aerodynamics optimization of a ducted coaxial rotor in

Research ArticleAerodynamics Optimization of a Ducted Coaxial Rotor inForward Flight Using Orthogonal Test Design

Yuening Jiang 12 Hai Li12 and Hongguang Jia13

1Changchun Institute of Optics Fine Mechanics and Physics Chinese Academy of Sciences Changchun 130033 China2University of Chinese Academy of Sciences Beijing 100049 China3Chang Guang Satellite Technology Co Ltd Changchun 130000 China

Correspondence should be addressed to Yuening Jiang atpynjiang163com

Received 30 September 2017 Revised 11 January 2018 Accepted 30 January 2018 Published 28 May 2018

Academic Editor Mickael Lallart

Copyright copy 2018 Yuening Jiang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To investigate the aerodynamic complexities involved in the combination of freestream and propellerrsquos suction flow field of ductedcoaxial rotors system in forward flight an orthogonal 11987116(43) test design has been applied to optimize the design parametersincluding forward speed pitch angle and axial spacing between rotors Multiblock grids and Multiple Frame of Reference (MFR)method are adopted for calculating aerodynamic performance of the system hover characteristic was compared with experimentaldata obtained from the test stand and the thrust performance is well predicted for various rotor spacing and a range of rpm Thissolution approach is developed for the analytical prediction of forward flight and the simulation results indicated that the designparameters influenced lift drag and torque reduced in the order wind speed gt rotor spacing gt pitch angle wind speed gt pitchangle and rotor spacing gt wind speed gt pitch angle respectively The optimal rotor spacing and pitch angle were determined tomaximize the aerodynamic performance considering high lift low drag and trimmed torque

1 Introduction

The small unmanned aerial vehicles (SUAVs) with ductedrotor configuration offer a number of significant advan-tages over other vertical take-off and landing (VTOL) flightvehicles [1] In recent decades they generated considerableinterests in both military and civilian applications Practicaluses for these flight vehicles have extended to aerial map-ping disaster surveillance and military reconnaissance [2]Security is notably improved through shrouding an isolatedrotor within a duct which decreases the possibility of rotorsstriking person or objects

The efficiency of aerodynamic configuration is critical forthe performance of VTOL vehicles [3] It has been observedthat the hovering rotor system produces more aerodynamicefficiency with duct which generates higher total thrustdue to low pressure region on the duct lip and intensifiesinflow distribution by accelerating flow towards the outboardsections of interior rotors [4 5] Since coaxial counterrotatingrotors produce the net thrust instead of an isolated rotordesign in conventional way the diameter of the rotors can

be decreased to take the same amount of weight [6 7]Compared to single rotor system the torque generated bycoaxial rotor can be opposed by the counterrotating rotortherefore no flow deflector or rudder reflection is required

Unlike the fixed-wing aircraft vehicles or conventionalrotational wing vehicles on the ducted contrarotating rotorsthe wake of each rotor is significantly interacted with oneanother and the tip-vortex is highly influenced by theshrouded duct structure [8ndash10] Additionally for a fixed pitchangle system the various flight velocities produce axial flowthrough the rotors that increase the angle of attack (AOA) ofblade section in the forward flight

Computational fluid dynamics (CFD) is adopted to ana-lyze complex viscous flow in a wide range of flight conditionsGenc [11] verified the 119896-119896119871-120596 transition model which pre-dicted more accurate laminar separation and reattachmentof thin airfoil by comparison with 119896-120596 SST transition model119896-120596 SST turbulence model and 119896-120576 turbulence model ThenGenc et al [12ndash14] numerically simulated the elimination ofseparation bubble in the application of transition models byfluent Lakshminarayan and Baeder [15] used compressible

HindawiShock and VibrationVolume 2018 Article ID 2670439 9 pageshttpsdoiorg10115520182670439

2 Shock and Vibration

Table 1 Forward flight aerodynamics factor-level form

Factor level Pitch angle (120572∘) Flight velocity (Vmsdotsminus1) Rotor spacing (Hmm)1 A1 85 B1 5 C1 382 A2 80 B2 10 C2 573 A3 75 B3 15 C3 6654 A4 70 B4 20 C4 76

Rotor Spacing

Z

YX

(a) Rotor spacing of the coaxial rotors

D

Y

LT

Z

YX

(b) Pitch angle and forward flight velocity

Figure 1 Configuration of VTOL aircraft in forward flight

RANS solver with sliding mesh interpolation scheme topredict instantaneous thrust and power influenced by theinteraction between coaxial rotors Singh et al [16] used low-and high-fidelity with loose coupling method to computa-tional simulated steady and unsteady performance of elasticcoaxial rotor with vibratory hubloads

Experiment techniques for aircraft vehicles have alsodeveloped significantly over time Schmaus and Chopra [17]evaluated the vibratory loads of rigid coaxial rotor for testingin the wind tunnel and explored the influence of rotorphase on vibratory hubloads Genc et al [18] performedan experimental study on the pressure distribution andaerodynamic forces of NACA2415 aerofoil at low Reynoldscarried out in the suction-type wind tunnel

Many experimental and numerical efforts had beendone to investigate the forward flight performance [19ndash23] However most previous studies were concentrated onoptimizing the shape of duct or measuring the aerodynamicstep-by-step Rarely has research been proposed to maximizethe fundamental aerodynamic performance issues whichare associated with the determination of the rotor spacingbetween upper and lower rotors taking into account bothattitude and speed of the ducted coaxial rotors configuration

In this work the identical three-dimensional ductedpropeller configuration has been established to validate theefficiency of numerical scheme in achieving high-fidelitypredictions of hybrid flow field and compared with theexperiments measured by the hovering aerodynamic perfor-mance test stand of our laboratory The aim of the hoverperformance investigation is to apply this analytical approachto forward flight Besides this solving method aims to formthe fundamental exploring correlation between vibratoryloads and blade loads thereby aiding in a better selectionof blade structural properties in manufacturing Orthogonal

test design is designed to analyze the dominant factor to eachaerodynamics Subsequently the variation trends of aero-dynamic performance are characterized with three leadinginfluence factors including pitch angle freestream velocityand rotor spacing The optimized rotor spacing and flightpitch angle are determined from a wide range of factors tomaximize forward flight performance of our system

2 Orthogonal Test Design

According to experimental purpose three influence factorsgiven by incident angle to the freestream in forward flight(120572∘) flight speed (Vmsdotsminus1) and rotor spacing (Hmm) arechosen and the level of factors have been decided Variationtendency of aerodynamic performance with proposed fourfactor levels for each influenced factor can be compared accu-rately and optimum parameter combination can be designedwith three factors taken into consideration Corresponding tothe four levels of pitch angles listed in Table 1 wind speed isgiven by 5ms 10ms 15ms and 20ms and rotor spacingrepresents the distance between top and bottom rotor rangingfrom 38mm to 76mm Figure 1(a) shows the longitudinalforces acting on the calculation configuration in forwardflight then lift and drag can be calculated as follows

119871 = 119879 sin120572 + 119884 cos120572

119863 = 119884 sin120572 minus 119879 cos120572(1)

where 119879 and 119884 refer to thrust and tangential force which canbe predicted by numerical approach

Orthogonal array 11987116(43) is adopted to optimize theprescription of forward flight ducted coaxial rotors [24]Table 2 summarizes the numerical calculation scheme

Shock and Vibration 3

Table 2 Test number of forward flight aerodynamics

Test number 120572∘ Vmsdotsminus1 Hmm1 A1 B1 C12 A1 B2 C23 A1 B3 C34 A1 B4 C45 A2 B1 C26 A2 B2 C37 A2 B3 C48 A2 B4 C19 A3 B1 C310 A3 B2 C411 A3 B3 C112 A3 B4 C213 A4 B1 C414 A4 B2 C115 A4 B3 C216 A4 B4 C3

3 Numerical Simulation

31 Solving Method The flow field is divided into multisub-domains to solve the complexity of suction flow and front-flow in forward flight Interface boundary condition has beenestablished between subdomains to keep flux conservationcoupled with unstructured overset mesh Figure 2 showsthe computational rotor Spatial discretization of inviscidterms is computing using Roersquos flux difference splittingformat and second-order central differencing is employedto compute viscous terms Time integration is discrete usingsecond-order implicit difference scheme Spalart-Allmarasturbulence model is employed to account for the turbulencein the vortex core attributed to the rotating effect

Multiple frames of reference (MFR) have been used toanalyze the situation involving domains that are rotatingrelative to stationary domains that allow for the adequate pre-dictions of complex flows dominated by transient interactionsof the relative movement between rotating and stationarydomains

Moving coordinate system rotates at the angular velocity997888rarr120596 relatively to the stationary coordinate system the unitvector 997888rarr119886 represents rotating axis as seen in Figure 3 Theorigin of rotation coordinate system is defined by the vector997888rarr1199030associatedwith stationary systemThus997888rarr120596 can be described as

997888rarr120596 = 120596997888rarr119886 (2)

Any certain point in the computational domain of rota-tion system is determined by position vector997888rarr119903 and the originpoint The transformation of velocity from static system torotated system can be realized as follows

997888rarrV 119903 =997888rarrV minus 997888rarr119906 119903 (3)

In (3) 997888rarrV 119903 and997888rarrV represent the relative velocity and the

absolute velocity respectively 997888rarr119906 119903 =997888rarr120596 times 997888rarr119903 is the converted

acceleration

Figure 2 Computational model of rotor

movingcoordinatesystem

y

stationarycoordinatesystem

axis ofrotationx

z

x y

R

CFD domainz

rarrr0

rarr

rarra rarrVt

rarrr

Figure 3 Sketch of multiframe reference model

Additional terms in momentum equation lead to theincrease of fluid acceleration derived from the multiplemotion individual problems As a consequence governingequations can be expressed in two ways The momentumequation which is produced on the basis of relative and abso-lute velocity separately forms the foundation of fluid govern-ing equationsThe governing equations of fluid mechanics interms of relative velocity can be written as follows

Continuity Equation

120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0 (4)

Momentum Equation

120597120597119905(120588997888rarrV 119903) + nabla sdot (120588

997888rarrV 119903997888rarrV 119903)

+ 120588 (2997888rarr120596 times 997888rarrV 119903 +997888rarr120596 times 997888rarr120596 times 997888rarr119903 )

= minusnabla119901 + nabla sdot 997888rarr120591 + 997888rarr119865

(5)

In (5) Coriolis acceleration term 2997888rarr120596 times997888rarrV 119903 and centripetalacceleration term 997888rarr120596 times 997888rarr120596 times 997888rarr119903 are two additional kinds ofacceleration

Energy Equation

120597120597119905(120588119864119903) + nabla sdot (120588

997888rarrV 119903119867119903) = nabla sdot (119896nabla119879 + 120591119903 sdot V119903) + 119904ℎ (6)

where 120591119903 represents the viscous stress term in the form ofrelative velocity derivation In (6)119864119903 = ℎminus119901120588+(12)(V2119903minus119906

2119903)

is defined to be the relative intrinsic energy and119867119903 = 119864119903+119901120588is relative total enthalpy


The controlling equations with respect to absolute veloc-ity format in rotation coordinate system can be reevaluated as(7)

120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0

120597120597119905120588997888rarrV + nabla sdot (120588997888rarrV 119903

997888rarrV ) + 120588 (997888rarr120596 times 997888rarrV )


120597120597119905120588119864 + nabla sdot (120588997888rarrV 119903119867 + 119901997888rarr119906 119903) = nabla sdot (119896nabla119879 + 120591 sdot V) + 119904ℎ

(7)

The Coriolis acceleration and centripetal acceleration areattributed to the individual 997888rarr120596 times 997888rarrV term

32 Boundary Conditions and Mesh Generation A cylindri-cal flow field has been established to surround the ductedrotors velocity inlet and pressure outlet boundary conditionswere specified on the far-field planes as shown in Figure 4The diameter and height of the column are 4D and 7D whereD represents the duct outer diameter and the calculationmodel is placed at 4D from inflow boundary The coaxialrotor is based on the NACA airfoil and it is paired withduct based on the NACA 0012 airfoil Shrouding the doublerotors configurations within the duct can be seen in Figure 5Unstructured overset grids have been used to allow forgrid densification at the blade tip clearance in achievinghigh-fidelity simulation of leakage vortex Nodes were alsoclustered at the duct lip and near the diffusional section ofduct

In this current study 25 35 45 and 55million numbersof grid nodes have been used to discuss the independenceof computing grid which maintain a marginal variation insolutions at a stage of grid quantity [12] Hovering thrust aswell as the trimmed torque of two counterrotating rotors forentire system is obtained by MFR model for all the grid sizesin Table 3 and compares with the experimental data Typicalconvergence trend of torque is readily discovered the numberof grid has been increased by 1million as the torque reduces towithin 1 with 55 million grids when the variation of thrustis less than 2 approximately The size of grid is determinedafter grid independence test and the computing results are inaccord with experiments well Spatial slice mesh of interiorrotational domains and exterior stationary domains aroundcoaxial rotors are shown in Figure 6 with adequate meshaccuracy and resolution

4 Experimental Investigation for HoverAerodynamic Performance

The hover efficiency affected by RPM and rotor spacing arecritical for the implement of duct coaxial rotor UAV [2526] In this section a hover test stands for ducted coaxialrotormodel which was established in order to experimentallymeasure the performance in hover as shown in Figure 7Theidentical 3-D geometries were tested to assess the effect ofmultiblock generation and MFR solve method by comparing

Rotational Zone 1

D4D

4D 7D

Velocity Inlet Pressure Outlet

Rotational Zone 2

Far Field

Stationary Zone

Stationary Zone

Figure 4 Computational domains of ducted coaxial rotors

Figure 5 Geometric model of ducted coaxial rotor

it with the experimental results The accuracy and efficiencyof current numerical simulation indicated that the applica-tion of our method is capable of continuing to be utilized forforward aerodynamic computation in the next section

The rotor and motor systems were mounted inverselyon hinges Two physical quantities can be simultaneouslymeasured by designed test stand (1) Thrust thrust wasmeasured by the weighing sensor which was placed betweenthe inner frame structure and external frame structure (2)Rotational speed considering the free rotation and indepen-dent transmission the rotational speed of each rotor wasseparately determined through an approach switch that wassensed by metal objects in the range of 5mm

Simulation of total thrust produced by the entire ductedcoaxial rotor system is validated by the experimental data inFigure 8 A wide range of rpm varying from 1000 to 7000were conducted to maximize the aerodynamic capability oftesting model The calculated thrusts agreed well with themeasurement data at low speed whereas at higher speedthe analytical result is slightly underpredicted for the giventhrust level and the disparities increased as the rotationalspeed raised The computation assigning identical rotationalspeed for the top and bottom rotors that generated thrustsin the same trends with variation of rpm while the upperrotor is more efficiency than lower one which is affected by


Table 3 Hovering thrust and trimmed torque versus mesh quantity based on MFR model at 6000 rpm

6000 rpm 25 times 106 35 times 106 45 times 106 55 times 106 Expt119879 (kg) 30588 32682 33991 34636 37318119876 (Nsdotm) 0111 0108 0106 0105 0103

Figure 6 Space grids slices of nested grid system (grid quantity 55 times 106)

Inner frame structure

External frame structure

Weighing sensor

Approach switch

Figure 7 Structural components of hover test stand

the contracted slipstream of upper one The thrust of ductstructure is seen to remain fairly equal to the lower rotor

Figure 9 shows the total thrust of the entire systemobtained from the test stand experiment for a range ofdistance between rotors varying from 3000 to 7000 Therotor spacing is given by 119867119877 = 025 035 045 055 and065 In hover performance the effect of rotor spacing is notsignificant for the thrust which approaches a constant valueranged from 025 to 04 while the thrust abruptly decreasedat 045

5 Results and Discussion

Since a variety of physical parameters influence the for-ward performance the optimization of the structure formof essential aerodynamic component and the aerodynamiccharacteristic is a critical step in the development of a SUAVThe angle of attack of duct freestream velocity and rotorspacing of the coaxial rotors are generally considered to be

Computational (Total)Computationla (Top rotor)Computational (Bottom rotor)Computational (Duct)Experimental (Total)

2000 3000 4000 5000 6000 70001000RPM

0

10

20

30

40

50

60

Thru

st (N

)

Figure 8 Hover performance comparison with experimental dataat different rpm

the most crucial factors The procedure traditionally used foroptimization the structural configuration of ducted coaxialrotors can be implemented by experimental investigation orcarried out step-by-step In the current research all selectedfactors were tested using an orthogonal 11987116(43) test design

Results of each scheme are summarized in Table 4the calculation scheme A1B4C4 provided the maximumlift (4982N) The minimum drag of total system and theminimum torque value trimmed of counterrotating coaxialrotor were 04707N (A2B1C2) and 00178Nsdotm (A4B2C1)


035 045 055 065025RPM

5

15

25

35

45

55Th

rust

(N)

300040005000

600065007000

Figure 9 Experimental thrust versus rotor spacing

Table 4 11987116(43) test results of aerodynamics

Test number LiftN DragN Torque Nsdotm1 243606 26550 minus005272 359317 132894 010873 422899 263460 021024 498214 411217 019285 331124 04707 011396 372669 93868 014727 437340 222020 018858 421831 393675 015149 338219 minus18496 0124610 368556 63430 0171411 350175 247934 0077312 434715 341595 0202913 333692 minus45041 0136614 271594 76410 minus0017815 403194 162937 0144616 480299 316043 02060

respectively By now we cannot determine the best combi-nation of levels depending on these consequences simplyFurthermore an orthogonal analysis has been exhibited interms of the test results of aerodynamics in Table 4 Thestatistical model including the sum of aerodynamic force 119879mean value 119898 and range value was computed to analysis11987116(43) calculation results in Table 5

According to the range value of factors the influence tothe lift drag and torque reduced in the order B gt C gt AB gt A gt C and C gt B gt A respectively Wind speedof freestream was demonstrated to be the most significantdetermination of lift and drag and the value of trimmedtorque is most decided by the spacing of rotors

Figure 10 compares the mean values of lift drag andtorque (119898119894) analytically calculated in Table 5 versus fourfactor levels Lift and torque show the same trends with rotorspacing which almost have no effect on drag force Widerotor spacing is one of the main contributors to lift force thatis capable of decreasing the interference between upper andlower rotors In order to optimize lift of system 76mmshouldbe adopted for the spacing of coaxial rotor Thrust remainsfairly constant value with rotor spacing in hover While inforward flight the thrust sharply increases with rotor spacingdue to flow asymmetry in freestream

Air volume intake into duct system correspondinglyincreases with freestream velocity as per unit time Differen-tial pressure between the upper and lower area of propelleris enlarged attribute to the more remarkable suction flowAs a consequence wind speed is found to be the mostdeterminant factor of lift in Figure 10(a) Meanwhile drag ishighlymagnifying due to inhibition effect of duct as the flightspeed increasingwhich can be seen in Figure 10(b) To reducethe drag of forward flight a small amount of wind speed is themost significant effect factor

Pitch angle of ducted coaxial rotor has no significantinfluence on the aerodynamic force In the meantime angleof attack marginally affects drag force that the increaseof deflection away from edgewise forward direction (pitchangle at 90∘) would lead to small amount of drag reductionThat is because at lower pitch angle a slight decrease ofnegative pressure zone occurs near internal lip of duct atwind side and the drag reduces with the pressure differentialbetween external and internal side Furthermore at upwindside the lessening of high pressure zone near internal lipat upwind side also contributes to the drag reduction Inforward flight for fixed rpmassuming in this calculations 70∘is more suitable for the ducted coaxial rotor system to achieveminimum power consumption on drag that contributes tobetter aerodynamic performance

6 Conclusions

For the rotary-wing aircraft vehicles various structure pa-rameters and flight conditions affect the inflow distributionmaking it very challenging to draw a general conclusion abouthow to practically analyze the aerodynamic characteristic andobtain the optimum performance

A representative ducted coaxial rotor configuration pro-posed in this work is motivated by the development of aVTOL aircraft In this present study MFR model is adoptedto predict the complex viscous flow of multirotors whichtransform the time-dependent formulation into steady stateapproximation The predictive capability of the new configu-ration as well as the SUAV is very high and validated by theexperimental results

In forward flight pitch angle freestream velocity androtor spacing between the counterrotating rotors are provedto be three dominant influence factors of aerodynamicperformance in previous efforts Three factors should betaken into consideration in order to optimize lift drag andtorque of the system The orthogonal 11987116(43) test designwas applied to select the optimum structure and forward


Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894


Pitch angleFreestream velocityRotor spacing

30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level

(a) Lift versus level factor


2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)

(b) Drag versus level factor


2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)

(c) Torque versus level factor

Figure 10 Trend of forward flight aerodynamics with diverse factors

flight parameters Mean values of lift drag and torquewith four levels of pitch angle freestream speed and rotorspacing have been compared and variation trend of the threeinfluence factors has been depicted Optimal rotor spacingand appropriate forward flight AOA have been decided The

flight speed should be determined by a compromise of highlift and low drag This study provides an efficiency approachto simulate the mixed flow field of multirotating domainsand static domain which gives out significant reference inengineering application


Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Knowledge InnovationProgram of the Chinese Academy of Sciences (Grant noYYYJ-1122) and the Innovation Program of UAV funded bythe Chang Guang Satellite Technology Co Ltd

References

[1] T E Lee Design and performance of a ducted coaxial rotor inhover and forward [Master thesis] Department of AerospaceEngineering University of Maryland College Park MD USA2010

[2] F Bohorquez Rotor hover performance and system design ofan efficient coaxial rotary wing micro air vehicle [PhD thesis]Department ofAerospace EngineeringUniversity ofMarylandCollege Park MD USA 2007

[3] V K Lakshminarayan and J D Baeder ldquoComputational inves-tigation of microscale coaxial-rotor aerodynamics in hoverrdquoJournal of Aircraft vol 47 no 3 pp 940ndash955 2010

[4] B G Jimenez and R Singh ldquoEffect of duct-rotor aerodynamicinteractions on blade design for hover and axial flightrdquo inProceedings of the 53rd AIAA Aerospace Sciences Meeting 2015USA January 2015

[5] J L Pereira Hover and wind-tunnel testing of shrouded rotorsfor improved micro air vehicle design [PhD thesis] Universityof Maryland College Park MD USA 2008

[6] X M He H C Zhao X D Chen Z L Luo and Y N MiaoldquoHydrodynamic performance analysis of the ducted propellerbased on the combination of multi-block hybrid mesh andReynolds stress modelrdquo Journal of flow control measurement ampvisualization vol 3 pp 67ndash74 2015

[7] O Rand and V Khromov ldquoAerodynamic optimization ofcoaxial rotor in hover and axial flightrdquo in Proceedings of the 27thInternational Congress of theAeronautical Sciences Nice France2012

[8] H W Kim and R E Brown ldquoModelling the aerodynamicsof coaxial helicopters ndash from an isolated rotor to a completeaircraftrdquo in Proceedings of the 1st EU-Korea Conference onScience and Technology EKC 2008 pp 45ndash59 August 2008

[9] M Ramasamy ldquoHover performance measurements towardunderstanding aerodynamic interference in coaxial tandemand tilt rotorsrdquo Journal of the American Helicopter Society vol60 no 3 Article ID 032005 2015

[10] H W Kim and R E Brown ldquoCoaxial rotor performanceand wake dynamics in steady and maneuvering flightrdquo inProceedings of the American Helicopter Society 62nd AnnualForum Proceedings Phoenix 2016

[11] M S Genc ldquoNumerical simulation of flow over a thin aerofoil ata high Reynolds number using a transition modelrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 224 no 10 pp 2155ndash21642010

[12] M S Genc U Kaynak and H Yapici ldquoPerformance of tran-sition model for predicting low Re aerofoil flows withoutwithsingle and simultaneous blowing and suctionrdquo European Jour-nal of Mechanics - BFluids vol 30 no 2 pp 218ndash235 2011

[13] M S Genc U Kaynak and G D Lock ldquoFlow over an aerofoilwithout and with a leading-edge slat at a transitional Reynoldsnumberrdquo Proceedings of the Institution of Mechanical EngineersPart G Journal of Aerospace Engineering vol 223 no 3 pp 217ndash231 2009

[14] M Genc G Lock and U Kaynak ldquoAn Experimental andComputational Study of Low Re Number Transitional Flowsover an Aerofoil with Leading Edge Slatrdquo in Proceedings of theThe 26th Congress of ICAS and 8th AIAA ATIO AnchorageAlaska

[15] V K Lakshminarayan and J D Baeder ldquoHigh-resolution com-putational investigation of trimmed coaxial rotor aerodynamicsin hoverrdquo Journal of the American Helicopter Society vol 54 no4 Article ID 042008 2009

[16] R Singh H Kang M Bhagwat C Cameron and J SirohildquoComputational and experimental study of coaxial rotor steadyand vibratory loadsrdquo in Proceedings of the 54th AIAA AerospaceSciences Meeting AIAA Paper January 2016

[17] J H Schmaus and I Chopra ldquoAeromechanics of rigid coaxialrotor models for wind-tunnel testingrdquo Journal of Aircraft vol54 no 4 pp 1486ndash1497 2017

[18] M S Genc I Karasu and H Hakan Acikel ldquoAn experimentalstudy on aerodynamics of NACA2415 aerofoil at low Re num-bersrdquo Experimental Thermal and Fluid Science vol 39 pp 252ndash264 2012

[19] H Xu and Z Ye ldquoNumerical simulation of unsteady flowaround forward flight helicopter with coaxial rotorsrdquo ChineseJournal of Aeronautics vol 24 no 1 pp 1ndash7 2011

[20] C P Coleman ldquoA survey of theoretical and experimentalcoaxial rotor aerodynamic researchrdquo NASA TP-3675 1997

[21] J Russell L Sankar C Tung J Russell L Sankar and CTung ldquoHigh accuracy studies of the tip vortex structure froma hovering rotorrdquo in Proceedings of the 28th Fluid DynamicsConference Snowmass VillageCOUSA

[22] R E Brown and A J Line ldquoEfficient high-resolution wakemodeling using the vorticity transport equationrdquoAIAA Journalvol 43 no 7 pp 1434ndash1443 2005

[23] S Sunada K Tanaka and K Kawashima ldquoMaximization ofthrust-torque ratio of a coaxial rotorrdquo Journal of Aircraft vol42 no 2 pp 570ndash572 2005

[24] Y Lei Y Bai and Z Xu ldquoWind Effect on AerodynamicOptimization for Non-planar Rotor Pairs using Full-scale Mea-surementsrdquo Journal of Intelligent amp Robotic Systems vol 87 no3-4 pp 615ndash626 2017

[25] K T Fang and C X Ma Design method Design Method ofOrthogonal And Uniform Test Science Press Beijing China2001

[26] V K Lakshminarayan and J D Baeder ldquoComputational inves-tigation of micro hovering rotor aerodynamicsrdquo Journal ofthe American Helicopter Society vol 55 no 2 pp 0220011ndash02200125 2010

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Table 1 Forward flight aerodynamics factor-level form

Factor level Pitch angle (120572∘) Flight velocity (Vmsdotsminus1) Rotor spacing (Hmm)1 A1 85 B1 5 C1 382 A2 80 B2 10 C2 573 A3 75 B3 15 C3 6654 A4 70 B4 20 C4 76

Rotor Spacing

Z

YX

(a) Rotor spacing of the coaxial rotors

D

Y

LT

Z

YX

(b) Pitch angle and forward flight velocity

Figure 1 Configuration of VTOL aircraft in forward flight

RANS solver with sliding mesh interpolation scheme topredict instantaneous thrust and power influenced by theinteraction between coaxial rotors Singh et al [16] used low-and high-fidelity with loose coupling method to computa-tional simulated steady and unsteady performance of elasticcoaxial rotor with vibratory hubloads

Experiment techniques for aircraft vehicles have alsodeveloped significantly over time Schmaus and Chopra [17]evaluated the vibratory loads of rigid coaxial rotor for testingin the wind tunnel and explored the influence of rotorphase on vibratory hubloads Genc et al [18] performedan experimental study on the pressure distribution andaerodynamic forces of NACA2415 aerofoil at low Reynoldscarried out in the suction-type wind tunnel

Many experimental and numerical efforts had beendone to investigate the forward flight performance [19ndash23] However most previous studies were concentrated onoptimizing the shape of duct or measuring the aerodynamicstep-by-step Rarely has research been proposed to maximizethe fundamental aerodynamic performance issues whichare associated with the determination of the rotor spacingbetween upper and lower rotors taking into account bothattitude and speed of the ducted coaxial rotors configuration

In this work the identical three-dimensional ductedpropeller configuration has been established to validate theefficiency of numerical scheme in achieving high-fidelitypredictions of hybrid flow field and compared with theexperiments measured by the hovering aerodynamic perfor-mance test stand of our laboratory The aim of the hoverperformance investigation is to apply this analytical approachto forward flight Besides this solving method aims to formthe fundamental exploring correlation between vibratoryloads and blade loads thereby aiding in a better selectionof blade structural properties in manufacturing Orthogonal

test design is designed to analyze the dominant factor to eachaerodynamics Subsequently the variation trends of aero-dynamic performance are characterized with three leadinginfluence factors including pitch angle freestream velocityand rotor spacing The optimized rotor spacing and flightpitch angle are determined from a wide range of factors tomaximize forward flight performance of our system

2 Orthogonal Test Design

According to experimental purpose three influence factorsgiven by incident angle to the freestream in forward flight(120572∘) flight speed (Vmsdotsminus1) and rotor spacing (Hmm) arechosen and the level of factors have been decided Variationtendency of aerodynamic performance with proposed fourfactor levels for each influenced factor can be compared accu-rately and optimum parameter combination can be designedwith three factors taken into consideration Corresponding tothe four levels of pitch angles listed in Table 1 wind speed isgiven by 5ms 10ms 15ms and 20ms and rotor spacingrepresents the distance between top and bottom rotor rangingfrom 38mm to 76mm Figure 1(a) shows the longitudinalforces acting on the calculation configuration in forwardflight then lift and drag can be calculated as follows

119871 = 119879 sin120572 + 119884 cos120572

119863 = 119884 sin120572 minus 119879 cos120572(1)

where 119879 and 119884 refer to thrust and tangential force which canbe predicted by numerical approach

Orthogonal array 11987116(43) is adopted to optimize theprescription of forward flight ducted coaxial rotors [24]Table 2 summarizes the numerical calculation scheme








997888rarr120596 = 120596997888rarr119886 (2)





acceleration



y


axis ofrotationx

z

x y

R

CFD domainz

rarrr0

rarr

rarra rarrVt

rarrr



Continuity Equation

120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0 (4)

Momentum Equation

120597120597119905(120588997888rarrV 119903) + nabla sdot (120588

997888rarrV 119903997888rarrV 119903)



(5)


Energy Equation

120597120597119905(120588119864119903) + nabla sdot (120588



2119903)




120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0





(7)






Rotational Zone 1

D4D

4D 7D


Rotational Zone 2

Far Field

Stationary Zone

Stationary Zone












Weighing sensor

Approach switch







2000 3000 4000 5000 6000 70001000RPM

0

10

20

30

40

50

60

Thru

st (N

)





035 045 055 065025RPM

5

15

25

35

45

55Th

rust

(N)

300040005000

600065007000









6 Conclusions





Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894



30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









997888rarr120596 = 120596997888rarr119886 (2)





acceleration



y


axis ofrotationx

z

x y

R

CFD domainz

rarrr0

rarr

rarra rarrVt

rarrr



Continuity Equation

120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0 (4)

Momentum Equation

120597120597119905(120588997888rarrV 119903) + nabla sdot (120588

997888rarrV 119903997888rarrV 119903)



(5)


Energy Equation

120597120597119905(120588119864119903) + nabla sdot (120588



2119903)




120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0





(7)






Rotational Zone 1

D4D

4D 7D


Rotational Zone 2

Far Field

Stationary Zone

Stationary Zone












Weighing sensor

Approach switch







2000 3000 4000 5000 6000 70001000RPM

0

10

20

30

40

50

60

Thru

st (N

)





035 045 055 065025RPM

5

15

25

35

45

55Th

rust

(N)

300040005000

600065007000









6 Conclusions





Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894



30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




120597120588120597119905

+ nabla sdot 120588997888rarrV 119903 = 0





(7)






Rotational Zone 1

D4D

4D 7D


Rotational Zone 2

Far Field

Stationary Zone

Stationary Zone












Weighing sensor

Approach switch







2000 3000 4000 5000 6000 70001000RPM

0

10

20

30

40

50

60

Thru

st (N

)





035 045 055 065025RPM

5

15

25

35

45

55Th

rust

(N)

300040005000

600065007000









6 Conclusions





Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894



30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Weighing sensor

Approach switch







2000 3000 4000 5000 6000 70001000RPM

0

10

20

30

40

50

60

Thru

st (N

)





035 045 055 065025RPM

5

15

25

35

45

55Th

rust

(N)

300040005000

600065007000









6 Conclusions





Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894



30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



035 045 055 065025RPM

5

15

25

35

45

55Th

rust

(N)

300040005000

600065007000









6 Conclusions





Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894



30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table5Analysis

oftestresults

LiftN

DragN

TorqueNsdotm

AB

CA

BC

AB

C119879 1

152404a

12466

4128720

83412

minus3228

74457

0459

0322

0158

119879 2156296

1372

14152835

71427

36660

64213

0601

0410

0570

119879 31491

661613

611614

0963446

89635

65488

0576

0621

0688

119879 4148878

183506

163780

51035

146253

6516

30470

0753

0689

1198981

38101b

3116

63218

020853

minus0807

18614

0115

0081

0039

1198982

39074

34303

38209

17857

9165

16053

0150

0102

0143

1198983

37292

40340

40352

15862

22409

1637

20144

0155

0172

1198984

37220

45877

40945

12759

36563

16291

0117

0188

0172

Rangev

alue

1855

c14711

8765

8094

3737

02561

0036

0108

0133

Optim

allevel

A2

B 4C 3

A4

B 1C 4

A1

B 1C 1

a 119879119894=sumtheam

ount

ofaerodynamic

forceat119860119894b 119898119894=1198791198943crang

evalue

=max119898119894minusmin119898119894



30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




30

33

36

39

42

45

48Li

ft (N

)

2 3 41Factor level



2 3 41Factor level

minus5

5

15

25

35

45

Dra

g (N

)



2 3 41Factor level

002

006

01

014

018

022

Torq

ue (N

middotm)








Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Acknowledgments


References





























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


aerodynamics optimization of a ducted coaxial rotor in

Documents