F. PEDORI, F. PRODI & E. WIRTH

Captures OJ Droplets by Simulated Hexagonal Plates: Preliminary Results

R eprinted from

R I VI S TA I TALI ANA DI GEOFI SI CA (Continu ntion of GEOFI S I CA E M E T E OROLOGI A )

Boll ettino dell 'Associazion e Geofisica I taliana

Vol. XX II (1973), N . 3/4, pp. 160-164

Captures oJ Droplets by Sinutlated Hexagonal Plates; Prelinl,inary Results

by F. PEDORI (*), F . PROD! (*) & E. WIRTH (**)

Imrodllction.

In c10uds with cold bases the precipitation can be formed through the ice phase before the coalescence process can be effective. The growth of ice partic1es is in turn due to tbree processes, mostly in sequence: growth by diffusion of water vapor, by capture of c10ud drop1ets, and by aggregation of ice crystals. The first process is welI described by the theory of the electrostatic analogue, at least in the semplification of a stationary crystal, and the agreement with the experimental growth rates is considered rather good. On the contrary the second and third have not yet been completely investigated. This is due [Q the complexity of these processes which require, to be properly described, a separate investigation of the dynamic behavior and the capture efficiency of the different types of ice crystals. Therefore quantitative theories of precipitation formation cannot be satisfacto­rily proposed.

These investigations might also give some hint abour which process, the freezing of a large drop and the formation of a graupel on an ice crystal, has to be considered the main source of hai I embryos. The latter process implies also an initial capture of c10ud drop1ets by the ice crystals, in fall conditions that can be different than those characteristic of stratus c1ouds.

In recent years several theoretical and experimental studies ha ve been performed on the terminaI velocity (CORNFORD, 1965; JAYAVEERA & COTTIS, 1969; JAYA­VEERA & RYAN, 1972) and fall behavior (LIST & SHEMENAUER, 1971; PODZIMEK, 1965) of ice crystals and models.

On the other side, the growth of ice parric1es by accretion of c10ud droplets has been theoreticalIy investigated by M ARWlTZ & AUER (1969) on the basis of the RANZ & WONG (1952) equations, and experimentally by STARR & MASON (1966) and SOOD & JACKSON (1969).

A combined experiment has been designed and perfor med to study the fall behavior in air of simulated hexagonal crystals and their collection effi ciencies for c10ud droplets. T he studies on the dynamics of fall

(*) Osservatorio Scientifico Sperimentale IFA-CNR, Verona, Italy .

(**) Permanent affi liation: Centrai Institute for Atmo­spheric Research, Meteorological Servi ce of Hungary, Budapest.

of the models have pointed out two characteristic fall patterns in the range of Reynolds numbers 50 to 200: oscillation and rotation (the latter along a helicoidal path). The results have been presented elsewhere (WIR­TH et al. , 1973). In the present paper the collection characteristics for c10ud droplets of the models in these two cases are compared and some preliminary results presented.

Experimem al lechniqlle .

In our studies on fall behavior in air, by stroboscopic photography, that have been previously mentioned paper models of hexagonal crystals of various sizes, thickness and density had been used. Instead, in de­termining the collection characteristics, only one kind of models was used, cut from sealing tape as the smooth surface was suitable [Q microscope investigation of the collected droplets (T able I).

T ABLE I : Physical properlies oj lhe models a'ld cloud dropler.s.

T hick- D en- R ey- T etm Mass D iam. ness sity nolds veloc. mg cm I-lm g cm- 3 no. cm S- l

- - -----

M odel L08 0.25 130 2.04 175 105

Parl icles 0.5 · 10-·'1 0·9 to 18 · 1 0 -.1.

The crystal mode1s ha ve been let [Q fall in a cy­linder fill ed with a c10ud of solid paraffin spheres of the same size range as for c10ud droplets (1- 18 f.l), after allowing enough ti me fo r turbulence [Q die down. The experimental arrangement is shown in Fig. 1.

The partic1es have been generated by atomizing paraffi n (p = 0.9 g cm- O) kept at a temperature above m.p. In this way the ex peri menta I difficulties connected with the use of water droplets had been avoided.

The model is collected on a grid at the bottom of the cylinder. T he front surface is then inspected at the microscope and the colIected pa rtic1es counted and sized in the 9 areas shown in Fig. 2. A re1easing devi ce has been set up to avoid unwanted initial mo­mentum of the models which could affect the entire fa ll behavior. T he models are held in a horizontal po-

3

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l

O

S,N,

RH [J*==

O; { ] C

\

C, P. D

_ f

\ \

S,H

Fig. I - Experimenral arrallgement. RH = re/casing hole; C = camera ; S = stroboscope; D = diaf ragm ; C.P.D . = cloud DJ paraffin drop/eu ; S. H . = sampling ho/es; S.N . =

spray ing noz zle; M .P. = me/zed poraffin ; G = grido

sition, onto a small suction head, connected to a pump. At the desired time they are released by simply switching off the pump. A shutter diafragm sepa­rated the releasing devi ce and the c10ud cylinder, which was opened immediately before rhe fall of the mode!.

The releasing phase and the final stage of motion were at firsr controlled by srroboscopic photography, thus carefully following rhe type of mori on of the mode!. These tests, with a second srroboscope and camera at

III AR EA

o O

O O

Fig. 2 - The hexagollal model div '-ded in zhree areas witlz tlle 9 eire/es inspected a l ell e microscope.

4

the end of the faH trajectory, had shown rhar rhe kind of motion could be derermined simply by the observa­tion of the releasing phase.

Immediately before each run, rhe size disrriburion of the paraffin spheres has been measured by sam­pling air rhrough membrane filters and sizing rhe collected parti cles at the microscope. T he effects of sedimenration and coagulation were considered negli­gible wirhin rhe duration of rhe individuaI runs . To experimentally derermi ne the collection efficiency of an ice crystal we consider thar rhe average number of particles collected by the crysral in each size class is given by :

N = B (D p, Dc) . S . Iz • 1/

where E (D P, Dc) is rhe collecrion efficiency of the crystal of size Dc for particles (droplets) of diameter Dp and average number concentration n. S is the projected area of the crystal as it faHs through a deprh h. The experimental parameters to be derermined in such. experiments are N, n, Dc, Dp , h. Monodisperse particles are generally used by different aurhors. How­ever, the purpose of rhis preliminary work was ro determine only rhe rario of the collection efficiencies of a fa lling crystal during oscillation and roration rather than to deri ve the indi viduaI absolure collecrion ef­ficiencies in rhe two cases . This is a more complex goal, and would ha ve required a measurement of rhe droplet concentration in addition to the size distri­bution during the experiment.

R esults and discussion ..

In Fig. 3 the results of th ree runs, as percent con­centration vs. size of the collected drop1ets on the crysrals after fall with oscillation (B) and roration (C) are shown.

The size distribution of cloud particles while air­bome is given in part (A).

In case of another run, the numbers of collected droplets after the two fall motions are given in T able III. Due to the not unifor m distribution of the dro­plets on the surface of rhe models, counting and sizing have been performed on each model in rhe circles (0.15 mm diameter) shown in Fig. 2. The rrailing surface of the plares was not exami ned for collected particles.

Experiments by STARR & M ASON (1966) have sug­gested that capture in the wake can be an important factor, as they found comparable numbers of parti cles on borh the front and the rear face of the mode!. However, it seems that in their experiment rhe kind of motion of the falling model has not been determined. If so, it should be improper to speak of a leading and traili ng surface of the model, as the discs and hexagonal plates rotate while fa lling in helical paths. An invesri­gation of the ca pture in the wake of hexagonal plates is planned in the next future.

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l-o

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, , , , ,~ Il

, , , .1-

-

-

.

. I--

Ih Ih 11--.. , , ~ ,~ " " , 6 J " Il " . , " " Il

" .. /"''' 'OIj

Fig. 3 - The resu/es Dj t"ree rum, as percenr. cOllcentration vs . size 0/ the droplets collected on the crystals after fa ll wich oscilla tion (B) alld rotati01l (C) . The size distribllt ;oll

oj cloud particles w hile a irborlle is gl'Ven in (A) .

The mai n result which can be seen from Fig. 3 and T able III is the differenr capture corresponding with the differem fa ll behavior of the crysrals : rotating models capture a larger number of small droplers. While fro m Fig. 3 only the size distribution of rhe collected drop1ets is observable, from T able III and similar observarions, rhe ratio of the collecrion effi­ciencies in each size class in the two cases can be derived. We have ro remark that in comparing the two fig ures, the numbers of particles collected by- the rotati ng model were obtained by multiplying by two the numbers counred on one side.

Although we did not measure the concentration of rhe particles in rhe cloud and it was not possib1e to deter mine the absolute capture efficiency, it is useful to show the calculations of the rheoretical collection

efficiencies from the equation of Ranz and Wong· A few semplifications ha ve been made, namely thar the models fall perfectly flat .along the vertical (no oscillation) with the average velocity (105 cm . sec 1) .

The hexagons have been approximared in one case ro discs wirh diameter rhe maximum diameter of the hexagons, and in another case ro discs having the same equivalent surface area. In this latter case the results of JAYAVEERA (1972) were followed, who found that the terminaI velociry of hexagons is exactly rhe same as that of the discs of equal mass and thickness .

The parameter of inertia 0/ is given by

1 8 '~ Dc

when pp I density of the particles

C (being negligi ble the correction of Cun­ningham in our case)

V terminaI velocity of the crysral

dynamic viscosity

diameter of rhe crystal and parti cles respectively.

The collection effi ciencies for droplets of various sizes in the above mentioned simplifications aIe shown in Table II.

TABLE II : The parameter oJ t'nenia \1)' alld the theoretical collection efficiellcies 0/ the model f or droplets oJ v arious sizes, f rom the equation oJ RANZ & WONG. Symbols with star

refe r to discs of equivalent surface area.

Panicle size, d I l'' 5 1" I O l'' 15 l'' 20 l''

'P' 0 .034 0 .1 7 1 0· 34 0. 51 0.68

B o? o o 0· 34 0 .63 0 ·77

\Ir* 0 .034 0 .1 80 0 ·36 0·54 0 .7 1

B o? * o o 0. 38 0 .67 0·79

From Table II (and other computations) we see that for particles 7 fJ. in size the rheoretical collection effi ciency should vanish while we find rhat the cry­stals collect many particles below this size. T he explanation is probably that the computations are based on a simplified flow field of the fluid . T his is already an approximation for the « perfectly flar » falling crysra!. When rhe crystal experiences an oscil­lation, or even a roration, the f10w field is more complex and needs a separate investigarion.

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T ABLE III : N umbers 01 col/ecLed d rop/ets, alter the fall mo,iom 01 oscillac;oll Qnd rocacioll, in the areas impeaed oj

one mode/o

3 < r 6 < r 9 < r 12 < r 15 < r

Size, !.1- ,;, 3 ,;, 6 ,;, 9 ,;, 12 ,;. 15 ,;, 18

---------

Oscillation 55 91 125 85 7 1 34

------------ - --R ot3tion 246 172 Il O 106 5° 4°

From Fig. 3 and Table III we can conclude that, for droplet sizes > 12 fL the ratio of the two capture efficiencies is close to I.

For small droplets (d < 12 fL m) the ratio of the effici encies as a fu nction of size is as follows:

r S 3 (1.,

Fig. 43 - S urjace 01 che model alld che drop/eu colleeted afler f all witlz rOlalio n. R emarll ch e higher concemracion on

che sweepillg edge .

3 < ,. ,;, 6 1'-E,ot.

E osc.

Erot . 6 < r ';' 12 1.1. --- = 1.2 .

E osc.

Another remarkable result concerns the distribution of droplets on the surfaces of the crystals characteristic of the two motions. In case of rotation the sweeping edge captures much more than the opposite one. This generaI beh avi or is generally hidden by the superim­posed rotation of the crystal around an axis per pendi­cular to its surface .

In one case this rotation was very slow and Fig. 4a shows what is the typical distribution in this condition.

Fig. 4b shows the surface of crystal which feli while oscillating. In this case the distribution is more uni­form with lower concentration of droplets in the centraI area.

The percent occourrence of droplets (> IO fL) is reported in Fig. 5 along a diameter of the crysta l in the three regions described in Fig. 2 . It res ults as an average of seven runs through a dense cloud.

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" .. 1.25 nlm . • ,

• •

"

'. ' · · •

_ 1.25 mQl _

• · • • • I

· Fig. 5 - P ercem OCClirren ce oJ dropleu > I O I-lm in che chree areas showJI in Fig . 2; after roeal ing (a) Qud osci llati"g Cb)

mOlion.

SOOD & JACKSON (1969) and STARR & MASON (1966) fou nd experimentally a non vanishing collection efficiency of discs and snow crystals for small parti cles in the I lO 5 fL range (Lycoperdon, Mullberry Pollen, B. subtilis spores and fluorescent particles).

However, a direct comparison with their data is impossible for the different experimental conditions and the lack of absolute values of collection efficiencies in our case.

Conclusion.

This experimental research has been initiated to investigate the possibility that the capture of cloud droplets by fa lling hexagonal plates could be differelll for the different fa ll behaviours. In fact two characte­ristic motions for falling hexagona l crystals had been identified : oscillation along a vertical path and rotation

Fig. 4b - Surl ace 01 the model which lell while oscil/ating. along an helicoidal trajectory.

6

A different capture has been confirmed by our experi ments only for small size (3 to 6 fL) droplets: in this range the collection is four times more effective for rotating crysta ls than for osciIlating ones.

Although the models are about IO times larger than current natural crystals for the shape considered, the behaviour evidenced may be significant also of natural behaviour.

It has been suggested that the turbulence in sheared regions of the c10ud may increase the collection of the crystals for the cloud droplets, and therefore favo ur the production of graupels as hailstone embryos. The present results, that show an enhanced collection effi ciency only for small droplets, which do not con­tribUle much ro mass increase, seem to roule out the possibily of higher graupel formation in sheared re­gions of the cloud.

REFERENCES

S. G. CORNFORD, 1965 : Pali sp eeds oj precipica tioll elemem s. Quart. J . R. Met. Soc. 9 1, 91-94 . - K. O. L. F . JAYA­VEERA, I972 : An equiv alem disc fo1' calculating th e terminaI v elocities oj p lau-lik e ice crystals. J. Atm . Sci. 29, 596-598.­K. O. L. F. JAYAVEERA & R. E . COTTIS, 1969: Pali ve­locùies oj plate- like and columnar ice crystals. Quart. J. R. M et. Soc. 95, 703-709. - K. O. L. F . J AYAVEERA & B. F. RYAN, 1972 : T erminai velocities oj ice cryslals . Quart. J. R. M et. Soc. 98, '93-197. - R. LIST & R. S. SCHE­MENAUER, 197 I: Free jall belzavior oj pla nar S1l0W cry sta ls, conical groupels alld small hai/o j. Atm. Sci. 28, 110-115. -J. D. MARWITZ & A. H . AUER, 1969 : I ce crySlal grow/h by diffusioll and accrel ioll. Proc. 7th In tern. Conf. on Con­densation and Ice Nuclei, Prague and Vienna, S ept. 1969, pp . 249-254. Czecholoslovak Acad. of Sco Prague, 1969. - J. PODZIMEK, 1965 : M ovemem oj ice par t ic/es in lh e

atmosp lzere. Proc. Intern. Conf. Cloud Physics, Tokyo and Sapporo, 224-23°. - W. E. RANZ & J. B. WONG, 195"' : Impacc;on oj dUSl and smoke p arlic/es 0 11 surface and body col/eccors. Industriai and Eng ineering Che m. 44, 137 1-13 8 1. - S. K. Sooo & M. R . JA CKSON, 1969 : Scave/lgi1lg 01 aWlospheric particula te maller by fal/ing hydrometeors, in Proc. Intern. Conf. 00 Condensation and Ice Nuclei, Prague and Vienna, Sept. , 1969, 299-302. Czechoslovak Acad. of Sci. Prague, 1969. - J . R . STARR & B. J. M ASON, 1966 : The ca,pture oj airborne partic/es by wa ler drops alld sùnulated S1l0W cryslals. 92, 490-499. - E. \VIRTH, M . MrSEROCCHI & F. PRO DI, I973 : Dynamics oj fa ll oj sùnu­laud hexago"al p lates ; prelimill ary l'esults. T o be submitted to I dòjàràs .

R iassumo - Sono state determinate le caratteris tiche di cattura di modelli di cri stalli esagonali (diametro maggiore 2.5 mm) in caduta attraverso una nube di particelle sferiche di paraffina, di nota distribuzione delle dimensioni. L e caratteristiche di cattura sono state poste in relazione ai due tipi di moto, studiati a pane, dei modelli : caduta con oscillazione lungo la verticale e con ro tazione lungo una traiettoria elicoidale. Si è osservato c he i modelli che ruo­tana catturano un maggior numero di goccioline di picco le dimensioni « I O tL) rispetto ai modelli che oscillano ; s i è cosi determinata l'efficienza di cattura relat iva nei due casi in funzione delle dimensioni delle particelle.

S ummary - The collection characteristics o f models of hexagonal plates (2.5 mm largest dia m.) falling in a c10ud of spherical paraffin particles o f known size distribution have been inves tigated for the two kinds o f motion observe d : osci l1ation along the vertical and rotatioo along an helicoidal path. The front surfaces of the crys tals ha ve been exa­mined at che microscope and the collected droplets counte d and s ized. Rotaring models capture more droplets in the small size range « IO ~m) than the osci llating ones . The relative collection effici ency for the two cases has been de­termined as a function of particle sizes.

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