# ASTM E799-03 (Reapproved 2015)

Designation E799 03 Reapproved 2015Standard Practice for DeterminingData Criteria and Processing for Liquid Drop Size Analysis1This standard is issued under the fixed designation E799; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice gives procedures for determining appro-priate sample size, size class widths, characteristic drop sizes,and dispersion measure of drop size distribution. The accuracyof and correction procedures for measurements of drops usingparticular equipment are not part of this practice. Attention isdrawn to the types of sampling spatial, flux-sensitive, orneither with a note on conversion required s notspecified. The data are assumed to be counts by drop size. Thedrop size is assumed to be the diameter of a sphere ofequivalent volume.1.2 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.3 The analysis applies to all liquid drop distributionsexcept where specific restrictions are stated.2. Referenced Documents2.1 ASTM Standards2E1296 Terminology for Liquid Particle Statistics With-drawn 199732.2 ISO Standards4133201 Particle Size Analysis-Laser Diffraction s92761 Representation of Results of Particle Size Analysis-Graphical Representation92722 Calculation ofAverage Particle Sizes/Diameters andMoments from Particle Size Distribution3. Terminology3.1 Definitions of Terms Specific to This Standard3.1.1 spatial, adjdescribes the observation or measure-ment of drops contained in a volume of space during such shortintervals of time that the contents of the volume observed donot change during any single observation. Examples of spatialsampling are single flash photography or laser holography.Anysum of such photographs would also constitute spatial sam-pling. A spatial set of data is proportional to concentrationnumber per unit volume.3.1.2 flux-sensitive, adjdescribes the observation of mea-surement of the traffic of drops through a fixed area duringintervals of time. Examples of flux-sensitive sampling are thecollection for a period of time on a stationary slide or in asampling cell, or the measurement of drops passing through aplane gate with a shadowing on photodiodes or by usingcapacitance changes. An example that may be characterized asneither flux-sensitive nor spatial is a collection on a slidemoving so that there is measurable settling of drops on the slidein addition to the collection by the motion of the slide throughthe swept volume. Optical scattering devices sensing continu-ously may be difficult to identify as flux-sensitive, spatial, orneither due to instantaneous sampling of the sensors and themeasurable accumulation and relaxation time of the sensors.For widely spaced particles sampling may resemble temporaland for closely spaced particles it may resemble spatial. Aflux-sensitive set of data is proportional to flux density numberper unit area unit time.3.1.3 representative, adjindicates that sufficient data havebeen obtained to make the effect of random fluctuationsacceptably small. For temporal observations this requiressufficient time duration or sufficient total of time durations. Forspatial observations this requires a sufficient number of obser-vations.Aspatial sample of one flash photograph is usually notrepresentative since the drop population distribution fluctuateswith time. 1000 such photographs exhibiting no correlationwith the fluctuations would most probably be representative.Atemporal sample observed over a total of periods of time thatis long compared to the time lapse between extreme fluctua-tions would most probably be representative.3.1.4 local, adjindicates observations of a very small partvolume or area of a larger region of concern.3.2 SymbolsRepresentative Diameters1This practice is under the jurisdiction ofASTM Committee E29 on Particle andSpray Characterization and is the direct responsibility of Subcommittee E29.02 onNon-Sieving s.Current edition approved March 1, 2015. Published March 2015. Originallyapproved in 1981. Last previous edition approved in 2009 as E799 03 2009.DOI 10.1520/E0799-03R15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume ination, refer to the standards Document Summary page onthe ASTM website.3The last approved version of this historical standard is referenced onwww.astm.org.4Available from American National Standards Institute ANSI, 25 W. 43rd St.,4th Floor, New York, NY 10036, http//www.ansi.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.1 Dpq is defined to be such that5Dpqp2q5iDipiDiq1whereD the overbar in Ddesignates an averagingprocess,pqpq the algebraic power of Dpq,p and q the integers 1, 2, 3 or 4,Di the diameter of the ith drop, andi the summation of Dipor Diq, representingall drops in the sample.0pand q values 0, 1, 2, 3, or 4.iDi0is the total number of drops in the sample, and someof the more common representative diameters areD10 linear arithmetic mean diameter,D20 surface area mean diameter,D30 volume mean diameter,D32 volume/surface mean diameter Sauter, andD43 mean diameter over volume De Broukere or Herdan.See Table 1 for numerical examples.3.2.2 DNf,DLf,DAf, and DVfare diameters such that thefraction, f, of the total number, length of diameters, surfacearea, and volume of drops, respectively, contain precisely all ofthe drops of smaller diameter. Some examples areDN0.5 number median diameter,DL0.5 length median diameter,DA0.5 surface area median diameter,DV0.5 volume median diameter, andDV0.9 drop diameter such that 90 of the total liquidvolume is in drops of smaller diameter.See Table 2 for numerical examples.3.2.3logDgm 5ilogDi/n 2wheren number of drops,Dgm the geometric mean diameter3.2.4DRR5 DVF3wheref 11e 0.6321, andDRR Rosin-Rammler Diameter fitting the Rosin-Rammlerdistribution factor see Terminology E1296.5This notation follows Mugele, R.A., and Evans, H.D., “Droplet Size Distri-bution in Sprays,” Industrial and Engineering Chemistry, Vol 43, No. 6, 1951, pp.13171324.TABLE 1 Sample Data Calculation TableSize Class BoundsDiameterin MicrometresClassWidthNo. ofDrops inClassSum of Dirin Each Size ClassAVol. in ClassBCum. by Vol.DiDi2Di3Di4240360 120 65 19.5 1035.91061.81091. 10120.005 0.005360450 90 119 48.2 19.6 8.0 3 0.021 0.026450562.5 112.5 232 117.4 59.7 30.5 16 0.081 0.107562.5703 140.5 410 259.4 164.8 105.2 67 0.280 0.387703878 175 629 497.2 394.7 314.5 252 0.837 1.2248781097 219 849 838.4 831.3 827.6 827 2.202 3.42610971371 274 990 1221.7 1513.7 1883.2 2352 5.010 8.43613711713 342 981 1512.7 2342.1 3641.1 5683 9.687 18.12317132141 428 825 1589.8 3076.1 5976.2 11657 15.900 34.02321412676 535 579 1394.5 3372.5 8189.2 19965 21.788 55.81126763345 669 297 894.1 2702.8 8203.5 24999 21.826 77.63733454181 836 111 417.7 1578.2 5987.6 22807 15.930 93.56741815226 1045 21 98.8 466.5 2212.1 10532 5.885 99.45352266532 1306 1 5.9 34.7 348.5 1534 0.547 100.000Totals of Dirin 6109 8915.3 10316562.6 10637729.0 109100695 1012entire sample DN0.5 1300 D10 1460 D21 1860 D32 2280 D43 2670D20 1650 D31 2060D30 1830DV0.5 2540 Worst case class width348.5377295 0.009 Relative Span 5 sDV0.92 DV0.5d/DV0.55 s3900 2 14200d/2530 5 0.986692676133453 0.21826 5 0.024Less than 1 , adequate sample size Adequate class sizesAThe individual entries are the values for each as used in 5.2.1 Eq 1 for summing by size class.BSUM Di3in size class divided by SUM Di3in entire sample.E799 03 201523.2.5 Dkub upper-boundary diameter of drops in the kthsize class.3.2.6 Dklb lower-boundary diameter of drops in the kthsize class.4. Significance and Use64.1 These criteria6and procedures provide a uni basefor analysis of liquid drop data.5. Test Data5.1 Specify the data as temporal or spatial. If the data cannotbe so specified, describe the sampling procedure. Also specifywhether the data are local that is, in a very small section of thespace of liquid drop dispersion, and whether the data arerepresentative that is, a good description of the distribution ofconcern. Report the fluids, fluid properties, and pertinentoperating conditions.5.1.1 A graph for reporting data is given in Fig. 1.5.2 Report the largest and smallest drops of the entiresample, the number of drops in each size class, and the classboundaries. Also report the sampling volume, area, and lapseof time, if available and applicable.5.3 Estimate the total volume of liquid in the sample thatincludes measured drops and the liquid in the sample that is notmeasured. The volume outside the range of sizes permitted bythe measuring technique might be estimated by graphicalextrapolation of a histogram or by a curve fitting technique.5.4 The ratio of the volume of the largest drop to the totalvolume of liquid in the sample should be less than the tolerablefractional error in the desired representation. See Table 1. Allof the drops in the sample at the large-drop end of the6These criteria ensure that processing probably will not introduce error greaterthan 5 in the computation of the various drop sizes used to characterize the spray.TABLE 2 Example of Log Normal Curve with Upper BoundData Collected May 2, 1979 Computer Analysis May 2, 1979Upper Bound Diameter m Normal Curve, Adjusted Data, Data, 360.00 0.006 0.005 0.005450.00 0.027 0.027 0.026562.50 0.109 0.108 0.107703.00 0.389 0.387 0.387878.00 1.227 1.224 1.2241097.00 3.421 3.426 3.4261371.00 8.407 8.437 8.4361713.00 18.109 18.124 18.1232141.00 34.080 34.024 34.0232676.00 55.551 55.811 55.8113345.00 77.828 77.637 77.6374181.00 93.648 93.568 93.5675226.00 99.481 99.453 99.4536532.00 100.000 100.000 100.000For Computing Curve AveragesLargest drop diameter 6532.00 mSmallest drop diameter 240.00 mFraction of normal curve 0.999995Normal Curve Simple CalculationGaussian Limits4.55457 to 4.53257D10 1464.91 1459.37 m length mean diameterD20 1646.44 1646.57 m surface mean diameterD30 1824.85 1832.39 m volume mean diameterD21 1850.45 1857.79 m surface/length mean diameterD31 2036.73 2053.27 m volume/length mean diameterD32 2241.75 2269.32 m sauter mean diameterD43 2615.67 2670.75 m mean diameter over volumeDV0.5 2534.53 2533.31 m volume median diameterDN0.5 1303.62 1304.71 m number median diameterAverage of Absolute Relative Deviation from DV0.5by Volume 0.311Relative Span DV0.900DV0.100/ DV0.5DV0.9DV0.1/DV0.5 3913.74 1437.21 2534.53 0.977Normal curve FsDd 51e2DEL lnsADXM2Dde2z2dzwhereA 1.8941,DEL 1.17206, andXM 7335.30.FD accumulative fraction of liquid volume in drops having diameter less than D.E799 03 20153distribution should be measured. This criterion is a good “ruleof thumb” to determine a minimum sample size. The value ofD10is greatly affected by the smallest drops measured.5.5 Ninety-nine percent of the volume of liquid representedby the data should be in size classes such that no size class hasboundaries with a ratio greater than 32. For the majority ofsize classes, this ratio should not exceed 54. The 99 condition mpts size classes having diameters smaller thanDV0.01. These criteria assure that processing probably will notintroduce errors greater than 5 in the computation of thevarious drop diameters cited in this practice. The criteria maybe relaxed for measurements where this degree of accuracy isunattainable.5.6 Dkub Dklb/Dkub Dklb multiplied by the liquid vol-ume in the kth class and divided by the total volume of liquidin the sample shall be less than 0.05 for every class. See Table1. Use of the same criterion for a size class created by lumpingthe estimated volume below the boundary of measurementprovides a test for determining the need for some type of curvefitting. It may be necessary to relax this requirement for caseswhere this degree of accuracy is unattainable.6. Data Processing6.1 Transations of Data6.1.1 If drop motions are essentially free from recirculationthrough the region of observation, spatial data can be trans-ed to flux-sensitive data by multiplying the number ofdrops in each size class by the average velocity of drops forthat size class at the sample location. If this transation ispered, the exact procedure shall be noted.6.1.2 If evaporation corrections are applied, the procedureshall be described and the magnitude of the corrections shall berecorded.6.1.3 If corrections are applied to account for drops outsidethe boundaries represented by the data, the procedure shall bedescribed. Likewise, if the overall distribution is established byblending several distributions, the procedure shall be de-scribed.6.1.4 If curve fitting for example, to the upper-limit lognormal, Rosin-Rammler or Nukiyama-Tanasawa equation isused in the data processing, the mathematical function7andminimization criteria, including any weighting factors applied7Examples are found in Mugele and Evans, loc. cit.; in Tishkoff, J. M., and Law,C. K., “Applications of a Class of Distribution Functions to Drop Size Data byLogarithmic Least Squares Technique,” Transactions of ASME, Vol 99, Ser. A, No.4, October 1977; and in Goering, C. E., and Smith, D. B., “Equations for DropletSize Distributions in Sprays,” Transactions of ASAE, Vol 21, No. 2, 1978, pp.209216.FIG. 1 Sample Data GraphE799 03 20154to the data, shall be given. The quality of fit shall be showngraphically or by tabular comparison with the data. When thereare corrections or transations, the comparison shall bemade with the adjusted data.6.2 Calculations Involving Size Classes6.2.1 When data are reported by size classes rather than asindividual drop diameters, the representative diameters, Dpq,may be calculated from summations defined as followsiDir5kDkubr112 Dklbr11 NkDkub2 Dklbr114wherer corresponds to the selected value of p or q in theexpression for Dpqas stated in 4.2.1, andNk the number of drops in the kth size class.This calculation is based on the assumption of a linearincrease in the accumulation of counts as a function ofdiameter within each size class. If the data satisfy the criteria in5.5 and 5.6, the results based on either of the following twoulas will differ by less than 8 from that based on theabove preferred Eq 1.iDir5kDkubr1Dklbr23Nk5iDir5kSDkub1Dklb2Dr3Nk66.2.2 To obtain the values described in 4.2.2, the fractionalvalues number, length, area or volume accumulated betwee