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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, 17–19 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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