ANALYSES OF THE COMBUSTIÓN PROCESSES IN GAS TURBINES*

* Paper presented at the IV International Congres* oí Combustión Processes, Zurich 1957

Gregorio MULLAN, I. A, Chieí oí the Aerodynamics Studies, oí Instituto Nacional

de Técnica Aeronáutica, Esteban Terrados.

Segismundo SANZ, I. A.

Chieí oí the Dept. oí Laboratories oí C. E. T. A.

1

Combustión oí a hydrocarbon requires the previous evaporation and

mixture with oxygen, In a combustión chamber oí a turoine combustión may

take place in many diverse ways.

If the hydrocarbon vapors íorm an almost homogeneous mixture with

air beíore combustión, combustión may be eííected by a fíame laminar or

turbulent according to the circumstances across the mixture.

The propagation oí ílame s laminar as well as turbulent has been the

subject oí intense studies in the last years, particularly because oí its great

interest in aviation propulsión systems. The re exists an extensive bibliography

in both the intrensic properties in the establishment oí such fíames in the rapid

currents that obtain in combustión chambers oí turbinas and after burners.

Typical examples oí the bibliography are given in reíerences (1) and (2)

indicating theoretical and experimental studies oí laminar flamas oí hydrocarbons

and reíerences (3) and (4) íor turbulent flamea and (5) and (6) on studies oí the

problem oí estábilshing one or the other in rapid currents. In each one oí the

reíerences íound in the bibliography are íound a complementary bibliography on

these qtwfetions, knowledge oí which i s rudimentary because oí the complication

oí the problem. The velocity oí propagation oí a laminar ílame across a mixture

oí combustible vapors and air i s independent oí the pressure and i s oí the order

oí a íew

- 2 -

centimeters per second. (1) That oí a turbulent fíame may be aeveral

times higher but at the most o£ some meters per second. This presente

grave needs for space in order to burn such mixtures, particularly if the

limitations imposed by the mentioned phenomenon oí stabilization are taken

into account and by those oí the thermal blockade. (7)

When combustión is produced in a very intense turbulent soné the

mixture between reactants and products makes the concept oí a fíame

front disappear, a combustión almost homogeneous oí the mixture obtains.

The ideal limit oí such type oí combustión corresponda to the so-called

perfectly mixed homogeneous reactor

studieé theoretically by Avery and Hart (8) and by DeZuboy (9) and whose

practlcal realizaron was approximated in the spherical burner oí Longwell (10).

The homogeneous combustión chamber determines the máximum energy that

may be Uberated per unit volume in a combustión chamber. JLongwell

in his spherical combustión chamber reached ratea oí the order oí 4 x 10° Kcal/

per hour at ambient pressure with a stoichiometric mixture compared with

the 2 x 10 Kcal/m per hour which is characteristic oí combustión chambers

oí industrial gas turbinas.

- 3 -

2

When the combustible penetratea in the liquid átate into the soné

of combustión of the chamber, evaporaron, misdng of the vapora with the

air and combustión are going on simultaneously atarting aome of the foilowing

typea of combustión according to the circumatances.

a. Propagation of a fíame of similar characteristics similar

to the premixturea mentioned in the No. 1 across the cloud formed

by the suspensión of smail dropleta of the combustible in the air.

b. Formation of individual flamea around or in the wake of the drops.

The first type of combustión i s produced when the sise of the drops

is so small that they are able to evapórate in the heated zone of a premixed

fíame. Thia occura with dropa with a díameter of the order of 5 microña

or leas. Experimente made by Browning Krall (11) with clouda formed

by drops of propane or kerosene with drop diameters leas than 1 micron

indícate that the characteristics of such flamee are very aimilar to the

prerrixed flamas of the aame fuel. For example, the velocity of the laminar

fíame is süghtly less caused without doubt by the heat of vaporixation of

the dropa. Theae flamea of carbón duat and other solid fuels present

characteristics similar to the foregoing. One essential difference rests

without doubt in the prepondurate influeene of the heat transmitted by

radiation in the dust flamea which makes the velocity of fíame acroaa duat

mixtures dependent not only on the air/fuel relation but aleo and very

conaiderably by the si se of the particlea of combuatible and by the geometry

of the fíame (12 to 14). The study of such flamea haa great practical intereat

- 4 -

because oí the possible employment of coal dust in the combustión chambars

of industrial turbinas.

The second type of combustión i s that which i s produced when the

sise of the drop exceeds several microns and it is that which i s going to

be considerad in the following with considerable detail from the theoretical

point of view as well as experimental.

3

The combustión of a drop of combustible is a very complicated

phenomena in which concurrently occur processes of heat transmission

by redi ation and convection in the atmosphere that surrounds the drop and

at the same time the evaporation of the drop, the diffusión and mixing of

the vapors and gases and finaliy the ignition and chemical reaction all

of which i s taking place in an environment which is not stationary. In

•tudying the procesa the principal object of analysis consists of determining

the conditions under which combustión may exist and the time required in

burning a drop of a given sise, that i s to say, the Ufe duration. One or

the other depends on the physical chemical properties of the combustible

and the atmosphere around it and of the state of movement relative to both.

S. S. Penner (15) in a aimplified dimane! onal atudy of the phenomenon

enumerated 23 distinct dimensionless parameters. This constitutes an

indi catión of the compli catión of the process.

- 5 -

Nevertheles8, in the moit «imple case of combustión oí an isolated

drop in the atmosphere of a cavity in which ia formed a fíame

of difusión aurroundlng the drop it i s possible to make a schematic modal

of the phenomenon which repreaents the modal very approximataly to the

real case and is susceptible to theoretical study. Such a modal is basad

on the following two eonsiderations:

a, That combustión i s effected in the vapor phaae and the denaity

of the liquid i s much greater than the former for that reaaon combustión

once initiated may be treated as a phenomon almost statiLonary.

b. The mixture of oxygen and vapora ia effected by laminar diffuaion

of reaction at the high temperatura that prevalía in the flama and which

permita the elimination of the chemical kenetics applying the classical

method of Burke and Schumann (16) to the fíame diffuaion that forms around

the drop. With such a hypotheais and if moreover the influence of free

convection due to the heating of the gases i s disregarded the model of

combustión that appears in schematic form in Figure 1 is obtained.

Surrounding the drop is the form of a

fíame of very small thickness dia-

grammed by a spherical surface

whose radius is several times largar

than the radius of the drop. Toward

the flama are diffueing the vapora of

the combuatible from the interior

and oxygen from the exterior. The

Frente ¿e Ihmajéa^

Fi 0 . t

- 6 -

diffusión ia produced acroaa an atmosphere oí inert gaaea and producta.

Theae in their turn diffuse from the fíame toward the exterior, The

fíame auppliea the heat necessary for the evaporation oí the combustible.

The concentration oí the vapore oí the combustible and oí oxygentn the

fíame are practically nil because both are consumad almost instantaneously

on arriving at the ñame because of its elevated temperatura. This model

was proposed by Godsave (17). A theoretical study completing the process

based on the model may be found in reíerence (18).

Letting P signiíy the density oí the liquid combustible, d the

instantaneous diameter oí the drop, m the mass of the combustible burned

in unit time at each instant a simple calculation gives

The fundamental result oí the analysis is that d2 i s a linear function oí the

time t oí combustión of the íorm. ¿» = i\ - Kt

úc « df - Kt (2)

in which K is a constant oí evaporation which depende only on the physical

chemical characteristics oí the procesa, di the diameter oí the drop at the

instant combustión is initiated and t the time measured starting from

this instant.

The previous result has been obtained from the hypothesis that

the heat that the drop receives by racüation originates from the fíame or

from the walls oí the combustión chamber is insignificant.

-7 -

Caiculations by Godaave (17) and by Hottel and bis coilaborators (19)

show that such heat i a small comparad to that which the drop receivea by

convection, in all caaes o£ practical ¿interest.

From the equations oí (1) and (2) there results

m • 4 7TP Kd (3) m = 4 * pe Kd (1) c

This shows that the masa burned per unit time is not proportional

to the suríace oí the drop.

This i s due to the approach oí the llame front to the suríace which

hastens the evaporation. This attributerf emphasiaes the interest in good

atomication. In efíect diminishing the sise oí the drops írom the jet atream

hastens combustión not only because the available liquid suríace i s increased

but also the combustión per unit suríace ia more rapid.

5

Numeroua experimental measurements have been made under

conditions that tend to reproduce Figure 1. Three oí the techniques utilised

with diverse methods are

a. Combustión oí drops that íall íreely or are thrown through the

atmosphere (19)* This method is appropriate to drop sises comparable

to those which are obtained in a combustión chamber but the results appear

to be masked by the iníluence oí the íorced convection, owning to the movement

oí the drop to which reíerence has been made previously.

b. Combustión oí drops suspended írom a fine filament oí silicon

or quarts (17) with which are elimínated the inconvenience oí the íorced

m {$ • •

convection but the dropa must be reiatively large (d^l mm) in order to

elimínate the influence o£ the Ülament.

c. The employment oí metallic apheres led by the combustible

by various procedures (20). With this method are obtained constant

diameters and a really stationary and eaay to control but must be used

with very large diameters.

All o£ the experimental results

confirm the lineal iaw ol equation 2.

Figure 2 shows «orne experimental

results obtained in the combustión

laboratory oí INTA or taken from

reference (21). It may be verified

moreover that the experimental

valúes oí the constant of evapora­

ron coincide very closely with the

theoretical valúes. This may be

seen in Table 1 (18) in which they are

compared for some typical fuels.

TABLA

K.

Teórico

0.86X1Ü-2 1.00X10-2 0.87X10-2

cm'/seg.

Combustible

K.

Teórico

0.86X1Ü-2 1.00X10-2 0.87X10-2

Exper.

n-Heptano Benceno Tolueno

K.

Teórico

0.86X1Ü-2 1.00X10-2 0.87X10-2

0.97X10-2 0.97X10-2 0.66X10-2

9

Table 2 gives the valué* of K for a large variety of combustibles both

simple and compound including the temperatures in which it was measured.

TABLA II

Combustible K. cmVseg.

Alcohol metílico . . . . 1.60X10-2 Alcohol etílico 0.99X10-2 n-Heptano 1.16X10-2 Isoctano 0.90X10-2 Benceno. . . . . 1.00X10-2 T r u e n o 0.91X10-2 Cetano . 1.44X10-2 Cvdoexano. . . . . 1.02X10-2 Metilnaftaleno 1.04X10-2 Nitrobcnceno 1.02X10-2 Gasolina motor 1.10X10-2 Keroseno 1.12X10-2 Aceite Diesel . . 1.11X10-2

Aceite pesado ÍP ,=0.918 gr'cm') . . . 1.05X10-

Accite pesado (P .=0.864 gr/cm*) . . . 0.93X10-2

ToK

1073 973 973 973 1000 1000 973 973 973 973 973 97.3 973

968

973

The formula (2) gives the time of l i te t.. of a drop of inltially

of diameter d¿

(4)

In Figure 3 are given the

Ufe span of drop» of diameters

between 10 and 200 microns for

some of the fuels given in Tables 1

and 2. In the calculations the ex­

perimental valúes of the constants

given in the se two tables ha ve

been used.

ito too

-10-

II the fuel evaporatea without combustión the lineal law 2 appliee

but the valué of the constant oí evaporation is lesa, which prolonga the

time of Ufe of the drop. At a temperature of the order of 1000'K the constant

of evaporation without combustión

is approximátely 1/2 that of evap­

oration with combustión. At

lower temperaturea it is

aeveral times leaa. In Figure 3

have been included Unes for drop Uves that evapórate without combustión

for typical fuels. These Unes have practical interest be cause it may occur

that the drops may not be able to maintain a surrounding fíame in spite of

the fact that the temperature of the atmosphere that surrounds them is

higher than that required for combustión perhapa for lack of oxygen or

because the drop i s moving sufficiently rapidly across the atmosphere.

(See paragraph 14 following)

When a drop of fuel penétrate» into an oxidisting atmosphere heated

to a temperature to that required for ignition of the drop there exists a

transition period before the initiaüon of combustión which ia composed of

2 parts. First the drop is heated expanding itself until its surface reaches

a temperature near that of ebollution. In this phase the evaporation is

very amall but the diameter increase. When the temperature of the drop

approsdmates the temperature of evollution intense evaporation is produced

but without combustión, Both phases appear ciearly in the higher curves

of Figure 2. The transitory effects increase the Ufe span of the drop by

-11-

.018

Acetre PtC3£L^ Pte.sG<- Foec

a fraction that liea between 15% for iight fuela to 50% for more heavy fuela,

at a temperatura of the order oí ÍGQQ'F.

In compound and heavy íuele the formation of interior bubblea of

vapor and cracking can maak the lineal law 2 giving place to curvea of

d vet or irregular forro like that ehown in Figure 4 taken from reference 21,

Nevertheleae the Ufe of a drop

approxlmatea being proportioned

to the aquare of ita diamate r and

one may continué to apply the law 4

in which K wiil be in thia caae an

apparent conatant of evaporation

for the drop.

The valué» of Tablea 1 and 2

ahow that the conatant of evapora­

ron variea relatively little between

fuela particularly if the enormoua

difference between the volatiUÜe»

of the fuela ia conaidered. A» the

quantitiea of air neceaaary for coro-Fig. 4

buation of theae fuela differ alao by amall quantitiea the reault ia that the

eyetem of combustión ia particularly auitable to burn any claaa of fuel and

for thia reaaon ia more adequate in industrial applicatión» in whioh economy

playa an important role.

. 1 2 .

O i í Figure 5 (Reí. 21) shows the

influence of temperatura of the a t -

mosphere that surrounds the drop

on the constant of evaporation. The

abrupt fall that is observed at temp­

eraturas higher than 1000a co r r e s -

ponds to the influence of disasso-

ciation when the temperature of

the fíame i s in that soné will be

above 3000-K. The influence of

the ambient temperature on the

valué of K in the soné of interest i s

somewhat less than the influence of

said temperature on the velocity of propagation of a premixed fíame.

The valué of K increases from 15 to 20% for each 100*C risa in

temperature.

The volume V of air required by a drop of diameter d for combustión is

V • 4/3TTd3v P c in wbich

.010

.005

/

V /

__ «X? IOCO HOO 1200 1300

Temperatura del aire TaaCK) —~-

Flg. 5

v is the weight of a ir per unit weight of fuel in a stoichiometric mixture

°* *ke * i ' . Sinos the mass m burned in unit time and P a i s the

is given by (3) the heat liberated per unit volume per unit time i s

-13-

q n 3q K P . iüí = .±±!í?.a- (5) V * 2 * (5)

vd'

in which q is the heating valué of the fuei per unit ol mase. This says

that the heat liberated i s directly proportional to the density of the air

and inversely proportional to the square of the drop diameter which again

shown the great importance of good atomisation and the convenience of

burning under pressure in order to basten combustión.

Using typical valúes of this physical chemical constant there is

8 3

obtained from (5) burning rate of the order of 10 Kcal/m per hour when

the temperatura of the air is some 1000*K for drope of 100 microns in

diameter. This valué i s some 40 times less than that which may be obtained

in a homogeneous ideal burner but it demonstrates the efttcacy of the

system of small drops and i s some 50 times larger than the valué obtained

in an industrial turbine.

Theoretical resulta indícate that K as well as the relation between

the radius of the fíame and of the drops are practicaliy independent of the

pressure (22). There exista little experimental Information about the

influence of pressure on the combustión of a drop. The most complete

work about this point is that by Hall and Diederichen (23) who tested with

drops suspended and pressures in the range of 1 to 20 atmoapherea

ahowing that the constant of evaporation increased approximateiy as the

1 /4 power of the pressure. This effect has been attributed to various

causes (18) but especially to the influence of free convection that i s produced

because of the heating of the gases around the drop. This combustión

hastens the combustión because the fíame draws near the drop, as is

. 1 4 .

shown in the schematic of Figure 1.

The quantative study of the poaaible influence of f ree conveetion

is of intereat to judge the valué of the experimental resulta since if this

influence is considerable the coincidence between theoretical and experimental

valúes may be accidental. The question i s very complicated and its technical

intereat limited for that reason we have limite d only indi cate d in the

bibliography (19) and (24) advice that the only experimental Information

concerne measurements in the absence of free conveetion (24) appears to

indícate that its effect is considerable,

Major technical interest i s found in the study of the influence oí

forced conveetion because in all technical applications the drope are in

movement.

Fríossling (25) proposed a semiemperical formula to calcúlate the

influence of forced conveetion in the evaporaron without combustión of a

drop. Letting m be the mase evaporated per unit time under the influence

of forced conveetion and m that which would be evaporated without conveetion

The formula of Frossiing gives -HL = <1 4- 03 sc ". ff« <h). (6)

,1 1 / 2 a ( 1 + Q S S . R ^ ) expresión, Se = -JL-. y Re

*» e p u Ce m - ~ ?DCP

in this expréssion S„ «-JJL-— and R^ • P a v d

r c PDC-, • ——«—

and are respectively the Schmidt number and the Reynolds number of the

phenomfenon. i s the coefficient of viscosity of the atmosphere that

surrounds the drop, D the coefficient of diffusión between the vapora

of the fuel and air. C spedrie heat at constant pressure Xét V * velocity

of the drop with respect to the afesne atmosphere that surrounds it.

-15-

Easily it may be understood that (o) may alio be written in the form

AI*2\ i 1/3 1/2

"3SJ « K l • Kfl+O.SS. R,» ) (?)

in which K is a constant oí evaporation with convection and

K the corresponding constant without convection* Slnce K depends on

the diameter oí the drop through Rc the results oí (7) i s that in this case

the lineal law (2) does not obtain yet when the solutions oí (7) draw very

near to it for normal valúes oí RA.

It has been suggested that the rule (7) of Fróssling i s also applicable

to the study oí the influence oí íor ce d convection in the combustión oí a

drop when Sc and R0 are assigned these valúes corresponding to the

temperaturas prevailing between the atmosphere that surrounds the drop

and the fíame. This cannot be put down until the presentaron oí suííicient

experimental Information in order to decide the question but the iníormation

existing (27) suggests the validity oí this rule or other similar ones, such

as proposed by Spalding (28) and by Ingebo (29) •

In INTA a program oí theoretical and experimental work on this partially

question has been íinished. (30) (31) (This program has beenXBJBBItoidaei» subsidised by the European Office ARDC. USAF through its contract

No. A.F.61 514-734C with INTA).

-16-

Figure 6 taken írom Reí. 26

reproduce* «orne oí the resulta ob-

tained with toluene. In it the traces

oí the curve that correapond to the

rule oí Froasling hav* been represented,

The meaaurementa made could not be

extended Mgher than the soné explored

becauae oí the extinction oí the fíame,

which will be shown later. Figure 6

showa that the íorced convection ia

aomewhat eííective in haatening the

combustión oí a drop but i í the phen-

omena oí extinction is taken into con-

sideration the time oí Ufe oí a drop may not be reduced probably more

than 30% to 40% aa a máximum,

13

A probiem oí great practical intereat in the combustión oí a drop

i a the determinan on oí the dietance oí travel or ita penetraron and oí ita

Ufe time when it movea acroaa an atmoaphere oí definit* characteriatica

with a certain initial velocity Vj and it evaporatea with or without

combustión along ita patfa. Thesüác diíñculty oí the probiem reata on the

íact the velocity varíes becauae oí ita aerodynamic reaifetance. Problema

oí this type have been atudied theoretically and experimentally by othera

-17-

among thom are Miesse (32) (33) aad El Wakil and collaborators (34)

(In the reference indicated may be found aa abundant bibUography on the

question). Takiag as a base these studies aad supposiag that the formula

of FrossUng i s applicable the reduction ia Ufe time and the peaetration

has beea calcúlated for a drop that moveí uader the conditioas indicated.

(The authors take pleasure ia expressing gratitude to Sr, Da Riva for his

valued cooperaron in making the calculations) The coefücieat of resistance

of the drop i s inverseiy proportionai to the Reynolds number of the movement

for the interval of Reynolds number s of practical interest. In this case

equation 7 may be integrated in expiicit form and starting this solution

the Ufe span of the drop may be calculated. The fundamental result is

coadeased ia Figure 7. In this ¿r

figure St i s the reduction of the

Ufe span of the drop taJdng as

unity the Ufe span in a quiet

atmosphere, <X and B are two

parameters defined by the fol-

lowing expressions.

o< ^ . s ^ c %R& í * -

¡ Ó- ?

in which R e l i s the initial Reynolds

number and the rest of the para­

meters have previously beea

define d.

a = 0.3 Se *<* Re, ' '••

^ 9 K ?c

(8)

(9)

-18—

Figure 7 shows that the fundamental variable in the Ufe ia the

páramete roe while the influence oí B ia very small. The Schmidt number

varias little from one íuel to another and haa valué a oí about 2. For thia

reaaon the important variable i a the Reynolda number.

14

The foregoing concluaiona are valid aa haa been aaid i í evaporation

i a produced with or without combuation.

Ií the evaporation ia without combuation the Ufe epan ia increaaed

doubUng itaelí íor temperaturee oí the order oí 1000'K. Thia problem

is intereating íor i í the velocity exceeda a certain valué the fíame íront ia

extinguished. Then the combustión oí the drop takea place in the wake

which reduces conaiderably the valué oí the constant oí evaporation aa ia

shown in Fig 7, or it may be totally extiagulahed ia which caae the drop ia

evaporated without combuation. Spalcüng (28) haa pointed out that the

oí the movement and the diameter oí the drop. Fig 6 gives aleo auch an

example, aome experimental valúes that we have obtained in thia relation.

The measurements were made at or near ambient temperatura and the v

indications are that the valué oí ¿ correaponding to extinction increaaea

conaiderably with the temperatura.

íor drop whoae diameters are oí the order oí 100 microns or leaa extinction

ia produced at velocitiea oí aome centimeters per aecond. Thia aignifiea

that mmm%wMWámú evaporation la producad without combuation in moat eaaea

oí practical intereat, the vapora burning later on rnixtag with air in one oí

the modea indicated at the beginning. Nevertheleaa the problem ia not

auíficiently clear.

- 1 9 -

1 5

Another important question i s the iníluence oí the proadmity oí other

drops on the velocity oí combustión oí each. There exist some preliminary

experimental studies on this question (36) (3?) and (38) wtách demónstrate

that the interaction is small unless the drops are very cióse to each other

and are very numerous. Flg 8 shows the results oí two cases oí interaction Dos gohs uno alhao <*> /a oía _.&»*°T?-*A*.e..*Z£Be

Una fila en la < filamento ¡ndinoabL'. £ * ^ . / £ _ £ * S É ° < es/e/a délooho 1 rihmen&wfca/J&élP.i^aíffiíb (37) and (38) D/jlr/ói/c/óo cúbica tkochüQofa&yuna enelepn/ro..

cu BICAL p/¿r£/&t/-no# br- <3 VKOFS W/7~H O/*"? "" TWíT CEtHTBK.

pooo

• 015

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k l « .

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i— i... H * " » - . ^ r2 p4 —

_ i i

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—

_ i i ; ! /

>»/ * >»

LÍT~ ! i i

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I

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r i "T I / I ~r

r — i - •

/

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M

— ... i i

i . i r*-i "i ' <1 — 1 "S? — » — * — ... i i r-. £T~

i A

—-

— I : I

| \

A

—-

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I i i —-

I i

—-i

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i . ¡ _i ~ r "t i i

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16

•U 6 8

'•' Distancia enlr? ¡os, centros de las goras cm. 2-Arista del cubo cm.

10

The preceding analysis íurnishes the baslc iníormation to attempt a

study oí major practical interest, that oí combustión oí a jet oí íuel. It

turas out to be dtfficult, nevertheless, to know how such iníormation ought

to be used in the attempt such study and logically the answer ought to

depend on the particular characteristics oí each burner, the conüguration

oí the cúrrente in the primary soné oí the chamber which vary widely írom

one to the other.

-20-

During the last yeara the re has been graat activity in accumulating

Information principally experimental about the combustión oí streams of

fuel. Frequently such Information has relerred only to partial aspects of

the problem, most easy to study like the statistical characteristics of the

streams (39) (49 their dynamics (41) (42) and (43) the diffusion and mixture

of the drops with the atmosphere that surrounds them (44) and (45) its

evaporation without combustión (41) (42) and (46) and finally the combustión

(47) (48) (49) (50) (51) • • • immHtéwtuum*

Some of such experimente have been made with ideal streams in which

all the drops are of the same s ise .

The measurements made have referred generally to the groes charac­

teristics of the stream, although in some cases the be ha vi o r of individual

drops has been observed. Such observations have shown that to attempt

to generalice the results obtained with isolated drops with those of streams

difficulties appear concerning the valúes that should be assigned to char-

acteristic parameters which are not well determinad.

Various works of review principally directed toward the burner

for reaction motors were presented in the two meetings for A. C. A. R. D.

in 1954 (52) (53) (54)

The methods that have been followed for the study of combustión of

streams may be put in three groups.

a. Methods basad on the extensión of the results obtained in

etudying the combustión of isolated drops. The take off point for

such studies i s established in the theoretical work of Probert (47).

-21 -

Gravaa and Garataln (53) havc calculated lome axamplaa of tha applicatión

oí thia method to determine tha efficiency of combustión and tha influence

of páramete re euch aa tha valúa of the conatant of evaporaron or the con-

centration of oxygen. Another example may ba found in Reí (51). Tha

comparieon between tha experimental raaulta and thoee redicted by thia

method ara not conclualva maldng it ne ce star y to continué the theoretical

work as well aa experimental In thia direction.

b. Extensión of methoda employed in the study of turbulent flamee,

diffusión o£ gases, of heterogenfeous combustión of jet streams.

An example of this method ia found in Reí (50). The problem consista

of determining the geometrical location of the points in which fuel and

oxygen are mixed in stoichiometric proportions.

c. Finally methoda baaed on the study of the influence of some

characteriotic parametera of the atream and of the atmosphere in

which it burns, in the characteristics of the combustión and the

efficiency of combustión. Examples of the appli catión of this method

are found in Reí (52) and (53). Thus when emperical Information ia

secured by thia method of great valué nevertheleaa the resulte have

limitad application be cause they depend considerably on the configuration

utiliaed. For thia reason it would be advisable to accumúlate pre-

liminary information concerning the influence of some fundamental

parameters that may be variad in a syatematic way in aimple and

well defined configuration aa haa been done for example by Woodward (57).

. 2 2 .

17

We have dona (57) some theoretical work on tbe applicatión of

Frobert's method in wbich baa been considerad both tba stationary

functiong región and tranaitory that corresponda to tbe beginning of

combustión of tbe atreaxn tbe altérnate correaponding to periodic combustión.

In thia work it baa been auppoeed that all of tbe dropa bave tbe aaxne

conatant of evaporation. How ligitimate thia hypotheaia ia and tbe valué

that ougbt to be aaaigned to thia conatant if it ia valid dependa on the

reaulta of experimental meaaurementa now in preparation. In tbeae the

sise diatribution function of dropa of Mugele-Evans has been uaed and

conaidered preferable to that of Roain-Rammler and Nukiyama-Tanasawa

becauae it permitted a prediction with cloae approximation and moreover

limited the máximum sise of tbe dropa. Let F be tbe fraction of volume

of tbe atream formad by dropa whoae díameter la leaa than d. Tbe formula

of Mugele-E vane givea for F the following expreaaion

r* - L I ; * í / £ /* X~A^ > 2 L dmái~á J

In thia expreaaion $ ia the integral error d n i a x ia the máximum diameter

ot O . drop. £ « d <f>.r. «wo c h . ~ c t . r i . t t e , - r . m . t . r . of th. dt.trlbution.

Fig 9 givea aome distributione correaponding to typical valué a of tbeae

paramttere. In tbis figure it ia aeen that increaaing & increaaea the

uniformity of the atream wbile increaaing $diminiahea the mean sise

of the drope.

-23-

If G is the volume oí íuel injected in the burner per unit tizne and

g the voluzne oí the drope that exiet in the chaznber* g is expressed as

a function oí G by means oí the formula

. ,^£, , , ., , . QJ^-J

J Vrr „ r <10>

in which I is given by the expression

C ' C '~* •——T~~ " é ki

4v 00

ty is the tizne oí combustión oí the drops oí máximum cüameter in the

strearn.

The znagnitude oí 10 i s oí interest be cause the intensity oí combustión

oí the burner should be inversely proportional to it.

As may be seen to increase £. that i s to increase the uniformity

oí the stream diminish the volume oí íuel in the chamber, In consequence

it is oí advantage to opérate with streams oí the highest possible uniformity

in order to diminish the volume oí the burner.

Combustión distorts the distribution oí the drops in sise conserving

nslirally the largest s ise . Itg 10 shows the íunctiona oí distribution in

the fíame corresponding to the three cases calculated.

-Z4-

For comparieon the re has

been included in thie figure the

corresponding distribution in the

•tream. In Table m have been

included the díamete re frem

Sauter corresponding to the

•tream and the fíame.

1.

fff

1.

fff e-¿5¿=/~7

.70

60

¿ r / O W / . .70

60

•

i i g » u / / 1 17/ J

yfj -

f'/P-U j j r / 1 V e * .$*•/ -

1 Si

F *

I

-

1 Si

F * t' 1 -¿ /jl .

1 Si

F * í» .5 #»-5

so .to

K

^ f--« *«¿

K

1 JO M .30 4fi SO .60 .70 -80 w r

dmax

Fig. 10

90 y*y y y /y

^y&' W

S0

£tl ¿fí y/

Ss

W

/ / t ^r-Z- ±

• £ í

t-u / trr r/ '

y jr ^e.-.s

• S í l" ly

< í

f r . 5 »ff

y y ivt Combustión

Chortv-j. JC

y y ivt Combustión

Chortv-j.

.ZP

y y

y 1 / &m.e *M

(0 y

y Jy y y /

y

JO .20 .36 m so .60 •TO .00 .90

h* TABLA ni

0.5 1 1.5 g _ 0.129 0 110 0.105 Gh

0.129 0 110 0.105

( ds ) dmdx chorro

= 0.269 -STBEAM

0.438 0.895

( f* )., = = 0.517 0.454 0.401 dmáx llama - / c - ^ / r f ^

-25-

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• 26~

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-27-

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-28-

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-29-

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-30-

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- 3 1 -

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