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Atomization and Sprays, vol . 4, pp. 351-367, 1994

DISCHARGE COEFFICIENT AND SPRAY ANGL EMEASUREMENTS FOR SMAL LPRESSURE-SWIRL NOZZLES

Javier BallesterLaboratorio de Investigación en Tecnologías de la Combustió n(LITEC) -CSICIDGA, 50015-Zaragoza, Spai n

César DopazoFluid Mechanics Group, School of Mechanical Engineering, Zaragoza, Spai n

An experimental study of the influence of atomizer dimensions and injection conditions o ndischarge coefficient and spray angle is presented . Simplex pressure-swirl nozzles atom-izing heavy oil have been examined . Twenty nozzles of different geometries have beeninvestigated, including orifice diameters down to 0 .45 mm. Inviscid theory results orpublished correlations validfor larger atomizers do not seem to apply for those ofsmallerdimensions, for which viscous effects are thought to play a major role . This role isanalyzed, and new correlations are proposed for discharge coefficient and spray coneangle .

INTRODUCTIO N

Pressure-swirl nozzles are commonplace in numerous engineering applications i nwhich a liquid must be broken down into droplets, such as in combustion, drying, o ragriculture. Their practical importance explains the considerable number of studies on thi stype of atomizer that can be found in the scientific literature since the 1940s . Most of themanalyze experimentally the performance of the atomizers . Droplet size is often the mainsubject of the experimental investigations . Discharge coefficient, spray angle, liquid fil mthickness, or velocity coefficient are also parameters of interest .

Most of the current knowledge on the behavior of pressure-swirl nozzles is of a nempirical nature . The complexity of the processes taking place from liquid injection tospray formation hampers the development of satisfactory predictive methodologies .

Drop size predictions would require the modeling of the liquid sheet breakup pro-cess, which remains to a large extent a poorly understood phenomenon . Pressure-swir lnozzles pose the additional difficulty of the the internal flow prediction . No attempt a tcomplete modeling of this flow has been published . The most comprehensive work on th esubject is that by Dumouchel et al . [1,2], who nevertheless neglect the modeling of th eair core .

The most common approach uses inviscid theory analysis of the flow [3,4] . Undercertain simplifying hypotheses, flow parameters at the exit orifice can be expressed as afunction of atomizer geometry and, more specifically, of the atomizer constant K . There-fore, parameters such as discharge coefficient, spray angle, or liquid film thickness canbe calculated .

Copyright C 1994 by Begell House, Inc .

351

352

J . BALLESTER AND C. DOPAZ O

However, the flow inside a pressure-swirl nozzle is characterized by high velocitie sand small dimensions . Consequently, viscous effects, which are neglected in the invisci dtheory, may play a significant role . Taylor [5] studied the boundary layers formed near th ewall of the swirl chamber and at the air core interface . He concludes that, under certai nconditions, most of the liquid emerges through one of the boundary layers . A recenttheoretical analysis [6] indicates that boundary-layer effects can range from dominant t onegligible depending on the injection pressure . Therefore, the inviscid theory approac hcan lead to important errors .

Comparisons between theory and empirical correlations show the effect of viscos-ity . The formation of boundary layers may cause, among other things, the reduction o ftangential momentum and, therefore, an increase in film thickness at the orifice . As aconsequence, measured discharge coefficients are usually higher than those predicte dtheoretically, with some exceptions reponed by Dombrowski and Hasson [7] . Apart fromthese considerations, published experiments tend to show that differences are not ver yimportant, and the predictions from the inviscid theory are usually accepted as reasonabl ygood estimates [7,8] .

The results of the present work display a significant disagreement with estimate sfrom the theoretical analysis . The atomizers used were designed for an experimental stud yof heavy oil combustion . The design was conducted in accordance with inviscid flowtheory and published correlations . The nozzles were expected to perform within certai nranges of discharge coefficient, cone angle, and drop size . However, in the first tests ,flow rates more than twice the calculated ones were measured . Therefore, the atomizershad to be redesigned, reducing their dimensions . A systematic study of the influence o fgeometry and injection conditions on discharge coefficient CD , cone angle 20, and dropsize was conducted . An important departure of CD and 20 from the theory was observed ,and is apparent in the results reported below .

In Section 2 the experimental facilities and measuring techniques are described .Section 3 presents the trends of the discharge coefficient CD as a function of test variablesand compares the present measured data with available theoretical predictions and result sfrom previous experimental studies, discussing possible explanations for the observeddiscrepancies . Spray cone-angle measurements, comparison with existing correlations ,and a discussion of the influence of viscosity on this variable are included in Section 4 .Tentative conclusions are drawn in Section 5 .

NOMENCLATUR E

A ;

total inlet slots are aA 0

exit orifice are a

C°

Discharge coefficien t

D o

exit orifice diameterD,

swirl chamber diameter

(t)D0D5

Lo

exit orifice length

LS

swirl chamber lengthOP

injection pressure

Q

fuel oil flow rat e

Tfo

fuel oil temperatureV

mean discharge velocity20

Maximum spray cone angl eLiquid viscosityLiquid densitySurface tension

[Ao(2 OP p i)

111

P r

a r

Q

K

atornizer constant

MEASUREMENTS FOR SMALL PRESSURE-SWIRL NOZZLES

3 53

2. EXPERIMENTAL FACILITIE S

The test rig used in the present experiments was designed for the atomization o fheavy oil using large-capacity pressure nozzles . A maximum injection pressure of 80 bar ,oil temperatures up to 150°C, and a flow rate up to 700 liters/h can be reached . However ,it was easily adapted to the conditions of the present study (Q = 20–60 liters/h, OP =12–20 bar.) . A detailed description of the facilities can be found in [9] .

The atomizer is vertically oriented, injecting the liquid downward . The spray isdischarged into an open quiescent environment . The cloud of droplets is collected by anextraction system placed under the atomizer .

The atomizers are simplex pressure-swirl nozzles and consist of three interchange-able parts :

An orifice plate (Fig . 1), containing the conical swirl chamber and the exit orifice .

• Inlet ports (Fig . 2)—three rectangular tangential slots drive the liquid to the swir lchamber .

• An assembly cap (Fig. 3), which holds the orifice plate and inlet ports an dattaches them to the barrel .

Several parts with different dimensions were manufactured, covering the followin gintervals :

• Da = 0 .44–1 .09 mm

• A . = 0.6745–1 .0096 mm2

• K = 0.11–0.3 9

A good surface finish turned out to be essential . Even microscopic imperfectionscaused deviation of the spray axis . The exact dimensions and the quality of the surface swere checked with the aid of a microscope .

The test fluid was heavy oil customarily used in utility boilers . Its physical prop-erties were detemined as a function of temperature (Table 1) . The oil temperatures were100, 110, 120, and 135°C . The pressures selected for injection were 12, 14, 17, and 2 0bar .

A total of 133 experimental runs were performed with different combinations of th evariables Do , A;, PP, and Tfo , corresponding to 20 atomizer geometries .

The spray angle was measured using low-speed photography . Plates 1 and 2 were

0 18.1 5

0 6

w/x#-Z##n rrMD o

2 .4

0 .25 1

Fig . 1 Orifice plate .

354 J. BALLESTER AND C . DOPAZ O

0.53

0 18 .1 501 3

01 0

0 6

0 .82 .65

18.3

0 8 .66

Fig . 2 Inlet ports .

obtained for the same spray with two different exposure times . In Plate 1 the movemen tof the spray is frozen, showing the appearance and growth of disturbances on the liqui dsheet and its final disintegration into drops . Plate 2 is an example of the photographs wit hexposure times of 1/60 s used to determine the spray cone angle . The exposure time i slong enough to record the average location of the envelope of the spray . The reportedangle corresponds to the tangent to the spray at an axial distance of about 3 mm from th eorifice (nozzle geometry made it impossible to record the first millimeters) . Nevertheless ,angle variations are assumed to be negligible over that distance, and that value is taken a sthe maximum angle of the spray . Differences between angles measured on different day sunder the same experimental conditions do not exceed 4° .


355

1

Fig. 3 Assembled nozzle .

Table 1 Physical Properties of Heavy Oi l

T/,, (°C) p r (kg/m3) p. (Pa s) o i (N/m )

20 983

30 977 1 .44

40 979 0 .735 0 .033 7

50 966 0.354 0 .032 360 959 .5 0 .222 0 .031670 959 0.126 0 .030980 0 .0805 0.030290 0 .0465 0.0295

100 0 .0332 0 .0289110 0 .0255 0.0285120 0 .0195 0 .0278

The discharge coefficient was calculated using the expression

CD

A0 (2 LLP pl)0.5

The oil flow rate was measured with a positive displacement meter . The readingvariations were less than 0 .2 liter/h for repetitions of the same experiment, giving arepeatability better than 1% for the reported values of CD .

356

J . BALLESTER AND C . DOPAZ O

Plate 1 Photograph of the spray with an exposure time of 0 .5 µs . Atomizer A-840a + P-50a ; AP= 12 bar; Tío = 120°C .Plate 2 Photograph of the spray with an exposure time of 1/60 s . Atomizer A-840a + P-50a ; AP= 12 bar, Tío = 120°C .

3. DISCHARGE COEFFICIEN T

The values of CD as a function of the injection pressure are shown in Fig . 4 forseveral atomizers .

The atomizers are designated as A-x + P-y, x and y indicating the total inlet port ssection and orifice diameter, respectively . For instance, part A-840 has a nominal tota lports section of 0.840 mm 2 , and píate P-80 has a nominal orifice diameter of 0 .80 mm .

According to the inviscid theory, áP should have no influence on the dischargecoefficient . The curves in the graph are nearly horizontal, but they exhibit a slightl yascending slope . The reason for this increase could be ascribed to a reduction in relativ ehead losses as the velocity increases . As a consequence of the small dimensions of thenozzle and the high viscosity of the liquid, the characteristics of the interna] flow depen don the injection pressure in the range of the tests conducted . A higher pressure would berequired to obtain values of CD independent of OP for these atomizers .

The variation of CD with oil temperature is represented in Fig . 5 . The evolution ofCD and 26 with temperature should be attributed to variations in viscosity, which change sover 250% within the temperature interval, and not to the density or surface tension ,which change less than 6% . In fact, all the curves in Fig . 5 exhibit the maximum in CDthat is characteristic of pressure-swirl atomizers as the fluid viscosity decreases . At low


357

Atomizer

---e— A-840a+P-110a

---ts-- A-840a+P-60b

--—A-840a+P-55b

- a A-840a+P-50a

-- +— A-840a+P-45c

- A-630a+P-110a

--♦-- A-630a+P-80a

--•— A-630a+P-60b--e— A-630a+P-55 b

A-630a+P-50a

—* — A-630a+P-45c0 .2

10

12

14

16

18

20

2 2

L*P (bar)

Fig. 4 Effect of

on Co . Tfo = 100°C .

CD

Ó0.3

0 . 4

0 . 5

0 . 6

0 .7

•

a

n 100 110 120 130 14

0 .63

0 .62

0 .5 9

0 .589

0 .6 1

CD

0 .6

---e—AP = 12 bar

---a—AP = 14 "

— $— .P = 17

— +—AP=20 "

o

Tfo (r)Fig. 5 Effect of Tfo on CD . Atomizer A-630b + P-55b .

temperatures, the viscous friction prevents the formation of a central air core and th eliquid exits as a full jet . The flow rate is a monotonically increasing function of temper-ature . As temperature increases, the tangential velocity of the liquid inside the swir lchamber causes the appearance of the air core, and the liquid emerges as an annular empt yjet. The consequence is the reduction of the effective exit area for higher temperatures .Therefore, CD follows a decreasing trend with viscosity, as can be seen on the right-han dside of the curves in Fig . 5 .

The changes in discharge coefficient with A ; and Do are shown in Figs . 6 and 7 . Al lthe measurements of CD are displayed as a function of the atornizer constant in Fig . 8 . Thegraph also contains the inviscid theory estimates for the lame experimental conditions, a swell as data points generated from the following published correlations:

358

*BALLESTER AND C' DOPAZO

0 . 7

0 . 6

0.5

CD

0 .4

0.3

0.5

0.6

0.7

0 .8

0 .9

D ymm }m ' _

Fig . 6 Effect o[Do on Co . Inlet purtsA-63Ou T~ = 100°C .

0.2 L-O .4

i1 1 .1

--e--&l" =12Ibear

--**—áP=l4 "

--*s--áP =l7 ~

_-**--AP =3O "

¿i

0.7

0 .75

0 .8

0 .85

0 .9

0 .95

1 .050 .5 8

0 .65

o AP =1%baar

--*--áR=l4 ^

=l 7__*--A p =20

0 . 7

0 .68

0 .62

0 .6

A . A/ (="2/

Jones [8l :

sDop, V\ - 0 .02

-0 .03

0 .05

0 .52 0 .23( --*-*— l

(

B

O-~

` 'CD = 0 .45

( 1 )/

D" /

Rizk and Lefebvre [10] :

0 . 25


359

i

0 .1

0 .2

0 .3

0 .4

0 .5

K

Fig . 8 Comparison among present measurements of C D , inviscid theory predictions, and available correla-tions .

Tanasawa and Kobayasi [11] (quoted by Dombrowski and Munday [12]) :

2

(4/ rr)K + 1 .2

-o . f 2*D a ;)CD = 1 — ardan 2 .13 [(417r)K + 1 ] 2 — 1

e

Despite the wide variety of experimental conditions, the results lie in a narrow band .This is an indication of the influence of K on the flow characteristics, as predicted by thetheory. However, dicharge coefficients measured in this work are much greater than thos eestimated from previous correlations and from the theory .

Published experimental results for CD are usually larger than the theoretical esti-mates . The difference is traditionally explained by the reduction in tangential momentu mcaused by the viscous forces . The consequence is an increase of the liquid film thicknes st the orifice and, therefore, of the effective exit cross section .

However, Fig . 8 indicates that departures from the theoretical conditions are muchmore important for the experiments reported in this work . When compared with thepublished correlations estimates, good agreement is observed only for the atomizers wit hthe largest orifice diameters (CD < 0 .32 in Fig. 8) . Larger differences appear as the orific ediameter becomes smaller . This change in behavior with variations in the scale of th eatomizer is discussed next .

The application of multiple regression techniques to all the data points yields thefollowing correlation:

CD = 1 .323 x 10-3K0.29D0-0 .82 p0 .03

(4)

The variables are expressed in SI units . The quality of the fit is shown in Fig . 9 .As indicated previously, the trends of CD were observed to depend on the range of

Do considered . For this reason, Eq . (4) does not represent the CD dependence accurately .

0.

0 . 6

0 . 5

0.4

0 .3CD

0 . 2

0.1

o Measurement sx Jones [8 ]+ Rizk et al [10]e Tanasawa et al [11 ]

Inviscid theory

(3)

360

J. BALLESTER AND C . DOPAZO

0. 8

0 .7

0 . 3

O .%.2

0 .3

0 .4

0 . 5

Esrimates

Fig . 9 Scatter of measurement data points of C D with respect to Eq . (4) .

Should only the data points for orifice diameters smaller than 0 .8 mm be included, th efollowing correlation is obtained :

CD = 1 .335 x 10-2K0•3D0-0.41 Po.o7

(5)

While the remaining terms are almost identical in both expressions, Eqs . (4) and(5), the exponent of Da is significantly different . The scatter of the data with respect t oEq. (5) is shown in Fig . 10. This graph also includes the data for atomizers with Do > 0. 8mm, which did not contribute to the calculation of the fit . For Do > 0.8 mm, Eq. (5)significantly overestimates the values of CD, with larger deviations for the smaller value sof CD , i .e ., the larger orifices .

Published correlations for orifice diameters ranging from around 1 mm [10] to 5 m m[8] show similar exponents, hence suggesting that all the atomizers in that scale interva ldisplay similar trends . However, the results reported here prove that this is not the cas efor smaller orifices . It seems logical to conclude, therefore, that the flow inside theatomizer exhibits different behavior depending on its size . The reason for these discrep-ancies is thought to be the dominant influence of viscous effects in the flow insideatomizers with smaller dimensions .

Viscosity, however, does not appear in the calculated correlations because CDdisplays a maximum in the temperature interval investigated (see Fig . 5) . Includin gviscosity as an additional variable in the correlations would therefore be meaningless .Cone angle correlations, on the other hand, will demonstrate the large influence ofviscosity on the flow inside the atomizers .

4. SPRAY CONE ANGL E

Available studies do not allow one to establish a general trend of the influence o fthe injection pressure on the cone angle . Dodge and Biaglow [13] did not find anynoticeable effect . De Corso and Kemeny [14] concluded that increases in .áP cause spra y

0.6 0 .7 0 .8


36 1

••

contraction as a result of air entrainment, but have no influence on the angle at the exi tof the atomizer . The measurements of Rizk and Lefebvre [15] and of Chen et al . [16]show a clear increase of the angle with AP . The review work by Lefebvre [17] includessome plots of measurements of cone angle as a function of injection pressure showing amaximum. This diversity of trends suggests that the effect of [PP is not always the same ,but might depend on some other parameters, such as the atomizer exact geometry o rdimensions .

Some examples of the variation of cone angle with injection pressure are shown inFig. 11 . An increase of 20 with AP is apparent, although the magnitude of this incremen tis not the same for all the cases .

A rice in the oil temperature results in an important increase in cone angle (Fig . 12) .This trend is in agreement with previous studies [7,8,15] . However, the influence o fviscosity is remarkably higher in the present work, as discussed in what follows .

As for CD , a comparison is presented between measurements and predictions fro mthe inviscid theory and from published expressions :

Tanasawa and Kobayasi [11] (quoted in [12]) :

20, = 180° — 2 arctan4

K (1 .37 + 26.9e -11 .1(1/D,))

(6)

Rizk and Lefebvre [15] :

o .1 t

200 = 6K-°.15 'LPDop t2

The results for cone angle are much more scattered than those for C D due to theinfluence of injection pressure and, particularly, of the viscosity . Therefore, in order to

0 . 8

0 . 7

0 . 6

0 . 5

0 . 4

0 .3

o Do<0.8mm

e Do>0.8mm

0 0.2

0 .3

0 .4

0 . 5

Estimares

Fig . 10 Scatter of measurement data points of Co with respect to Eq . (5) .

0 .7 0 . 80 .6

(7)

36 2

J . BALLESTER AND C. DOPAZO

Atomizer

--e— A-630a+P-60b

--e— A-630a+P-55b

—8—A-525a+P-80a

— e A-525a+P-60b

--t— A-525a+P-55b

—1. A-525a+P-50a

12

Fig.11

14

16

18

20

2 2

AP (bar)

Effect of OP on spray cone angle . Tfo = 100°C .

Jnlet Ponis. áP

—e —A-840a, 12 bar---s-- " , 14---e-- " , 1 7--e— " , 20

--t—A-630b, 12 bar"

,14"

1 7

" , 20

Tfo ( ce')

Fig. 12 Effect of Tfo on spray cone angle . Plate P-55b .

provide a clearer picture, the results are separated into four graphs (Figs . 13a, 13b, 13c ,13d), corresponding to the four oil temperatures . Although some dispersion is still ap-parent in the graphs, this strategy makes it possible to draw some tentative conclusions :

• Inviscid theory predictions produce higher values than those obtained from pub-lished correlations and the results of the present work.

The expression proposed by Rizk and Lefebvre [15] provides good estimates fo rK ? 0 .2 and Tfa = 100°C .

▪For K < 0.2, i .e ., plates with larger orifices, the discrepancy between measure-


363

¡o

+

+

0 .05

0 .1

V ' l5

0 .2

0 .25

0 .3

0 .35

0 . 420

O

--Inrmd theory

o Meusomeír=ts

x Bizlc et al [15]+ Tommm~oa:al [11 ]

1 6

1 4

120

100

208 0

6 0

40

K

o 0+ +

0.05

0 .1

0 . 15

0 .3

0 .25

0 .3

0 .35

0 . 420

O

--Inviscid d=ry

o Mean=ent /

x Riak a al [15]

+ TuuusonmwxuJ[ll]

1 6

1 4

1 2

zO V

208 0

6 0

40

K

Fig . 13 Comparison among present measurements o[syray cone angle, inviscid theory predictions ,and available correlations : (a) Tft, = 100°C; (b) Tia = 110°C ; (c) Tfi, = 120°C ; (d) Tfa = 135°C .

ments oodthc inviscid thenrxlneconocs less important . Furtboumcases, úhocxpccumioumF

The large differeoceobetween theory and experiments can aloobe explained bmth ercductiooin the taogeoúa7cmmpmueot of the liquid velm :tYcouoedby the v¡s000VDricúuu .Tbiocoouluoimoiacoofirmedby the o}eazcouvecgeoce o[coeuaurcnneoLmood the theoret-ical curve as oil temperature increases .

The expression proposed by Rizk and Lefebvre [15] provides good estimates mftb ccone angle fbrK � 0 .2 and T' = 100°C . However, despite including viscosity, the in-crease of 20 is not followed by this correlation and, for 135 "C, differences from th e

364

J . BALLESTER AND C . DOPAZO

1 6

1 4

1 2

10 0

208 0

60

40

20

(C)

t

-

i_ - ...ami -*_--.*. ... .

j

8 1

05

0 .1

0 .15

0 .2

0 .25

0 .3

0 .35

0 . 4

K

Inviscid theory

o Measuremcnts

x Rizk et al [15 ]

+ Tanasawa et al [11 ]

1 6

1 4

1 2

1 0

2080

— Inviscid theory

o Measurements

X Rizk et al [15]

+ Tanasawa et al [11 ]

0 .2

K

0 .250 .1 0 .15

60

4 0

20

(d)0.3

0 .35

0 .4

Fig . 13

present data are very important . Therefore, that expression cannot be considered t orepresent the behavior of the atomizers tested in this work .

The expression of Tanasawa and Kobayasi [111 includes only geometric parameter sand cannot predict the effect of viscosity .

Multiple regression calculations for spray cone angle also showed that the exponentaffecting the exit orifice diameter depends on the range of Do over which calculations aremade, as already observed for Co. The expression obtained when all the data points areconsidered is (in SI units)

20 = 16.156K 0 .39D 1* .13µ* 0 .9

0 .39

(8)


365

°4 p .: é .*

ee ° o

__

20 40 60 80 10

100

0

o Do < 0.8 mme Do>0.8mm

8 0

6 0

40

20

Estimates

Fig . 14 Scatter of measurement data points of 20 with respect to Eq . (8) .

Figure 14 shows the degree of agreement between the correlation and the measure-ments .

When the experimental points obtained for Do > 0 .8 mm are excluded, the best fi tis given by

20 = 0.2197K—0.39D0.63µ, 0 .91 áp0.42

(9)

Differences between measurements and estimates are smaller for this expression(Fig . 15) . However, cone angle is underestimated for orifice diameters larger than thos ein the considered range .

With the exception of Do , the powers affecting K, µl , and [XP remain remarkablyconstant in both equations . Therefore, the influence of those variables seems to be ap-proximately the same over the range of atomizers used in the tests .

The powers in both correlations are much larger than those in the expressio nproposed by Rizk and Lefebvre [15] . The second term in Eq . (7) is the Reynolds numberat the exit orifice, and it appears as 20 —Re2 .22 . If variables in Eqs . (8) and (9) are groupedin a similar way, it results in 20 Re2 .9 . The important difference again suggests th edecissive influence of viscous effects on the flow inside the atomizer for the experiment sreported here when compared with previous results .

5. CONCLUSION S

An extensive series of measurements of discharge coefficient and spray cone angl efor pressure-swirl nozzles atomizing heavy oil have been presented . The influence of oi ltemperature, injection pressure, and nozzle geometry has been examined . The atomizerdimensions belong to a range not covered by the available open literature . The mostsignificative findings are as follows .

366

J. BALLESTER AND C. DOPAZO

o

O

oo

•p O

--- —

"es

-.;

20 40 60 80 100

100

80

20

o

Estimares

Fig. 15 Scatter of measurement data points of 20 with respect to Eq. (9) .

Measurements of CD and 20 display much higher deviations from the invisci dtheory than reported for larger atomizes . The application of either theoretical estimation sor published correlations to the design of small-size nozzles would result in very importan terrors .

• Empirical correlations for discharge coefficient and spray cone angle have beenobtained. The expressions derived when all the measurements are included [Eqs . (4) and(8)] are different from the equivalent ones when only results corresponding to the smalle rexit orifices are considered [Eqs . (5) and (9)] .

The observed differences in the behavior of small-size atomizers in relation t oprevious studies is attributed to the significant role of viscous effects . The large influenceof viscosity is corroborated by the magnitude of its power in the spray cone anglecorrelations .

REFERENCES

1. C . Dumouchel, M . Ledoux, M . I . G. Bloor, N. Dombrowski, and D . B . Ingham, The Desig nof Pressure Swirl Atomizers, Twenty-Third Symp. (Int .) on Combustion, The Combustio nInstitute, Pittsburgh, Pa ., pp. 1461-1467, 1990 .

2. C. Dumouchel, M. I . G. Bloor, N. Dombrowski, D. B . Ingham, and M. Ledoux, ViscousFlow in a Swirl Atomizer, Chem . Eng. Sci., vol . 48, no. 1, pp. 81-87, 1993 .

3. G . I . Taylor, The Mechanics of Swirl Atomizers, 7th Int . Congress of Applied Mechanics, vol .2, pt . 1, pp. 280-285, 1948.

4. E. Giffen and A . Murascew, Atomization of Liquid Fuels, Chapman & Hall, London, 1953 .5. G. 1 . Taylor, The Boundary Layer in the Converging Nozzle of a Swirl Atomizer, Quan. J .

Mech. Appl . .Math ., vol . 3, pt . 2, pp. 129-139, 1950.6. C. Dumouchel, M . 1 . G. Bloor, N . Dombrowski, D . B . Ingham, and M. Ledoux, Boundary-

Layer Characteristics of a Swirl Atomizer, Atomization and Sprays, vol . 2, pp . 225-237, 1992 .7. N. Dombrowski and D . Hasson, The Flow Characteristics of Swirl (Centrifugal) Spray Pres -

sure Nozzles with Low Viscosity Liquids, AIChE J ., vol . 15, 1969 .


367

8. A. R. Jones, Factors Affecting the Performance of Large Swirl Pressure Jet Atomizers, CEG BRep . R/M/N1054, Marchwood, Southampton, UK, 1982 .

9. J . M . Ballester, Experimental Study of the Influence of Spray Characteristics on Heavy Oi lCombustion (in Spanish), Ph .D. thesis, University of Zaragoza, 1992 .

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11. Y. Tanasawa and K . Kobayasi, Tech . Rep . Tohoku Univ ., vol . 20, 1955 .12. N. Dombrowski and G . Munday, Spray Drying, in Biochemical and Biological Engineering

Science, Academic Press, New York, vol . 2, chap. 16, 1968 .13. L . G. Dodge and J . A . Biaglow, Effect of Elevated Temperature and Pressure on Sprays fro m

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discharge coefficient and spray angl e … journals cd/23atspray.pdf · atomization and sprays,...

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