ENGINEERING RESEARCH -INSTITUTE UNIVERSITY- OF MICHIGAN ANN ARBOR DRAG COEFFICIENTS FOR BRURNING.KEROSENE DROPS JAY A. BOLT LOUIS W. WOLF Project 2253-3 U. S. AIR FORCE WRIGHT AIR DEVELOPMENT CENTER CONTRACT NO AF33 (616)-2436 November, 1954

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ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN --- Foreword This report was prepared by -the Engineering Research Institute of the University o- Michiganm on Uo S. Air Force Contract- Noo AF33(616)24136, 'The work was: sponsored. by the Wright Air levelopment Center,with Jack Wo Fulton acting as project coordinator. The work was conducted at_ the University of Michigan under Projects 1988 and. 2253-3o ii

ENGINEERING RESEARCH INSTITUTE ~* UNIVERSITY OF MICHIGAN NOMENCLAUrE A Projected area. of.the drop, ft 0D Coefficient of drag. (dimensionless) D Diameter off drop> fSt F Drag forcee lbs M Momentum of. drop, mv-. lb-sec m Mass of drop, slugs v Velocity of drop, ft/sec Pa Density of 'air' slugs/ft3 Ok Density -of kerosene, slugs/fts iii

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN -DRAG-C QEFFIC.ENTS FOR' BURNNG K OSETE DROPS iI ROD.'UICTION: In. ac.ordance with 'the desire of the proj:ect sponsor, brief re"*' ports covering pecific phas-s o thi researh i-stigation will be repared as thework:roeeds- It. -is hoped that this method.ill be more effective: in making the infortion aile t interested groups th the usual Ypraetice of waiting until the completion of.the project.- write a.single large r reporto $IRCE QF DATA The-. data for -these-, calculabions were taken from Appeidix B o:f the report -by Bolt, Boyle, -ad Mi-r:skyl covering:the size -and -velocity of drops of burning kerosene trow.n -from aspinning dlisco By photographing drops:in -the- brning:zone twice with a known interva (see Fig0 1),: both the- diameter 'and tihe velocity were dAeterminedo, It-w::.as pointed aout.. t'hat:.an accuray of- 5 in diameter and 03 ft per seen velocity was oh tained, The temperature of the atmosphere surrounding:the drops was measured with an ptical pyrometer and fond. to be 2 F It is.: assumed for thse. purposes that.:the only force re.sisting the motion -of the d&rop is 'the drag -fore~: ~~~~~ag e.~) I

Fig. 1

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN where M = my then F;.(D:. (1) Drag is. usualy expressed in the f:lloi.ng form: F 2 A v - =t: (2) When -the two expressions are combined, 3av % dt(3) C.LCULA4TIO]. The data from several -phtographs for dros 9.and 13.. in orig — inal -size were averaged The -:burning time was plotted.against D3v and. the derivative determined from the slope of the curve,: The drag coefficient -was then determined by formula. 5 The results c-an be Fig0 2 and Table 1: where the- drg 'coefficient is platt-ed against Reynolds number* These, d.ta, can be:.o, sidered. ccate-to 15 per -cent, but the satter probably results from the -action of 'c.-.mbu'st:ion Fig- 3.;oi.par.es these resul-ts -with data..ob.tained for solid spheres movig in my different fluids, The dataof Gunn and KinzerS for water drops falling in still air, and of Fledderman and Han-. son4 for the -evaporatin of hee:spra:s asre pltted for reference: S

1000 I7 -N I I I I I1 I II I I 50.0 10.0 5.0 -v C.) w a ir Lu 0 (9 cD a 1.0.5 1% Ie I Ell I I= I I, L (I) 1. BURNING KEROSENE DROPS 2..SOUD SPHERES IN DIFFERENT FLUIDS A~l~~~:5|~3. l3WATER FALLING IN STILL AIR 4.EVAPORATING HEXANE IN AIR O KEROSENE 130F DROPS A KEROSENE 90F DROPS I.I -: -I I ':I WI.I I (4) I 5 < 1 111 1I I I IAIna 3.5 I. 5. 10 50 100 Soo,000 5).1.5 0 I - * VVV *~Vv -IAyp REYNOLD S NUMBER Re COEFFICIENTS OF DRAG OF BURNING FUEL DROPS COMPARISION WITH NON-BURNING CONDITIONS Fig. 2

100.01 I I 0 s5( Iz iLL om o L.~ c 0 cr I( SOLID SPHERES IN DFFERENT FLUIDS 5.0 0 KEROSENE 130, DROPS A KEROSENE 90p DROPS _ _.1I.5 10 REYNOLDS NUMBER Re 5 10

ENGINEERING. RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - DRAG WCO:EFFTIC IET~I OFBR KANl("SEE DROPS 130it DPrQ 9Ot DUrops Re C..D Re........ '................'.......,. ~' m '......... '....?-." L......~ ',.I..-.I.................. _ I. I. I - ~1 -- o423 0 307 0:255 -25375 oZ163.O124:40712.0409 85,6 85,*2 82,2 82.5 81.6 11 i4.8 80.8 84.5 94.5.825,835.,686:617 * 583 4.67.336.282.260 *191.1324..... ~~~7r2 28.6 37.3 57.3 32,0 39*1 62.5 50.2 49.0 57.6. -.-....i~ I~i~_ L- l:i.~ ~ --- -.... I- 0 - - - - - - The re s show correlate reasnably well with those for solid spheres. However, wrknow in pogreis:sh d give — better results since.it will deal with dta on single drops~ rather th:- with statistically -aazed data, I.1 6

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN — BIBLIOGRAPHY 1. Bolt, J. A. Boyle, T. A*, and Mirsky, W*, t''The Generation and Burning of Uniform-Size Liquid Fuel Drops": Univ. or Mich, Ann Arbor, Mich., Eng. Res. Inst., Project M988, May, 1953. Uniformly sized drops (90 and i30o) of kerosene burning in air were were photographed at known intervals -From the photograph the size and velocity-of the drops were determined.. 2. Goldstein, S., Modern Developments in Fluid ics, Oxord University -Pzress, 1938, Vor. l 16 A graph is presented of drag coeficients for solid spheres moving in various fluids at different Reynolds numbers. 3- Gunn: Ross,- and Kinser, Gilbert D., 'jT- The Terminal Velocity of Fall for Water Droplets in Stagnant Air", Journal of Meteorology 6_ No. 4, 243-248, August, 1949. The terminal velocity- and drag coefficient for distilled water droplets falling through still air are determined for drops ranging in size' from 0.2 +Lg to 100,000,g, The overall accuracy of the measurements was better than 0.7 per cent* 4. Fledderman, R. Ge. and Hanson, A- R.y The Effects of Turbulence and. Wind Speed on the Rate of Evaporation of a Fuel Spray"t Univ. of Mich, Ann Arbor, Micho, Eng. Res, Inst., Project CM667,% June,1951. From work done with fuel sprays evaporatinging a wind tunnel; drag coefficients were calculated for hexane drops. The results-deviated considerably from the. data for solid spheres. i 7

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