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Analysis and Design of a Small-Scale Wingtip-Mounted

Pusher Propeller

Tom C. A. Stokkermans∗, Sebastiaan Nootebos†and Leo L. M. Veldhuis‡

Delft University of Technology, 2629 HS Delft, The Netherlands

The wingtip-mounted pusher propeller, which experiences a performance beneﬁt from the

interaction with the wingtip ﬂowﬁeld, is an interesting concept for distributed propulsion. This

paper examines a propeller design framework and provides veriﬁcation with RANS CFD sim-

ulations by analysing the wing of a 9-passenger commuter airplane with a wingtip-mounted

propeller in pusher conﬁguration. In the taken approach, a wingtip ﬂowﬁeld is extracted from

a CFD simulation, circumferentially averaged and provided to a lower order propeller analysis

and optimisation routine. Possible propulsive eﬃciency gains for the propeller due to installa-

tion are signiﬁcant, up to 16

%

increase at low thrust levels, decreasing to approximately 7.5

%

at the highest thrust level, for a range of thrust from 5

%

up to 100

%

of the wing drag. These

gains are found to be independent of propeller radius for thrust levels larger than 30

%

of the

wing drag. Eﬀectively, the propeller geometry is optimized for the required thrust and to a

lesser degree for the non-uniformity in the ﬂowﬁeld. Propeller blade optimization and instal-

lation result in higher proﬁle eﬃciency in the blade root sections and a more inboard thrust

distribution.

Nomenclature

b=Wing span, m

CD=Drag coeﬃcient

CL=Lift coeﬃcient

Cp=(p−p∞)/q∞pressure coeﬃcient

CQ=Q/ρ∞n2D5

ptorque coeﬃcient

CT=T/ρ∞n2D4

pthrust coeﬃcient

c=Chord, m

Dp=Propeller diameter, m

D=Wing drag, N

hi=Average cell size of grid i, m

J=V∞/(nDp)advance ratio

L=Wing lift, N

n=Propeller rotational speed, s−1

P=Shaft power, W

p=Static pressure, Pa

Q=Torque, Nm

Q0=Torque distribution, Nm ·m−1

q=Dynamic pressure, Pa

Rp=Propeller radius, m

Rp,ref=Reference XPROP propeller radius, m

r=

Radial coordinate in propeller reference frame, m

T=Thrust, N

T0=Thrust distribution, N ·m−1

U∗

s=

Standard deviation of a ﬁt based on theoretic order

of convergence

Uφ=Estimated discretization uncertainty

V=Velocity, m ·s−1

x=Axial coordinate, m

y=Vertical coordinate, m

y+=Dimensionless wall distance

z=Lateral coordinate, m

α=Angle of attack, deg

β=Blade pitch angle, deg

ηp=TV∞/Ppropeller propulsive eﬃciency

ρ=Density, kg ·m−3

ϕ=Propeller blade phase angle, deg

φi=Numerical solution obtained using grid i

ω=Vorticity, s−1

Subscripts

0=Extrapolated

0.7Rp=Radial coordinate, in which r/Rpis equal to 0.7

a=Axial

c=Chord based

iso =In isolated condition

h=Hub

k=Kink

p=Propeller

r=Root

t=Tangential, tip

∞=Freestream

∗

Ph.D. Candidate, Flight Performance and Propulsion Section, Faculty of Aerospace Engineering, AIAA Member, t.c.a.stokkermans@tudelft.nl.

†M.Sc. Graduate, Flight Performance and Propulsion Section, Faculty of Aerospace Engineering

‡Full Professor, Head of Flight Performance and Propulsion Section, Faculty of Aerospace Engineering, AIAA Member.

1

I. Introduction

Today’s research on propellers is driven by their potential for reduced fuel consumption compared to turbofan

propulsion. Not only the high propulsive eﬃciency of the propeller itself, but also its location on the airframe can

enhance the overall eﬃciency of the aircraft. Wingtip-mounted propellers have been envisaged for their favorable

interaction eﬀects. For the tractor propeller variant, the interaction of the wing with the slipstream results in a reduction

of the wing induced drag if the rotation direction of the propeller is opposite to that of the wingtip vortex [

1

–

3

]. The

pusher propeller variant experiences a reduction in shaft power due to the swirling vortex inﬂow from the wingtip in

case the propeller rotates against the direction of the wingtip vortex [

2

,

4

–

6

]. Moreover, the modiﬁcation of the wingtip

vortex may reduce wing induced drag as well. Yet, the ingestion of the non-uniform inﬂow ﬁeld may result in a noise

penalty for the pusher variant. Adverse aeroelastic eﬀects due to the large weight of an engine at the tip of a wing and

the large yawing moment arm of the thrust vector in case of a one-engine-inoperative condition have prevented the

application of wingtip-mounted propellers up to now. However, the emergence of electric propulsion in aircraft allows

almost penalty-free downscaling of the propeller due to the scale independence of the electric motor [

7

]. This makes it

possible to distribute the propulsion for instance through a hybrid-electric architecture, and enables to scale down the

wingtip-mounted propeller like proposed in the SCEPTOR concept [8].

a) Modified Learfan 2100 b) Modified Tecnam P2012 Traveller

Fig. 1 Impression of airplane concepts with small-scale wingtip-mounted pusher propellers.

In this research the pusher variant is investigated in the context of distributed propulsion. An impression of such a

concept, combining i.e. fuselage boundary layer ingestion and wingtip-mounted pusher propellers through a hybrid

electric architecture, is shown in Fig. 1 a. A more conventional airplane layout with small-scale wingtip-mounted

pusher propellers is sketched in Fig. 1 b. The design freedom to scale propellers and to distribute propulsion, results in

a non-unique thrust requirement. For example, the propeller can be designed to balance just the induced drag of the

wing or balance the entire cruise drag of the aircraft. The resulting performance beneﬁt of propeller installation at the

wingtip may depend on the thrust level. Hence the following research question: How does propeller scale inﬂuence the

propulsive eﬃciency beneﬁt and the upstream aerodynamic loading on the wing? Up to now, only research on a full

scale wingtip-mounted pusher propeller has been performed, with a propeller not speciﬁcally designed for this task

[

4

]. The inﬂow to the propeller is non-uniform, especially when the propeller becomes smaller relative to the wingtip

ﬂowﬁeld. For a boundary layer ingestion propeller, Ref. [

9

] has shown that maximizing the propulsive eﬃciency gain

requires a diﬀerent design to cope with the non-uniform inﬂow experienced on the aft fuselage. Analogue to that, the

wingtip-mounted pusher propeller may also beneﬁt from design optimization, resulting in the second research question:

To what extent can the propulsive eﬃciency beneﬁt be increased by designing the propeller for the non-uniform inﬂow

experienced at the wingtip?

This research, which is regarded as an extension of Ref. [

10

], gives insight in these questions by analysis of a

speciﬁc case through the following steps:

1)

CFD analyses of the wing are performed in order to quantify the wing performance and extract the wingtip

ﬂowﬁeld.

2)

A lower order propeller analysis and optimisation routine PROPR is established and validated for uniform inﬂow.

3) The wingtip ﬂowﬁeld is fed to PROPR for analysis and design optimization.

4)

The upstream eﬀect of the propeller designs on the wing performance is analyzed through CFD analyses of the

wing with an actuator disk representation of the propeller.

5)

The accuracy of PROPR for the non-uniform wingtip ﬂowﬁeld is checked through a fully resolved propeller–wing

CFD simulation.

2

II. Computational Methods

A. RANS CFD Simulations

Four diﬀerent types of RANS CFD simulations were performed in order to establish the wing performance and wingtip

ﬂowﬁeld, to estimate the upstream eﬀect of the propeller on the wing and to verify the accuracy of PROPR:

•Isolated wing simulations

•Isolated propeller simulations

•Wing simulations with actuator disk propeller representation

•A propeller–wing simulation

The wing used for these simulations was derived from the Tecnam P2012 Traveller [

11

], a twin-prop 9-passenger

commuter airplane with a maximum take-oﬀmass of 3600

kg

. Only the wing was taken into account, without the

original propeller and nacelles. A sketch of the wing is shown in Fig. 2 a. A minimum radius nacelle was added at

the tip of the wing, extending aft of the trailing edge to accommodate a propeller in pusher conﬁguration. The nacelle

radius was kept equal to the propeller hub radius

Rh

. Hence, so far there is no provision to accommodate an electric

motor. The wing parameters are given in Table 1 and are partly based on Ref. [12].

a) Wing model with nacelle and spinner. b) XPROP propeller model.

y

x

z

ypxp

zp

xp

Rp

Rh

n

yp

0.21b

0.29b

cr = ck

ct

Fig. 2 Isometric view of the wing and TU Delft research propeller XPROP.

The propeller in the isolated propeller and propeller–wing simulations is the 6-bladed XPROP propeller, shown in

Fig. 2 b, a research propeller from Delft University of Technology typical for turboprop airplanes. An extensive grid

study and experimental validation for this propeller was performed in Ref. [

13

], and the same propeller grid density

was used in this research. The spinner was modiﬁed to convert it into a pusher propeller. The propeller was used in its

original size with a radius of

Rp,ref =

0

.

2032 m and hub radius of

Rh=

0

.

23

Rp,ref

. Simulations were also performed

with proportionally scaled versions of smaller and larger size.

Table 1 Wing model parameters.

Parameter Value

Span b13.55 m

Root and kink chord cr,ck2.06 m

Tip chord ct1.38 m

c/4 sweep, dihedral, twist 0◦

Root and kink airfoil NACA23015

Tip airfoil NACA23012

Cruise speed 80 m/s

Cruise altitude 3048 m

Cruise angle of attack 3◦

Cruise lift coeﬃcient ≈0.35

3

Symmetry BC Pressure

outlet BC

Pressure

farfield BC

OD

ID

WD

PD SD

OD:

ID:

WD:

PD:

SD:

Outer Domain

Inner Domain

Wing Domain

Propeller Domain

Slipstream Domain

15cr

cr

y

x

5cr

20cr

Fig. 3 Computational domain and boundary conditions for the wing simulations.

The RANS equations for compressible ﬂow were used with a 2

nd

order accurate scheme in ANSYS

r

Fluent 18.1

[

14

], a commercial, unstructured, ﬁnite volume, cell-centered solver. For the propeller–wing simulations time-dependent

solutions were found by a 2

nd

order backward Euler scheme with a time step equivalent to 2

deg

of propeller rotation.

Discretization of the advection term was done with an upwind scheme using the Barth–Jesperson boundedness principle

[

15

]. For the equation of state, an ideal gas was assumed and Sutherland’s law was used to predict the corresponding

dynamic viscosity. Standard atmospheric conditions at the cruise altitude were assumed. The turbulence model was

selected based on the ﬁndings of Kim and Rhee [

16

], who tested several turbulence models to simulate the wingtip

vortex of an isolated wing. The eddy viscosity model in their research that best agreed with experimental data in terms

of static pressure and axial velocity in the wingtip-vortex core was the Spalart–Allmaras (SA) one-equation model [

17

]

with modiﬁcation proposed by Dacles-Mariani et al. [

18

] to prevent build-up of turbulence viscosity in vortex cores.

Therefore, this model was selected for the current research. Values for the inlet turbulence quantities were based on the

recommendations by Spalart and Rumsey [

19

], which resulted in an eddy viscosity ratio of 0

.

21044 for the SA model.

In order to fully resolve the boundary layer, the y+value on the no-slip walls of the model was less than one.

The computational domain and boundary conditions for the wing simulations are shown in Fig. 3. The outer

dimensions of the domain were chosen to be suﬃciently large with respect to the wing chord, in order to minimize the

inﬂuence of the boundary conditions on the ﬂow properties near the wing. At the domain inlet, a total-pressure jump

with respect to the undisturbed static pressure was set to reach the cruise speed. Furthermore, the undisturbed total

temperature was speciﬁed. At the domain outlet, the static pressure was prescribed to be on average equal to undisturbed

static pressure. On the outboard side of the domain, a Riemann-invariant pressure farﬁeld condition was speciﬁed

with a Mach number, static pressure and static temperature complying with the inlet conditions. On the inboard side

side, a symmetry boundary condition was imposed. The wing, nacelle, propeller and spinner were modeled as no-slip

walls. The computational domain was divided in several domains for reﬁnement of the grid. The propeller domain (PD)

was connected to the other domains through sliding mesh interfaces to allow grid rotation for simulation of propeller

motion. This domain could be replaced by a domain without propeller blades for the isolated wing simulations and

wing simulations with actuator disk representation of the propeller. The actuator disk model described in Ref. [

20

] was

used, requiring the propeller blade radial distribution of thrust and torque as input. Grids were constructed by means

of ANSYS

r

Meshing. For regions adjacent to no-slip walls, the unstructured grid was made up of a triangular wall

mesh, followed by layers of semi-structured prismatic elements of the inﬂation layer. For the remainder of the domain

tetrahedral elements were used. Grid density in the whole domain was controlled by wall reﬁnement of all no-slip walls,

volume reﬁnement of the domains, a 1

st

layer thickness of the inﬂation layers, and growth rates of the inﬂation layers

and the remainder of the grid. Grid study results for the isolated wing are shown in Section III.

The computational domain and boundary conditions for the isolated propeller simulations are described in Ref. [

13

].

Since the wake of a propeller with axisymmetric nacelle is cyclic with the number of the blades, only a single blade was

modeled in a wedge shaped domain with appropriate boundary conditions. The movement of the propeller and spinner

was simulated with a rotating reference frame.

4

B. Propeller Analysis and Optimisation Routine: PROPR

To perform quick propeller analyses and to aerodynamically design the propeller for optimized performance, a

PRopeller analysis and OPtimisation Routine named PROPR was set up based on XROTOR [

21

]. The software program

uses discrete line vortices forming a semi-rigid wake to iteratively determine the induced velocities and has been used

before by Refs. [

9

,

22

–

25

] for both uniform and non-uniform inﬂow. XFOIL [

26

] was selected for airfoil analyses. All

details of PROPR are described in Ref. [

10

]. Twenty radial sections were used to deﬁne the propeller geometry and

provide XROTOR with airfoil data. Each radial section was supplied with the correct non-uniform ﬂowﬁeld. Fully

turbulent ﬂow for the airfoil data was assumed to allow comparison with the fully turbulent CFD simulations and to

increase stability of running XFOIL in an optimization framework. The non-linear part of the lift curve was modiﬁed

using an empirical model by Snel et al. [

27

] to correct two dimensional data for three dimensional rotational eﬀects.

Comparison of PROPR results with validation data is provided in Section IV.

III. Isolated Wing Analysis

CFD analyses of the wing were performed at 3

deg

angle of attack to represent a cruise condition. A grid dependency

study was performed to estimate the discretization uncertainty and to select an appropriate grid density. All reﬁnements

were varied systematically, except for the inﬂation layer, which was kept constant in line with Roache [

28

]. To estimate

discretization uncertainty, the least-squares version of the grid convergence index (GCI) proposed by Eça and Hoekstra

[

29

] was applied, with the alteration of using only the theoretical order of the solver of 2 to estimate the extrapolated

grid results. Table 2 gives an overview of the grid sizes and wing lift and drag found for each grid. Table 3 presents the

extrapolated lift and drag

φ0

, the standard deviation of the ﬁt based on the theoretical order of convergence

U∗

s

and the

estimated discretization uncertainty

Uφ

for grid 2. The uncertainty of 0

.

49% and 3

.

10% for the lift and drag coeﬃcient

respectively was deemed acceptable for this study.

Table 2 Overview of grids and resulting isolated wing performance.

Grid No. of cells hi/h1CL[-] CD[-]

4 8,561,478 1.82 0.3434 0.01638

3 16,315,794 1.47 0.3440 0.01622

2 32,756,863 1.16 0.3447 0.01600

1 51,424,220 1.00 0.3452 0.01585

Table 3 Grid extrapolation results and estimated discretization uncertainties for grid 2.

CLCD

φ00.3458 0.01568

U∗

s(%) 0.08 0.57

Uφ(%) 0.49 3.10

From the solution on grid 2 the ﬂowﬁeld that was fed to PROPR was extracted from the propeller plane, the plane

where the propeller will be installed. The ﬂowﬁeld at the wingtip is visualised in Fig. 4 by means of streamtraces and

the wingtip vortex is shown by an axial vorticity isosurface. On the isosurface and the propeller plane the velocity

magnitude is plotted and on the wing surface the pressure coeﬃcient distribution is shown. In Fig. 5 this ﬂowﬁeld

at the propeller plane is given for the left wingtip as seen from behind, by means of contour plots of the axial and

tangential velocity components. These velocity components are most relevant for the propeller aerodynamic loading

and, together with the propeller rotational speed and propeller induced velocities, determine the local blade section

angle of attack and dynamic pressure. The tangential velocity component is deﬁned positive in the rotation direction of

the propeller, which is running counterclockwise for the left propeller when seen from behind. In PROPR, the inﬂow

ﬂowﬁeld is radially varying but assumed to be circumferentially constant. Therefore a circumferential average of this

ﬂowﬁeld was taken, which will impact the resulting propeller response as follows: In the axial velocity contour plot

the reduced velocity in the wake of the wing is clearly visible and its eﬀect on the propeller will be averaged. In the

tangential velocity plot a region of strong negative velocity and a region of positive velocity can be observed which

have an opposite eﬀect on the propeller. These regions will also be circumferentially averaged in a net negative velocity.

5

(V − V∞) / V∞

−0.40

−0.35

−0.30

−0.25

−0.20

−0.15

−0.10

−0.05

0.00

0.05

Cp

−1.25

−1.00

−0.75

−0.50

−0.25

0.00

0.25

0.50

0.75

1.00

axial vorticity isosurface at ωx = −900 s-1

propeller plane

Fig. 4 Visualisation of wingtip ﬂowﬁeld and pressure coeﬃcient distribution on the wing surface.

−0.4 −0.2 −0.0 0.2−0.4 −0.3 −0.2 −0.1 0.0

(Va − V∞) / V∞Vt / V∞

zp

yp

Rp,ref

zp

yp

Rp,ref

Fig. 5 Contour plots of axial and tangential velocity components at the propeller plane behind the left wingtip.

The dashed line shows the propeller disc area for the reference XPROP propeller.

The resulting propeller designs for this ﬂowﬁeld are presented in Section V and the consequence of circumferential

averaging will be further discussed in Section VII.

IV. Isolated Propeller Analysis

To establish conﬁdence in PROPR, two comparisons were made. The ﬁrst was with in-house windtunnel data of

the XPROP propeller in uniform ﬂow. In Fig. 6 a comparison is presented of the thrust and torque coeﬃcient versus

advance ratio for

V∞=

30 m/s. Although at high advance ratios a signiﬁcant deviation starts to appear for both thrust

and torque coeﬃcient, in the region of interest where

CT

is higher, the match with the experimental data is satisfactory.

The second comparison was made with a CFD model of the isolated propeller from Ref. [

13

]. In Fig. 7 the thrust

and torque distribution over a propeller blade are plotted for both PROPR and the CFD model for

V∞=

30 m/s and an

advance ratio of

J=

0

.

74. This corresponds to a thrust of 16% of the isolated wing drag. The integrated loading is

overestimated by PROPR with 4

.

5% and 7

.

6% in thrust and torque respectively. The shape of the thrust and torque

distribution from PROPR and the CFD model are very similar except for at the tip of the blade. The local rise in thrust

and torque in the CFD model due to the tip vortex is not captured in the PROPR results because of the single lifting line

representation of the blade. Considering that in these comparisons acceptable agreement was found, a design study was

performed with PROPR. This is presented in the next Section V.

6

0.35

0.00

0.30

0.25

0.20

0.15

0.10

0.05

−0.05

Thrust coefficient CT

0.50 0.75 1.00 1.25 1.50

PROPR

Experiment

0.06

0.00

0.05

0.04

0.03

0.02

0.01

Torque coefficient CQ

Advance ratio J

0.50 0.75 1.00 1.25 1.50

Fig. 6 Propeller performance from PROPR and inhouse windtunnel test for V∞=30 m/s and β0.7Rp=30◦.

180

Thrust distribution T´ (N / m)

Radial coordinate r / Rp

0.2 0.3

PROPR

CFD

160

140

120

100

80

60

40

20

00.4 0.5 0.6 0.7 0.8 0.9 1.0

14

Torque distribution Q´ (Nm / m)

0.2 0.3

12

00.4 0.5 0.6 0.7 0.8 0.9 1.0

10

8

6

4

2

Fig. 7 Blade loading distributions from PROPR and CFD model for V∞=30 m/s, β0.7Rp=30◦and J =0.74.

7

V. Propeller Design Study

In this section the design optimization results from PROPR for a propeller placed in the wingtip ﬂowﬁeld are

discussed. The diﬀerent propeller designs are given in Table 4. The original XPROP propeller was tested in isolated and

installed condition. The XPROP propeller was also optimized for minimum power in terms of blade pitch distribution

and chord distribution, keeping the airfoil sections the same. This was done for isolated and installed conditions,

denoted isoOpt and insOpt respectively. The former was tested both in isolated and installed conditions, while the latter

was only tested in installed conditions. Note that these optimizations were performed for each thrust level separately

and that for each thrust level the performance is given for optimum operating conditions in terms of β0.7Rpand J.

Table 4 Overview of diﬀerent propeller geometries used in design study.

Propeller name Description

XPROP-iso Original XPROP propeller operating in isolated condition

isoOpt-iso Optimized for isolated condition, operating in isolated condition

XPROP-ins Original XPROP propeller operating in installed condition

isoOpt-ins Optimized for isolated condition, operating in installed condition

insOpt-ins Optimized for installed condition, operating in installed condition

0.10 0.14 0.17 0.21 0.24 0.27 0.31 0.34 0.38 0.41

Propulsive efficiency ηp (%)

100

90

80

70

100

95

90

85

Power P / Piso (%)

XPROP-iso

isoOpt-iso

XPROP-ins

isoOpt-ins

insOpt-ins

80

0.44 0.48

Thrust over drag ratio T / Diso

Fig. 8 Propeller optimization results showing the propulsive eﬃciency and power versus the thrust to wing

drag ratio at constant radius Rp/Rp,ref =1.00 for isolated and installed conditions.

A. Propeller Optimization for Constant Radius

First, a design sweep was performed for a range of thrust levels, keeping the propeller radius equal to that of the

original XPROP propeller

Rp,ref

. In Fig. 8 the propeller performance is shown for a range of design thrust levels with

respect to the isolated wing drag

T/Diso

. The propulsive eﬃciency

ηp=TV∞/P

is plotted, as well as the relative power

required with respect to the XPROP-iso propeller

P/Piso

. Dashed lines refer to performance in isolated conditions, solid

lines indicate installed propeller performance. Put in perspective, the wing induced drag is about 40% of the total wing

drag in this condition, so a range of thrust levels is plotted from 25% up to 115% of the wing induced drag.

8

A number of trends can clearly be observed: The propulsive eﬃciency decreases with increasing design thrust in both

the isolated and installed cases. This is expected since the propeller radius was kept constant. The possible eﬃciency

gains due to installation and optimisation of the propeller are signiﬁcant. Comparing insOpt-ins with XPROP-iso results,

up to 20% increase in eﬃciency is achieved at lower design thrust levels by the combined eﬀect of optimisation and

installation, decreasing to approximately 10% and remaining constant at higher thrust levels. Although a more fair

comparison is that of the insOpt-ins with the isoOpt-iso propeller, both optimised for their respective ﬂowﬁeld. Then,

an eﬃciency increase up to 15% remains at the lowest thrust level, decreasing to 9% at the highest thrust level.

Looking at the power plot, the eﬀectiveness of geometrical optimization in both isolated and installed conditions

at low and high thrust levels is clearly visible. This eﬀect diminishes at more average thrust levels, as the XPROP

propeller is apparently designed for those thrust levels. The reduction in required power is signiﬁcant when installing

the propeller, even for the XPROP with non-optimized geometry. Reductions up to 20% are achieved when comparing

insOpt-ins with XPROP-iso results, although looking at the most fair comparison with the isoOpt-iso propeller, a bit

lower maximum power reduction of up to 15% is found. Note that the installed propeller with optimized geometry for

isolated conditions (isoOpt) yields almost identical power reductions compared to the installed propeller with optimized

geometry for installed conditions (insOpt). Thus, eﬀectively the propeller geometry is optimized for the required

thrust level and to a lesser degree for the non-uniformity in the ﬂowﬁeld. Only at the very high design thrust levels of

T/Diso ≥0.42 a noticeable diﬀerence in performance between the two diﬀerent optimized propellers is observed.

With increasing thrust, the power reduction due to installation converges quickly to a nearly constant value, meaning

that the eﬀective power reduction that can be achieved by installation of the propeller almost does not change with thrust

requirement. One would expect that the eﬀective power reduction would decrease with increasing propeller design

thrust, as there is only a ﬁnite amount of energy to be ‘extracted’ from the wingtip ﬂowﬁeld present in the installed case.

Because of the limited maximum thrust that can be delivered by the XPROP propeller it is not possible to investigate the

eﬀective power decrease at even higher thrust levels for the current propeller radius. The experimental work done by

Patterson et al. [

4

] gives already an indication of the power reduction found at higher thrust levels, considering that the

size of that propeller and its thrust relative to the wing was much larger. At similar lift coeﬃcient the power reduction

was found to be 14%, although this was for a non-optimized propeller design. Considering that this is of similar order

to what was found in this study thus far, it may be that over a larger thrust range this relative power reduction stays

more or less constant. To conﬁrm this, in Section V.C the higher thrust regime up to a thrust equal to the cruise drag of

the wing will be investigated with larger radius propellers.

B. Blade Loading and Geometry Changes Due to Optimization

The resulting changes in the propeller blade loading and geometry due to optimization and installation are discussed

for two diﬀerent design thrust levels:

T=

0

.

21

Diso

and

T=

0

.

39

Diso

. First, the results from optimization of the XPROP

propeller with

T=

0

.

21

Diso

are discussed. In Fig. 9 the blade pitch angles, chord fractions, the proﬁle eﬃciency and

thrust distribution over the entire blade radius are shown. It is seen that the chord distribution of the insOpt and isoOpt

propellers are nearly identical, even though the insOpt propeller was subjected to the non-uniform wingtip ﬂowﬁeld

during optimization. In both cases, the chord lengths were reduced by as much as 40% compared to the XPROP

propeller. A slight increase in blade pitch angle in the root sections is observed. Both the optimized isoOpt and insOpt

propellers show signiﬁcantly higher eﬃciency in the root sections. Presence of the non-uniform inﬂow enables further

eﬃciency gains. Combined, this leads to a higher local proﬁle eﬃciency for the insOpt propeller, especially for the

root sections (

r/Rp<

0

.

4). A clear trend is visible in the thrust distribution over the blade. Geometry optimization

of the XPROP propeller causes the thrust distribution to shift inboard towards the root. Furthermore, the maximum

value decreases. The same behavior to an even greater extent is observed when investigating the insOpt propeller. The

combination of higher proﬁle eﬃciency and the production of thrust there where the proﬁle eﬃciency is higher makes

this the most eﬃcient propeller of the three.

Second, the optimization results with

T=

0

.

39

Diso

are discussed. In Fig. 10 it is seen that the local blade chord

lengths are increased in both the isoOpt and insOpt propeller designs compared to the original XPROP propeller. This

geometry change due to optimization shows a reverse trend than what was seen for the lower design thrust in Fig. 9,

where the chord fractions were decreased due to optimization. The local blade pitch angle is higher for both the isoOpt

and insOpt propeller design, as was the case for the propellers optimized for

T=

0

.

21

Diso

. Also the improvements in

local eﬃciency are similar, except for at the tip. Note that the eﬃciency of the XPROP propeller is relatively low in the

tip region (

r/Rp>

0

.

85) due to tip stall. Optimization of the propeller geometry reduces this tip stall and the overall

eﬃciency distribution is again an almost ideal constant distribution. Finally, again an inboard shift in thrust distribution

is observed for the optimized propeller geometries.

9

Radial coordinate r / Rp

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

Profile efficiency (%)

100

80

60

40

20

200

150

100

50

0

T´ (N / m)

Blade pitch angle β (deg)

20

30

40

50

60

70

Chord c / Rp

0.20

0.15

0.10

0.05

XPROP-iso

isoOpt-iso

insOpt-ins

Fig. 9 Propeller blade loading and geometry changes due to optimization for T =0.21Diso.

Radial coordinate r / Rp

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0

Profile efficiency (%)

100

80

60

40

20

200

100

0

T´ (N / m)

Blade pitch angle β (deg)

20

30

40

50

60

70

Chord c / Rp

0.20

0.15

0.10

0.05

XPROP-iso

isoOpt-iso

insOpt-ins

300

400

Fig. 10 Propeller blade loading and geometry changes due to optimization for T =0.39Diso.

10

C. Propeller Optimization with Varying Radius

The performance of the propeller placed in the wingtip ﬂowﬁeld was also investigated for propeller radii diﬀerent

from the XPROP propeller. The radius was varied between 0

.

75

−

1

.

50

Rp,ref

, where

Rp,ref

is the radius of the XPROP

propeller. A design thrust range up to

T=Diso

was analysed for the largest radius propeller. The hub dimension was

kept constant and was not scaled with propeller radius. In this analysis the performance of the propeller optimized

for installed condition and operating in installed condition, insOpt-ins, was compared to a propeller of equal radius

optimized for isolated condition operating in isolated condition, isoOpt-iso. This is the most fair comparison since

both propellers are optimised for their respective ﬂowﬁeld. The propeller performance results are given in Fig. 11 as

a function of thrust level. For any given thrust level, the propulsive eﬃciency

ηp

increases with increasing propeller

radius for all propeller designs. This is a straight forward result since, with increasing radius and equal thrust, more

mass is accelerated by the propeller but with a lower velocity increase. The corresponding advance ratio is also higher

for larger radii propellers due to the large reduction in required rotational speed n.

80

85

90

95

100

105

1.0

1.2

1.4

1.6

1.8

2.0

0.75Rp,ref

1.00Rp,ref

1.25Rp,ref

1.50Rp,ref

0.0 0.2 0.4 0.6 0.8 1.0

6

8

10

12

14

16

18

0.0 0.2 0.4 0.6 0.8 1.0

82

84

86

88

90

92

Propulsive efficiency ηp (%)ηp − ηp, iso (%)

Power P / Piso (%) Advance ratio J

Thrust over drag ratio T / Diso

Fig. 11 Optimization results with varying propeller radius for installed condition with insOpt-ins design com-

pared to isolated condition with isoOpt-iso design.

The gain in eﬃciency by installation of the propeller at the wingtip,

ηp−ηp,iso

, varies less with propeller radius.

Only for low thrust levels of less than 30% of the wing drag, signiﬁcant diﬀerences occur in the eﬃciency gain. While

the eﬃciency gain decreases with thrust level, it does so at a reducing rate, decreasing to a still signiﬁcant gain of 7

.

5%

when the thrust equals the wing drag

T=

1

.

00

Diso

. As discussed earlier for the optimisation results at equal radius, the

power ratio

P/Piso

seems to level oﬀto an approximately constant value at larger thrust levels. This is also happening

for the other propeller radii, however the relative power reduction reduces for larger propeller radii, reducing to a 9%

reduction due to the wingtip ﬂowﬁeld for 1.50Rp.

11

VI. Actuator Disk–Wing Analysis

The upstream eﬀect of the propeller designs on the wing performance was analyzed through CFD analyses of the

wing with an actuator disk representation of the propeller. These simulations are of similar computational cost as the

isolated wing simulations but do provide the required time-averaged upstream eﬀect of the propeller at much reduced

computational cost compared to the fully resolved propeller–wing simulation in Section VII. In Fig. 12 the wing lift

coeﬃcient

CL

and lift-over-drag ratio

L/D

are plotted as a function of propeller thrust for a number of cases with

varying propeller radius from Fig. 11. Results are also shown for the isolated wing.

0.0 0.2 0.4 0.6 0.8 1.0

0.3446

0.3447

0.3448

0.3449

0.3450

0.3451

0.3452

0.0 0.2 0.4 0.6 0.8 1.0

21.30

21.35

21.40

21.45

21.50

21.55

21.60 Prop off

0.75Rp,ref

1.00Rp,ref

1.25Rp,ref

1.50Rp,ref

Thrust over drag ratio T / Diso

Wing lift coefficient CL

Wing lift-over-drag ratio L / D

1.50Rp,ref no swirl

Fig. 12 Wing performance as function of propeller thrust investigated with an actuator disk.

The changes in wing lift coeﬃcient due to propeller thrust are quite small and are only just larger than the estimated

discretization uncertainty given in Table 3. Despite this, an increasing trend in

CL

is visible with increasing propeller

thrust level. This could be explained by a slightly stronger suction over the wing due to the presence of the propeller.

Contrary to the lift coeﬃcient, the lift-over-drag ratio decreases with increasing propeller thrust. Apparently the

propeller slightly reduces the wing eﬃciency. Another observation is that with increasing propeller radius, the upstream

eﬀects of the propeller on the wing reduce. For the 1

.

50

Rp

case an additional simulation was performed where no

swirl component was introduced by the actuator disk, denoted no swirl. It shows that the swirl component has only a

minor impact on the wing loading. Thus, the reduction of swirl in the wingtip ﬂowﬁeld due to the propeller does not

cause a signiﬁcant change in wing loading and the observed changes are mainly an eﬀect of the axial velocity increase.

However in general, it is concluded that the upstream eﬀect of the propeller on the wing loading is very limited for the

investigated thrust range. A closer look at the downstream interaction of the wing on the propeller is presented in the

next section.

VII. Propeller–Wing Analysis

To check the accuracy of PROPR for the non-uniform wingtip ﬂowﬁeld, and to investigate the unsteady behaviour

of a wingtip-mounted pusher propeller, a fully resolved propeller–wing CFD simulation was performed. The original

XPROP propeller was simulated installed on the wingtip at optimum operating condition in terms of

β0.7Rp

and

J

at a

thrust of T=0.30Diso.

In Fig. 13 a the normalized blade thrust and torque as function of blade phase angle are shown, as deﬁned in Fig. 14

b. In addition, the mean of the thrust and torque obtained from the transient CFD simulation are shown, as well as the

thrust and torque values calculated using PROPR. As expected, the blade thrust and torque vary considerably over a

rotation due to the circumferential non-uniformities in the ﬂowﬁeld that were shown in Fig. 5. Following the trajectory

of the blade, clear trends are observed:

•ϕ=0◦: Initial position, blade pointing up and perpendicular to the wing surface.

•ϕ=90◦: Blade is fully outboard and subjected to the largest negative tangential velocities, thus highest thrust.

12

36031527022518013590450 36031527022518013590450

1.2

1.1

1.0

0.9

0.8

0.7

0.6

1.2

1.1

1.0

0.9

0.8

0.7

0.6

Propeller blade phase angle φ (deg)

Blade thrust T / TPROPR

Blade torque Q / QPROPR

CFD

PROPR

CFD mean

Fig. 13 Installed XPROP propeller blade thrust and torque evolution over a complete rotation for

T=0.30Diso.

•ϕ=

180

◦

: Blade is again perpendicular to the wing but now pointing down. Thrust delivered with inﬂow from

under the wing is slightly lower.

•ϕ=

270

◦

: At this angle the blade is fully immersed in the wake region of the wing, showing a clear local peak in

thrust, due to the lower axial velocity. This causes an increased angle of attack of the blade sections.

Identical trends are observed when investigating the torque evolution. The diﬀerence in mean thrust and torque

obtained between CFD and PROPR are very similar to those obtained for the isolated propeller in Section IV. The blade

thrust and torque are overestimated 3

.

3% and 4

.

0% by PROPR respectively. This provides conﬁdence in the validity of

PROPR given these non-uniform ﬂowﬁelds.

To get some more insight in the blade loading evolution, in Fig. 14 a the propeller blade thrust distribution is plotted

at various blade positions as deﬁned in Fig. 14 b. The blade distribution from PROPR is also shown. It is seen that the

thrust distribution over the blade from PROPR is nearly identical to that found in the transient CFD simulation over

blade 1. Blade 2 and 3 are subjected to the largest tangential velocity ﬁeld and indeed show the highest thrust. Most

notably, these blades experience a signiﬁcantly higher thrust at the root sections of the blade. Blade 5 experiences the

lowest blade loading because, as was shown in Fig. 5, the tangential velocity ﬁeld at this location is near zero. A drop in

thrust near the root occurring over blade 6 is seen, because it is immersed in a ﬂowﬁeld with locally positive tangential

velocity. Blade 6 experiences this positive tangential velocity near the root, because it crosses the tip vortex of the wing.

This becomes clear from Fig 15, where a tangential and an axial vorticity isosurface is shown at such levels that they

identify the propeller blade tip vortices and wingtip vortex respectively. The propeller blades are at the same position as

in Fig. 14 b. It is clear that blade 6 is starting to cross the wingtip vortex.

13

1

2

3

4

5

6

Thrust distribution T´ (N / m)

Radial coordinate r / Rp

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

100

0

50

−50

150

200

250

300

350

CFD - blade 1

CFD - blade 2

CFD - blade 3

CFD - blade 4

CFD - blade 5

CFD - blade 6

PROPR

a) Propeller blade thrust distribution comparison. b) Definition of blade positions.

yp

zp

φ

5

6

4

3

2

1

Fig. 14 Comparison of XPROP propeller blade thrust distributions at diﬀerent blade positions for

T=0.30Diso.

a) Side view of vorticity isosurfaces.

b) Rear view of vorticity isosurfaces.

ωx = −900 s-1

ωt = 800 s-1

wingtip vortex

blade tip vortices

Fig. 15 Vorticity isosurfaces identifying the XPROP propeller blade tip vortices and wingtip vortex.

14

VIII. Conclusions

A design framework for wingtip-mounted pusher propellers was established and veriﬁed with RANS CFD sim-

ulations. It was found that the following approach is valid: First a wingtip ﬂowﬁeld was extracted from an isolated

wing simulation. Then, this ﬂowﬁeld was circumferentially averaged and used in a validated lifting-line based propeller

analysis and optimisation routine named PROPR for aerodynamic design optimization. The upstream eﬀect of the

propeller on the wing performance was investigated with an actuator disk representation of the propeller in multiple

wing simulations and was found to be very limited for the tested thrust levels. This was a requirement for the taken

approach. However, a trend of increasing wing lift coeﬃcient and decreasing lift-over-drag ratio was observed with

increasing propeller thrust, which may become signiﬁcant for higher thrust levels than currently investigated. At last,

the resulting propeller performance from PROPR was in line with time-averaged propeller loading of fully resolved

propeller-wing RANS CFD simulations, providing conﬁdence in the validity of the approach. This was despite the large

ﬂuctuation found in the transient propeller blade loading due to circumferential non-uniformities in the inﬂow ﬁeld.

With this design framework for wingtip-mounted pusher propellers, various conclusions on propeller design for

wingtip-mounted pusher propellers are drawn:

•

The possible propulsive eﬃciency gains for the propeller due to installation are signiﬁcant: Up to 16% increase in

eﬃciency was achieved at the lowest investigated thrust level of 5% of the wing drag, decreasing with a reducing

slope to approximately 7.5% for the highest investigated thrust level of 100% of the wing drag.

•

The propulsive eﬃciency gain was only signiﬁcantly dependent on the propeller radius for low thrust levels of

less than 30% of the wing drag.

•

It was found that eﬀectively the propeller geometry is optimized for the required thrust level and to a lesser degree

for the non-uniformity in the ﬂowﬁeld.

•

Propeller blade optimization and installation result in higher proﬁle eﬃciency in the blade root sections and a

more inboard thrust distribution over the blade.

Considering the propulsive eﬃciency beneﬁts found in this study, wingtip-mounted pusher-propellers should be

considered for (hybrid)-electric concepts. The propeller thrust should then be a design variable, determining together

with the wing lift the resulting eﬃciency beneﬁt from this aerodynamic interaction.

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