numerical simulation of airfoil aerodynamic penalties and

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2013 Article ID 590924 13 pageshttpdxdoiorg1011552013590924

Research ArticleNumerical Simulation of Airfoil Aerodynamic Penalties andMechanisms in Heavy Rain

Zhenlong Wu Yihua Cao and M Ismail

Beijing University of Aeronautics and Astronautics Beijing 100191 China

Correspondence should be addressed to Zhenlong Wu jackilongwugmailcom

Received 19 July 2013 Revised 21 September 2013 Accepted 22 September 2013

Academic Editor N Ananthkrishnan

Copyright copy 2013 Zhenlong Wu 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

Numerical simulations that are conducted on a transport-type airfoil NACA 64-210 at a Reynolds number of 26times106 and LWC of25 gm3 explore the aerodynamic penalties andmechanisms that affect airfoil performance in heavy rain conditions Our simulationresults agree well with the experimental data and show significant aerodynamic penalties for the airfoil in heavy rainThemaximumpercentage decrease in 119862

119871is reached by 132 and the maximum percentage increase in 119862

119863by 476 Performance degradation

in heavy rain at low angles of attack is emulated by an originally creative boundary-layer-tripped technique near the leading edgeNumerical flow visualization technique is used to show premature boundary-layer separation at high angles of attack and theparticulate trajectories at various angles of attack A mathematic model is established to qualitatively study the water film effect onthe airfoil geometric changes All above efforts indicate that two primary mechanisms are accountable for the airfoil aerodynamicpenalties One is to cause premature boundary-layer transition at low AOA and separation at high AOAThe other occurs at timesscales consistent with the water film layer which is thought to alter the airfoil geometry and increase the mass effectively

1 Introduction

The aerodynamic penalty of aircraft flight through heavy rainhas been deemed to be a critical cause in many severe avia-tion accidents The Eastern Flight 066 accident at KennedyAirport (NTSB 1976) is a telling example though the factorof heavy rain was not taken into consideration at that time[1]Three years later another Flight named 693 a Boeing 727-25 civil airplane suffered from an intense rainfall associatedwith wind shears on its eventual routine to the AtlantaInternational Airport [2] Several severe aviation accidents in1981 aroused peoplersquos consciousness of the seriousness of raininfluence on aircraft flight [3]

Investigation of rain effect on aircraft flight was begunwith the wind tunnel test and the earliest was conducted byRhode in 1941 [4] It dealt with the situation of an aircraftencountering heavy rain at moderate cruising altitude ofabout 5000 ft and concluded that the heavy rain exposuretime is not sufficient to force the aircraft to the ground In1982 Haines and Luers did a research concerning the fre-quency and intensity of very heavy rains and their effects ona landing aircraft [1] In 1987 Hansman and Criag compared

the aerodynamic performance degradation of NACA 64-210NACA 0012 and Wortman FX 67-K170 airfoils under thelow Reynolds numbers in heavy rain conditions and exploredthe various mechanisms underlying by forcing boundary-layer to transition [5] In other similar wind tunnel exper-iments laminar flow airfoils were also found to experienceperformance degradation approximately equivalent to thatcaused by tripping the boundary layer to turbulence [6ndash8]In 1992 Bezos et al determined the severity of rain effectthe aerodynamic penalty over a range of rain intensities andthe importance of surface tension interactions of water asa scaling parameter [9] Thompson and his team examinedanother NACA 4412 airfoil in moderate rain in wind tunnelThey primarily placed emphasis on the correlation of surface-film behavior including rivulet formation [10] Subsequentlythey went on a further examination on the aerodynamicefficiency of the same airfoil in moderate rain [11] Compar-isons with different flow patterns showed the aerodynamicdegradation depended on the location of rivulet formationand the diameter of these rivuletsThe latter factor was foundto be more important to aerodynamic performance

2 International Journal of Aerospace Engineering

Numerical simulation approach was introduced anddeveloped with the development of computer technology In1995 Valentine and Decker studied the NACA 64-210 airfoilaerodynamic performance [12] and the track of raindropsin flow over the airfoil [13] by numerical simulation In1999 Thompson and Marrochello calculated the location ofthe oneset of rivulet formation in the surface-water flowover a wing with a NACA 4412 airfoil and compared theresults with wind-tunnel experiments [14] In 2003 Wan andWu also conducted the numerical simulation of heavy raineffect on airfoil [15] The water film layer and vertical rainmass flow rate on the airfoil upper surface were added thusincreasing the airfoil roughening effects In 2010 Wan andPan studied the cruise and high-lift NACA 64-210 airfoilaerodynamic efficiency in heavy rain via a two-phase flowapproach [16] Later he reinvestigated the high-lift NACA64-210 with the consideration of proper modeling of discretewater droplets shear flow between airfoil elements [17] andstudied aerodynamic performance of a 3D blended-wing-body aircraft under severe rain through a two-phase flowapproach [18] Zhang and Cao and Ismail et al studied aero-dynamic characteristics of the NACA64-210 and NACA 0012airfoils in rain and preliminarily explored the mechanism[19 20]

As is presented above present research methods ofrain effect on aircraft aerodynamic performance are mainlywind-tunnel test and numerical simulation However forthe former method in one hand the result of model testin wind tunnel may not be directly used for large-scaleaircraft due to the complexity ofmultiphase environment Forexample theWeber number of water cannot bemaintained asuniformmeanwhile On the other hand if the scale of modelis decreased then the testing velocity must be increasedproportionally to a uniform Reynolds number thus the windtunnel test will be much more expensive and complex tomanipulate So numerical simulation method may as wellbe accepted as a good approach to deal with the involvedproblem

In numerical simulations two approaches have been usedto model multiphase flows that is the Eulerian approachand the Lagrangian approach They have been reviewed byValentine and Decker [13] The Eulerian approach treatsthe continuous fluid phase and the dispersed particle phaseas continuum while the Lagrangian approach solves time-averaged Navier-Stokes equations for the continuous fluidphase first and then integrates the Lagrangian motion equa-tion for the dispersed phase this model is called discretephase model (DPM) There are two models including a one-way coupled model and a two-way coupled model in theLagrangian approach The former model assumes that theparticles motion is affected by the continuous phase butthe continuous phase is not affected by the presence of thedispersed phase The latter takes the two-way exchange ofmass momentum and energy between the two phases intoconsideration

Though rain effect on airfoil aerodynamic performanceand some mechanisms have been exposed by wind-tunneltests little work of numerically studying the mechanisms

has been done For example Wan and others mainly dis-cussed airfoils aerodynamic performance in rain conditionsat low angles of attack The rain effect of airfoil at highangles of attack is little concerned neither is the mechanismresearched

The present study uses the discrete phase model (DPM)in Fluent to study the typical commercial transport airfoilNACA64-210 aerodynamic performance in heavy rain butmainly it places emphasis on themechanism explorationTheraindrops in our study are assumed to be nonevaporatingnondeforming spheresThe objective of our study is fourfoldfirst to determine the aerodynamic penalties of the airfoilover a wider range of attack angle second to investigate thepremature boundary-layer transition and separation mecha-nism leading to the dynamic penalty at low and high anglesof attack respectively using a CFD method third to trackthe particulate trajectory at various angles of attack fourthto acquire the water-film-layer influence on the geometricchanges of airfoil in different rain rates and at different anglesof attack

2 Numerical Approach

21 Fluid Phase Previous wind-tunnel experiments per-formed by Hansmann and Barsotti [8] suggested that pre-mature boundary-layer transition causes the aerodynamicpenalty of natural laminar airfoils at the low Reynolds num-bers in heavy rain conditions To investigate this hypothesisHansman Jr and Craig [5] placed boundary-layer transitionelements on the suction and pressure surfaces of airfoil toforce airfoil boundary layer to transition Trip strips 025 inwide and madeup of sand grains ranging in diameter from0025 to 0040 inch were placed at the 5 25 50 or 75chordwise station on the top and bottom surface of airfoilTrip strips on the lower surface of the airfoils resulted inmin-imal performance changes whereas forcing boundary-layertransition on the upper surface resulted in fairly significantperformance changes Therefore the location of the lowertrip strip was generally fixed at 5 chord and the upper tripstrip location was varied To investigate the hypothesis froma perspective of computational fluid dynamics we developa CFD (Computational Fluid Dynamics) method to emulatethe forced boundary-layer transition that is to give a normaland outward increment as modeling the trip strip like a stepto the specified-position section of the airfoil as shown inFigure 1(d) This is a new method so we name it numericalboundary-layer-tripped technique in this paper We also putthe trip at 5 25 50 and 75 chordwise stations on the topsurface and at 5 on the bottom surface of a NACA 64-210airfoil for our study The width and height of the incrementhave the same ratio to the chord length as that of the trip inHansmanrsquos experiment

The computational domain consists of an extruded O-type grid around the NACA 64-210 airfoil The first stepin computational fluid dynamics is to examine the griddependency on numerical results Generally the more nodesare distributed the more accurate solution will be acquiredhowever the more expensive computational memory and

International Journal of Aerospace Engineering 3

(a) (b)

(c) (d)

Figure 1 (a) O-type computational domain of meshes for both the original and numerically tripped NACA 64-210 airfoils (b) near mesh ofthe original airfoil (c) near mesh of the airfoil tripped at 5 chordwise station (d) close view of the tripped position on the 5 chordwisetripped airfoil

Table 1 Lift and drag coefficients for different sizes of the original airfoil mesh

Mesh size 119862119871AOA 0∘ 119862

119871AOA 10∘

LWC 0 gm3 25 gm3Δ119862119871

LWC 0 gm3 25 gm3Δ119862119871

80 times 100 0161 0155 0006 1081 1029 0052100 times 100 0157 0152 0005 1077 1028 0049100 times 120 0156 0151 0005 1076 1027 0049120 times 120 0155 0151 0004 1075 1027 0048

119862119863AOA 0∘ 119862

119863AOA 10∘

LWC 0 gm3 25 gm3Δ119862119863

LWC 0 gm3 25 gm3Δ119862119863

80 times 100 0020 0022 0002 0078 0082 0006100 times 100 0019 0020 0001 0075 0080 0005100 times 120 0019 0020 0001 0074 0080 0006120 times 120 0019 0020 0001 0074 0079 0005LWC liquid water content AOA angle of attack 119862119871 lift coefficient 119862119863 drag coefficient

time will be required Table 1 shows the effect of mesh sizeon lift and drag coefficients for the original airfoil at angles ofattack (AOA) of 0∘ and 10∘ in the dry and rain conditions Itindicates that the aerodynamic penalties due to rain are notgreatly affected by the number of grid cells Considering ourcomputational limits we choose the mesh with 12000 gridcells for a further study as shown in Figures 1(a) and 1(b)Theheight of the first cell adjacent to the original airfoil surface isset to 1times 10minus5m and the stretching ratio of themesh is 11Themesh of 5 chordwise position tripped NACA 64-210 airfoilis shown in Figures 1(c) and 1(d) and the number of cellsis 34 632 The height of the first cell adjacent to the tripped

airfoil surface is also set to 1 times 10minus5m as well as the stretchingratio of 11The origin is set at the airfoil leading edge with theX-axis pointing to the right and Y-axis upward The circularouter boundary of the two O-type computational domains isset as the velocity-inlet condition and the airfoil surface asno-slip wall condition The chord length is 0762m and thefree-stream Reynolds number of air is set to 26 times 106 equalto a dynamic pressure of 30 psf in order to be consistent withparameters of theory of wing section [9] It is stated here thatthe results of which airfoil is not stated explicitly in all belowfigures are about the original NACA 64-210 airfoil includingthe experimental and the numerical ones


The incompressible air flow field is solved by FLUENTa common commercial flow field solver the details of whichcan be referred to in the help literature [21] and will not berepeated here For a Reynolds number of 26 times 106 the flowcharacteristic is considered as turbulent so turbulencemodelis added to solve the Navier-Stokes equations During thecalculation of the original and tripped airfoils in dry con-dition the steady pressure-based solver is chosen of whichthe segregated SIMPLE algorithm is adopted to discretizethe pressure-velocity coupling term The pressure term usessecond-order scheme and the QUICK scheme is used in themomentum term discretization

Airfoil aerodynamic performance is measured by liftand drag coefficients in this research which are definedrespectively as follows

119862119871=

119871

(12) 120588119886V2

infin119888

119862119863=

119863

(12) 120588119886V2

infin119888

(1)

where 119862119871is the lift coefficient and 119862

119863is the drag coefficient

119871 is the lift119863 is the drag 120588119886is the density of air V

infinis the air

free-stream velocity and 119888 is the chord length of the airfoil ofinterest

22 Particulate Phase

221 Scaling of Rain Model To study the heavy rain effectfirst of all it is necessary to measure the intensity andfrequency of heavy rain To study the heavy rain effect firstof all itrsquos necessary to measure the intensity and frequency ofheavy rain Usually the rainfall rate 119877 in millimeter per houror the Liquid Water Content LWC in gram per cubic meteris chosen to categorize different intensities of rain A rainfallof 100mmh or greater is often deemed as heavy A rainfall of100mmh or greater is often deemed as heavy

The LWC can be written as a function of119873(119863) as follows

LWC = int+infin

0

120588119908

120587

61198633119873(119863) 119889119863 (2)

where 120588119908

is the density of water Integrating the aboveformula we may attain the correlation of LWC and 119877 by

LWC = 0054119877084 (3)

Subsequently it is necessary to establish the size distri-bution of water droplets under different rain rates Manyresearchers like Best [22] Ulbrich [23] and so on haveestablished various raindrop size distribution formulas forvarious situations Marshall and Palmer developed the classicformula of drop size distribution in 1948 based on massiveexperimental data [24] It is shown as follows

119873(119863) = 1198730EXP (minus119868119863) (0 le 119863 le 119863max) (4)

where 119873(119863) (mminus3mmminus1) is the number density of sphericalraindrops of diameter 119863 (mm) per cubic meter of air 119863max

is the maximum drop diameter and 1198730and 119868 (mmminus1) are

parameters of 119873(119863) and have different values for differenttypes of rain For storm-type heavy rainfall 119868 varies withrainfall rate 119877 as 119868 = 3119877minus021 and 119873

0has the constant value

1198730= 1400mminus3mmminus1 [25] correspondinglyHere it is assumed that raindrops have beenwith uniform

velocity before hitting the aircraft surface that is withoutacceleration So it is important to determine the terminalvelocity of raindrops It has been developed by Markowitz[26] as follows

119881 (119863) = 958 1 minus EXP [minus( 119863177

)

1147

] (5)

where 119881(119863) is the terminal velocity A correction for it aloftis given by Markowitz as

119881 (119863) = 1198810 (119863) (1205880

120588119886

)

04

(6)

where 1198810(119863) is the terminal velocity consistent with the

density of air aloft 1205880

222 Wall-Film Model In our study the wall-film modelin Fluent [21] is mainly adopted to model the interactionof particle and wall surface It allows a single-componentliquid drop to impinge upon a boundary surface of arbitraryconfiguration and form a thin liquid filmThemajor physicalprocesses that affect the liquid film includemass andmomen-tum contributions to the film thanks to drop impingementdroplet splashing effects evaporation shear forces on thefilm dynamic pressure effects gravity driven flow convectiveheat and mass transfer flow separation and sheet breakupas shown in Figure 2(a) In present study we ignore the filmevaporation to simplify our solution so it is unnecessary toconsider the effects of the thin liquid film on the air flow

The main assumptions for the film model are as follows

(i) The layer is thin less than 500 microns in thicknessdue to the assumption of a linear velocity profile inthe film

(ii) The temperature in the film particles changes rela-tively slow due to the use of an analytical integrationscheme

(iii) The film temperature is always below the boilingtemperature for the liquid

(iv) Film particles are assumed to be in direct contact withthe wall surface and the heat transfer from the wall tothe film occurs through conduction

The wall interaction regimes are calculated for a drop-wall interaction based on local informationThe four regimesincluding stick rebound spread and splash are based on theimpact energy andwall temperature as shown in Figures 2(b)and 2(c) (Tb is the liquid boiling temperature and Tw is thewall face temperature) Below the liquid boiling temperaturethe impinging droplet can either stick spread or splashwhile above the boiling temperature the particle can eitherrebound or splash As to our case of which the temperature


Impinging droplets Splashing

Liquid film layer

Evaporation

Convective heat transfer

Wall Conduction Flow separationand

sheet breakup

(a)

Stick Rebound

Spread Splash

(b)

Tb Tw

Stick

Spread

Splash

Rebound

E

(c)

Figure 2 (a) Mechanisms of mass momentum and energy transfers for the wall-film model (b) the four impingement regimes included inthe model (c) simplified decision for wall interaction criterion

is below the boiling point particles stick spread and splashresulting in aerodynamic efficiency degradation of an aircraft

The criteria by which the regimes are partitioned arebased on the impact energy and the boiling temperature ofthe liquid The impact energy 119864 is defined by

1198642=1205881199081198812

119903119863

120590119908

(1

min (ℎ0119863 1) + 120575bl119863

) (7)

where120588119908is thewater density119881

119903is the particle relative velocity

in the frame of the wall (ie 119881119903= 119881119901minus 119881wall) 120590119908 is the water

surface tension and ℎ0is the total height of the wall film 120575bl

denotes the thickness of the boundary layer and is defined by

120575bl = radic120583119863

120588119908119881119903

(8)

The sticking regime is applied when the dimensionlessenergy 119864 is less than 16 and the particle velocity is set equalto the wall velocity In the spreading regime the probabilityof the drop having a particular direction along the surfaceis given by an analogy of an inviscid liquid jet with anempirically defined radial dependence for the momentumflux If the wall temperature is above the boiling temperatureof the liquid impingement events below a critical impactenergy (119864) result in the particles rebounding from the wallSplashing occurs when the impingement energy is above acritical energy threshold defined as 119864cr = 577 Besides in our

study we sample a cumulative probability distribution func-tion (CPDF) which is acquired from theWeibull distributionfunction and fitted to the data from Mundo et al [27] todetermine the different diameter of each splashed parcelTheequation of the cumulative probability distribution functioncan be expressed as

pdf(119889119894

119863119901

) = 2119889119894

1198632

119901

exp[minus(119889119894

119863119901

)

2

] (9)

and it represents the probability of finding drops of diameter119889119894in a sample of splashed raindropsBilanin [28] has investigated the evaporation of the

particles near the surface and found that evaporation does notaffect the airfoil aerodynamic efficiency so in our study weignore the vaporization of water film Since the film particlevaporization is ignored only the momentum and energyconservation equations remain in the conservation equationsfor wall-film particles

Conservation equation of momentum is as follows

120588119886ℎ

119889997888119881119901

119889119905+ ℎ(nabla

119904119901119891)119888= 120591119892

997888119905119892+ 120591119908

997888119905119908

+119875 imp119888 minus imp119888

997888119881119901+119865119899119888

+ 120588119886ℎ (997888119892 minus

997888119886119908)

(10)


Water-film layer

Airfoilh(i)

Figure 3 Illustration of the water film development

where 119888 denotes the current face where the particle locates ℎdenotes the current filmheightwhere the particle locatesnabla

119904is

the gradient operator as to the surface 119901119891is the film pressure

120591119892and 120591119908are respectively the magnitude of the shear stress

of the air flow on the film surface and the magnitude of thestress of the film exerted by the wall 997888119905

119892and 997888119905

119908are the unit

vectors in the direction of the relative motion of the film andthe wall 119875 imp119888 denotes the impingement pressure on the film

surface imp119888 is the impingementmomentum source 119865119899119888

isthe force to keep the film on the surface and 120588

119886ℎ(997888119892 minus

997888119886119908) is

the body force term in which 997888119886119908is the acceleration of the

relative wall motionConservation equation of energy is as follows

119898119901119862119901

119889119879119901

119889119905=

120581119860119901

ℎ(119879119908minus 119879119901) + ℎ119891119860119901(119879119886minus 119879119901) (11)

where119898119901is the particle mass 119862

119901is the equilibrium concen-

tration of the rain droplet120581 is the liquid thermal conductivityℎ is the film height where the particle locates ℎ

119891is the film

heat transfer coefficient 119860119901is the area of the film particle

119879119901 119879119908 and 119879

119886 respectively denote the temperature of the

particle wall and air The first term on the right-hand sidedenotes the thermal conduction from the wall to the filmparticle and the second term denotes the thermal convectionfrom the top surface to the film particle

223 Mathematic Modeling for Water Film In this part anumerical model for the water film based on [1] is adopted tocalculate water film thickness by airfoil location and rainfallrate In each grid cell the film thickness is resulted fromwaterremaining after the gains and losses due to the incomingrain and film flow After a time an equilibrium thickness iscompleted in each cell Herewewillmainly examine the effectof water film on the airfoil geometric changes qualitativelyso for simplicity the pressure gradient and thermodynamicinfluences are neglected It is assumed that the water filmdevelops normally to the airfoil surface as shown in Figure 3The main program is acquired and shown as follows

The raindrop local collection efficiency within every gridcell symbolized as 120573(119894) can be expressed as

120573 (119894) =119899 (119894)

1198990

119884max minus 119884min119904 (119894)

(12)

where 119899(119894) is the number of raindrops within cell 119894 1198990is the

total number of raindrops which can have an impact on theairfoil surface 119884max and 119884min represent the maximum andminimum vertical position respectively 119904(119894) is the arc lengthof cell 119894 and is shown as follows

119904 (119894) = radic(119909 (119894 + 1) minus 119909 (119894))2+ (119910 (119894 + 1) minus 119910 (119894))

2 (13)

where 119909(119894) and 119910(119894) represent position of cell 119894 in 119883 and 119884direction respectively Consider

120573 =sum119873

1120573 (119894)

119873 (14)

where 120573 is the average collection efficiency at the airfoilsurface 119873 is the total number of cells adjacent to the airfoilsurface

The air shear stress within every cell 120591(119894) can be expressedas

120591 (119894) =1

2119862119891 (119894) times 120588119886 times V

2 (15)

where119862119891(119894) is the air coefficient of friction and V is the average

velocity of cells at the airfoil surface as follows

V =sum119873

1V (119894)

119873 (16)

where V(119894) is the velocity of air in cell 119894The resulting film is a balance betweenwater runback and

rain water reception For the film in each cell the equilibriumcondition of the mass balance can be expressed as

119889119898119894

119889119905=120588119908

119860int

119911=ℎ

119911=0

119909=119894Δ119909

119906 119889119911 minus120588119908

119860int

119911=ℎ

119911=0

119909=(119894+1)Δ119909

119906 119889119911 +120597119898119894

120597119905 (17)

where 119906 = 120591119911120583119908is the film velocity at height 119911 120583

119908is the

molecular viscosity of waterThe first and second terms at theright side represent respectively mass flux into the 119894th cell(119909 = 119894Δ119909) of Area119860 and out of the cell (119909 = (119894 + 1)Δ119909) due tofilm flowThe third term represents mass flux into the ith celldue to rain

The change rate of raindrop mass in cell 119894 (119889119898119889119905)(119894) iscalculated from (12)119889119898

119889119905(119894)

=1

2120588119908

times 120591 (119894) [((119873 minus (119894 + 1)) ℎ0 (119894)

119873)

2

minus ((119873 minus 119894) ℎ0 (119894)

119873)

2

]

sdot1

120583119908119904 (119894)

+ LWC times 120573 (119894) times Vinfin

(18)


where ℎ0(119894) is the initial thickness of water film in cell 119894 and

set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)

After all a new water film thickness in cell 119894 ℎ(119894) resultsfrom [1]

ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)

where Δ119905 is the time stepExperimental research shows that once the water

droplets impact the thin water film layer scallops will formand the water remaining in the scallops will form convex filmlayers thus increasing the roughness of the original waterfilm Based on Macklinrsquos research [29] the present programassumes the convex film layers to be cylindrical so as to takethe water film roughness into consideration

From Driling [30] the correlation equations for equiva-lent sandgrain roughness developed from experimental datacan be expressed as the function of the average height of theconvex film that is

119896119904

119896

= 00164Λ

37 Λ le 493

139Λminus19 Λ ge 493

(21)

where 119896119904is equivalent sandgrain roughness 119896 is the average

height of convex filmΛ is the correlating parameter and bothcan be referred to [1]

The original NACA 64-210 airfoil in wet condition ofLWC = 25 gm3 is simulated and the results are comparedwith the wind-tunnel experimental ones in [9] The windtunnel experiment was conducted by Bezos et al in theNASA Langley 14- by 22-Foot Subsonic Tunnel in 1992to determine the aerodynamic penalty associated with asimulated heavy rain encounter The model was comprisedof a NACA 64-210 airfoil section with a chord of 25 fta span of 8 ft and was mounted on the tunnel centerlinebetween two large endplates The rain simulation systemmanifold which was located 10 chord lengths upstream ofthe model produced liquid water contents ranging from 16to 46 gm3 Aerodynamic measurements in and out of thesimulated rain environment were obtained to measure theairfoil aerodynamic coefficients In our rain calculations thepressure-based unsteady solver with the first-order implicitscheme is adopted the calculation condition of rain is shownin Table 2

3 Results and Discussions

31 Validation To get a better numerical accuracy two tur-bulence models namely the Spalart-Allmaras model (abbre-viated as SA model) and K-E model are chosen to get thelift and drag coefficients of the airfoil over a wider range ofattack angles in the dry condition and the results of bothare compared with the experimental data from wing sectiontheory [9] as is shown in Figures 4 and 5 It can be seen that

0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t

Angle of attack (deg)

Experimental (wing section theory)Numerical (SA model)Numerical (K-E model)

Figure 4 Lift coefficient comparison between numerical andexperimental results

Table 2 Calculated rain condition

Variable ValueLWC(gm3) 25Raindrop arithmetic meandiameter(mm) 1

Air freestream velocity(ms) 484632Raindrop vertical velocity(ms) minus4Air density(kgm3) 1225Airfoil chord length(m) 0762Air freestream Reynolds number 26 times 10

6

Reference pressure(Pa) 101325 times 105

Reference temperature(K) 273

both the turbulence models have the same accuracy of liftcoefficient at low angles of attack while the SA model has abetter tendency at high angles of attackWhat is more the SAmodel has fairly satisfactory results of drag coefficient at lowangles of attack Hence the SA model is chosen as the majorturbulence model and all the results below are achieved by it

32 Lift and Drag Force Data Figures 6 and 7 present thelift and drag coefficient polar data in dry and wet condi-tions for numerical and wind tunnel experimental approachrespectively It shows a decrease in lift and an increase indrag due to the heavy rain effect for both approaches Forour simulation the maximum percentage decrease in 119862

119871is

reached by 132 and the maximum percentage increase in119862119863by 476 for the airfoil in the rain condition And for

the experiment the maximum percentage decrease in 119862119871is

reached by 137 and the maximum percentage increase in119862119863by 563 Our simulation shows good agreement with


00

01

02

03

04

Dra

g co

effici

ent

0 5 10 15 20Angle of attack (deg)


Figure 5 Drag coefficient comparison between numerical andexperimental results

0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t


Experimental (dry)Experimental (wet)

Numerical (dry)Numerical (wet)

Figure 6 Lift coefficient versus AOA for numerical and experimen-tal results

the experiment Although the numerical lift data in bothconditions are larger than the experimental data the trendmatches well The numerical drag coefficients correspondwell with the wind tunnel experimental data before AOA =13 degree but smaller than the experimental data at higherangles of attack

Figures 8 and 9 show the pressure contour and the stream-lines around the NACA 64-210 airfoil at AOA = 14 degreein the dry and wet conditions respectively The operatingpressure is 101325 Pa In the dry condition the boundarylayer has no rain-induced changes at the moment While inthe wet condition the boundary layer has separated due to

00

01

02

03

04

Dra

g co

effici

ent




Figure 7 Drag coefficient versus AOA for numerical and experi-mental results

70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000

Figure 8 Pressure distribution and streamlines around the airfoilin the dry condition

minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X

Figure 9 Pressure distribution and streamlines around the airfoilin the rain condition


0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t


Original airfoil ( dry)

minus2

Original airfoil (LWC = 25 gm3)

75 chordwise tripped airfoil (dry)50 chordwise tripped airfoil (dry)25 chordwise tripped airfoil (dry)5 chordwise tripped airfoil (dry)

Figure 10 Numerical lift coefficient comparison for differenttripped positions

X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity

Figure 11119883-velocity distribution of air around the original airfoil

rain The two contours reveal that premature boundary-layerseparation may happen for airfoil in rain at high angles ofattack this conclusion is consistent with that in [5] Besidesthe difference of the pressure on the upper and lower surfacesof the airfoil leading edge decreases with rain thus the liftdecreases in the rain

33 Forced Boundary-Layer Transition Results To prove ourhypothesis of premature boundary layer transition at lowangles of attack theNACA64-210 airfoil with tripped bound-ary layer is emulated in the dry condition Figure 10 showsthe numerical lift coefficient comparison for the originalairfoil in dry and wet (LWC 25 gm3) conditions and thetripped airfoil with different tripping positions in the drycondition Evidently trip strips at 5 chord on the top surface

X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity

Figure 12 119883-velocity distribution of air around the 5 chordwisetripped airfoil

minus243e + 00

512e + 01

Figure 13 Raindrop traces at AOA = 0 degree

best modeled the wet conditions However the high-AOAbehavior of the NACA 64-210 airfoil is not emulated by thetripping technique possibly because the tripped position isaft of the leading-edge separation point The overall abilityto model aerodynamic performance degradation in heavyrain condition with our numerically tripped boundary-layertechnique suggests that the aerodynamic degradation resultsfrom premature boundary-layer transition at low angles ofattack which is also consistent with that in [5] Figures 11and 12 show the component of air velocity in the119883 directionnamely 119883-velocity distribution near the leading edge of theoriginal airfoil and the 5 chordwise tripped airfoil at thesame AOA of 8 degree in the dry condition It can be clearlyseen that the negative 119883-velocity appears at the trippedlocation compared with the smooth original one whichmanifests that the premature boundary-layer transition isgained

34 Tracking the Particulate Trajectories From Figures 13 1415 16 17 and 18 the raindrop traces colored by particulate119883-velocity at AOA = 0 4 8 12 16 and 20 degrees at timeof 119905 = 0125 s are shown At AOA = 0 degree raindropsconcentrate on both the top and the bottom surfaces of theairfoil At AOA = 4 degree there have been few raindropson the top surface but still many flowing from the stagnation


486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n

Upper surface Lower surface

(times108dr

ople

tsm

3)

Figure 19 Droplet concentration within the second cell layer fromthe airfoil surface at AOA = 8 degree

point to downstream on the bottom At AOA = 8 degreethe discrete phase has developed a full separation on thebottom surface so there are almost no raindropsMeanwhilethe discrete phase begins to separate on the top surface Asthe angle of attack increases further the separation extentbecomes larger coupling with the presence of the continuousphase separation At AOA = 20 degree a maximum degree ofcoupled separation is reached and large-scale vortexes appearresulting in the runback of rivulets on the upper surfaceThe patterns should be viewed qualitatively however ourgrid is nonuniform and resolution decreases away from theairfoil surface Turbulent dispersion of the small splashed-back droplets is not modeled and thus the contours showmean trajectories

Figure 19 shows the droplet concentration within thesecond cell layer from the airfoil surface at AOA of 8 degreesSince the freestream raindrop number density is of the orderof 103 raindropsm3 and is well below the minimum valueof 121 times 105 of the droplet concentration it can be assumedthat the vast majority of droplets in the second cell layeris owing to splashback For an angle of attack of 8 degrees


LWC = 39gm3

LWC = 25 gm3

Dry airfoil

Figure 20Water film thickness comparison between different LWCconditions at AOA = 14 degree

AOA = 0degree

Dry airfoil

AOA = 14degree

Figure 21 Water film thickness comparison at different angles ofattack and LWC = 25 gm3 condition

the stagnation point is slightly below the leading edge somore splashed-back raindrops from impacts at the leadingedge are carried over the upper surface than the lower surfaceWhat is more the downward component of raindrop velocityleads to more impacts on the upper surface especially forlarger raindrops which have higher vertical velocities

35 Geometric Changes Based onWater Film Layer Figure 20shows the leading-edge water film thickness comparisonbetween LWC = 25 gm3 39 gm3 and the dry condition atAOA of 14 degrees and time of 0125 s It can be concludedthat as the LWC increases the water film thickness increasessimultaneously at the same angle of attack which conformsto the objective fact For the condition of LWC = 25 gm3 theresulting average film thickness for the top and bottom sur-faces of a 1-meter-chord-length airfoil is respectively 03502and 03167mm And for the condition of LWC = 39 gm3it increases up to 03794 and 03469mm respectively Asanalyzed in Subsection 4 of this part for an angle of attackof 14 degrees more raindrops have an impact on the topsurface and certainly form a thicker film Besides the filmthickness increases with the increasing rain rate (or liquidwater content) The water film increases the weight changesthe geometry of surface and may cause vital aerodynamicperformance degradation of aircraft

Figure 21 shows the leading-edge water film thicknesscomparison for AOA = 0 and 14 degrees and LWC = 25 gm3at the same time From the figure we can see that in the sameLWC conditions water films have approximately the samethickness at the stagnation point at different angles of attackBut at higher angles of attack water films on the bottomsurface get thicker this is because that at higher angles ofattack water collection efficiency gets larger on the bottomsurface andwater on both surfaces runs faster to downstream

4 Conclusion

In summary numerical experiments at a Reynolds Numberof 26 times 106 and LWC of 25 gm3 have been conducted inthe dry and wet conditions to compare the quantitative andqualitative aerodynamic penalties of NACA 64-210 airfoilwith wind-tunnel experiments in heavy rain conditions Anumber of mechanisms underlying are found by numericalsimulation approach The innovative points of present studyare fivefold as follows

(i) Aerodynamic penalties of NACA 64-210 airfoil over awider range of AOA up to 20 degrees are determinedAirfoil aerodynamic performance in rain conditionsat high AOA more than 15 degree has little beenstudied by numerical simulation before The numer-ical simulation shows a shift of stall angle from 15degrees in the dry condition to 13 degrees in thewet condition For our simulation the maximumpercentage decrease in 119862

119871is reached by 132 and

themaximumpercentage increase in119862119863by 476 for

the airfoil in the rain condition The numerical dragcoefficients correspond well with the wind tunnelexperimental data before AOA = 13 degrees

(ii) A newly creative boundary-layer-tripped techniqueis developed to prove that the airfoil aerodynamicdegradation results from premature boundary-layertransition in heavy rain conditions at low angles ofattack which is consistent with the correspondingreference

(iii) The pressure distribution contour and the stream-lines around the airfoil are attained by using flow-visualization technique so as to illustrate the hypoth-esis that premature boundary-layer separation mayhappen for airfoil in heavy rain conditions at highangles of attack which is also consistent with thecorresponding reference

(iv) The trajectories of raindrops at various angles ofattack are tracked by flow-visualization techniqueand the corresponding flow characteristics are dis-cussed in detail Impact and splash of raindropsflow and runback of rivulets and continuous phaseand discrete phase coupled separation are displayedBesides a detailed analysis of raindrop splashback isgiven

(v) Amathematic water-filmmodel is established and thecorresponding program is developed to get the waterfilm on the airfoil surface and the effects of LWC


and AOA on water film thickness are discussed Thewater film alters the airfoil geometry effectively butthis effect is most likely exaggerated in our study dueto the small scale

It is recognized that because of the small-scale test caseand specified flight conditions the results of our testsmay notbe extrapolated to larger scales cases and various real flightconditions However the physical mechanisms of rain effectsand their importance may be similar So it is believed thatall efforts in this study can be a preliminary evaluation ofpotential heavy rain mechanisms induced at larger scales andan important reference for civil aviation community

Nomenclature

AOA Angle of attackEXP Abbreviation of exponent function119862119871 Lift coefficient

119862119863 Drag coefficient

119877 Rain rate (mmsdothminus1)LWC Liquid water content (gsdotmminus3)119863 Equivolume spherical diameter of

raindrop (mm)119881(119863) Terminal velocity of raindrop (msdotsminus1)119894 Index of individual mesh cellΔ119905 Time step119905 Total computational timepsf Pounds per square foot119883-velocity Component of velocity in the119883

(horizontal) direction

References

[1] P A Haines and J K Luers ldquoAerodynamic penalties of heavyrain on a landing aircraftrdquo Tech Rep CR-156885 NASA 1982

[2] J K Luers and P A Haines ldquoHeavy rain influence on airplaneaccidentsrdquo Journal of Aircraft vol 20 no 2 pp 187ndash191 1983

[3] J K Luers and P A Haines ldquoThe effect of heavy rain on windshear attributed accidentsrdquo in Proceedings of the 19th AerospaceSciences Meeting Paper 81-0390 1981

[4] R V Rhode ldquoSome effects of rainfall on flight of airplanes andon instrument indicationsrdquo NASA TN-903 1941

[5] R J Hansman Jr and A P Craig ldquoLow reynolds number testsof NACA 64-210 NACA 0012 and wortman FX67-K170 airfoilsin rainrdquo Journal of Aircraft vol 24 no 8 pp 559ndash566 1987

[6] B A Campbell and G M Bezos ldquoSteady state and transitionalaerodynamic characteristics of a wing in simulated heavy rainrdquoTech Rep TP-2932 NASA 1989

[7] L P Yip ldquoWind tunnel investigation of a full-scale canard-configured general aviation aircraftrdquo Tech Rep TP-2382NASA 1985

[8] R J Hansman Jr and M F Barsotti ldquoThe aerodynamic effectof surface wetting effects on a laminar flow airfoil in simulatedheavy rainrdquo Journal of Aircraft vol 22 no 12 pp 1049ndash10531985

[9] G M Bezos R E Dunham Jr G L Gentry and W EdwardMelson Jr ldquoWind tunnel aerodynamic characteristics of atransport-type airfoil in a simulated heavy rain environmentrdquoTech Rep TP-3184 NASA 1992

[10] B E Thompson J Jang and J L Dion ldquoWing performance inmoderate rainrdquo Journal of Aircraft vol 32 no 5 pp 1034ndash10391995

[11] B E Thompson and J Jang ldquoAerodynamic efficiency of wingsin rainrdquo Journal of Aircraft vol 33 no 6 pp 1047ndash1053 1996

[12] J R Valentine and R A Decker ldquoA Lagrangian-Eulerianscheme for flow around an airfoil in rainrdquo International Journalof Multiphase Flow vol 21 no 4 pp 639ndash648 1995

[13] J R Valentine and R A Decker ldquoTracking of raindrops in flowover an airfoilrdquo Journal of Aircraft vol 32 no 1 pp 100ndash1051995

[14] B E Thompson and M R Marrochello ldquoRivulet formation insurface-water flow on an airfoil in rainrdquo AIAA Journal vol 37no 1 pp 45ndash49 1999

[15] T Wan and S-W Wu ldquoAerodynamic analysis under the influ-ence of heavy rainrdquo Journal of Aeronautics Astronautics andAviation A vol 41 no 3 pp 173ndash180 2009

[16] T Wan and S P Pan ldquoAerodynamic efficiency study under theinfluence of heavy rain via two-phase flow approachrdquo in Pro-ceedings of the 27th International Congress of the AeronauticalSciences 2010

[17] TWan and C J Chou ldquoReinvestigation of high lift airfoil underthe influence of heavy rain effectsrdquo in Proceedings of the 50thAIAA Aerospace Science Meeting including the New HorizonsForum and Aerospace Exposition Nashville Tenn USA 2012

[18] T Wan and B C Song ldquoAerodynamic performance study ofa modern blended-wing-body aircraft under severe weathersimulationrdquo in Proceedings of the 50th AIAA Aerospace ScienceMeeting including the New Horizons Forum and AerospaceExposition Nashville Tenn USA 2012

[19] R-M Zhang and Y-H Cao ldquoStudy of aerodynamic character-istics of an airfoil in rainrdquo Journal of Aerospace Power vol 25no 9 pp 2064ndash2069 2010

[20] M Ismail C Yihua ZMing andA Bakar ldquoNumerical study ofairfoils aerodynamic performance in heavy rain environmentrdquoWorld Academy of Science Engineering and Technology vol 67pp 1052ndash1060 2012

[21] Fluent 63 Userrsquos Guide 2006[22] A C Best ldquoThe size distribution of raindropsrdquo Quarterly

Journal of the Royal Meteorological Society vol 76 no 327 pp16ndash36 1950

[23] C W Ulbrich ldquoNatural variations in the analytical form ofthe raindrop size distributionrdquo Journal of Climate amp AppliedMeteorology vol 22 no 10 pp 1764ndash1775 1983

[24] J S Marshall and W M K Palmer ldquoThe distribution ofraindrops with sizerdquo Journal of Meteorology vol 5 no 4 pp165ndash166 1948

[25] J Joss and A Waldvogel ldquoRaindrop size distribution andsampling size errorsrdquo Journal of the Atmospheric Sciences vol26 no 3 pp 566ndash569 1969

[26] A H Markowitz ldquoRaindrop size distribution expressionsrdquoJournal of AppliedMeteorology vol 15 no 9 pp 1029ndash1031 1976

[27] C Mundo M Sommerfeld and C Tropea ldquoDroplet-wallcollisions experimental studies of the deformation and breakupprocessrdquo International Journal of Multiphase Flow vol 21 no 2pp 151ndash173 1995

[28] A J Bilanin ldquoScaling laws for testing airfoils under heavyrainfallrdquo Journal of Aircraft vol 24 no 1 pp 31ndash37 1987


[29] W C Macklin and G J Metaxas ldquoSplashing of drops on liquidlayersrdquo Journal of Applied Physics vol 47 no 9 pp 3963ndash39701976

[30] R E Dirling ldquoAmethod for computing roughwall heat transferrates on re-entry nosetipsrdquo in Proceedings of the 8th AIAAThermophysics Conference Palm Springs Calif USA 1973

International Journal of

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Numerical simulation approach was introduced anddeveloped with the development of computer technology In1995 Valentine and Decker studied the NACA 64-210 airfoilaerodynamic performance [12] and the track of raindropsin flow over the airfoil [13] by numerical simulation In1999 Thompson and Marrochello calculated the location ofthe oneset of rivulet formation in the surface-water flowover a wing with a NACA 4412 airfoil and compared theresults with wind-tunnel experiments [14] In 2003 Wan andWu also conducted the numerical simulation of heavy raineffect on airfoil [15] The water film layer and vertical rainmass flow rate on the airfoil upper surface were added thusincreasing the airfoil roughening effects In 2010 Wan andPan studied the cruise and high-lift NACA 64-210 airfoilaerodynamic efficiency in heavy rain via a two-phase flowapproach [16] Later he reinvestigated the high-lift NACA64-210 with the consideration of proper modeling of discretewater droplets shear flow between airfoil elements [17] andstudied aerodynamic performance of a 3D blended-wing-body aircraft under severe rain through a two-phase flowapproach [18] Zhang and Cao and Ismail et al studied aero-dynamic characteristics of the NACA64-210 and NACA 0012airfoils in rain and preliminarily explored the mechanism[19 20]

As is presented above present research methods ofrain effect on aircraft aerodynamic performance are mainlywind-tunnel test and numerical simulation However forthe former method in one hand the result of model testin wind tunnel may not be directly used for large-scaleaircraft due to the complexity ofmultiphase environment Forexample theWeber number of water cannot bemaintained asuniformmeanwhile On the other hand if the scale of modelis decreased then the testing velocity must be increasedproportionally to a uniform Reynolds number thus the windtunnel test will be much more expensive and complex tomanipulate So numerical simulation method may as wellbe accepted as a good approach to deal with the involvedproblem

In numerical simulations two approaches have been usedto model multiphase flows that is the Eulerian approachand the Lagrangian approach They have been reviewed byValentine and Decker [13] The Eulerian approach treatsthe continuous fluid phase and the dispersed particle phaseas continuum while the Lagrangian approach solves time-averaged Navier-Stokes equations for the continuous fluidphase first and then integrates the Lagrangian motion equa-tion for the dispersed phase this model is called discretephase model (DPM) There are two models including a one-way coupled model and a two-way coupled model in theLagrangian approach The former model assumes that theparticles motion is affected by the continuous phase butthe continuous phase is not affected by the presence of thedispersed phase The latter takes the two-way exchange ofmass momentum and energy between the two phases intoconsideration

Though rain effect on airfoil aerodynamic performanceand some mechanisms have been exposed by wind-tunneltests little work of numerically studying the mechanisms

has been done For example Wan and others mainly dis-cussed airfoils aerodynamic performance in rain conditionsat low angles of attack The rain effect of airfoil at highangles of attack is little concerned neither is the mechanismresearched

The present study uses the discrete phase model (DPM)in Fluent to study the typical commercial transport airfoilNACA64-210 aerodynamic performance in heavy rain butmainly it places emphasis on themechanism explorationTheraindrops in our study are assumed to be nonevaporatingnondeforming spheresThe objective of our study is fourfoldfirst to determine the aerodynamic penalties of the airfoilover a wider range of attack angle second to investigate thepremature boundary-layer transition and separation mecha-nism leading to the dynamic penalty at low and high anglesof attack respectively using a CFD method third to trackthe particulate trajectory at various angles of attack fourthto acquire the water-film-layer influence on the geometricchanges of airfoil in different rain rates and at different anglesof attack

2 Numerical Approach

21 Fluid Phase Previous wind-tunnel experiments per-formed by Hansmann and Barsotti [8] suggested that pre-mature boundary-layer transition causes the aerodynamicpenalty of natural laminar airfoils at the low Reynolds num-bers in heavy rain conditions To investigate this hypothesisHansman Jr and Craig [5] placed boundary-layer transitionelements on the suction and pressure surfaces of airfoil toforce airfoil boundary layer to transition Trip strips 025 inwide and madeup of sand grains ranging in diameter from0025 to 0040 inch were placed at the 5 25 50 or 75chordwise station on the top and bottom surface of airfoilTrip strips on the lower surface of the airfoils resulted inmin-imal performance changes whereas forcing boundary-layertransition on the upper surface resulted in fairly significantperformance changes Therefore the location of the lowertrip strip was generally fixed at 5 chord and the upper tripstrip location was varied To investigate the hypothesis froma perspective of computational fluid dynamics we developa CFD (Computational Fluid Dynamics) method to emulatethe forced boundary-layer transition that is to give a normaland outward increment as modeling the trip strip like a stepto the specified-position section of the airfoil as shown inFigure 1(d) This is a new method so we name it numericalboundary-layer-tripped technique in this paper We also putthe trip at 5 25 50 and 75 chordwise stations on the topsurface and at 5 on the bottom surface of a NACA 64-210airfoil for our study The width and height of the incrementhave the same ratio to the chord length as that of the trip inHansmanrsquos experiment

The computational domain consists of an extruded O-type grid around the NACA 64-210 airfoil The first stepin computational fluid dynamics is to examine the griddependency on numerical results Generally the more nodesare distributed the more accurate solution will be acquiredhowever the more expensive computational memory and


(a) (b)

(c) (d)



Mesh size 119862119871AOA 0∘ 119862

119871AOA 10∘

LWC 0 gm3 25 gm3Δ119862119871

LWC 0 gm3 25 gm3Δ119862119871


119862119863AOA 0∘ 119862

119863AOA 10∘

LWC 0 gm3 25 gm3Δ119862119863

LWC 0 gm3 25 gm3Δ119862119863







119862119871=

119871

(12) 120588119886V2

infin119888

119862119863=

119863

(12) 120588119886V2

infin119888

(1)




infinis the air





LWC = int+infin

0

120588119908

120587

61198633119873(119863) 119889119863 (2)

where 120588119908


LWC = 0054119877084 (3)









119881 (119863) = 958 1 minus EXP [minus( 119863177

)

1147

] (5)


119881 (119863) = 1198810 (119863) (1205880

120588119886

)

04

(6)












Liquid film layer

Evaporation



sheet breakup

(a)

Stick Rebound

Spread Splash

(b)

Tb Tw

Stick

Spread

Splash

Rebound

E

(c)




1198642=1205881199081198812

119903119863

120590119908

(1

min (ℎ0119863 1) + 120575bl119863

) (7)






120575bl = radic120583119863

120588119908119881119903

(8)



pdf(119889119894

119863119901

) = 2119889119894

1198632

119901

exp[minus(119889119894

119863119901

)

2

] (9)




120588119886ℎ

119889997888119881119901

119889119905+ ℎ(nabla

119904119901119891)119888= 120591119892

997888119905119892+ 120591119908

997888119905119908

+119875 imp119888 minus imp119888

997888119881119901+119865119899119888

+ 120588119886ℎ (997888119892 minus

997888119886119908)

(10)


Water-film layer

Airfoilh(i)



119904is




119892and 997888119905

119908are the unit




119886ℎ(997888119892 minus

997888119886119908) is



119898119901119862119901

119889119879119901

119889119905=

120581119860119901

ℎ(119879119908minus 119879119901) + ℎ119891119860119901(119879119886minus 119879119901) (11)




119891is the film


119879119901 119879119908 and 119879





120573 (119894) =119899 (119894)

1198990

119884max minus 119884min119904 (119894)

(12)




2 (13)


120573 =sum119873

1120573 (119894)

119873 (14)



120591 (119894) =1

2119862119891 (119894) times 120588119886 times V

2 (15)



V =sum119873

1V (119894)

119873 (16)



119889119898119894

119889119905=120588119908

119860int

119911=ℎ

119911=0

119909=119894Δ119909

119906 119889119911 minus120588119908

119860int

119911=ℎ

119911=0

119909=(119894+1)Δ119909

119906 119889119911 +120597119898119894

120597119905 (17)


119908is the



119889119905(119894)

=1

2120588119908

times 120591 (119894) [((119873 minus (119894 + 1)) ℎ0 (119894)

119873)

2

minus ((119873 minus 119894) ℎ0 (119894)

119873)

2

]

sdot1

120583119908119904 (119894)


(18)



set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)


ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)




119896119904

119896

= 00164Λ

37 Λ le 493


(21)






0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







6





119871is





00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)



Mesh size 119862119871AOA 0∘ 119862

119871AOA 10∘

LWC 0 gm3 25 gm3Δ119862119871

LWC 0 gm3 25 gm3Δ119862119871


119862119863AOA 0∘ 119862

119863AOA 10∘

LWC 0 gm3 25 gm3Δ119862119863

LWC 0 gm3 25 gm3Δ119862119863







119862119871=

119871

(12) 120588119886V2

infin119888

119862119863=

119863

(12) 120588119886V2

infin119888

(1)




infinis the air





LWC = int+infin

0

120588119908

120587

61198633119873(119863) 119889119863 (2)

where 120588119908


LWC = 0054119877084 (3)









119881 (119863) = 958 1 minus EXP [minus( 119863177

)

1147

] (5)


119881 (119863) = 1198810 (119863) (1205880

120588119886

)

04

(6)












Liquid film layer

Evaporation



sheet breakup

(a)

Stick Rebound

Spread Splash

(b)

Tb Tw

Stick

Spread

Splash

Rebound

E

(c)




1198642=1205881199081198812

119903119863

120590119908

(1

min (ℎ0119863 1) + 120575bl119863

) (7)






120575bl = radic120583119863

120588119908119881119903

(8)



pdf(119889119894

119863119901

) = 2119889119894

1198632

119901

exp[minus(119889119894

119863119901

)

2

] (9)




120588119886ℎ

119889997888119881119901

119889119905+ ℎ(nabla

119904119901119891)119888= 120591119892

997888119905119892+ 120591119908

997888119905119908

+119875 imp119888 minus imp119888

997888119881119901+119865119899119888

+ 120588119886ℎ (997888119892 minus

997888119886119908)

(10)


Water-film layer

Airfoilh(i)



119904is




119892and 997888119905

119908are the unit




119886ℎ(997888119892 minus

997888119886119908) is



119898119901119862119901

119889119879119901

119889119905=

120581119860119901

ℎ(119879119908minus 119879119901) + ℎ119891119860119901(119879119886minus 119879119901) (11)




119891is the film


119879119901 119879119908 and 119879





120573 (119894) =119899 (119894)

1198990

119884max minus 119884min119904 (119894)

(12)




2 (13)


120573 =sum119873

1120573 (119894)

119873 (14)



120591 (119894) =1

2119862119891 (119894) times 120588119886 times V

2 (15)



V =sum119873

1V (119894)

119873 (16)



119889119898119894

119889119905=120588119908

119860int

119911=ℎ

119911=0

119909=119894Δ119909

119906 119889119911 minus120588119908

119860int

119911=ℎ

119911=0

119909=(119894+1)Δ119909

119906 119889119911 +120597119898119894

120597119905 (17)


119908is the



119889119905(119894)

=1

2120588119908

times 120591 (119894) [((119873 minus (119894 + 1)) ℎ0 (119894)

119873)

2

minus ((119873 minus 119894) ℎ0 (119894)

119873)

2

]

sdot1

120583119908119904 (119894)


(18)



set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)


ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)




119896119904

119896

= 00164Λ

37 Λ le 493


(21)






0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







6





119871is





00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119862119871=

119871

(12) 120588119886V2

infin119888

119862119863=

119863

(12) 120588119886V2

infin119888

(1)




infinis the air





LWC = int+infin

0

120588119908

120587

61198633119873(119863) 119889119863 (2)

where 120588119908


LWC = 0054119877084 (3)









119881 (119863) = 958 1 minus EXP [minus( 119863177

)

1147

] (5)


119881 (119863) = 1198810 (119863) (1205880

120588119886

)

04

(6)












Liquid film layer

Evaporation



sheet breakup

(a)

Stick Rebound

Spread Splash

(b)

Tb Tw

Stick

Spread

Splash

Rebound

E

(c)




1198642=1205881199081198812

119903119863

120590119908

(1

min (ℎ0119863 1) + 120575bl119863

) (7)






120575bl = radic120583119863

120588119908119881119903

(8)



pdf(119889119894

119863119901

) = 2119889119894

1198632

119901

exp[minus(119889119894

119863119901

)

2

] (9)




120588119886ℎ

119889997888119881119901

119889119905+ ℎ(nabla

119904119901119891)119888= 120591119892

997888119905119892+ 120591119908

997888119905119908

+119875 imp119888 minus imp119888

997888119881119901+119865119899119888

+ 120588119886ℎ (997888119892 minus

997888119886119908)

(10)


Water-film layer

Airfoilh(i)



119904is




119892and 997888119905

119908are the unit




119886ℎ(997888119892 minus

997888119886119908) is



119898119901119862119901

119889119879119901

119889119905=

120581119860119901

ℎ(119879119908minus 119879119901) + ℎ119891119860119901(119879119886minus 119879119901) (11)




119891is the film


119879119901 119879119908 and 119879





120573 (119894) =119899 (119894)

1198990

119884max minus 119884min119904 (119894)

(12)




2 (13)


120573 =sum119873

1120573 (119894)

119873 (14)



120591 (119894) =1

2119862119891 (119894) times 120588119886 times V

2 (15)



V =sum119873

1V (119894)

119873 (16)



119889119898119894

119889119905=120588119908

119860int

119911=ℎ

119911=0

119909=119894Δ119909

119906 119889119911 minus120588119908

119860int

119911=ℎ

119911=0

119909=(119894+1)Δ119909

119906 119889119911 +120597119898119894

120597119905 (17)


119908is the



119889119905(119894)

=1

2120588119908

times 120591 (119894) [((119873 minus (119894 + 1)) ℎ0 (119894)

119873)

2

minus ((119873 minus 119894) ℎ0 (119894)

119873)

2

]

sdot1

120583119908119904 (119894)


(18)



set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)


ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)




119896119904

119896

= 00164Λ

37 Λ le 493


(21)






0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







6





119871is





00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Liquid film layer

Evaporation



sheet breakup

(a)

Stick Rebound

Spread Splash

(b)

Tb Tw

Stick

Spread

Splash

Rebound

E

(c)




1198642=1205881199081198812

119903119863

120590119908

(1

min (ℎ0119863 1) + 120575bl119863

) (7)






120575bl = radic120583119863

120588119908119881119903

(8)



pdf(119889119894

119863119901

) = 2119889119894

1198632

119901

exp[minus(119889119894

119863119901

)

2

] (9)




120588119886ℎ

119889997888119881119901

119889119905+ ℎ(nabla

119904119901119891)119888= 120591119892

997888119905119892+ 120591119908

997888119905119908

+119875 imp119888 minus imp119888

997888119881119901+119865119899119888

+ 120588119886ℎ (997888119892 minus

997888119886119908)

(10)


Water-film layer

Airfoilh(i)



119904is




119892and 997888119905

119908are the unit




119886ℎ(997888119892 minus

997888119886119908) is



119898119901119862119901

119889119879119901

119889119905=

120581119860119901

ℎ(119879119908minus 119879119901) + ℎ119891119860119901(119879119886minus 119879119901) (11)




119891is the film


119879119901 119879119908 and 119879





120573 (119894) =119899 (119894)

1198990

119884max minus 119884min119904 (119894)

(12)




2 (13)


120573 =sum119873

1120573 (119894)

119873 (14)



120591 (119894) =1

2119862119891 (119894) times 120588119886 times V

2 (15)



V =sum119873

1V (119894)

119873 (16)



119889119898119894

119889119905=120588119908

119860int

119911=ℎ

119911=0

119909=119894Δ119909

119906 119889119911 minus120588119908

119860int

119911=ℎ

119911=0

119909=(119894+1)Δ119909

119906 119889119911 +120597119898119894

120597119905 (17)


119908is the



119889119905(119894)

=1

2120588119908

times 120591 (119894) [((119873 minus (119894 + 1)) ℎ0 (119894)

119873)

2

minus ((119873 minus 119894) ℎ0 (119894)

119873)

2

]

sdot1

120583119908119904 (119894)


(18)



set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)


ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)




119896119904

119896

= 00164Λ

37 Λ le 493


(21)






0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







6





119871is





00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Water-film layer

Airfoilh(i)



119904is




119892and 997888119905

119908are the unit




119886ℎ(997888119892 minus

997888119886119908) is



119898119901119862119901

119889119879119901

119889119905=

120581119860119901

ℎ(119879119908minus 119879119901) + ℎ119891119860119901(119879119886minus 119879119901) (11)




119891is the film


119879119901 119879119908 and 119879





120573 (119894) =119899 (119894)

1198990

119884max minus 119884min119904 (119894)

(12)




2 (13)


120573 =sum119873

1120573 (119894)

119873 (14)



120591 (119894) =1

2119862119891 (119894) times 120588119886 times V

2 (15)



V =sum119873

1V (119894)

119873 (16)



119889119898119894

119889119905=120588119908

119860int

119911=ℎ

119911=0

119909=119894Δ119909

119906 119889119911 minus120588119908

119860int

119911=ℎ

119911=0

119909=(119894+1)Δ119909

119906 119889119911 +120597119898119894

120597119905 (17)


119908is the



119889119905(119894)

=1

2120588119908

times 120591 (119894) [((119873 minus (119894 + 1)) ℎ0 (119894)

119873)

2

minus ((119873 minus 119894) ℎ0 (119894)

119873)

2

]

sdot1

120583119908119904 (119894)


(18)



set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)


ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)




119896119904

119896

= 00164Λ

37 Λ le 493


(21)






0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







6





119871is





00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











set as

ℎ0 (119894) =

0 120573 (119894) = 0

00005 120573 (119894) = 0(19)


ℎ (119894) = ℎ0 (119894) +1

120588119908

119889119898

119889119905(119894) Δ119905 (20)




119896119904

119896

= 00164Λ

37 Λ le 493


(21)






0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







6





119871is





00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

01

02

03

04

Dra

g co

effici

ent




0 5 10 15 2000

02

04

06

08

10

12

14

Lift

coeffi

cien

t







00

01

02

03

04

Dra

g co

effici

ent





70001000

12000

0

02

04

0

minus02

minus06

minus04

minus02 102 04 06 08

10000

11000

X

Y

10000

11000


minus05

minus04

minus03

minus02

minus01

0

01

02

03

04 9000

10000

8000

9000

Y

0minus06

minus02 02 04 06 08

X



0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10 12 14 16 1800

02

04

06

08

10

12

14

Lift

coeffi

cien

t



minus2




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

006

70

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity




X

Y

minus002 0 002 004 006 008 01

minus004

minus002

0

002

004

00670

60

50

40

30

20

10

0

minus10

minus20

x-v

eloc

ity


minus243e + 00

512e + 01





486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










486e + 01

minus787e + 00


628e + 01

minus181e + 01


663e + 01

minus194e + 01


minus124e + 01

609e + 01


579e + 01

minus258 + 01


00 01 02 03 04 05 06 07 08

0

1

2

3

4

5

6

7

Chordwise positionm

Spla

shed

-bac

k dr

ople

t con

cent

ratio

n


(times108dr

ople

tsm

3)





LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










LWC = 39gm3

LWC = 25 gm3

Dry airfoil


AOA = 0degree

Dry airfoil

AOA = 14degree





4 Conclusion













Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Nomenclature






References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









numerical simulation of airfoil aerodynamic penalties and

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