ANALYSES OF THE COMBUSTIÓN PROCESSES IN GAS TURBINES...
Transcript of ANALYSES OF THE COMBUSTIÓN PROCESSES IN GAS TURBINES...
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
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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.
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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
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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.
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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
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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.
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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
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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
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.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
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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
.010 ,
.90.5-
k l « .
i j " i
í 1 — i — ~ -
í T " i
i 1 I 1 J
•""T " —
! i
i— i... H * " » - . ^ r2 p4 —
_ i i
" 7 / I >»/ * >»
—
_ i i ; ! /
>»/ * >»
LÍT~ ! i i
' /
I
* >»
r i "T I / I ~r
r — i - •
/
— 1 "S? — » —
M
— ... i i
i . i r*-i "i ' <1 — 1 "S? — » — * — ... i i r-. £T~
i A
—-
— I : I
| \
A
—-
—
I i i —-
I i
—-i
~| ! j - 1 í
—-i
_i ! < i j í
i . ¡ _i ~ r "t i i
— : L J
¡ I I í
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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