Experimental determination of the droplet impingement ...

Copyright ©1997, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, January 1997A9715262, AIAA Paper 97-0179

Experimental determination of the droplet impingement characteristics of apropeller

Jonathan ReichholdIllinois Univ., Urbana

Michael BraggIllinois Univ., Urbana

Dave SweetBFGoodrich Aerospace, Uniontown, OH

AIAA, Aerospace Sciences Meeting & Exhibit, 35th, Reno, NV, Jan. 6-9, 1997

One of the most powerful tools in the analysis of aircraft icing is the knowledge of where the water in a given cloud willimpinge on a surface. The determination of where a structure will accrete ice is expressed by the impingement efficiency,beta. An improvement to the dye-tracer method for the experimental determination of impingement efficiency is presented.The improved method, which saves both time and expense, was then used to determine the impingement efficiency on afour-bladed, constant chord propeller with a nacelle. The propeller impingement tests showed the limitations of the currentdroplet impingement test techniques and found impingement efficiencies greater than one for a large portion of the propellerblade. Using blade-element theory it is shown how impingement efficiencies greater than one can occur for the case of apropeller. Suggestions are also made as to how the dye-tracer test method can be improved. (Author)

Experimental Determination of the Droplet ImpingementCharacteristics of a Propeller

Jonathan Reichhold* and Michael Bragg^University of Illinois at Urbana/Champaign

Urbana, Illinois

Dave Sweet*BFGoodrich Aerospace - Deicing Systems

Uniontown, Ohio

ABSTRACT

One of the most powerful tools in an analysis ofaircraft icing is the knowledge of where the water in agiven cloud will impinge on an surface. Thedetermination of where a structure will accrete ice isexpressed by the impingement efficiency, p. Animprovement to the dye-tracer method for theexperimental determination of impingement efficiencyis presented. The improved method, which saves bothtime and expense, was then used to determine theimpingement efficiency on a four-bladed, constantchord propeller with a nacelle. The propellerimpingement tests showed the limitations of the currentdroplet impingement test techniques and foundimpingement efficiencies greater than one for a largeportion of the propeller blade. Using blade-elementtheory it is shown how impingement efficiencies greaterthan one can occur for the case of a propeller.Suggestions are also made as to how the dye-tracer testmethod can be improved.

INTRODUCTION

The design of aircraft for safe operation in icingenvironments requires a knowledge of where the waterin an icing cloud will impinge. This information isnecessary for the efficient design of the aircraft iceprotection systems. Knowing the extent and mass of theimpinging water, along with the flight and cloudconditions, determines the energy per unit area whichmust be supplied and the surfaces locations which mustbe protected.

* Formerly Graduate Research Assistant, Dept. ofAeronautical & Astronautical Engineering. CurrentlyEngineer at The Boeing Company, Seattle, WA.Member AIAA7 Professor, Dept. of Aeronautical and AstronauticalEngineering, Associate Fellow AIAA+ Manager of Research and DevelopmentCopyright © 1997 by J. D. Reichhold andM. B. Bragg. Published by (he Americaninstitute of Aeronautics and Astronautics,Inc. with permission.

Droplet impingement information is also afundamental input in the prediction of the ice accretionswhich form on aircraft. The early methods to computeice growth used a knowledge of the dropletimpingement information to approximate the ice whichformed on structures. More recent computationalmodels utilize droplet impingement information directlyin a time stepped manner to compute the formation ofice over time on a structure. These newercomputational methods have evolved into highlyspecialized tools allowing the prediction of iceformations in aircraft development programs.Knowledge of the ice formations allows for thedetermination of the effects icing will have on theaerodynamics of a structure. The aerodynamics of theresultant structure with ice are important for theevaluation of aircraft safety margins.

The determination of droplet impingementinformation is most often accomplished by means ofcomputational codes. These computational methodsdetermine the mass of water which will impinge on asurface by the numerical solution of water droplettrajectories. While these codes do provide an efficientmeans to compute the droplet trajectories for a largenumber of structures, all computational methods requireverification. These computational tools have beenverified using the dye-tracer technique.

The dye-tracer method of droplet impingement wasdeveloped by von Glahn, et al.1, in the 1950s. The dye-tracer method is based upon the injection of a knownconcentration of dyed water into a wind tunnel bymeans of spray nozzles to create a 'cloud' of water.The dye laden water contained in the resultant spraycloud was then allowed to impinge on a model whichhad been covered with an absorbent medium. Theabsorbent medium, typically a blotter paper strip,absorbed the dye in the spray cloud at the point ofdroplet impact. In a similar manner, a freestreamreference collector was mounted in the test section todetermine the mass flux of water at specified locationsin the freestream over given spray times.

The mass of dye deposited at each location on theabsorbent mediums, from the model and freestream,

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was directly proportional to the mass of water whichimpinged on the model at the corresponding location.After the dye was allowed to impinge on the model for agiven time, the absorbent material was removed andreduced by means of a colorimetric analysis todetermine the mass of dye which had impinged atseveral discrete locations on the paper.

In the NACA tests of von Glahn, dye extraction wasaccomplished by punching holes out of the data strips.The cut outs were then dissolved in a aqueous solutionto separate the dye from the paper medium. Next, thepaper strands remaining in the mixture were filtered out.The remaining dye and water solution was thenanalyzed with a colorimeter to determine theconcentration of dye in the solution. From the dyeconcentration, knowing the amount of water used toextract the dye from the paper, the mass of dye in thesolution was therefore determined.

A modified means of reducing the mass of dye fromthe paper strips was developed by Papadakis, et al.2, inthe late 1980s. Papadakis replaced the colorimetricanalysis, which had been expensive, time consuming,and destructive, with a laser reflectance method.Instead of punching holes from the data strips, the laserreflectance data reduction used the reflected laserintensity from the data strip to determine the mass ofdye in the paper itself. This method of data reductionwas based upon diffuse reflective spectroscopy whichstates that the intensity of the reflected light wasproportional to the mass of dye in the paper.

In 1995 Bragg, et al.3, further improved the dyeextraction method by using a digital camera to create animage of the dye laden strips. The digital image wasthen reduced by means of image analysis routines. Thisnewer method provided a much faster and lessexpensive means to reduce the data strips. The theoryand implementation of this method will be discussedbriefly and are covered in further detail by Reichhold4.

THEORY AND IMPLEMENTATION

The study of icing frequently requires thedetermination of droplet impingement parameters. Themost frequently used droplet impingement parametersarc the impingement efficiency, p\ and the collectionefficiency, E. The impingement efficiency is the massflux of water impinging on a surface non-dimensionalized by the freestream mass flux. Afterutilizing conservation of mass the resultant equationfor fi is given by Eq. I. Note that Fig. 1 illustrates thevariables in the context of the propeller. Thecollection efficiency is the total mass flux impingingon a body non-dimensionalized by the mass flux in the

freestream through a characteristic area. In practice thecollection efficiency is defined as the integral of theimpingement efficiency from the maximum uppersurface impingement location, su, to the minimum lowersurface impingement location, SL, Eq. 2.

E = - 5-dA

(1)

(2)

Fig. 1 Droplet trajectory parameters in 3-D

Dye Tracer Impingement TestsThe goal of the present study was to determine the

impingement efficiency about a three-dimensional,rotating propeller. In order to accomplish this task, theUIUC 3-D tunnel, Fig. 2, was modified to include aspray system and propeller test stand. The UIUC tunnelhad a maximum test section velocity of 45 ft/sec (withpropeller and spray system installed) and used a spraysystem composed of five NASA standard spray nozzles.The spray system used the hardware from the tests of

Fig. 2. UIUC 3-D tunnel setup.

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Fig. 3. Propeller model as tested. Fig. 4. Freestream reference collector.

Papadakis2 for both the water and air injection systems.The system of Papadakis was modified for these testssuch that the air and water solenoids were controlled bya computer data acquisition system.

The model constructed for these tests was a four-bladed propeller which was mounted on a special teststand in the wind tunnel. Each of the four blades of thepropeller were manufactured from a single mold andwere based on a constant chord, Clark-Y airfoil section.The propeller blades further incorporated a twist of2.75°/inch. Fully assembled the propeller used had adiameter of 3 feet and was typically rotated at a constantspeed of 500 RPM. The complete model, as tested, isshown in Fig. 3.

In order to determine the freestream LWC values forthe calculation of (3, a reference collector wasassembled. The freestream reference collector usedcontained four, 20-inch collectors which were mountedperpendicular to the airflow and V2 a propeller diameterin front of the nacelle. The reference collector wasrotated during testing to provide an average value forthe freestream reference value at each radial location.The freestream reference collector is illustrated in Fig.4.

The water used in these tests was saturated withFD&C Blue Dye No. 2 to a concentration of 0.5 g/L ofdeionized water. The dye laden water was injectedthrough the spray nozzles, using the spray system, atknown air and water pressures for a given spray time.The pressures at the nozzles were monitored with two0-250 psig pressure transducers on the water supplylines and a 0-100 psig transducer on the air line. Theair and water on/off states were controlled by solenoidvalves which were computer activated by a relay switch.Before testing the spray system was calibrated using aPDPA system4. The spray calibration results were usedto determine the air and water pressures used in thepropeller testing.

The dye laden water in the reultant spray cloud wasthen allowed to impinge for a given amount of time on

both the model and reference collector which werecoated with paper. In the original tests of von Glahnand Papadakis a blotter paper had been used to collectthe dye on the models. In the current tests, a form ofchromatography paper was used. It was determined thatthis paper formed to the model contour without thewrinkling which was found with the blotter paper. Anadded benefit of this paper was the high level ofconsistency in paper color, unlike the blotter paperwhich was composed of courser wood pulp.

For the propeller testing it was further found that thepaper strips had to be protected on the inner radial sidefrom run back. This was accomplished by placing aguard strip of paper on the inner radial side of eachcollector strip. The radial locations tested and the guardstrips locations are illustrated in Fig. 5.

as0.90

0.3S

0-!S

if Data Strip•Gaurd Strip

Figure 5. Main blotter strip locations tested.

After the dye deposition had been accomplished inthe wind tunnel, the data strips were taken to NASALewis Research Center for digitization. Beforediscussing the specifics of the digitization a brief


discussion of the theory behind the method should bepresented.

The main theoretical background for the digitizationis that of diffuse-reflective spectroscopy and morespecifically the theory of Kubelka and Munk5. Thetheory of Kubelka-Munk (KM) relates the transmittanceand reflectance of monochromatic light off a plane-parallel layer composed of light-scattering and light-absorbing particles whose dimensions are much smallerthan the layer thickness, i.e. the paper thickness. TheKubelka-Munk theory is the main theoreticalbackground behind the chemical practice of thin-layerchromatography which determines chemicalcomposition and quantities of samples of a material onchromatography paper. The Kubelka-Munk theory isreally a set of ordinary differential equations whichwere solved by Kortiim5 for the case of a thin layer of asubstance on a backing paper. The equation for thereflectance and transmittance is therefore given by Eq.3a and 3b, respectively.

_ l - R g [ a - h - c o t h ( b - S - X ) ]~ a + b - c o t h ( b - S - X )

(3a)

dyes used in these experiments this was the case, basedupon an analysis of Papadakis" data.

In order to use the analysis technique of either laserreflectance or digital imaging the dye must not beallowed to soak into the paper beyond the upper layer ofthe paper. If the dye is assumed to be a transparentlayer on a totally reflecting substrate, i.e. the undyedpaper, and, using the undyed paper as a reference(100% reflectance of the incident light), it can beassumed that the Kubelka-Munk remission function canbe applied as follows7:

(5)

Equation 5 relates the normalized intensity (Inc = R),the molar absorption coefficient (e), the concentrationof dye (c), and the scattering coefficient (S). If it isfurther assumed that the scattering coefficient of the dyelayer was constant, the equation for the concentration is:

S-KM(In c) = B-KM(I n c ) (6)

a • sinh(b • S • X) + b • cosh(b • S • X)<3b)

where:

a = -S+K

In the above equation R is the percent reflectance ofthe incident light (I/I0), T is the normalizedtransmittance, S is the scattering coefficient of the dyein this case, X is the thickness of the dye layer, and Rg isthe reflectance of the backing paper.

In the practice of thin-layer chromatography it isfrequently assumed that the thickness of the dye layer isinfinite from a optical point of view. Assuming that, forthe moment, that the layer is infinitely thick then theKubelka-Munk remission function can be used asexpressed in Eq. 4. In this equation, K is theabsorptivity coefficient of the dye layer.

(4)2-R.

It was found by Huf6 that a layer could beconsidered infinitely thick from an optical point of viewwhen the quantity b-S-X was greater than 2. For the

The interesting thing about this equation is that B isa constant which will depend only on the choice of dyeand paper. The concentration, c, of a substance isrelated to the mass of the substance by the followingrelationship:

mass K • X= c • X = ———unit area (7)

In order to determine the dye concentration, basedupon the normalized reflected light intensity, acalibration would then be required in a manner similarto that used to determine the dye mass by von Glahn1.

The definition of (3 is the mass flux of waterimpinging on a surface non-dimensionalized by themass flux of water in the freestream. In the experimentthe definition of (i was defined as the mass of waterwhich impinged on the model over a given time non-dimensionalized by the mass of water which wasdeposited on the reference collector for the same lengthof time. Because the dye concentration was heldconstant throughout the tests, the equation for p" can beexpressed as the mass of dye deposited on the papernon-dimensionalized by the dye deposited on thefreestream collector, Eq. 8. In this equation acorrection factor, Efs, was applied to account for thecollection efficiency of the freestream collector.

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(mass ofdye)prope,,er

—— • (mass ofdye)freesll.ean cMeaor(8)

= E is •B-KM

B-KM f s

In Equation 8 the quantity B is a constant which canbe cancelled. Now, the equation for P is given by Eq. 9.

/J = Efs • KM/KMfs (9)

The data reduction procedure was, therefore,reduced by eliminating the need to determine theconstant required for the dye mass determination, Eq. 6.This relationship was found to hold for airfoil datastrips which were tested previously3 and the relationshipwas used in the propeller testing.

Digital Imaging ProcedureThe freestream and model data strips were all

imaged at the NASA Lewis Research Center using a 14-bit, liquid-cooled, CCD-array camera. As shown in Fig.6 the dye-laden strips were placed under a photographicgrade non-reflective glass, next to a scale (to provide areference length) and illuminated by two light sources.The light sources used were air cooled halogen bulbs.The light from the halogen bulbs was filtered through ayellow band pass filter around 600 nm ± 25 nm andpassed through a diffusion filter to reduce the peak lightlevels. Before digitization, care was taken to producethe most uniform lighting possible in order to reduce thecorrection factor for light intensity variations. Theresulting light reflected from the dye-laden paper wasthen imaged by the digital camera through a 412 - 52Snm band pass filter in order to increase the pixelsensitivity in the blue region and decrease theabsorption of extraneous light. The camera took imagesconsisting of a 512 by 512 pixel array, each pixelresolved in intensity to 14 bits. Each final image was anaverage of 8 separately acquired images with the blackimage subtracted. The digitized image was then storedfor later analysis. An example of image taken duringthe tests is shown in Fig. 7. Notice in this image thatseveral strips were recorded at the same time, lined upby the leading edge marks, and that each imageincluded a length scale and color reference.

After collecting all of the images, a flatfield imagewas created using the camera, the lens, the filters, thelights and a light integrating sphere. This flatfield imageset, which consists of a dark image (ID), a bias image,and a flatfield image (IFF). is later applied in the imageanalysis routines to reduce the non-uniformity in pixelresponse across the CCD array. In order to correct the

Fig. 6. Digitization setup.

ReferenceColorStrip

«*V-iiifc*V.' '•: ' 'saj^r-s"•'";.•;" -•;'-•'>

3'-$*

IFigure 7. Example image acquired of data strips.

intensity, I, of an image the flatfield images wereapplied to the intensity of each pixel of the image byuse of the Eq. 10 in order to arrive at a new flatfieldcorrected image, IFFC-

(10)

The flatfield correction corrected for variation in thecamera response due to angularity of light with thespherical lens and also corrected for pixel-to-pixelsensitivity in the CCD array to light levels.

The digitized images were processed using asoftware package called PV-Wave™, with speciallydeveloped processes (programs) to manipulate theimages. Each digitized image was read into PV-Wave™, alons with the white reference and flatfield

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images, and the length scale was then definedautomatically using the digitized scale, which typicallyyielded 0.3 mm per pixel. The user was then promptedto enter two points which defined a box around the areato be interrogated. The leading edge of each strip wasmarked at the time of the tests and the programautomatically determined this location by interrogationof the image. After the leading-edge location wasdetermined, and the user entered the interrogationlimits, the program iterated from the user specifiedupper surface s/c location to the user specified lowersurface s/c location determining the left and right edgesof the paper at each location using a gradient approach.At each s/c location the pixels from the left to rightedges of the strip were then averaged for a single value.At this point in the reduction process, a 1-D array oflight intensity values versus surface distance on themodel existed.

Some non-uniformity of the incident lighting at thetime of digitization was unavoidable, and led to a non-uniformity in the reflected light. This non-uniformitywas corrected by normalizing (dividing) the entireimage by the reference "white" image, which includedthe same non-uniformity, for every pixel in the imageThis yielded the normalized intensity In given by:

In(S)=I(S)/Iw r(S) (11)

Numerically this was implemented by averaging agroup of pixels in the white reference image centered onthe same pixel locations as the row on the strip beinganalyzed. This value was then used as the Iwr(S) valuein Eq. 11. The normalization effectively reduces theeffects of non-uniformity in the lighting at the time ofthe digitization.

After normalization the image was further correctedfor any changes in the image due to slight variations inthe mean incident light intensity. This wasaccomplished by using the white (non-dye-laden) regionon either end of the strip being reduced to determine acorrection factor. The correction factor, the white pixelintensity from the reference image taken at thecorresponding location, IWr(Send). divided by theintensity of the above white region, I(Send). was thenmultiplied by the normalized intensity. Then thenormalized corrected intensity becomes:

(12)

With normalization and the correction factorapplied, values of normalized corrected intensity, Inc, of1.0 were found at the end of each strip, where no dye ispresent, and values less than one between the limits of

impingement where dye was present. The minimumnormalized corrected intensity occurred where the dyeconcentration was a maximum.

Using the Kubelka-Munk remission function thenormalized, corrected light intensities were thentransformed into a new variable, KM. The freestreamvalue of the Kubelka-Munk variable, KMFS, wasdetermined by a similar data reduction process on thereference collector blotter strips. Using all of theabove, |}(S) was then given by Eq. 9. All valid caseswere then averaged to form a single beta curve.Typically 12 data strips were averaged for a singlecurve.

The collection efficiency of the freestream referencecollector, Erc, was determined using the numericalresults of Lewis and Brun8. Lewis and Brunnumerically determined the collection efficiency ofrectangular bodies and used the results to determine anequation for the collection efficiency.

Uncertainty AnalysisAn uncertainty analysis has been performed on the

propeller droplet impingement experiment for thepurpose of identifying the parts of the experiment wherea reduction in uncertainty will most improve theaccuracy of the final propeller droplet impingementdata. The analysis will ultimately provide an estimateof the uncertainty in the final data to facilitate its use forcomputer code validation. An analysis of theuncertainty in the airfoil droplet impingement data haspreviously been published in Ref. 3. The analysispresented here is based on the work of Kline andMcClintock9 and the more recent work of Coleman andSteele10 where the uncertainty estimate means that theodds are 20 to 1 that a single sample will lie within ±the uncertainty estimate from the true value.

Using the dye tracer method of dropletimpingement, the equation for p was given by Eq. 13where the variables are defined below. Using Eq. 13,the uncertainty of p can be estimated by Eq. 14. Theuncertainty in all three of these quantities must bedetermined.

(13)

md(s, r) mass of dye deposited on a propellerstrip per unit area

mjj-s(s, r) mass of dye deposited on referencecollector strip per unit area

Erc Collection efficiency of the referencecollector


s surface location in chordwise directionon the propeller strip

r radial location on the propeller strip

(14)

Uncertainty in the mass in the freestream andpropeller dye mass at any location will be dependentupon the uncertainty in several different quantities: thepropeller speed, the radial location of measurement, thetest section velocity, the LWC and MVD of the spraycloud, the timing, the blade setting, the concentration ofthe dye, the errors in the camera, and the freestreamturbulence. The last uncertainty, due to freestreamturbulence, was initially neglected in the uncertaintyanalysis.

Neglecting the freestream turbulence term at thispoint, the uncertainties, wmd/nid, in the mass of dyedeposited on the propeller and freestream referencecollector were determined to be ± 2.4% for a 20 micronMVD spray cloud at the 70% radial location. Theuncertainty in the reference collector efficiency at thesame location and conditions was determined to be ±2.9%. Combining the uncertainties listed above, theuncertainty in the impingement efficiency, for the 20(im MVD spray cloud, was found to be ±4.42% over theentire propeller.

The calculated uncertainty for this case is much lessthan the values determined by Papadakis, et al.2, of 10-25% or Bragg, et al.3, of 15.44%. Several differentfactors worked together to make the magnitude of theuncertainty found in this analysis so low. One factorwhich has been neglected is the error in the referencecollector efficiency, Erc, as a function of the radius forthe rotating collector used in the testing. Untilcomputational methods exist to predict the collectionefficiency for this rotational case, the 2-D, non rotating,values determined using the formulas of Lewis andBrun have been used in the reduction.

The other major omission in this error analysis hasbeen the unsteadiness of the freestream due to tunnelturbulence and spray cloud unsteadiness. There is nosimple way to calculate this uncertainty a priori. Bragg,et al. , dealt with this uncertainty by taking twice thestandard deviation of the freestream dye mass, asmeasured on the reference collector, to obtain a 95%confidence level (20:1 odds) for the uncertainty. Usingthis approach, the uncertainty in the propeller tests, as afunction of the radial location, was determined from thefreestream reference collector data. It was found thatthe twice the standard deviation of the dye mass on thefreestream reference collector was between 3%-14.4%.

Based upon the factors previously analyzed theexpected uncertainty in the dye mass on the freestreamreference collector was at most 1.5%-3%. Thefreestream turbulence and spray cloud unsteadiness,based upon the comparison of the test data and theuncertainty analysis presented in this chapter, dominatesthe uncertainty of the droplet impingement tests. Basedupon this difference in uncertainty, between the derivedand experimental values, the impingement testing hasthe possibility of being very accurate if the freestreamturbulence in the spray cloud could be made moreuniform and repeatable.

The deviation in the mass of dye collected on thefreestream collector, the standard deviation in thepropeller data at each radial location, and the collectorefficiency at each radial location were used to calculatethe uncertainty in the impingement efficiency, wp/fj.Figures 9 summarizes these data for the 20 [im MVDspray cloud using the data of the baseline geometrypropeller tests. In this figure the uncertainty ispresented as the percentage of wp/p. Notice that at thes/c = 0.0 - 0.01 location, which correspond to thelocations of Proax, has the minimum uncertainty levels,wp/P, of 8%-16%. In Figure 9 also notice that theuncertainty in P increased as the impingement limitswere approached. The increase in uncertainty at theouter edges of Fig. 9 correspond to the locations whereP approached zero. At the impingement limits a slightuncertainty in P will result in a large percentageuncertainty. The uncertainty in the impingementefficiencies shown in Fig. 9 provide further illustrationthat the derived uncertainty of approximately 4% for the20 MVD case was optimistic. Based upon theexperimental data the uncertainty in the impingementefficiency in these tests was therefore less than or equalto 16% at Pmax and increased as the impingement limitswere approached to 30%-50%.

0.02 O.M

Figure 9. Uncertainty in 20 n.m MVD data


RESULTS AND DISCUSSION

The baseline" propeller was a four-bladedconfiguration with POJSR = 40° and a 10"-diameter,axisymmetric nacelle. The first propeller impingementexperiments used a 20 um MVD spray cloud and theresults are included in Fig. 11. Figure 11 presents theexperimentally determined impingement efficiency (P)as a function of the radial and chordwise location.

3.5————— Beta(r25)— — Beta(r35)....... Beta (r45)——-X—— Beta(rSO)— - - - - Beta(r55)_ _ _ _ Beta(r65)

Beta (r70)Beta (r75)Beta (r85)Beta (r90)Beta(r95)

-0.1 -0.05 0 0.05 0.1

Figure 10. 20 urn MVD data.

0.15

The values of (3, in Fig. 10, were found to vary withboth radial location and chordwise, S/C, location.Maximum values of f$ were found to occur for thisbaseline case at S/C locations of approximately 0.005.As the radial location of the measurement was movedoutward from r/R = 0.25 to 0.95, the maximum value ofthe impingement parameter, Pmox, varied from 0.93 to3.12, Fig. 10.

In general the lower surface impingement movedtoward the stagnation line on the propeller (S/C = 0.0 -0.01 for the current geometry and conditions), when theradial location analyzed was varied between 0.25 andapproximately 0.70 - 0.75. When the radial location ofmeasurement was increased further the lower surfaceimpingement limits were found to move outward again.On the upper surface, the impingement limits were

again moved towards the stagnation line as the radiallocation analyzed was increased but, for the uppersurface past the r/R = 0.50 location, the upper surfaceimpingement limits were found to move away from thestagnation line of the propeller.

The variation in the impingement limits is partiallyexplained by the variation in the lift coefficient withradial location. Figure 11 shows the predicteddistribution of C, using a three-dimensional panel codefor a propeller, BetaProp", and a two-dimensional striptheory. Both methods show that the sectional liftcoefficient increased with radial extent on the blade upto the 0.55-0.65% radial location. The sectional liftcoefficient of the blade was directly proportional to thesectional angle of attack of the propeller blade at eachradial location. Increasing the angle of attack on anairfoil will move the lower surface impingement limitsfarther aft while the upper surface impingement limitwill be moved toward the stagnation point. Theimpingement limits of the baseline propeller data, Fig.11, follows the trends which would be expected basedupon the predicted variation in the sectional Cr values.

C 0.2

Figure 11. Variation in Ce for propeller.

Notice in Fig. 10 that the maximum impingementefficiencies for the baseline data were greater than unityfor the majority of the radial locations. In typicalimpingement calculations, i.e. for non-rotatingstructures, values of P greater than one are not usuallyfound, p was defined as the mass flux striking a surfacenon-dimensionalized by the freestream value. Thefreestream mass flux was based upon the freestreamvelocity, while each location on the propeller sees aneffectively larger approach velocity based upon theadditional angular velocity due to the rotation of thepropeller. Therefore, the propeller, as the radialdistance was increased, swept out more water in thespray cloud and its impingement increased. Since Pwas based upon the freestream value, P increased in theradial direction and significantly exceeded one for themajority of the baseline data, Fig. 10.


_1_1_JLJ_J_JL

Figure 12. Illustration of control volume used.

The trend of an increase in P as the radial location isincreased can be mathematically related to theimpingement on an airfoil using blade element theories.Figure 12 illustrates the reference frame and variablesused for the derivation of the three-dimensional value ofP from the two-dimensional blade clement theory.Figure 12 presents a slice of the propeller bladesurrounded by a control volume which was the fixedframe of reference for the following derivation. In thisfigure, the air approaches the blade clement from rightto left due to the rotation of the propeller and throughthe top of the control volume due to the freestreamvelocity. In order to simplify the equations, the effectsof the inflow (w) were ignored. In this analysis, in amanner consistent with the derivation of airfoilimpingement codes, the freestream mass whichimpinges on the model is assumed to start an infinitedistance from the propeller. For the derivationpresented, all of the mass which impinges on thepropeller was assumed to pass through the area A^ effwhich is perpendicular to the effective velocity, Veff, ofeach propeller section. In this frame of reference theequation for the conservation of mass becomes:

LWCeffVeffAmeff=LWCsVsAs (15)

LWCSVS

LWCeffVeff(16)

The three-dimensional impingement efficiency isnon-dimensionalized by the freestream mass flux, andnot the effective values, as shown in Eq. 17.

03-0 =LWCSVS

LWC V (17)

Combination of Eq. 16 and 17 yields:

03-D = 02-D ' LWCV (18)

Now, in order to simplify the analysis, theconcentration of water (frequently called the liquidwater content, LWC) in the freestream, LWC_, isassumed equal to the LWC at the effective area of the 2-D slice from the blade element theory. The waterconcentration is not a vector quantity and, therefore, theassumption of equality between the effective waterconcentration and the water concentration in thefreestream will be valid unless significant levels ofpropeller stream tube contraction occur. Thiscontraction will later be included, but was ignored atthis point such that Eq. 18 becomes:

03-D = 02-DVeffV.

(19)

If it is further assumed that the induced velocity, w,was negligible then, from Fig. 12, the effective velocityat the propeller location was:

r •> -> ->ilVeff=[vl+ft)2r2] (20)

Using Eq. 20 in Eq. 19 it can be found that:

r 2 2 2lI/2

03-D = 02-D ,, (21)

Where the subscript ( )eff quantities represent theeffect! ve values of the various quantities which wouldpass through the area A_ eff if the airfoil segment, asassumed in blade element theory, were stationary andfixed at the effective angle of attack, a. In this frame ofreference the definition of the impingement efficiencywould be:

Simplifying Eq. 21 it was found that:

03-D = 02-DfflV (22)

Based upon this simplified approach for thederivation of the impingement efficiency, and assuming


the maximum two-dimensional impingement efficiency,as typically assumed, was one, then the propellerimpingement efficiency, p3.D, can exceed one if co isgreater than zero. Therefore, as the radial location ofthe impingement measurement on the propellerincreased, the maximum impingement efficiency, Pmax,increased, in a manner consistent with the test data, Fig.11.

An example of using this idea with Bragg'sAIRDROP12 code is shown in Fig. 13 for the baselinepropeller case. In order to determine the data of Fig.13, the propeller was modeled using the same modifiedstrip theory analysis that was used to design thepropeller. From this analysis the C( values for the radiallocations of interest were obtained. The C, values werethen matched with the 2-D airfoil flowfield results todetermine the effective airfoil angle of attack as afunction of radial location on the propeller. The dropletinertia parameter and Reynolds number were calculatedusing the airfoil chord as the characteristic length andthe effective velocity as the characteristic velocity.Using this angle of attack, the inertia parameter andReynolds number were calculated and input into the 2-D droplet impingement code for the radial locations ofinterest. In order to compute the 3-D impingementvalues which corresponded to the propeller cases, the 2-D p values were then multiplied by the velocity ratioderived previously, Eq. 22.

-0.2 -0.15 -0.1 -0.05 0.05 0.1 0.15

Figure 13. 2-D determined P values.

The 2-D calculated pmax appropriately increased,Fig. 13, as the radial location analyzed was increased,but the theoretical values were lower in magnitude thanthe experimentally determined values, Fig. 10. Thelimits of impingement on the upper surface werepredicted reasonably well by the 2-D strip theoryapproach, Fig. 13, when compared to the experimentaldata. Fig. 10. However, on the lower surface, theexperimentally determined increase in SL withincreasing radial location was predicted, but the

magnitude of the change was greatly over predicted bythe theory. Overall, however, the 2-D method and theexperimental data agree for this case with regards to theimpingement limits.

In the above derivation the influence of the otherpropeller blades, the propeller thrust (and therefore theinflow), and the contraction of the stream tube havebeen neglected. These quantities are all likely toincrease the water concentration near the propellerwhich was previously assumed equal to the freestreamvalue. If now the effective water concentration near thepropeller were allowed to vary from the freestreamvalue, then Eq. 22 must be rewritten as shown in Eq. 23.

LWC eff T a>vl'riH (23)

For the actual propeller run in this report, thrust wasproduced and the area of the stream tube of air whichpassed through the propeller was contracted from alarger area in the freestream. The contraction of theairflow stream tube will increase the waterconcentration near the propeller, LWCcff. As the thrust,and therefore, the stream tube contraction increase, themaximum impingement efficiency will increase. Theincrease in the levels of P with increasing thrust can befound in the engine nacelle impingement data ofPapadakis2. In addition to the stream tube contractiondue to the thrust, the spinner and nacelle will furtheralter the effective LWC seen by the propeller andincrease P based upon Eq. 24. Based on all of thesefactors, the 3-D impingement measured on the propellershould be larger than the values predicted by the two-dimensional strip analysis.

All of the data presented in this report arepreliminary. Later analysis of the data revealed that thedata at the outer radial locations, r/R > 0.50, maycontain an error in the freestream measurements. Thisissue is still being pursued at this time.

SUMMARY AND CONCLUSIONS

The digital imaging and- image analysis datareduction scheme presented in this report offers asignificant savings in both time and expense overcurrent methods. This method was used to study theimpingement efficiency on a propeller. The propellerimpingement testing was the first of its kind andtherefore needs to be analyzed in more detail before theconfidence in the data can be increased. The propellertests illustrated that for rotating systems theimpingement efficiency can be greater than one, a factthat was explained using blade element theory.


RECOMMENDATIONS

The following recommendations are suggested inorder to further improve droplet impingement testing:

1. Reduce the turbulence level and, therefore, thespray cloud unsteadiness in the wind tunnel ifmixing can be maintained.

2. The linear relationship between the dye massand the KM variable needs further verification.

3. A light box should be used for the imagingoperations to eliminate outside lightinterference

4. The freestream reference collector needs to beimproved for both propeller and airfoil testing.

5. A large number of repeat runs are suggested toreduce the statistical uncertainty of the data.

ACKNOWLEDGEMENTS

The authors would like to thank the followingindividuals and organizations for supporting thisresearch: Michael Cebryznski who aided in taking allof the wind tunnel data, Abdi Khodadoust whoperformed the airfoil verification tests, NASA Lewisand Tim Bencic for the use of the digital camera andspray system, BFGoodrich Aerospace for funding thisresearch, and all of the graduate and undergraduatestudents whose long hours helped see this projectthrough.

5 Kortiim, G., Reflexions Spectroscopie, Springer-Verlag, Berlin, 1969.6 Huf, F. A., Anal. Chim., Acta 90, p. 143, 1977.7 Huf, F. A., "In Situ Evaluation of Thin-LayerChromatograms," Quantitative Thin-LayerChromatography and Its Industrial Applications, editorLaszlo R. Treiber, Chromatographic Science Series,Vol. 36, Marcel Dekker, Inc. New York, pp. 17-66,1987.8 Lewis, William and Brun, Rinaldo J., "Impingementof Water Droplets on a Rectangular Half Body in aTwo-Dimensional Incompressible Flow", NACA TN3658, 1956.9 Kline, S.J. and McClintock, F.A., "DescribingUncertainties in Single Sample Experiments",Mechanical Engineering, Vol. 75, pp. 3-8, Jan. 1953.10 Coleman, H.W. and Steele, W.G., Experimentationand Uncertainty Analysis for Engineers, John Wileyand Sons, Inc., New York, 1989." Farag, K. Private Communication, January 1996.12 Bragg, M. B., "Rime Ice Accretion and Its Effects onAirfoil Performance," Ph.D. Dissertation, The OhioState University, Columbus, OH, 1981, and NASA CR165599, March 1982.

REFERENCES

1 von Glahn, U. H., Gelder, T. F., and Smyers, W. H.,Jr., A Dye Tracer Technique for ExperimentallyObtaining Impingement Characteristics of ArbitraryBodies and a Method for Determining Droplet SizeDistributions, NACA TN 3338, March 1955.2 Papadakis, M., Elangonan, R., Freund, G. A., Jr.,Zumwalt, G. W., and Whitmer, L., An ExperimentalMethod for Measuring Water Droplet ImpingementEfficiency on Two- and Three-Dimensional Bodies,NASA CR 4257 (DOT/FAA/CT-87/22), Nov. 1989.3 Bragg, M. B., Cebrzynski, M., Reichhold, J. D.,Sweet, D., Waplcs, T., and Shick, R., "An ExperimentalMethod for Water Droplet Impingement Measurement",1995 American Helicopter Society/Society ofAutomotive Engineers International Icing Symposium,Montreal, Canada, Sept. 18-21, 1995.4 Reichhold, J. D., "Experimental Determination of theDroplet Impingement on a Propeller Using a ModifiedDye-Tracer Technique", M.S. Thesis, University ofIllinois at Urbana/Champaign, Urbana, IL, Jan. 1997.

IIAmerican Institute of Aeronautics and Astronautics

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