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PROPELLER OPTIMIZATION STRIVE TO PERFORMANCE / ACOUSTIC TRADE-OFF

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PROPELLER OPTIMIZATION STRIVE TO PERFORMANCE / ACOUSTIC TRADE-OFF

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This paper describes the design of a propeller-based electric-propulsion system for hover condition. The design procedure harnesses modeFRONTIER optimization framework with various single-and multi-objective hybrid optimization schemes. Several analyses were integrated to the design framework and propeller geometry optimizations were conducted. The multi-objective problem consisted of trade-off between the contradicting goals of performance (required electric power at hover) and acoustics (tonal overall sound-pressure-level). Using various hybrid optimization schemes, the Pareto tradeoff fronts were found for 2, 3, and 4 bladed propellers. These propellers are compared to an off-the-shelf propeller blade (Mejzlik 18x6) which is used as a reference. This reference propeller proves to be good design , compared to the optimized results. Still, from the optimized Pareto results, 4 propeller configurations were chosen to be fabricated and tested. These configurations are optimized by their acoustic or performance trade-off. These optimized propellers represent a good compromise , which is better than the reference propeller.
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EUROGEN 2021
14th ECCOMAS Thematic Conference on
Evolutionary and Deterministic Methods for Design, Optimization and Control
N. Gauger, K. Giannakoglou, M. Papadrakakis, J. Periaux (eds.)
Streamed from Athens, Greece, 1719 May 2021
PROPELLER OPTIMIZATION
STRIVE TO PERFORMANCE / ACOUSTIC TRADE-OFF
Ohad Gur1, Jonathan Silver2, Radovan Dítě3, and Raam Sundhar3
1 Mechanical Design Department
2 Aerodynamic Department
IAI Israel Aerospace Industries, Lod, 70100, Israel
e-mail: {ogur,jsilver}@iai.co.il
3 Aerospace Engineer
Mejzlik Propellers s.r.o., Brno-Židenice, 61500, The Czech Republic
e-mail: {dite,sundhar}@mejzlik.eu
Abstract
This paper describes the design of a propeller-based electric-propulsion system for hover
condition. The design procedure harnesses modeFRONTIER optimization framework with
various single- and multi-objective hybrid optimization schemes. Several analyses were inte-
grated to the design framework and propeller geometry optimizations were conducted.
The multi-objective problem consisted of trade-off between the contradicting goals of perfor-
mance (required electric power at hover) and acoustics (tonal overall sound-pressure-level).
Using various hybrid optimization schemes, the Pareto tradeoff fronts were found for 2, 3,
and 4 bladed propellers. These propellers are compared to an off-the-shelf propeller blade
(Mejzlik 18x6) which is used as a reference. This reference propeller proves to be good de-
sign, compared to the optimized results. Still, from the optimized Pareto results, 4 propeller
configurations were chosen to be fabricated and tested. These configurations are optimized
by their acoustic or performance trade-off. These optimized propellers represent a good com-
promise, which is better than the reference propeller.
Keywords: Propeller, Performance, Acoustic, Electric, UAM, Optimization, MDO
O. Gur, J. Silver, R. Dítě, and R. Sundhar
1 INTRODUCTION
Urban Air Mobility (UAM) development has been expanding since the publication of
UBER-Elevate white paper published in 2016.[1] Since then, numerous manufacturers have
been developing various UAM configurations. For example Refs. [2] and [3] show two possi-
ble configurations for such vehicles; most of which are multi-propeller based. This makes the
propellers a critical item in these vehicles, especially at hover conditions. At hover the propul-
sion system performance is at its highest required power,[4] thus propeller required-power at
hover impacts the overall vehicle performance. In addition, the acoustic signature at hover is
the highest and together with new regulations [5] the importance of optimized hovering propel-
lers increases dramatically.
In this paper the design procedure for hover propellers is depicted. The design procedure
which includes both analyses, validation, and optimization will be reviewed. From this design
process, several propellers were chosen to be fabricated.
Although UAM requires high thrust, an equivalent small propeller is specified, thus the en-
tire design, fabrication and testing procedures are simpler and more rapid. Still, all results are
highly related to all hovering configuration, with the appropriate scaling.
This makes the discussed design procedure very useful for future, large scale hovering-
propeller design, especially confronting the complex performance/acoustic tradeoff.
2 DESIGN SPECIFICATION
As a reference propeller, the Mejzlik 18×6 is used. Figure 1 shows the Mejzlik 18×6 pro-
peller and Figure 2 depicts its geometric properties as function of radial coordinate, r, i.e.
pitch, β, chord-to-radius ratio, c/R, and thickness-ratio, t/c, distribution. A design criterialimits
the propeller radius to R 0.23 m, which is the radius of the reference Mejzlik 18×6 propeller.
The propeller in the current effort is specified according to its produced thrust. At design
conditions, the Mejzlik 18×6 gives thrust of T = 2.8 kgf which is established as the required
thrust for hover (static operation) for all presented designs. The propulsion system is based on
Sobek 20-38 Spider brushless DC motor, with Kontrol-X 55LV electronic speed controller,
ESC. The acoustic signature is optimized for an observer which is located at azimuth angle,
θ=100º, relative to the propeller axis, as depicted in Figure 3. This angle fits the azimuth
which generally exhibits the highest sound-pressure-level signature for operated propellers.[6]
The above specifications allow the design of propeller with various goals. The most im-
portant is the required battery power, electric power, Pe. Different from other design efforts
which refer to the shaft power, here the battery power is the most important, thus the electric
propulsion system is to be considered through the design iterations.[7] The second parameter
to minimized is the acoustic signature as heard by the observer. This will be considered as the
overall sound pressure level, OASPL, at the position of the observer. In the current effort, on-
ly the tonal component will be used as design goal. The tradeoff between these two goals is to
be found using optimization.
O. Gur, J. Silver, R. Dítě, and R. Sundhar
Figure 1: Mejzlik 18×6 Propeller, front and top views
Figure 2: Mejzlik 18×6 Propeller, front and side views
Figure 3: Design conditions of observer-propeller attitude
R=0.2293 m
θ=100º
Thrust
Hover
Propeller
Observer
O. Gur, J. Silver, R. Dítě, and R. Sundhar
3 PROPELLER’S ANALYSES
To allow proper optimization, the required analyses should be both accurate and efficient,
i.e. using low computer resources. In this case, three analyses are used: propeller performance,
electric system, and propeller acoustic analysis.
3.1 Propeller Performance Analysis
The propeller performance model is based on blade-element model (BEM) which was ex-
tensively validated in the past.[8] Although, most past validation cases were of axial flight re-
gime, in the current case hover condition is treated which was also validated.[7]
BEM analysis uses a 2-D aerodynamic database based on the geometry of the propeller
cross sectional airfoils. Accuracy of the 2-D aerodynamic database is an important part of
BEM level-of-confidence. Thus, substantiation of the current database was conducted using
EZair RANS (Reynolds Average Navier-Stokes) software.[9] In addition, some installation
losses, due to the propeller and test rig interaction, were implemented on the BEM analysis.
3.2 Electric System Analysis
In the current effort a simple motor model is used to find the required electric power. The
model is based on four parameters: speed constant, Kv, armature resistance, Ra, no-load cur-
rent, I0, and controller efficiency, ηc.[10] The model is based on the following assumptions:
a. Power factor is equal to unit. This assumption is applicable to small brushless Perma-
nent Magnet (PM) motors.
b. Magnetic losses (eddy/Foucault Current and magnetic hysteresis) can be neglected.
3.3 Acoustic Analysis
The current acoustic model predicts only the tonal noise of the propeller. The model is
based upon Farassat’s formulation[11] as used in former design cases[12]. The model went
through extensive validation for various cases of propeller on various flight regimes.[13],[14]
4 OPTIMIZATION
Design technique is similar to former cases accomplished with the same tools. These tools
include using the validated analysis tools (BEM, electric model, and acoustic model) together
with Esteco’s modeFRONTIER framework.[13],[7]
Figure 4 presents a screen capture of modeFRONTIER framework. This design environ-
ment enables the integration of different simulation models into a single synergetic design
tool. In addition, it allows the use of various optimization procedures, thus a multi-
disciplinary design optimization, MDO, tool is obtained. In the current case, first the propeller
performance is calculated and then the propeller acoustic is estimated. The use of mode-
FRONTIER enables an easy usage of any of the input or output parameters, either as design
variables or to include it in the goal function and constraints.
In addition, a geometric pre-analysis and performance post-analysis, are implemented us-
ing Excel spread sheet. The geometry pre-analysis is used to parametrize the design variables
which are the pitch, β, thickness-ratio, t/c, and chord-to-radius ratio, c/R, distribution along
the blade. The current effort uses a Bezier spline to achieve smooth distribution of the geome-
try, hence 6 design parameters are used for each distribution. Thus, the design problem con-
tains total of 18 design variables. All airfoils are based on the Mejzlik 18×6 cross sections,
and the propeller radius is fixed to R=0.23 m.
O. Gur, J. Silver, R. Dítě, and R. Sundhar
To ensure the structural properties of the optimized designs, two geometric constraints are
satisfied. First the blade thickness distribution should not be lower than the original Mejzlik
18×6. Thin blade might be “soft” or exposed to high stresses, which might cause unacceptable
aeroelastic behavior, and high deflections. In addition, the root chord should not be larger than
the Mejzlik 18×6’s root chord. This might cause a very thick hub which increases the propel-
ler weight.
To overcome these issues, the design procedure incorporated two geometric constraints
over the thickness distribution and root chord. The first constraint limits the thickness distri-
bution and the second the rood chord. The thickness distribution, t (not t/c) has to be higher or
equal to the Mejzlik 18×6 up to r/R=0.90, with a tolerance of 0.1 mm. The blade tip (0.9< r/R
<1) was freed from this constraint the impact over the design was high and it seems the im-
portance of this constraint, at the very tip of the blade, is less important. The root chord is lim-
ited to c/R < 0.15. Note that the Mejzlik 18×6’s c/R = 0.14 at the root (Figure 2), thus small
increase of the root chord is allowed.
The performance post-analysis excel module is used to find the propeller-motor matching
speed. Using the performance calculation, for given propeller geometry, several rotational
speeds are calculated. To find the correct rotational speed, which the propeller produces the
required thrust, T =2.8 kgf, a linear interpolation is used. Then, using the electric model the
electric power, Pe, is found.
Figure 4: modeFRONTIER design framework screen capture
Performance
Calculation
Acoustic
Calculation
Electric system / Propeller Matching
Geometric
pre-analysis
O. Gur, J. Silver, R. Dítě, and R. Sundhar
Separate optimizations procedures were conducted for 2,3, and 4 bladed propellers. The
aim is to find, for different number-of-blades, the tradeoff between the electric power and the
overall sound-pressure-level, OASPL, as defined in the problem specification of section 2.
For each specific number-of-blades, the first stage is to find the Utopia Point in the design-
goal space. For a multi-objective problem containing two different cost-functions, this is ac-
complished by two separate single-objective optimizations; the first using the electric power
as an objective and the second using the OASPL as the design goal objective. To demonstrate
the procedure, the 2-bladed case is considered in what follows.
The single-objective optimizations are conducted using hybrid-optimization scheme based
on the available methods in modeFRONTIER. This hybrid scheme can be easily transfer to
any other available optimization framework.
First, pilOPT scheme is used. This is highly autonomous method which uses multi-strategy
self-adapting algorithm. No design-of-experiment, DOE, is required, nor any other a-priori
definition. pilOPT harnesses both surrogate-based (response surface) methods and implicit-
optimization methods, thus combines both local and global search techniques.
Using pilOPT, some candidates for further optimization are chosen. These are used as ini-
tial guess for constrained gradient-based optimization. In the current effort, sequential quad-
ratic programming, SQP, is used. Each initial guess is optimized into better design; thus a
population of optimized solutions are gathered. These are finally used as the initial population
for genetic algorithm, GA, scheme, which hopefully finds the global-optimal solution.
Figure 5 shows the results for the two single-objective procedures, conducted for the 2-
bladed case. The left column is the minimum electric power, Pe, while the left column is the
minim overall sound-pressure-level OASPL. The upper charts show the progress of the cost-
function as function of the iteration, Lower charts includes the same results in cost-function
space.
Each analysis lasts about 5 sec. on a desktop computer using 8 parallel threads of calcula-
tion. The entire optimization scheme last about 5÷10 hours, mostly over-night. Some differ-
ences between the two cases are visible, mostly for the ratio between the SQP and GA
analysis. While the min. Pe case uses much more iteration of SQP, the min. OASPL uses more
iterations of GA scheme.
In addition, for the min Pe, the SQP procedure went into a local minimum. Then, the GA
scheme escaped from this minimum into better region, supposedly global minimum. This is
very common for gradient based methods such as SQP to converged to a local minimum. GA
is less accurate with its minimum location, but it is capable of hopping to various minimum
regions, i.e. global search capabilities. In comparison to the minimum Pe, the minimum
OASPL case exhibits the ability of SQP to locate an optimum which later was improved by
the GA scheme. This Hybrid usage of various different scheme, harnesses each scheme’s
strength to a synergetic optimization procedure.
Note that the designer should carefully monitor the optimization and decide when to move
from one method to the other, and which DOE to re-use when transferring from pilOPT to
SQP and then from SQP to GA.
Gathering both results of the two single-goal optimization is presented in Figure 6. On this
figure also the reference Mejzlik 18x6 propeller is presented as a green circle. The cloud of
results can be used to substantiate DOE which is then used to optimize the Pareto frontier.
This is done using a multi-goal scheme, in the current case mainly by MOGA and NSGA
schemes. The final Pareto frontier after optimization is presented as a black curve in Figure 6.
Note that the cloud of results from the two single-objective optimizations, draw the final Pare-
to with relatively good accuracy. Thus, the Utopia-point estimation, actually plays an im-
portant role for the multi-objective scheme.
O. Gur, J. Silver, R. Dítě, and R. Sundhar
Figure 5: 2-blades Utopia Point, single-objective optimization results
Left: minimum electric power, Pe, Right: minimum overall sound-pressure-level OASPL
Figure 6: 2-blades single-objective results compared to the reference Mejzlik 18x6 and final Pareto frontier
Min. Pe
Min. Pe
Min. OASPL
Min. OASPL
O. Gur, J. Silver, R. Dítě, and R. Sundhar
The multi-goal optimization was conducted 3 times for 2, 3, and 4 blades configurations.
Each uses the same procedure mentioned above. Pareto frontiers which resulted from the op-
timization are presented in fig. 7. Propellers based on the Mejzlik 18×6 blades are also
marked by red circles. The design influence of number-of-blades is prominent increased
number-of-blades causes both OASPL decrease and Pe increase a tradeoff which the de-
signer should consider carefully.
From these Pareto frontiers, 4 propeller configurations were chosen these are marked
with arrows in fig. 7 and include:
a. 2 blades, minimum Pe (2B min Pe)
b. 2 blades, minimum SPL (2B min SPL)
c. 3 blades, minimum Pe (3B min Pe)
d. 4 blades, minimum Pe (4B min Pe)
These selections are based on motivation for improving the already adequate Mejzlik 18x6,
on different aspects. The minimum Pe is being chosen as improved Pe without penalizing the
OASPL. Similarly, min. OASPL is chosen with no penalty over Pe.
The propeller characteristics are depicted in table 1, and their blade geometric parameters
in fig.8. The clear difference is the rotational speed. This appears both as the mechanism of
reducing the OASPL for the 2 blades propeller and for achieving the proper thrust for the 3
and 4 bladed propeller. To reduce the rotational speed, thus achieving min SPL for the 2 blad-
ed propeller, the pitch was increased and the chord slightly increased as well.
For the 3 and 4 blades, the rotational speed had to decrease to achieve the required thrust,
T=2.8 kgf. The chord cannot decrease due to the geometric constraint, thus the chord re-
mained similar and thickness remains above the Mejzlik 18×6 blade. To maintain high
enough rotational speed, the pitch decreases for the 3 and 4 bladed propellers, thus the electric
efficiency, ηe, and figure-of-merit, FM, remain relatively high.
While the 3-bladed propeller exhibits high FM and low ηe, the 4-bladed exhibits low FM
and high ηe. Generally, all tradeoff in such complex design case, is beyond simple intuition
and it is a result of handling with all constraints while striving to minimize all design goals.
This proves the advantage of such MDO (multidisciplinary design optimization) framework,
which takes contradicting requirements and find the best compromise.
O. Gur, J. Silver, R. Dítě, and R. Sundhar
2B min Pe
2B min SPL
3B min Pe
4B min Pe
Figure 7: Pareto frontiers for the optimized results
Red circles mark the results for propeller based on Mejzlik 18×6 blades
2-Blades
Mejzlik 18×6
2-Blades
min.Pe
2-Blades
min.SPL
3-Blades
min.Pe
4-Blades
min.Pe
Electric Power, Pe, W
445
425
445
455
495
Shaft Power, Pshaft, W
340
335
345
350
375
Engine Speed, Ω, rpm
5,100
5,200
4,600
4,700
4,500
Figure-of-merit, FM
0.68
0.69
0.67
0.66
0.62
Electric efficiency, ηe
0.77
0.79
0.77
0.67
0.76
Tonal OASPL, dB
66.1
66.1
64.7
56.9
48.3
Table 1: Optimized propeller characteristics
O. Gur, J. Silver, R. Dítě, and R. Sundhar
Figure 8: Optimized blade geometries
O. Gur, J. Silver, R. Dítě, and R. Sundhar
5 CONCLUSIONS
In this paper a comprehensive and methodic design process for hover-propeller is de-
scribed. The design process has to have a detailed specification which is based, in the current
case, on an existing propulsion system with of-the-shelf propeller. In the basis of the design
process are 3 analytic models: blade-element model for the propeller performance estimation,
electric model for the propulsion system characteristics, and acoustic model which analyzes
the propeller tonal sound-pressure-level. Each of these models was previously validated ver-
sus various results in the literature.
These analyses were incorporated in a design framework based on modeFRONTIER soft-
ware and a multidisciplinary-design-optimization environment was substantiated. This envi-
ronment includes, beside the analyses, various definitions of design variables, constraints, and
design goals. Hence a multi-objective optimization problem is defined.
The design framework was run 3 times for designing 2, 3, and 4 bladed propellers. First, a
Utopia-point was found using a single-goal optimization process, which resulted with mature
design-of-experiment for the final multi-goal scheme. The optimization harnesses various
schemes such as multi-strategy, gradient-based, and evolutionary.
The optimization scheme was resulted with a Pareto frontier which exhibits the tradeoff
between the propulsion-system performance and its acoustic signature. From these tradeoffs,
optimized propeller configurations were chosen. These are to be fabricated and tested. The
test results for both performance and acoustics is to be compared with the design trends, thus
the design process is to be validated.
In the current effort 4 propeller were resulted. Two of them are 2 bladed, minimal electric
power and minimal acoustic signature. In addition, 3 bladed and 4 bladed propellers for min-
imum electric power were chosen. The four propellers exhibited some improvements over the
reference of-the-shelf propeller. These improvements can be chosen by the designer according
to the resulted Pareto frontiers. This demonstrates the use of Pareto tradeoff results as a quan-
titative, important decision support tool, during design process.
ACKNOWLEDGMENTS
The research was funded by Israel-Europe Research & Innovation Directorate, ISERD, of
the Israel Innovation Authority, and DELTA-2 programme of the Technology Agency of the
Czech Republic, TAČR. The authors thank these two organizations for their generous contri-
butions.
O. Gur, J. Silver, R. Dítě, and R. Sundhar
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... Pareto frontiers which resulted from the optimization are presented in Fig. 13. The optimization method and additional details concerning the solution procedure are available in Ref. [18]. ...
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Propeller design is a complex task that involves a variety of disciplines, such as aerodynamics, structural analysis, and acoustics. A new method of designing an optimal, propeller that is based on a multidisciplinary design optimization approach is presented. By combining various analysis tools with an optimization tool, a powerful and flexible design method is obtained. During the design process, three different optimization schemes are used, leading the design to its optimal goal. This new method is applied to the design of a propeller for an ultralight aircraft. Several optional designs for different design goals are presented. The results of the new method are compared with the results of the classic design method based on Betz's condition, which considers only the aerodynamic performance of the propeller. The importance of addressing the characteristics of the entire air vehicle, its aerodynamic characteristics, and its propulsion system (engine, gear box, etc.), rather than only the isolated propeller is emphasized.
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A review of propeller noise prediction technology is presented which highlights the developments in the field from the successful attempt of Gutin to the current sophisticated techniques. Two methods for the prediction of the discrete frequency noise from conventional and advanced propellers in forward flight are described. These methods developed at MIT and NASA Langley Research Center are based on different time domain formulations. Brief description of the computer algorithms based on these formulations are given. The output of these two programs, which is the acoustic pressure signature, is Fourier analyzed to get the acoustic pressure spectrum. The main difference between the programs as they are coded now is that the Langley program can handle propellers with supersonic tip speed while the MIT program is for subsonic tip speed propellers. Comparisons of the calculated and measured acoustic data for a conventional and an advanced propeller show good agreement in general.
Fast-Forwarding to a Future of On-Demand Urban Air Transportation
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This Passenger Drone Is Set to Have Its First Test Flight Next Week
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on unmanned aircraft systems and on third-country operators of unmanned aircraft systems
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