1、Designation: E 799 03Standard Practice for DeterminingData Criteria and Processing for Liquid Drop Size Analysis1This standard is issued under the fixed designation E 799; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of
2、 last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 size
3、s,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 (methods
4、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 analysis applies to all liquid drop distributionsexcept where specific restrictions are stated.2. Referenced Documents2.1 ASTM Standards: ASTM Standard:E
5、1296 Terminology Relating to Liquid Particle Statistics22.2 ISO Standards:133201 Particle Size Analysis-Laser Diffraction Methods392761 Representation of Results of Particle Size Analysis-Graphical Representation392722 Calculation of Average Particle Sizes/ Diametersand Moments from Particle Size Di
6、stribution33. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 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. Exam
7、ples 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 concentration:number per unit volume.3.1.2 flux-sensitive, adjdescribes the observation of mea-surement of the traffi
8、c 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
9、 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
10、 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-sensit
11、ive set of data is proportional to flux density: numberper (unit area 3 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
12、of time durations. Forspatial observations this requires a sufficient number of obser-vations. A spatial sample of one flash photograph is usually notrepresentative since the drop population distribution fluctuateswith time. 1000 such photographs exhibiting no correlationwith the fluctuations would
13、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 part(volume or area) of a larger region of conc
14、ern.3.2 Symbols:SymbolsRepresentative Diameters:3.2.1 ( Dpq) is defined to be such that:4Dpqp2q!5(iDip(iDiq(1)where:D= the overbar in Ddesignates an averagingprocess,(pq)pq = the algebraic power of Dpq,p and q = the integers 1, 2, 3 or 4,1This practice is under the jurisdiction of ASTM Committee E29
15、 on Particle SizeMeasurement and is the direct responsibility of Subcommittee E29.04 on LiquidParticle Measurement.Current edition approved May 10, 2003. Published August 2003. Originallyapproved in 1981. Last previous edition approved in 1998 as E 799 92(1998).2Annual Book of ASTM Standards, Vol 14
16、.02.3Available from American National Standards Institute, 11 W. 42nd St., 13thFloor, New York, NY 10036.4This notation follows: Mugele, R.A. and Evans, H.D., “Droplet Size Distribu-tion in Sprays,” Ind. Engnrg. Chem. Vol 43, No. 6 (1951), pp. 1317-1324.1Copyright ASTM International, 100 Barr Harbor
17、 Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.Di= the diameter of the ith drop, and(i= the summation of Dipor Diq, representingall drops in the sample.0=pand q = values 0, 1, 2, 3, or 4.(iDi0is the total number of drops in the sample, and someof the more common representative
18、diameters are:D10= 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 Her-dan).See Table 1 for numerical examples.3.2.2 DNf,DLf,DAf, and DVfare diameters such that t
19、hefraction, f, of the total number, length of diameters, surfacearea, and volume of drops, respectively, contain precisely all ofthe drops of smaller diameter. Some examples are:DN0.5= number median diameter,DL0.5= length median diameter,DA0.5= surface area median diameter,DV0.5= volume median diame
20、ter, andDV0.9= drop diameter such that 90 % of the total liquidvolume is in drops of smaller diameter.See Table 2 for numerical examples.3.2.3log Dgm! 5 (ilog Di!/n (2)where:n = number of drops,Dgm= the geometric mean diameter3.2.4DRR5 DVF(3)where:f = 1 1/e .6321DRR= Rosin-Rammler Diameter fitting t
21、he Rosin-Rammler distribution factor (See TerminologyE 1296)3.2.5 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 Use54.1 These criteria5and procedures provide a uniform basefor analysis of liquid drop
22、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 d
23、escription of the distribution ofconcern). Report the fluids, fluid properties, and pertinentoperating conditions.5.1.1 A graph form 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. A
24、lso 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 not5These criteria ensure that processing probably will not introduce error greaterthan5%inthecom
25、putation of the various drop sizes used to characterize the spray.TABLE 1 Sample Data Calculation TableSize Class Bounds(Diameterin Micrometres)ClassWidthNo. ofDrops inClassSum of Dirin Each Size ClassAVol. %in ClassBCum. %by Vol.DiDi2Di3Di4240360 120 65 19.5 3 1035.9 3 1061.8 3 1091. 3 10120.005 0.
26、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 8.43613711
27、713 342 981 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 46
28、6.5 2212.1 10532 5.885 99.45352266532 1306 1 5.9 34.7 348.5 1534 0.547 100.000Totals of Dirin (k = 6109 8915.3 3 10316562.6 3 10637729.0 3 109100695 3 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
29、Relative Span 5 DV0.92 DV0.5!/DV0.55 390014200/2530 5 0.986692676 1 33453 0.21826 5 0.024Less than 1%, adequate sample size Adequate class sizesAThe individual entries are the values for each k as used in 5.2.1 (Eq 1) for summing by size class.BSUM Di3in size class divided by SUM Di3in entire sample
30、.E799032measured. (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
31、 tolerablefractional error in the desired representation. See Table 1. Allof the drops in the sample at the large-drop end of thedistribution 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 measu
32、red.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 3:2. For the majority ofsize classes, this ratio should not exceed 5:4. The 99 %condition exempts size classes having diameters smaller
33、 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) multipli
34、ed 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 TableI. Use of the same criterion for a size class created by lumpingthe estimated volume below the boundary of measurementprovides a test for determining the
35、 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 Transformations of Data:6.1.1 If drop motions are essentially free from recirculationthrough the region of observation, spatial data can be
36、trans-formed 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 transformation isperformed, the exact procedure shall be noted.6.1.2 If evaporation corrections are applied, the procedureshall
37、 be described and the magnitude of the corrections shall berecorded.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 0.10
38、9 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 99.4536532.00 100.000 100.0
39、00 100.000For Computing Curve AveragesLargest drop diameter = 6532.00 mSmallest drop diameter = 240.00 mFraction of normal curve = 0.999995Normal Curve Simple Calculation(Gaussian Limits4.55457 to 4.53257)D10= 1464.91 1459.37 m (length mean diameter)D20= 1646.44 1646.57 m (surface mean diameter)D30=
40、 1824.85 1832.39 m (volume mean diameter)D21= 1850.45 1857.79 m (surface/length mean diameter)D31= 2036.73 2053.27 m (volume/length mean diameter)D32= 2241.75 2269.32 m (sauter mean diameter)D43= 2615.67 2670.75 m (mean diameter over volume)DV0.5= 2534.53 2533.31 m (volume median diameter)DN0.5= 130
41、3.62 1304.71 m (number median diameter)Average of Absolute Relative Deviation from DV0.5by Volume = 0.311Relative Span = (DV0.900DV0.100)/ DV0.5(DV0.9DV0.1)/DV0.5= (3913.74 1437.21)/2534.53= 0.977Normal curve % FD! 51=p*2DEL lnSADXM 2 DDe2z2dzwhere:A = 1.8941DEL = 1.17206XM = 7335.30F(D) = accumulat
42、ive fraction of liquid volume in drops having diameter less than D.E7990336.1.3 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 p
43、rocedure 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 function6andminimization criteria, including any weighting factors appliedto the data, shall be given. The qual
44、ity of fit shall be showngraphically or by tabular comparison with the data. When thereare corrections or transformations, the comparison shall bemade with the adjusted data.6.2 Calculations involving size classes:6.2.1 When data are reported by size classes rather than asindividual drop diameters,
45、the representative diameters, Dpq,may be calculated from summations defined as follows:(iDir5 (kDkubr 1 12 Dklbr 1 1! NkDkub2 Dklb!r 1 1!(4)where:r = 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 calculat
46、ion 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 twoformulas will differ by less than 8 % from that based on theabove (preferr
47、ed) Eq 1.(iDir5 (kDkubr1 Dklbr23 Nk(5)(iDir5 (k SDkub1 Dklb2Dr3 Nk(6)6.2.2 To obtain the values described in 4.2.2, the fractionalvalues (number, length, area or volume) accumulated betweenthe minimum drop size in the sample and the upper bounds ofthe respective size classes shall be plotted against
48、 the corre-sponding upper bound diameters, see Fig. 1. The desired valuescan then be read from the graph. The calculations shall be madefor the fractional accumulations based on the procedures from6.2.1.6Examples are found in Mugele and Evans, loc. cit.; in Tishkoff, J. M., and Law,C. K. “Applicatio
49、ns of a Class of Distribution Functions to Drop Size Data byLogarithmic Least Squares Technique,” Trans. of ASME, Vol. 99, Ser. A, No. 4, Oct.1977; and in Goering, C. E. and Smith, D. B.,“ Equations for Droplet SizeDistributions in Sprays,” Trans. of ASAE, Vol. 21, No. 2, 1978, pp. 209216.FIG. 1 Sample Data GraphE7990346.2.3 In plotting histograms of the data, the ordinate foreach size class shall be the incremental fractional values(number, length, area, or volume) per unit length increase indiameter accord
