapolated. The
outlet has to cover also the cylindrical walls
because of the way the angle of attack is
recreated in these simulations. The semi-
cylindrical surfaces cannot be considered
walls because the inlet flow determines the
angle of attack, not the rotation of the body as
it would be the case in an experimental
procedure.
Mesh Refinement
Mesh refinement was not made
systematically but was instead local. At first
the meshing process was made automatically
but was then refined locally. A hexahedral grid
type was chosen for all the mesh because of
its simplicity in defining wake refinement and
its superior speed to mesh. A prism layer was
used near the body with 20 layers, all
amounting to 1% of the base cell size (cell size
that every other parameter is related to). To
compare between meshes, axial and normal
forces coefficients were observed since these
are the values from which the rest of the
results are computed from. Refinement
convergence criteria was decided to be 0.001
(
size of the first cell closer to the surface is
correct for Mesh 6. The difference between
Mesh 7 and Mesh 6 is 0.0002 (0.4%) for the
normal and axial force coefficients so further
refinement was not made. The slight
fluctuation of wall y+ value between Mesh4,
Mesh5 and Mesh6 is due to the unsteady
nature of the flow. These simulations were
made for angle of attack of 8º where the model
starts to become accurate. Mesh 6 is the final
mesh used for this project.
Mesh Nº of cells (in millions)
𝑪𝑨𝑭 𝑪𝑵𝑭 Wall y+
Mesh 1 0.88 -0.0034 0.5127 4.01 Mesh 2 2.38 0.0287 0.6636 2.02 Mesh 3 2.57 0.0294 0.6532 2.05 Mesh 4 12.16 0.0479 0.7418 0.95 Mesh 5 15.00 0.0486 0.7363 0.98 Mesh 6 15.05 0.0489 0.739 0.99 Mesh 7 18.29 0.0487 0.7388 0.99
Table 3 – Mesh refinement process
Results
Configs 𝑷𝒊𝒏𝒏𝒆𝒓(kW)
𝑷𝑻𝒊𝒑
(kW)
𝒙𝑳𝑬(m)
𝑫𝒊𝒏𝒏𝒆𝒓(m)
𝑫𝒕𝒊𝒑(m)
Ref 20 kw 50 kw 0 0.75 1.5 X1 20 kw 50 kw 0.1 0.75 1.5 X2 20 kw 50 kw 0.2 0.75 1.5 DS 20 kw 50 kw 0 0.50 0.75 DL 20 kw 50 kw 0 m 0.9 1.5
Po
we
r I30 30 kw 50 kw 0 m 0.75 1.5 T70 20 kw 70 kw 0 m 0.75 1.5 T20 20 kw 20 kw 0 m 0.75 1.5
Table 4 - Table of configurations
Table 4 summarizes the parametric
changes made to the propellers in power and
geometry in every configuration. Only for the
reference solution (solution to which every
other result is compared) the variation of angle
of attack has been from 0° to 12°. For the rest
of the cases only the point of maximum lift was
interesting studying. For almost all of the
different propellers configurations, 𝐶𝐿 reaches
a maximum value at the angle of attack of 8°.
This is the reason why the results for other
configurations are only presented for angles
7° to 9°. Unfortunately this model is no longer
accurate after separation is reached because
it ceases to be a steady flow and it does not
take into account possible vortex shedding,
producing results that do not correspond with
reality. That is why it shows a slight increase
of 𝐶𝐿 between the angles of 9° and 10° even
though the values of both simulations have
stabilized.
2D simulations for NACA 2412 wing
profile without nacelles were made using the
program Xfoil [7] where the maximum angle of
attack was found to be at 13.8° with a 𝐶𝐿 𝑀𝑎𝑥
of 1.52 (presented in the annex). In figure 4
the 𝐶𝐿 𝑀𝑎𝑥 for the Reference solution is equal
to 0.85 at 8°. Not only the finite wing has a
decrease of lift but the presence of propellers
causes it to stall sooner at 8º. The results of
the rest of the parametric changes are
presented in phases, depending on the design
modifications made.
Figure 3 shows the wall shear stress
in the x-direction for the reference solution for
9°, after the maximum angle of attack. There is clearly a separation happening more in one
side on the left of the propeller. This is due to
the rotation of the propeller that increases the
local angle of attack on the left side of the
propeller forcing it to stall first. This means the
chosen wing airfoil cannot stall abruptly for
DEP systems.
In figure 4 every case for geometry
and power change are presented and the first
thing noticeable is that all cases have very
close values, stalling near the same angle of
attack. For X1 configurations 𝐶𝐿 𝑀𝑎𝑥 value
decreases to 0.84 at an angle of 8 degrees.
The variations of the lift coefficient are seen to
vary 0.004 (0.47%) from the Reference
configuration, while the drag coefficient varies
0.00026 (0.5%) with 𝐶𝐷 being 0.051 (figure 4).
The case of X2 has no decrease of 𝐶𝐿 𝑀𝑎𝑥,
remaining at a value of 0.85 to an angle of also
8 degrees, and the drag coefficient is
unaltered. This is a very low and not relevant change to conclude such differences.
Smaller propellers’ diameters are also tested (DS table 4). The value of 𝐶𝐿 𝑀𝑎𝑥 seems
to increase to 0.88 (3.7 %), for the larger
diameter configuration, this value drops
slightly to 0.84 (0.59 %). The drag coefficient
doesn’t change much for both cases in relation
to the reference solution, which leads to
conclude that this difference in lift is due to
different rotation rates of the propellers. For
simulations where larger propeller diameters
were tested (DL), the rotation rate is around
2400 rpm, while in the case of the smaller
diameters, propellers rotation is around the
speed of 5500 rpm. This also explains why the
drag for the larger diameter case is the same
as the reference solution even though the
affected area is bigger. In the case of the
smaller diameters, the higher rotation rate
increases the drag even though less area is
affected by the propellers. Looking at the lift
the Small Diameter case has higher values,
since the flow over the wing is less disturbed.
For I30 configuration, 𝐶𝐿 increases to
0.87 at 8° of angle of attack. It’s an increase of
0.021 (2.5 %) in 𝐶𝐿 for 50 kW of total power
increase. The reason for this increase is due
to the higher induced velocity over the wing
that ultimately generates higher lift. Obviously
that also means higher drag which in this case
is a 0.001 (1.5 %) of difference of 𝐶𝐷 for the
same angles, in this case 8°. There is a
significant change in drag but the lift is not
changing enough, leading to conclude this
increase in power is not worth it. The overall
change in 𝐶𝐿 is not big enough.
Others studied effects were the ones
created by the increase and decrease of
power in the tip propellers. Both higher and
lower power changes were tested. For the
case of T20, the lift not only gets bigger to a
value of 0.872, a change of 0.02 (2.4 %), but
also happens in a higher angle of attack of 9°.
However for the T70 case the change in lift is
not noticeable, being 0.85 for the angle of 8°.
The drag difference is clearly more noticeable
with changes of 0.016 (32%) for the T20 case,
and 0.0003 (0.6%) for the T70 case. Either
one of these parametric changes bring
benefits in terms of lift, but only T20 presents
also a decrease in drag, concluding that the tip
(or “cruise”) propeller does not bring benefits
when at a higher power than the “high-lift”
propellers.
Finally a change in inflow velocity is studied
and a clear change in results happens. Two
different cases of 77.2 m/s (150 knots) and
31.38 m/s (61 knots) were tested. The
maximum angle still seems to be at 8° for the
77.2 m/s. There is an increase of 0.042 (4.95
%) for the lift coefficient and decrease of
0.0027 (5.45 %) for the drag coefficient. This
shows that lower cruise velocity produces
higher L/D ratios, 16.86 for 110.6 m/s and
18.71 for 31.38 m/s, both at 8°.
Shown in figure 9, there are the lift
coefficients for different speeds. First the
maximum angle of attack is at 12° for 31.38
m/s, and 𝐶𝐿 and 𝐶𝐷 have respectively, an
increase of 0.409 (48.12%) and an increase of
0.098 (194.10%). Not only stall happens later,
as the overall lift coefficient of the wing is
higher. Clearly this type of “high-lift” devices
behave better and bring more efficiency at
lower speeds.
Figure 3 - Wall Shear Stress in the positive x-direction for Reference solution case at 9°
Figure 4 - Lift coefficient for all of the propeller change cases
Figure 5 - Cl/Clref vs angle of attack for all of the propeller change cases
Figure 6 – Drag coefficient for all of the propeller change case
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Lift
Co
effi
cien
t
Angle of attack (°)
DEFAULTX1X2DSDLT20I30T70
0,92
0,94
0,96
0,98
1,00
1,02
1,04
1,06
6 7 8 9 10 11
CL
/ C
Lref
Angle of attack (°)
X1X2DSDLT20I30
0,03
0,04
0,05
0,06
0,07
0,08
0,09
0,10
6 7 8 9 10 11
Dra
g C
oef
fici
ent
Angle of attack (°)
DEFAULT
X1
X2
DS
DL
T20
I30
T70
Figure 7 – Lift coefficient for all the cases with one propeller turned off
Figure 8 - Cl/Clref for all the cases with one propeller turned off
1,05
1,10
1,15
1,20
1,25
1,30
6 7 8 9 10 11 12 13 14 15
Lift
ceo
ffic
ien
t
Angle of attack (°)
61knots
1prop
2prop
3prop
4prop
5prop
0,92
0,93
0,94
0,95
0,96
0,97
0,98
0,99
1,00
6 7 8 9 10 11 12 13 14 15
Cl/
Clr
ef
Angle of attack (°)
1prop
2prop
3prop
4prop
5prop
Figure 9 - Lift coefficient for all the cases with one propeller turned off
Figure 10 – Lift coefficient change for velocity change, and without propellers
----------------
Conclusion
A series of different cases have
converged successfully showing both
expected and unexpected results.
2D simulations show that 𝐶𝐿 increases
with higher velocity (110.61 m/s) but stall first
than for lower velocities (31.38 m/s). The
same can’t be said for the 3D cases. With
propellers at lower velocities stall seems to
also be occurring later as it would be
expected, but because of the propellers 𝐶𝐿 is
much higher than for lower velocities. There is
also a slight increase comparing with the
geometry without propellers. Here the
comparison is difficult since the virtual disk are
not present anymore in NoProp case (figure 9)
producing much less drag. This means DEP is
producing higher 𝐶𝐿 overall but stalls first. Also
DEP systems seem to work much better at
lower velocities, and should not be used at
higher velocities.
Parametric changes to diameter and
distance to the leading edge seem to have
produce no conclusive data, even for higher
velocities. However power changes hints that
0,05
0,07
0,09
0,11
0,13
0,15
0,17
0,19
0,21
0,23
7 8 9 10 11 12 13 14 15
Dra
g co
effi
cien
t
Angle of attack (°)
61knots
1prop
2prop
3prop
4prop
5prop
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Lift
Co
effi
cien
t
Angle of attack (°)
DEFAULT
150 knts
61knots
the tip propeller should not have relatively
more power than the smaller ones. Vortices
produced by the propellers seem to be
interfering with one another, producing more
harm than good.
Finally the propellers that seemed to
influence more the lift are the ones positioned
more to the tip of the wing. However without
the fifth propeller (counting from the hub to the
tip of the wing) 𝐶𝐿 is slightly higher than without
the fourth propeller. As explained before, one
possible explanation is the influence of
different vortices produced. One possible
explanation is the influence of different
vortices produced from the fifth and the tip
propeller on one another. This may cause an
increase of dynamic pressure over the wing
due to not contra-rotating propellers.
Acknowledgement
The author would like to thank first
and foremost Prof. Dr. -Ing. Andreas Henze
and Prof. Dr. Luís Eça for all the guidance and
support in the making of this work. This project
was possible thanks to the opportunity given
by Prof. Dr. –Ing. Wolfgang Schröder who
made it possible to work at the Aerodynamic
Institute of RWTH Aachen, and also to
Michael Kreimeier for the opportunity to work
on this project. This project belongs to the
Aeronautics and Aerospace Department of
RWTH Aachen that was done in collaboration
with the Aerodynamic Institute of the same
university.
References
[1] Felder J.L., Brown G.V., DaeKim H., and
Chu J., (2011) Turboelectric Distributed
Propulsion in a Hybrid Wing Body Aircraft.
NASA Glenn Research Center, USA.
[2] Moore, M. D. and Fredericks, W. J., (2014) Misconceptions of Electric Aircraft and their Emerging Aviation Markets," AIAA SciTech, American Institute of Aeronautics
and Astronautics.
[3] Menter F.R., (1994) Two-Equation Eddy-
Viscosity Turbulence Models for Engineering
Applications. AIAA Journal, 32(8):1598-1605
[4] STAR-CCM+ User Guide. Star-CD version
4.02 (2006)
[5] Hepperle M.. (2013). Java PROP – Design
and Analysis of Propellers. Accessed in 15-
03-2016 at: http://www.mh-
aerotools.de/airfoils/javaprop.htm
[6] Adkins C. N.. Liebeck R.H.. (1994) Design
of Optimum Propellers. Douglas Aircraft
Company. Long Beach. California. Journal of
Propulsion and Power. Vol 10. No. 5.
[7] XFoil Subsonic Development System
Website, Drela M.. Youngren H., Accessed on
06-04-2016 at:
http://web.mit.edu/drela/Public/web/xfoil/
http://www.mh-aerotools.de/airfoils/javaprop.htmhttp://www.mh-aerotools.de/airfoils/javaprop.htm