Journal of Research of the National Bureau of Standards Vol. 49, No. 5, November 1952 Research Paper 2365

Analytical and Experimental Studies With Idealized GasTurbine Combustors1

Fillmer W. Ruegg and Howard J. Klug

Problems of flow, heat release, and mixing in gas turbine combustion chambers are dis-cussed and analyzed. The analysis is based on an idealized or equivalent chamber in whichthe end result is the same as in the conventional chamber, but in which the functions areseparate and distinct. A large primary zone is advantageous, but the combustion processstill is burdened by an inverse relationship between primary air and fuel. Conditions favor-able to combustion in the primary zone over the whole range of operation are realized bymeans of a mechanical control. Agreement between analysis and experiment was demon-strated by tests of a chamber with a mechanical control. Comparison of the field of mixingof primary flame gas and secondary air with other studies of mixing revealed a general simi-larity, but a slower rate of mixing that is ascribed to the effects of a large difference of temper-ature or density in these experiments.

1. Introduction

Although jet propulsion for aircraft has become apractical reality, many problems connected with itare still only partially solved. One of these problemsis the development of combustion chambers for turbo-jet engines that will give satisfactory performanceunder all service conditions. Satisfactory perform-ance implies that a continuous supply of exhaust gasat the desired temperature is furnished the turbine,and that response to demands for changes of condi-tions is positive and occurs in a minimum of time.Other desirable characteristics are high combustionefficiency, small loss of pressure, uniformity of tem-perature in the exhaust, minimum size and weightconsistent with required performance and life, andease of manufacture and maintenance. Some com-promises have been necessary in designing combus-tion chambers, since some of these features have beenfound to be obtained only at the expense of others.

Problems of flow and combustion in conventionalcombustion chambers are so complicated and inter-related that development of chambers has progressedlargely by empirical methods. Although develop-ment by these methods has produced immediate re-sults, in the long run a fundamental understandingof the problem is advantageous and will promotedesign on a more rational basis. It is the purpose ofthis paper to separate and examine some of the func-tions of conventional gas turbine combustion cham-bers in an attempt to arrive at a better understandingof their influence on the performance of the chamberas a whole.

2. NomenclatureA — Area, ft2.c— Effectiveness of mixing.C= Coefficient in mixing length equation.

Cp = Specific heat at constant pressure, Btu/lb°F.d,D= Diameter, ft.

g=Standard acceleration of gravity, ft/sec2./= Mixing length, ft.

i The work described in this report was sponsored by the Bureau of Aeronautics,Department of the Navy.

L = Length of potential core, ft.p = Absolute static pressure, lb/ft2.

pt = Absolute total pressure, lb/ft2.q=ipV2; dynamic pressure, lb/ft2.r = Radius, ft.

rm = Radius at which T (or V) is halfway between T(or V) at axis and that of secondary stream, ft.

#=Gas constant, ft-lb/lb ° F.T— Absolute temperature, ° R.V= Velocity, ft/sec.W= Weight flow per unit time, lb/sec.x = Axial distance from station 3, ft.y=Lateral distance, ft.z = Upper limit of probability integral,e = Emissivity.

7}b = Combustion efficiency.p = Density, slugs/ft3.<T= Scale factor.

rnt^= Turbulent shear stress, lb/ft2.

SUBSCRIPTS

1 to 4 = Stations in the chamber./=Fuel.i=Indicated.p = Primary.s = Secondary.

3. Combustion Chamber

Combustion chambers for gas turbines have beendeveloped and modified according to the require-ments of the system in which they are intended tobe used. Although each chamber may be differentfrom any other, it appears that most designs differin detail only, and not in principle. An examina-tion of the conventional combustion chamber revealsthat there are four main functions that it mustperform, (1) separation of the air into primary andsecondary streams, (2) maintenance of a stable pilotzone, (3) combustion of fuel with the primary air, and(4) mixing of the burned gases with secondary air.

Design features may be illustrated by the schematicdrawing in figure 1. A protected, turbulent zone oflow velocity is established at A inside of the dome ofthe perforated liner, and when fuel is injected intothis zone a mixture is formed which is capable ofsustaining a stable flame. More air enters the linerbetween A and B and combustion proceeds as it

279223977—52-

PERFORATEDLINER

FIGURE 1. The conventional chamber.A Turbulent zone of low velocity; A to B, primary zone; B to C, mixing of

secondary air with products of combustion from primary zone.

mixes with fuel. Velocity of the mixture in this zoneis probably higher than the velocity of the flame inthe mixture, but combustion is piloted by the flamefrom A. The air that takes part in the combustionin this zone is known as primary air. Secondary airenters and mixes with the products of combustionbetween B and C, thereby reducing the gas tem-perature to a safe operating level. Completenessof combustion is promoted if the air is admittedgradually into the liner and in a manner so that itdoes not quench the flame and cause blowout.

There is no assurance that all of the air that entersthe liner between A and B takes part in the combus-tion process, and therefore it may be said that theseparation into primary and secondary air is notdistinct.

Gas turbine combustors must be capable 01 oper-ating over a wide range of exhaust to inlet temper-ature ratio, and generally this flexibility is attainedby injecting atomized liquid fuel into the pilot zoneat A. This method of fuel injection providesheterogeneous mixtures that are capable of sup-porting stable combustion, even though their qualitymay differ substantially from stoichiometric. Itdoes not follow that combustion must always beefficient with this system. Actually, it may be goodover only a narrow range of conditions, and maybecome poor when others are imposed.

Loss of pressure due to flow friction is high, andproblems of flow and combustion are complicatedand interrelated. Flow is turbulent, and in someregions within the primary zone, it may actually bein an upstream direction. Combustion and mixingwithin the liner nowhere occur as distinct, individualprocesses. Although these conditions appear to bebeneficial from the standpoint of performance andflexibility, they make a detailed analysis of theconventional chamber almost an impossibility.

If a chamber is designed to carry out the functionsenumerated above as separate and distinct opera-tions, then an analysis of its performance becomespossible. A chamber designed for this purpose maybe called an idealized or equivalent chamber,equivalent in the sense that the end result is thesame as in the conventional chamber. The dif-ferences between this chamber, represented byfigure 2, and one of conventional design are apparent.Stations A, B, and C in each figure represent locationswhere the same respective operations are performed.In this equivalent chamber the air is separated intotwo distinct streams, and the drop in pressure due toflow friction that each experiences is made to occur

© © ©

FUELINJECTION LOSS OF PRESSURE DUE"

TO FLOW FRICTIONPILOT ZONE

FIGURE 2. The equivalent chamber.A, Turbulent zone of low velocity; A to B, primary zone; B to C, mixing of

secondary air with products of combustion from primary zone.

in a manner that is subject to analysis. A throttlingprocess is assumed for the primary air, and thesecondary air is assumed to go through a throttlingprocess followed by a reversible expansion. Fuel isinjected and combustion is stablized after the primarythrottling process, and is assumed to be completewithin the primary zone. The size of the pilot zonehas been diminished to that which would exist at aflame holder, and combustion may be said to occuras in ramjet chambers. Since combustion is made tooccur at a fixed temperature ratio in a stream thathas a uniform, measureable velocity, the process issubject to treatment by both analytical and experi-mental methods. Mixing of the burned gas withsecondary air occurs only after combustion iscomplete, and the changes resulting from this processalso may be predicted and measured.

4. Analysis of the Equivalent CombustionChamber

The method used in the analysis depends on thefact that each function of the combustion chamberis considered to be performed as a distinct, individualoperation. Changes of temperature, pressure, etc.are calculated for each, and from these the perform-ance of the chamber as a whole is derived.

Before these calculations may be made, it is neces-sary to specify some of the conditions at which thechamber is required to operate. Although anypractical chamber must be able to operate over awide range of conditions, there is usually some con-dition whers it performs best, and it is desirable thatthis should coincide with the condition that is usedmost often in service. For the purpose of this anal-ysis, an exhaust to inlet temperature ratio of 3.2 isa suitable specification, because it is close to thatused in practice and is also a convenient workingcondition for experimental purposes.

As combustion is usually best when the mixture ofair and fuel is at or near stoichiometric, this conditionmay be used as the basis of a second specification.A mixture of this quality would give an exhaust toinlet temperature ratio of about 7.25 across theprimary zone.

Some loss of pressure in conventional chambersoccurs when the air flows through the perforationsof the liner. In order to approximate this conditionin the chamber represented in figure 2, it is necessary

280

to introduce loss of pressure in the flow of air in amanner that its effects can be determined analyti-cally and experimentally. Once the magnitude ofthe loss of pressure due to friction is specified, theconfiguration of the chamber may be calculated tosatisfy all of the above specifications, provided theconditions of the flow in the chamber are also speci-fied. However, the solution of the problem wouldapply only to the set of conditions of flow that werespecified. Because an infinite number of conditionsis possible and as all of them cannot possibly behandled, it is necessary to make a choice. Theproblem is simplified if it is considered that thevelocity of flow in the chamber approaches zero, andthis assumption is used throughout these analyses.Combustion chambers of gas turbines are operatedat relatively low velocities; hence such an assumptionwould not cause serious errors.

Other simplifying assumptions may be made with-out serious error. These are: rise of temperature inthe primary zone may be accomplished withoutadding fuel to the flowing stream; specific heat, cp,of the gas is independent of temperature; loss ofpressure due to friction does not occur except wherestated; velocity of flow is uniform in each zone acrossplanes in the duct normal to the flow; and secondaryair receives no heat before it mixes with the gas athigh temperature from the primary zone.

The problems of flow, heat release, and mixingmay be handled by using Bernoulli's equation andthe conservation of momentum equation. Since itis considered that the velocity of flow approacheszero, Bernoulli's equation for incompressible, fric-tionless flow may be written

(1)

where pt and p are constant at all points in the flow.The conservation of momentum equation for heatrelease or mixing is

p + P V2=constant, (2)

and when heat release occurs where V approacheszero, eq 2 may be written

The subscripts 1 and 2 in eq 2a indicate the state ofthe gas before and after heat release, respectively.When these equations are applied to cases where V\is appreciable, it is equivalent to considering that thefluid is incompressible, or that density is dependentonly on temperature. The condition for continuityof flow may be written

pAV— constant. (3)

Equations 1,2, and 3 and the gas law, p=gpRT, aresufficient for the analysis of the problems of flow inthe equivalent combustion chamber.

4.1. Effect of Size of the Primary Zone

Two design conditions of temperature rise in thechamber have been specified, but nothing has beensaid about the size of the primary zone. It wouldbe possible to specify arbitrarily a size based onresults of practical experience, but there is no assur-ance that the decision on this basis would be themost logical. A determination of the effect of sizeof the primary zone by analytical means probablywould provide a sound basis on which to make achoice of size. This determination is attempted inthe analysis that follows.

A list of the design conditions, in which thenumerical subscripts refer to the stations in thechamber indicated in figure 2, is presented below.The subscripts p and s refer to primary and secondaryair, respectively.

(1) TJT^S.2; (2) TtJ^ = 7.25; (3) Aps/q2,s=2=loss of pressure due to flow friction; (4) ApP/q2,p=10=loss of pressure due to flow friction; (5) pz,s=Pz,P.

At low velocity, loss of pressure due to frictionmay be expressed as a constant number of velocityheads, q, where q=ipV2. The losses indicated inthe third and fourth specifications were chosen inan attempt to approximate those in practical cham-bers. The fifth specification is that pressure isuniform across the plane of station 3. Tollmien [1] 2

calculated that the pressure at the plane of thedischarge of a free, round jet differs from the am-bient by an amount equal to about one-tenth per-cent of the dynamic pressure of the jet. A pressuredifference of this small magnitude would have nosignificance in the present analysis. A variation ofserious magnitude probably would not be encoun-tered except where the velocity of flow in the primarystream at station 3 equaled the acoustic velocityin the stream. Conditions such as this are notencountered in present-day engines, and consequentlyare not considered here.

The above specifications provide sufficient infor-mation to permit a calculation of the effect of linersize, d2j on the problems of flow, heat release, andmixing in the equivalent chamber.

If WP and Ws are the rates of flow of the primaryand secondary streams, respectively, then whenmixing of these streams occurs between stations 3and 4, a heat balance may be written

WP(T*,P- TJcp= Tx)cp. (4)

Noting that cp is assumed to be independent oftemperature, eq 4 may be written

W

Ff 1

(5)

and when the first and second specifications aresubstituted, the right member of eq 5 is equal to

2 Figures in brackets indicate the literature references at the of this paper.

281

10

aT~ 2

0

-9S

P

\

(o)

60

50

c£* 40

30

20

10

0

3

,11\1

(d)

—

1 (g)

60

50

cr* 40

V\

p

(b)

_ 40CT

^ 30

k 20

10

0

.06

0.2 0.3 0.4 0.5 0.6 0.7

(e)

/

1

\(h)

\

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7(d2 / D)2

FIGURE 3. Effect of size of primary zone.

t.2

1.0

•5 0.8o

K 0.6o

2! 0.4

0.2

0.0

( d 3 / D ) 2 - ^ ^

/ \

(D/d3)2-

(c)

50

> 40

?_ 30

10

0

\ v\ — —

(f)

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.35. In other words, 35 percent of the air mustenter the primary zone to fulfill the conditions ofspecifications (1) and (2). The air that enters theprimary zone can be regarded as the central coreof the stream at station 1. Since it is consideredthat the properties of the flow are uniform at thisstation, the diameter of this central core of primaryair can be expressed by the equation

(6)'W, + W.

Bernoulli's equation, eq 1, may be used to deter-mine the changes of pressure between stations 1 and2 as d2 is changed. Thus

1 - 2 = I — - (7)

and the ratio of the velocities for both primary andsecondary air may be determined by the continuityequation as follows:

(8)

V (9)

Since (dJD)2=Wp/(WP+Ws), the pressure changesmay be expressed by the equations

WP+W0'

wP+ws

D2

- 1

(10)

(11)

These were evaluated and plotted versus (d2/D)2 infigure 3, a. When (d2/p)2 is greater than 0.35, theprimary air diffuses into the primary zone, itsvelocity decreases, and its pressure increases. When(d2/D)2=0.6, the velocity of the primary air as estab-lished by eq 8 is about 58 percent of Vx.

Loss of pressure in the primary zone is the sum ofthat due to friction and combustion. This may bewritten

(12)

where the second term on the right side is determinedby eq 2a, which is the loss due to combustion on thebasis of the momentum equation. <z2,P/<Zi is given byeq 8, and the pressure loss thus may be expressed interms of qx by the following equation:

282

This was evaluated and the results are plotted infigure 3, b.

Calculation of the change of pressure in thesecondary air is based on the assumption thatPz,p=pz,s- In order to fulfill this condition, it isnecessary to change dz with d2i and the requiredchange may be evaluated by using eq 1 and 3.Change of pressure in the secondary air may bewritten

p2,s—Pz,s=qz,s—q2,s+Aps, (14)

and this may be solved for pziS. Eq 7 and 12 may becombined to yield

and since it is considered that Pz,P=pz,s, the rightside of eq 15 may be substituted for pz,s ineq 14. By this method the following relation isderived,

s — &Ps) — (Pl—P2)s. (16)

Now qz,s may be related to #i by the continuityequation, and this relation leads to

qi \dl—dlJ(17)

and when this is solved for (dz/D)2, the following isderived

D

(-)V qi /

1 / 2 D 2 (18)

These equations furnish sufficient information toevaluate the change of pressure and of dz as d2 ischanged. Thus eq 14 and 16 evaluate (p2,s—pz,s)and eq 16 and 18 evaluate (dz/D)2. Changes of pres-sure between stations 2 and 3 are plotted in figure3, b, and (dz/D)2 is plotted in figure 3, c. Both areplotted against (dJD)2, which defines the size of theprimary zone. Figure 3, b, shows that the pressureloss decreases rapidly as the size of the primary zoneis increased. However, the velocity in the secondaryzone becomes high, and a point is reached (when(d2/D)2=0.Q) where the loss in pressure across thethrottle is so high that there is no need for more dropin pressure by expansion in the nozzle at station 3.At this point dz=D. If the primary zone were madestill larger, the loss of pressure in the secondary airwould be so high that an enlargement or diffuserwould be necessary to recover and thus maintain theequality of pressure across station 3. Thus dz wouldhave to become larger than D, and this is shown infigure 3, c, by the curve of (D/dz)2, where this ratiobecomes zero when (d2/D)2=0.65. For all practicalpurposes, it may be said that the area of the primaryzone in this chamber cannot exceed 60 percent of thetotal area. This area of the primary zone depends,

of course, on the relative pressure losses in the pri-mary and secondary zones. For example, if nofriction loss were assumed, the maximum area wouldbe 66 percent, whereas if both the assumed losseswere doubled, the maximum area would decrease to58 percent of the total.

At station 3 the primary air at high temperatureand the secondary air begin to mix, and the resultingchanges of pressure may be calculated by the equa-tion for the conservation of momentum. For thiscase it may be written

This equation may be arranged to the more con-venient form

d

and the change of pressure is determined by evalu-ating each of the separate terms and taking thesum. These terms may be evaluated by using thecontinuity equation and the gas law, and alwaysconsidering that p is dependent only on temperature.Thus

(20)

d2Vwd\

( 2 2 )

The values of these terms were determined from theprevious relations, and the sum expressed as (pz—p±)lqx is plotted versus (d2/D)2 in figure 3, d. The over-all change of pressure from station 1 to 4, which wasevaluated by a summation of the successive changes,is plotted versus (d2/D)2 in figure 3, e.

Although the over-all change of pressure is informa-tive, it does not allow ready comparison with thechange of pressure of other combustion chambers.In order to make a comparison on this basis, it wouldbe necessary for each chamber to have inlet andexhaust ducts of the same relative size. However,if the loss of pressure is expressed in the fundamen-tally more useful form of total pressure, a comparisonis possible without this information about size. Lossof total pressure may be written

4 g 4 . x (23)

The first two terms on the right side were evaluatedpreviously (see fig. 3, e, and eq 20), and the loss oftotal pressure was determined and is plotted versus(d2/D)2 in figure 3, f. Inspection of this curvereveals the advantage of a liner of large size. Whenthe liner of this chamber occupies 60 percent of thetotal area, the loss of pressure is about half that whenthe liner occupies 35 percent of the area.

283

Little is known about the factors that control therate of mixing of gas streams under conditions thatexist in combustion chambers. In practical chambersthe rate is accelerated by the turbulent flow of theair through the perforations of the liner. Althoughthis is accomplished at the expense of loss of pressure,it is compensated for by the consequent reduction inlength of the chamber. One of the factors that mayinfluence the rate of mixing is the ratio of the velocityof the gas streams at station 3. The ratio of ^tP/^sfSmay be determined from eq 21 and 22, and notingthat jT3t3,/Ti = 7.25, the velocity ratio may be derived,and equals

V3,s Tx \djD D

l - ( ^

This was evaluated and the ratio is plotted versus(d2/D)2 in figure 3, g. It increases with an increase ofthe size of the liner, notwithstanding the fact thatV2tP, and therefore V3tP, decreases. The degree ofexpansion required in the secondary stream alsodecreases, and V3, decreases at a greater rate thanV3,P.

Squire and Trouncer [2] analyzed the problem ofincompressible mixing of a round jet in a generalstream, and the results were used here in an attemptto determine the effect of liner size on the mixing ofthe primary and secondary streams. Although theconditions existing in a combustion chamber differin many respects from those assumed in the analysis,it is possible that the two cases would exhibit similarbehavior.

In the analysis [2] the momentum transfer theorywas used to determine the way in which velocity istransferred between two round streams. Turbulentshear stress, r, defined by the equation

(25)XdF)

was equated to the change of momentum flux of themixing region with axial distance. Mixing length, Z,was assumed equal to the width of the mixing regionmultiplied by a constant of proportionality, C. Theconstant G was considered a characteristic of theturbulent motion, and appeared in the end result asa constant to be evaluated experimentally. It wasalso assumed that the variation of velocity acrossthe mixing region was similar to that determined bythe cosine equation

v-vsF r =o- ] T6~ )' (26)

where rm is the radius at which velocity is half }between axial and secondary stream velocity. Re-gions in the flow and significance of terms in eq 26are illustrated in figure 4.

Extent of the potential core of undisturbed pri-mary stream, L/d2, was found to increase as the ratio

Secondary stream, Vs

^ - ^f I . Mixing Region

Primary stream, v D —*• 2r, Potential "—^-^ ,__ _ vw .3'P Core "" *^ r=

FIGURE 4. Diagram of mixing field.

of primary to secondary stream velocity, V3tP!V-6tSdecreased and approached unity. Beyond L, the rateof decay of velocity along the axis was not influencedgreatly by V3tP/V2fS, and therefore for the presentpresent purposes L may be regarded as an inversemeasure of the effectiveness of the mixing process inbringing the two streams to a uniform state. Inother words, at a given value of axial distance x,(x^>L), decay along the axis would be less completewhen L is large.

Squire and Trouncer present values of L/d2 andVS,P/VS,S, and in this analysis the variation ofV3fp/VZfS with d2/D has been determined. A combi-nation of the two sets of information will allowdetermination of L as a function of d2i and this ispresented in figure 3, h. In their analysis the constantG was regarded as independent of V3)P/V3tS, and thissame assumption is made here. At small values ofd2, L is also small, and mixing would probably begood. As d2 is increased, V3tP/V3tS increases slowly,but not sufficiently to counterbalance increase of d2yand L increases. However, a point is reached whereV3tP/V3fS increases at a rate sufficient to counter-balance increase of d2, and L begins to decrease.When (d2/D)2=0.6, L is well below the maximum,and it may be said that mixing probably would berelatively effective at this condition. In connectionwith these conclusions, it must be remembered thatthere are differences between the conditions assumedin the theory and those existing in a chamber. Alarge difference of temperature, confinement of themixing region by the walls of the chamber, and arelatively large primary stream would probablyinfluence the mixing in a manner that would requireexperimental determination.

This analysis has indicated the effect of the size ofthe primary zone on the problems of flow, heat re-lease, and mixing in the equivalent chamber. Aprimary zone of large size appears to offer the advan-tages of low velocity in the primary zone, and re-duced loss of pressure across the chamber. Lowvelocity probably would simplify the problem ofmaintenance of a stable flame, and a reduction in theloss of pressure would increase the "mechanicalefficiency" of the chamber and thereby increase theover-all efficiency of the engine in which it would beused. With regard to the problem of mixing, theanalysis indicates no serious disadvantage attachedto a large primary zone. Maximum area of theprimary zone in the equivalent chamber is found tobe 60 percent of the total chamber area. Measure-ments of practical chambers indicate that the area

284

of|the primary zone is generally about 60 percent ofthe total, and this point of similarity between analy-sis and practice is gratifying. For these reasons thesize of the primary zone is fixed at the maximumvalue in the analysis that follows.

4.2. Analysis of Operation of the EquivalentCombustion Chamber

The only means of control over the over-all tem-perature ratio in conventional chambers is by thevariation of the rate of fuel injection into the pri-mary zone. This may be approximated for pur-poses of analysis by assuming that the temperatureratio, T2<p/Th in the primary zone is allowed tochange, while holding the configuration of the cham-ber constant, as determined above. Before pro-ceeding to the calculations, it is advantageous to listthe following complete specifications for this combus-tion chamber:

(1) d22=0.6D2; (2) ds=D; (3) Ap5/q2tS=2=\oss of

pressure due to flow friction; (4) App/q2tP=10=lossof pressure due to flow friction; (5) P3s=P3P',(6) TJTt varies with TZJTX.

The problem is to evaluate the distribution of airbetween the primary and secondary zones on thebasis that pZfP will always equal pz,s. Exhaust toinlet temperature ratio, TJTh can be determinedonce the distribution is known. Loss of pressure inthe primary zone is given by eq 12, and by using^q 1? P2,P may be written in terms of pu as follows:

(27)

Combining these two equations gives

Q?,P- l ) - « i . (28)

/

Loss of pressure in the secondary air is given by eq14, and by evaluating p2fS in terms of pi and com-bining, there results

Pi — P3,s=2q2tS+q3,s—2i. (29)

Equating 28 and 29 on the assumption that P3,P=P3,Syields

(30)Z2, V

Since d% is specified equal to Dy q2,s=(L3,s, and eq 30will yield a relation between q2tP, q2>s and T%,v\TXi asfollows:

(31)q, >P

(Aps/q2tS)+l

This equation, when combined with the equation ofcontinuity of flow,

W, , Ws (32)

will yield a relation that will predict how the airdivides between the primary and secondary zones asTz,pjTi is changed. Thus the continuity equationmay be written in the form

wp 1

w,+w. 1+V2,s D2-tV,

(33)2,P

and since T72,s/^

/2,j>=(g'2.s/g'2,?)1/2, the fraction of air

going into the primary zone is

W, + W. 2,i,+2cr3,i,/r1)-iT/2/z>2 \

Ap.lqi.+ l J Ul )(34)

Equation 5 expresses the relation between TJTX andWP/(W?+WS), and this may be combined with eq34 to yield

IJTT—l

= 1+"2,i,+2(r3.,/r,)-ni/2/g2 AAP,/2s.,+i J \di V

(35)

This expresses the relation between the overalltemperature ratio and the temperature ratio in theprimary zone, and is plotted in figure 5, a. Therelation between TA/Tt and Wpf(Wp+W8) is plottedin figure 5, b.

Inspection of these curves reveals some interestinginformation concerning the operation of the chamber.Although TztP]Ti increases with TJTU the fraction ofair going into the primary zone decreases. This maybe interpreted to mean that as more fuel is injectedinto the primary zone, the flow of air into it willdecrease. Thus the length of the flame will increasewith T4/T1, and at values higher than the designcondition it may extend downstream beyond theprimary zone. Mixing with secondary air may notbe complete by the time the gas enters the turbine,and the turbine may be exposed to gas at excessivelyhigh temperatures. A further possibility is that theconditions may not be favorable for combustionbeyond the primary zone. The flame may bequenched by the large quantity of excess air, andcombustion efficiency will then be low. In addition,the pilot zone may become so rich in fuel that it willnot support combustion, and rich blowout will occur.

Conversely, at low values of TJTi, the mixture inthe primary zone will be lean in fuel, and combustionmay be poor. As TJTX is decreased, a point will bereached where the mixture in the primary zone willbe too lean to support combustion, and lean blowoutwill occur. Moreover, the velocity in the primaryzone increases and adds to the difficulty. Theseeffects are observed in testing of practical chambers,although not exclusively because of the reasonsenumerated.

285

(a )

30

2 0

0

—i_ •

__ P _

s

- —-

(d)

30

ia^" io

0

-

A practical chamber ^ — -

The Equivalent chamber

(g)

0.6

0.4

a.

^ o.i

on

—

— —— —

\ •

(b)

a*.

——

. *

- P —

s

1

( c ) "

— • —. - — •

•

(e)

50

_ 20r

?

no

0

— —» •

, . 1 —

( f )

(h)

FIGURE 5. Effects in the chamber with a large primary zone.

In contrast to the air distribution determinedabove, a distribution is shown based on maintenanceof near stoichiometric conditions in the primaryzone. Equation 5 was used with a constant value ofTitP/Ti equal to 7.25, and the dotted curve labeled"ideal" in figure 5, b,i s the result. This ideal distri-bution is radically different and points out the factthat the conventional chamber has proper distribu-tion only at the design condition, that is, at the valueof TJTi where the two curves cross.

Both the type of mixture of air and fuel and thevelocity of the air in the combustion chamber in-fluence the lean and rich limits of combustion.Heterogeneous mixtures are used exclusively becausethe range of combustible limits is relatively widecompared to that of homogeneous mixtures. It isprobably true that low velocity tends to widen thelimits in all chambers of this type.

When the distribution of the air is known, thechanges of pressure and velocity in the chamber maybe determined. Because the fraction of air goinginto the primary zone changes with TJTU it is evi-dent that the streamlines of this air will diverge orconverge on going from station 1 to 2, depending onthe quantity that is flowing. If this fraction issmaller than that of the fraction of the area includedby the primary zone, the streamlines will diverge, andthe air will diffuse into the primary zone. Change ofpressure between stations 1 and 2 may be determinedas before by eq 5 to 11, remembering in this case thatthe fraction of primary air is the variable. A plot ofthese is presented in figure 5, c, for both primary andsecondary air streams. At all values of TJTi theprimary air in this chamber diffuses into the primaryzone, whereas the secondary air expands.

The changes of pressure between stations 2 and 3are evaluated by combining eq 28 and 10 for theprimary zone, and 28 and 11 for the secondary zone.Thus by this method

and(36)

(37)

These changes were evaluated, and the results areplotted in figure 5, d. For this chamber the loss instatic pressure from station 2 to 3 does not changegreatly with TJTt.

Mixing of the primary and secondary streamsbegins at station 3, and the change of pressure thatresults may be calculated as before by eq 19 through22. This is plotted in figure 5, e, and the over-allchange of pressure from station 1 to 4 is plotted infigure 5, f. Loss of total pressure may also beevaluated as before (see eq 23), and is plotted infigure 5, g. In this equivalent chamber the totalloss is about 6qi.

Observed loss of total pressure in a practical com-bustion chamber is also shown for comparison.These data were observed when V\ was equal to 70ft/sec, and displacement of the curves from each otheris an indication of the relative magnitude of the lossof pressure due to friction. Loss of pressure in acombustion chamber is undesirable, because it lowersthe over-all efficiency of the engine in which it isused, and from this standpoint it appears that thisequivalent chamber would be superior. However,size and performance of the chambers in other re-spects must also be considered before an effective

286

comparison can be made. Combustion efficiency,stability, etc. are very important, but all the factorsthat influence these are not thoroughly understood.Such factors as pressure, temperature, character ofthe mixture of air and fuel, etc. may not have thesame effects in all combustion chambers, and theseare not considered in this analysis. Their influencein any one chamber is determined almost exclusivelyby experiment.

The ratio of the velocities of the primary to sec-ondary air at station 3, Vz,p/Vz,8 was evaluated asbefore (see eq 24) and is plotted versus T^Ti infigure 5, h. It increases with TJTU and probably themixing process will be most effective in bringing thegas to a uniform state when outlet temperature ishigh. Effective mixing is needed most at this con-dition of high temperature.

The combustion chamber described and analyzedis similar to practical chambers in which over-allratio of temperature TJTi is controlled by rate offuel injection into the primary zone. In the analysisthis method of control is simulated by variation oftemperature ratio, Tz,p/Tly in the primary zone. Ithas been pointed out that this system of control hascertain undesirable effects in the combustion chamber.When the conditions of operation deviate from thedesign point, the quality of the mixture of air andfuel in the primary zone also deviates from the qual-ity that is most favorable for combustion. Hencethe efficiency of combustion probably would decrease,and at extreme conditions the mixture would becomeeither too rich or lean to support combustion. It isrecognized that this system has certain advantages,such as simplicity of control, because all that is re-quired is a control of the rate of fuel injection intothe primary zone. However, the advantages ofmaintaining conditions for good combustion are alsoapparent, and some effort may well be made toinvestigate the requirements for this objective.

4.3. Analysis of Operation of a Chamber with aControlled Primary Zone

As stated before, combustion is usually best whenthe mixture of air and fuel is near stoichiometric,and hence T^V\TX may be selected to be equal to7.25 as before. The problem then is to select amethod and determine the conditions that are nec-essary to hold T^p/Ti constant while TJTX is varied.Probably the first method that comes to mind is thevariation of the size of the mixing section, since thismethod was used in the first analysis. In that anal-ysis d2 was varied, and dz was changed simultane-ously to hold TzJTi constant. This method wouldrequire an adjustable nozzle at station 3, and in serv-ice it probably would be impractical. However, anadjustable throttle, or valve, also may be inserted inthe secondary zone for this purpose. Although thismethod of control introduces loss of pressure due tofriction, it has certain advantages from the stand-point of mechanical simplicity. A combustion cham-ber with such a device is represented by figure 6,where the throttle takes the form of two perforated,thin annuli. The pressure drop in the secondary

© ©

SECTION X-X

FIGURE 6. Diagram of the chamber with the controlled primaryzone.

stream is adjusted by rotating one annulus relativeto the other, thus providing larger or smaller open-ings as desired. This is only one of many possibleschemes that might accomplish the same object. Itwill, however, serve for the purposes of this analysis.

The specifications for this case are (1) Tz,p/T1 =7.25; (2) d2

2=0.35D2; (3) d3=D; (4) App=0; (5)P3,s=Ps,p; (6) TJTX varies with A^s/g2,s.

Stations in the chamber are shown in figure 6.It will be noted that d2 was specified small (0.351/2Z>),and this was done for several reasons. Experimentalwork was planned on this chamber, and it appearedthat conditions in a small primary zone would bemore favorable in the proposed experiments to awell-regulated combustion process. In a large zonethe velocity of the primary stream would be low,and probably the flame would seat at the fuel in-jector under some conditions, and under otherswould require a flame holder for stabilization. In asmall zone, velocity would be relatively high, andcombustion could be well regulated and performedin a homogeneous mixture of air and fuel with theseat of the flame at any desired position. A largeprimary zone would require a throttle in the pri-mary stream, with attendant increase of mechanicalproblems and unknown effects on the flow condi-tions and combustion process. Another reason fora small zone was that a study of the mixing processof flame gas and secondary air could be made underconditions more nearly comparable with those as-sumed in theoretical studies of spread of free jetsand of mixing of coaxial streams. The particularsize chosen for the primary zone is that for whichthe flow of air will be undisturbed when operatingat the design condition of TJT1=3.2. At this de-sign condition primary air is 35 percent of the total(see eq 5). With regard to the specification of nopressure loss due to friction in the primary zone,this is not a serious departure from reality becausethe loss can be made small when combustion is per-formed under the conditions mentioned. Thesespecifications of the method of combustion and of

223977—52- 287

0.6

0.5

^ 0.4

#0.3

01

0.0

60

50

S"~ o

/

(b)

> /

s

50

40

xf 30

cT 20

c^ 10

0

- i n

P

s

+**

(c)

^ P

I

^ 2 0

10

0

30

25

y/

(d)10

8

^ ~ 6

sr 2

0

-2

— - ^

(e)60

50

•^40

°-30

Sao

10

0

(f)

(g) •

. — •

(h)

FIGURE 7. Effects in the chamber with the controlled primary zone.

pressure loss in the primary zone, although practicalin the laboratory, probably would not be practicalin actual engines where flexibility of operation isimportant.

The fraction of air going into the primary zoneunder the conditions specified may be calculatedagain by eq 5, using TZtPlTl constant at 7.25. Re-sults of these calculations are shown in figure 7, a.Change of pressure in the primary and secondaryair between stations 1 and 2 may be calculated byusing eq 10 and 11, and these changes are shown infigure 7, b.

Loss of pressure in the primary zone is

(38)

and in order to evaluate 38 it is necessary to expressq2t p in terms of-gi. By Bernoulli's equation, eq 1,q2t p may be written

Q.2,p=(pi— P2)P+qi, (39)

and since (Pi—p2)p is determined by eq 10, eq 38and 39 may be combined to yield:

(P2 — Pd)p = ^ (40)

This was evaluated and is plotted in figure 7, c.As it is considered that the pressure is uniform

across station 3, Pz,s=P\P and (p2—p^)s may bedetermined as follows:

(P2 — Pz)s= (Pl—P2)p+ {P2 — PZ)P— (P1—P2),. (41)

All of the terms on the right side have been evaluated,and their sum is plotted in figure 7, c.

The magnitude of this pressure change is variableover the operating range, and the variation is accom-plished by changing the opening of the adjustablethrottle shown in figure 6. The pressure change isexpressed in terms of qh but it is also of interest todefine the change of pressure with respect to q2>s, asthis may be of aid in the design of the throttle.Equation 9 is the relation between #i and q2>s, and itmay be applied for this purpose as follows:

<[2,s

2— Pz)s gl

gl Q2,s(42)

This relation was evaluated and (p2—pz)s/q2,s isplotted versus TJTi in figure 7, d. When thethrottle is opened, the fraction of air going into theprimary zone decreases, thereby decreasing TA/Ti.If the throttle were removed entirely (A_p4 — 0),TJTi would be about 1.8. Lower values of T±\Tlcould only be achieved by decreasing T3tP/Ti or byinsertion of a throttle in the primary zone.

Change of pressure due to mixing of the secondaryand primary streams may be calculated by eq 19to 22. The term rf3 in these equations for this caseis equal to D, and when this substitution is made,(Pz—Pi)/qi can be evaluated. Figure 7, e, is aplot of this quantity. The over-all change of pres-

288

sure, (pi—Pi), which was evaluated by adding thesuccessive changes, is plotted in figure 7, f.

Loss of total pressure may be determined by eq 23.When qjqi, expressed by eq 20, is substituted in 23the following relation is derived:

<Zi 2,4 T4

T V(43)

This was evaluated and is plotted versus TJTi infigure 7, g. Inspection of this curve reveals that theloss is substantially higher than in the previouscase at the higher values of TJTX. The previouscase was calculated on the basis that pressure waslost due to friction in the primary zone, but in thiscase none was assumed. In any practical applica-tion of a chamber of this type, some means of stabi-lizing the flame would be necessary, and this wouldintroduce loss of pressure in the primary zone. Themagnitude of the loss of pressure required in serviceprobably would be comparable to that in the con-ventional chamber. If this loss had been considered,the over-all loss of total pressure would have beenhigher than indicated in figure 7, g, and higher thanthat of the conventional chamber.

The ratio of the velocities of the primary and sec-ondary streams at station 3, Vz,P/VZf,, was evaluatedand is plotted in figure 7, h. This ratio increaseswith T4/7\, and if this increase is a sign of an increasein the effectiveness of mixing, uniformity of temper-ature in the exhaust will be good in this chamberunder conditions of maximum temperature rise.

The problem of control in combustion chambersof this type would be more difficult than that of aconventional chamber. A mechanism would be re-quired to adjust the throttle in the secondary air inresponse to change of T4 or to change of over-all air-fuel ratio. Another method, analagous to that usedin reciprocating engines, would be manual control ofthis throttle, with fuel rate automatically controlledin accordance with throttle opening. The problemsof manufacture, installation, and maintenance wouldbe more complicated, but improved performance overa wider range might compensate for the addedmechanical complications.

5. Experimental Program

The specifications for the preceding analysis werechosen with the thought that experimental workwould be undertaken to check the results of theanalysis. It is relatively simple to match experimentand analysis insofar as the physical size of the cham-ber and temperature rise therein are concerned, butdeviation in other respects probably would influencethe results. The mere fact that combustion occursrequires addition of mass (of fuel) to the flowingstream. Specific heat is not independent of temper-ature, loss of pressure due to friction cannot belocalized, and exchange of heat between primary andsecondary streams before mixing cannot be pre-vented. Although uniform velocity can be providedacross the plane of the chamber entrance in the ex-

periments, the flow will take up a nonuniform dis-tribution at other stations. Operation of the cham-ber at a finite velocity of flow would also introducesome deviation due to compressibility, but not ofserious magnitude if the flow Mach number is notabove 0.1. Influence of compressibility on the flowrelations is discussed in detail in reference [3]. Somedeviation between theory and experiment is to beexpected, but probably is not of serious magnitude.

5.1. Experimental Apparatus

The experimental combustion chamber was con-structed of standard 6 in. pipe with a 4-ft coaxialliner, 3%6 in. inside diameter and a wall thicknessof Ke in. The pipe was cut and flanged as illustratedin figure 8 for accessibility to the liner. A schematicdrawing of the system, in which the location of thestations is shown, is also presented in figure 8.Dimension X was 10 in. in the experiments on flowand heat release, and 8 ft in the experiments onmixing. Uniform velocity across the plane of theentrance to the chamber was provided by a nozzleof 12-in. diameter at the inlet and 6 in. at the outlet,or chamber, end. Throttles were placed in thesecondary or primary zones as required to controlthe air distribution between zones. The throttlein the secondary zone was made of two thin annulicontaining equally spaced %-in. holes. Rotationof one annular plate with respect to the other con-trolled the opening and thereby the distribution.Throttles in the primary zone consisted of disks withvarious sized holes at their centers.

Flow of air to the chamber was metered by acalibrated orifice located in the system far upstreamfrom the burner. Liquid propane flowed from aweighing tank through a rotameter to a vaporizertube in the shape of a hairpin mounted in the systemfar downstream from the liner. Gaseous propanefrom the vaporizer flowed to the multihole fuelinjector located in the liner about 6 in. downstream

© © ®©INLET TO FUEL t FLAME r SPARK ELECTRODE

INJECTOR X H O L D E R / VALVE•THROTTLE

(B-C) = 48", MIXING ZONE

FIGURE 8. The experimental chamber.

289

from station 2. The injector was made of threeconcentric but not coplanar rings of tubing mani-folded together and drilled with numerous smallholes. The injector shown in figure 8 was usedonly in the preliminary experiments and was madeof two concentric rings. Mixing of the fuel withprimary air took place between the injector andflame holder, and the flame was initiated by a sparkat the flame holder. The spark was turned offafter smooth combustion was established and theflame was stabilized at the flame holder. The flameholder was a ring of triangular cross section, 2%-in.outside diameter and l)s-in. inside diameter. Itwas placed 18 in. upstream from the end of theliner (station 3). A water-cooled valve was placedat the outlet of the pipe system, and this was usedto control the chamber pressure.

Initial attempts to operate the chamber wereuniformly unsuccessful because of rough or inter-mittent combustion. Numerous changes in theprimary zone and downstream portions of the systemmade no improvement whatsoever, and it was notuntil an orifice plate was installed 5 ft upstream fromthe nozzle that smooth combustion was possible.This orifice plate was replaced by one perforatedwith numerous smaller holes, and all experimentsreported herein were made with this plate in thesystem. It is probable that this improvement wasdue to change of the effective length of the columnof gas in the system.

Instrumentation was added for the measurementsof temperature, pressure, and flow in the chamber.Total-pressure tubes were installed at stations 1 and2p. A pitot-static tube was also used at station 2p.Static-pressure wall taps were located at stations0,1, 2p, 2s, 3s, 3p, and 4. Temperature was measuredat station 0 and also at a point far downstream fromstation 4 by silver-shielded Chromel-Alumel thermo-couples. The pipe system contained two right-anglebends beyond station 4 to insure that the gas waswell mixed by the time it reached the last thermo-couples. The reading of this thermocouple was con-sidered the average temperature of the exhaust gas,T4. Some tests were conducted with insulationaround the pipe beyond station 3 to determine themagnitude of the heat loss from the system. Tem-peratures in the system were high, and the pipe wasnot insulated in the majority of tests because ofpossible damage to the system by the prevailinghigh temperature.

oINCH

FIGURE 9. Iridium—iridium-rhodium thermocouple

In the experiments in which mixing of primary andsecondary streams was studied, most of the aboveinstrumentation was removed to prevent interferencewith the flow distribution in the chamber. Con-siderable trouble with asymmetrical flow conditionsin the mixing zone was experienced, and it wasnecessary to rebuild the system on this account.The wall thickness of the liner was increased to 3/32in., and the liner was mounted coaxially in a 21-ftlength of 6-in. pipe. Dimension X, figure 8, inthese experiments was 8 ft. Elimination of flangedjoints in the vicinity of the liner by this means madesubstantial improvement in the mixing zone. Theliner of heavier construction warped less, and thisalso probably helped to improve the conditions forthe mixing study.

Instrumentation in the mixing zone of the chamberconsisted of water-cooled total-pressure tubes, bareChromel-Alumel thermocouples of 22-gage wire, andiridium—50 percent iridium, 50 percent rhodium(Ir-IrRh) thermocouples of about 20-gage wire.Three of the Chromel-Alumel thermocouples weredriven by electric motors to traverse the pipe at aspeed of 2 in./min. This was equal to the chartspeed of the temperature recorder, and by this meansa full-scale profile of temperature was obtained.One motorized couple was located 32 in. and 2 were48 in. from station 3 and at right angles to each other.Other Chromel-Alumel thermocouples were handoperated, and were located in the mixing zone be-tween the motorized couples.

In order to measure the higher temperatures in themixing zone, Ir-IrRh thermocouples [4] in water-cooled supports were used. One of these thermo-couples with its support tube is shown in figure 9.In this instance the wires are bent at right angles tothe tube in an effort to gain depth of immersion inthe gas. Only one bent couple was used, othersprojected straight into the stream at least %6 in.These Ir-IrRh couples were operated by hand andwere used in the first 32 in. of the mixing zone.

5.2. Experimental Procedure and Results

The burner was ignited at an air velocity at sta-tion 1 of about 20 ft/sec, and after smooth combus-tion was established, the rates of air and fuel wereincreased simultaneously until the velocity at station1 was about 60 ft/sec. Measured temperature atstation 4 was maintained nearly constant during thisoperation because this would indicate nearly con-stant fuel-air ratio in the primary zone (at a giventhrottle opening). Injection of the propane vaporthrough the multihole injector provided nearlyhomogeneous mixtures of air and fuel. Limits ofsmooth combustion in homogeneous mixtures arenarrow, and the method of control was useful inkeeping within the limits while changing conditionsin the burner. After the burner was brought nearthe desired operating condition, final adjustmentswere made of fuel and air rates and burner pressurelevel. The fuel was adjusted until the burnersounded smoothest. This criterion did not neces-sarily guarantee the same fuel-air ratio in the primary

290

zone in all tests, but it was adopted because opera-tion otherwise (under conditions of resonant com-bustion) would affect adversely the accuracy of themeasurements of flow and pressures. Althoughresonance was not eliminated completely, the dataindicate that its effects were reduced to a tolerablemagnitude.

Because the primary zone was operated at nearlyconstant mixture ratio, the desired range of condi-tions of over-all temperature rise was attainedthrough the use of throttles.

The rate of air flow was about 1.25 lb/sec in themajority of tests. Temperature of the air variedfrom 560° to 610° R, and pressure generally wasabout 1.5 atmospheres absolute. Some variationfrom these conditions was tried but with no effect onthe results.

Dynamic pressure, q_\, at the inlet to the chamberunder these conditions of flow was about 1.2 in. ofwater. Temperature ratio in the primary zoneTz,p/Ti, was calculated to be in the range of 6.6 to 7.1,for mixtures of 0.06 part of gaseous propane and 1part of air by weight over the range of values of Txmentioned.

Experimental work on the chamber was dividedinto two parts, one in which problems of flow andheat release were studied and the other in whichmixing of primary and secondary streams wasstudied. Results of the former will be describedfirst.

a. Experiments in Flow and Heat ReleaseAs mentioned before, fuel rate was adjusted in

these experiments until combustion was smoothest,and consequently the fuel-air ratio in the primaryzone was not constant in all tests. Tests in which

06

0.5

"~w 0.4

J-03

the metered fuel-air ratio was 0.06 ±.005 were se-lected, and the results of these tests are reportedherein. Selection by this rule reduced the spread ofthe data somewhat and did not change the basicrelations.

Values of measured average temperature (T±) aftermixing of the gases by passage around two bends inthe system indicated either low combustion efficiency(85 to 90 percent) or large heat losses. Analysesof the mixed outlet gas in three tests by a gravimetricmethod [5] indicated a combustion efficiency of 98percent, while a heat balance based on T4 and theassumption of an adiabatic system indicated effi-ciency of about 90 percent. When insulation wasinstalled around the pipe beyond station 3, efficiencybased on T4 ranged between 92 and 100 percent,and it was concluded that loss of heat from the systemwhen uninsulated was large. Prevailing tempera-tures in the system were high, and it appeared advis-able to operate without insulation for reasons ofsafety. On the assumption that the low values ofefficiency were caused by heat loss and not by poorcombustion, data in this report are based on tempera-ture T4 calculated on the basis of 100-percentcombustion of the mixture of total air and fuel.Cool secondary air contacted the walls of the 6-in.pipe down to and somewhat beyond station 3, andit is expected that loss of heat from the gas down tostation 3 and somewhat beyond would have beennegligible. The majority of the observations weremade in this upper section of the burner, and this isconsidered a justification for ignoring the heat loss.

Results of the tests are presented graphically infigure 10, and results of the last analysis (fig. 7) areincluded for comparison. The portion of the air

rIwf/wp

f t

o

*

s*—.•

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(b)

•

o

s

50

40

• •

(c)

•

y•

—

(d)

/

IO

8

f 6c? 4'roS. 2

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y30

w 20

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3

FIGURE 10. Results in the experimental chamber

291

1.0

0.8

0.6

0.4

^" 0.2

? 0.0

-0 .2

-0.4

-0.6

-0 .8

i n

•

•

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••

/

/

'/

•

/

•

/

0 0 0.2 0.4 0.6 OB 1.0 1.2 14 1.6 1.8

FIGURE 11. Static and dynamic pressure changes in theprimary stream.

that entered the primary zone, figure 10, a, wasdetermined from pressure q2)P given by a pitot-statictube at station 2p in the primary zone, or by thedifference of pressure from a total head tube andstatic pressure wall tap. The data are displacedfrom the theoretical curve, but compare well withcurves based on known combustion characteristicsof propane-air mixtures. These curves were cal-culated for fuel-air mixtures of 0.055 and 0.065 inthe primary zone, which is the range in the testsreported. These curves take into account thevariation of specific heat with temperature and theadded mass of fuel.

Division of the air into primary and secondarystreams between stations 1 and 2 is accompaniedby pressure changes, and results of measurements ofthese are presented in figure 10, b. The data areagain displaced from the theoretical curve, but thesame general relationship as predicted by Bernoulli'sequation is evident. Some of the displacement isfor reasons enumerated above. A comparison of themeasured data for the primary stream with the curvecalculated from eq 1 is presented in figure 11, wherethe line represents the equation. In general itappears that the equation is applicable. Becausemagnitudes of the pressures are small, and anyeffect of resonant combustion in the chamber onthe measurements would be large on a percentagebasis, it is difficult to decide which of the readingsare correct. Several chemical analyses of the exhaustgas at station 3p were made, and the fuel-air ratioscalculated from these analyses were in good agree-ment with those calculated from values of q2tP derivedfrom eq 1 and the observed value of (pi~p2)p/qi. Thisis not regarded as conclusive evidence that measured

18

16

14

Q.

I 1 2

+ 10

CO

o.

r*—" i A

2l

0

/

/

•

••

••

X-0T3,p/Ti)-i]2+2-

/

•

•> • •

•

.02 .04W f /W.

.06 .08

FIGURE 12. Pressure drop in the primary zone.

values of (pi—p2)p were always correct. Thesechemical analyses also indicated essentially com-plete combustion (based on oxygen consumed)across station 3p, and it was concluded that theflame holder was not too close to station 3.

Change of pressure between stations 2 and 3 in thesecondary- zone is plotted in figures 10, c, and 10, d, andthe data, although displaced from the theoreticalcurves, are in good agreement with the theory. Pres-sures between these two stations were also measuredin the primary zone, and these are compared to thosepredicted by the conservation of momentum equationin figure 12. In this figure observed values of(P2—Ps)P/g_2y v were plotted versus fuel-air ratio in theprimary zone, and the theoretical curve is based oncalculated values of flame temperatures of propane-air mixtures. Velocity, and therefore dynamic pres-sure, in the primary zone is increased by the additionof fuel to the air stream, and observed q2,p was cor-rected as indicated in the figure to account for this.Observed pressures were not corrected for the mo-mentum of the fuel, which in these experiments wasinjected downstream with a pressure drop in the in-jector of from 20 to 60 lb/in.2. With no burning, ob-served pressure drop was about 2q2tP, which is due tofriction in the primary zone. This value of 2q2tP wasadded to the theoretical to account for the frictiondrop. In the neighborhood of fuel-air ratio of 0.06,observed pressure drop is in good agreement with thetheoretical, but at lean condition the observed valuesare low. The reason for the low observed values isnot clear, but it could be either incomplete combus-tion in the primary zone or an effect of resonance. Ifcombustion were not complete in the primary zone,

292

it did go to completion between stations 3 and 4 be-cause observed values of T4 indicated normal com-bustion efficiency.

One of the basic assumptions in the analysis of theflow in the combustion chamber was that pressurewas uniform across the plane of station 3. Some de-viation from this condition was observed; it wasfound that pressure of the secondary stream exceededthat of the primary stream by about 0.1 q3,p in mostcases, and by as much as 0.3 qs,p in some. However,conditions at the static pressure wall tap may havebeen affected adversely by warping and scale forma-tion caused by the high temperature of the liner. Inany event it appears that the pressure differences arenot large enough to detract from the value of theanalysis on the basis of equal pressure. A strongflow of the secondary air into the primary jet is indi-cated by the surplus of pressure in the secondarystream.

Mixing of the two streams takes place beyond sta-tion 3, and the observed pressure changes betweenstations 3 and 4 are plotted in figure 10,e. Compari-son with the theoretical indicates that the observedpressure changes are large, probably because of wallfriction and turbulence caused by the velocity differ-ence between the primary and secondary streams.Measurement of the friction drop with no burningindicated it to be about 25 percent of the dynamicpressure of the stream, which is a normal loss for thislength of 6 in. pipe. During burning, average condi-tions of flow across the mixing section would give adynamic pressure equal to qxTAjTi, and hence thewall-friction drop on this basis would be equal to0.25 (Tt/TJft. If the data at the condition 77

4/771=4

is used as an example, the observed {jps—pSlQi w a s

about 1, and correction by the friction drop (Apjqi =0.25 274/!Ti = l) would lead to (pz—2>4)/ffi=0, which isto be compared to the theoretical value of —2. Thedifference is probably due to high level of turbulencein the mixing streams.

Over-all loss of pressure in the experimental cham-ber is plotted in figure 10, g, and compares well withthe calculated values.

b. Experiments in Mixing

The combustion chamber was operated over arange of values of TJT\ of from 1.5 to about 4 bychanging the size of the throttle and its position.Corresponding values of the velocity ratio, Vz>sJV3tP,were 1.5 to about 0.1. The mixture in the primary'zone was adjusted until it was on the lean side ofstoichiometric by observation of the flame tempera-ture while decreasing the fuel rate from the condi-tion of excessive richness. Observations of tempera-ture were made in the mixing zone after the leancondition was established to reduce effects of reac-tion of the flame gas with secondary air duringmixing. Only one measuring instrument was usedat a time to avoid disturbance of the flow.

Accuracy of the temperature measurements of thehot gases was not of a high order, because only arough calibration of the Ir-IrRh thermocouple was

available, and because corrections to the indicatedtemperature were large. At high temperature, heatlost by radiation is large, and consequently thejunction would be at a temperature lower than thatof the gas. Corrections were calculated by a methodthat is based on the assumption that the heat lostfrom the thermocouple by radiation is equal to thatgained by forced convection. The equation bywhich the corrections were determined is

J- gas TiKad* (44)

Tt is the temperature indicated by the thermo-couple, TwaU was assumed equal to the gas tempera-ture next to the wall of the pipe, hrad is Stefan'sradiation constant (1.7X10"9 Btu/ft2/°R4 hr), hconv,is the coefficient of convective heat transfer. Forbare thermocouples, heonv=225^G/6 Btu/ft2/°R hr,which is an empirical relation to take into accountthe effect of mass rate of flow G expressed in poundsper square foot per second. A quick determinationof the emissivity, e, of the Ir-IrRh thermocouplesindicated it to be 0.26, and e for the Chromel-Alumelthermocouples was considered to be 0.9.

As an example of temperature arrived at by thismeans, temperature of the flame gas at station 3,TZtP, in 13 tests averaged 4,350 °R with a rootmean square deviation of 140° F. This averagetemperature is about 300° F greater than the cal-culated flame temperature of a propane and airmixture near stoichiometric condition. It is notknown whether the calculated corrections were toolarge or whether the calibration of the thermocoupleis responsible for the difference. Some of the devia-tion mentioned was probably caused by inability tomaintain the same fuel-air ratio in all tests.

Some measurements of dynamic pressure were alsomade in the mixing zone, and velocity was calculatedfrom these measurements and observed tempera-tures and static pressures.

In the description of the experimental results thatfollows, the data were correlated with the ratio ofvelocity of the secondary to primary stream, Vz, s/VZt p.The values of this ratio reported were estimated fromthe observed rate of fuel injection (on the assumptionof a constant fuel-air ratio of 0.062 in the primaryzone) and the observed temperature and pressure inthe chamber. The difference between these estimatesand some measurements was not larger than 10percent. Because the velocity measurements werenot considered accurate, the estimated values wereaccepted as adequate for the present purpose.

1. Axial Distribution of Temperature. Mixing ofthe primary flame gas and secondary air takes placein a system bounded by the walls of the 6-in. pipe,and the gas will approach an average or mixed tem-perature T4 as it travels downstream from station 3.Temperature at the axis of the burner, Tr=0> wasexpressed in the dimensionless form (Trss0—TA)/(T3 v— T4) and correlated with distance x from station3 by an empirical equation similar to that derived by

293

Pai [6] for two-dimensional jet mixing. The equationinvolved the probability integral, as follows:

3, V

The first member of eq 45 represents experimentalobservations (at various values of x), and values of zwere selected to make the two members of the equa-tion equal.

In these experiments it was not possible to makeaccurate measurements of T4, because both velocityand temperature gradients existed in the stream, andno bends were used in the system to mix the gas.Previous experiments in which mixed temperature,T4, was measured, indicated relatively large heat lossfrom the system. These measurements were madedownstream of the mixing zone, and if these wereused as a guide to establish T4 in the present experi-ments, T4 by this method would probably be lowerthan the true value at station 4. Calculation of T4on the assumption of 100-percent combustion effi-ciency, and no heat loss would give high values.Both methods were used to establish values of T4,and although some difference was noted, the correla-tion obtained was not basically changed. The wallof the pipe was relatively cool in the first half of themixing section, and it seemed logical to conclude thatT4, based on 100-percent combustion and no heatloss, was nearer the true value, and this value of T4was used in the correlation to be described.

Values of z in eq 45 were determined from theobserved axial temperature at various values of x,and these values of z were plotted against the corre-sponding values of x. It was,found that plots of logz against x/rz,p, where rz,p is the radius of the liner,could be represented by straight lines. Plots of thiskind are shown in figure 13 for three different condi-

tions of Vzt8IVztV<^\. The three lines have the com-mon point 2=1.5, x/rztP=9, and therefore a generalequation can be written

In z=— (46)

where k is a constant, and c is the slope of the lines.When VzJ8Vz,p>l, the same relationship was ob-served, but only two out of five tests gave plots thatpassed through the common point.

A Maclaurin expansion of the probability integralwould indicate that (Tr=0-TA)/(ThP-T4) = z to afirst approximation. This approximation is goodwhen £<0.7, and in this range temperature can beapproximated by

7 7 7 / 7 7

•z=ke-cx<rB.v, (47)

and differentiation of this would lead to

t -L 4

dx(48)

and from this it appears that c is a measure of theeffectiveness of the mixing in bringing the tempera-ture at the axis to the mixed temperature T4.

Slope c was correlated with Vz,8/Vz,p in figure 14,and the data suggest a parabolic relationship, with ca minimum at a velocity ratio of unity

These results have been presented thus far withoutreference to or comparison with the theory of mixingof jets. The mixing of streams, different in bothtemperature and velocity, has received very limitedattention, and consequently the present results willbe compared with the theory for incompressible flowpresented in reference [2] and utilized in a previous

2.0

i.o0.90.8

0.7

0.6

^0.5

0.4

0.3

0.2

OJ

(A) Vt,sl

\

C= -.167

V\

\\ -\° \

\

A

20 25 30 5

\

C=-|40

\\

\

\

\

\

\

B

\

\

C=-.IO8* \

\

•

\• \

<

c

9\

15x/r.

20 25 30 5 10 20 25 30

FIGURE 13. Correlation of axial temperature with distance hy the probability integral.2; T4/Ti=3.8. (B) V3ft/Vi>p=0.17; T4/Ti=3.3. (C) T'WT/3.P=0.38; 7VTi-2.3.

294

section of this report. A comparison will be pre-sented also with the recently presented experimentalresults of Forstall and Shapiro [7] obtained in thestudy of coaxial streams at a common temperature.It is expected that differences shown by the compari-sons would be caused by the large difference of Tem-perature or density between the streams in the pres-ent experiments. Hereinafter, comparison with thework of Squire and Trouncer [2] is referred to as acomparison with the theory, and the results of For-stall and Shapiro are referred to as the "other experi-ments. "

Figure 15 is a comparison of the characteristics ofthe mixing as observed along the axis of the burnerwith the theory and also with the other experiments.Because a jet in a general stream would mix andeventually approach the properties of the stream, thedimensionless fractions of temperature (and velocity)contain the temperature (and velocity) of the sec-ondary stream in order to make the comparison.In general, it may be said that in the medianrange, temperature expressed this way varies in-versely with axial distance, and this is in agreementwith the other experiments but not with the theory.

At the condition of V3fS/V3tP=0.375, limited infor-mation about axial velocity in the mixing zoneindicates that it is transferred at a slower rate thantemperature. Three other tests at the conditionV3fg/F3>p=0.25 also indicated this. Comparison ofthe data on velocity with the other experimentalresults indicates a somewhat slower rate of transferin the present experiments.

When V3JV3fP was 0.125, the data show thattransfer of temperature in the present experimentsapproximates that of velocity in the other experi-ments. However, in the expectation that velocitywould be transferred in this case also at a slower ratethan temperature, it appears that the rate of transferis less in the present experiments than in the otherexperiments. One set of data points in this figurewas for the condition V3JV3tP=0.18, and this was

1.6

> 0.8

O4

o

\

c

1̂ —•08 JO •12

- C

.14 .16 .18

FIGURE 14. Effectiveness of mixing.

included because it illustrates more clearly theinverse relationship of temperature and distance.In this system temperature approaches T4 as mixingbecomes complete, not Tu and the completely mixedcondition would be attained when (Tr=Q— Tx)l(T9iP-T1) = (TA-Tl)/(T3iP-T1). The latter frac-tion is 0.47 when F3,,/T

/3,J,=0.125, and the x data

points show the beginning of a slower approach oftemperature (at the lower values) to the mixed con-dition. At V3tS/V3>p=0.18, the fraction was 0.33,and the slower approach to the mixed conditionoccurred downstream from the place where theobservations were made in this case.

It will be noted that the straight lines wereextended to a value of unity for the temperaturefraction, and at both conditions of V3JV3iP<Cl theaxial distance is about llr3>p. This same value ofllr3yp was noted when V3'S/V3ip was 0.55, whichleads to the conclusion that the burner can beassigned a characteristic length. The general inverserelationship of temperature and axial distance, andthe characteristic length, would be of general utilityin making an approximation of the temperaturefield. In the theory the extent of the potential coreof velocity is variable, whereas in the present experi-

30 40 50 60

FIGURE 15. Axial temperature and velocity distribution., Temperature; , velocity.

295

i I i i r

0 4 .8 1.2 1.6 2.0 24 2.8 0 .4 .8 1.2 1.6 2.0 2.4 2.8

FIGURE 16. Lateral temperature profile.Cosine curve; , Tollmien's curve; # , x/n,p=9; X, z/r3,P=18;

O / = l l ; A, x/n,p=27.

ments it appears that the extent of the potentialcore of temperature (for purposes of approximation)can be regarded as constant.

Data at the conditions of T73tS/T73>2,>l are also

included in figure 15, but comparison is not possiblebecause this condition is not investigated in refer-ences [2 and 7]. The same inverse relationship isevident, but here there appears to be no evidence ofa characteristic length.

2. Lateral Distribution of Temperature. Numeroustraverses of temperature were made in the mixingzone of the chamber to investigate the lateral spreadof temperature in the two coaxial streams. Thegeneralized profiles were compared with that of thecosine curve as assumed by Squire and Trouncer in[2], and with that calculated by Tollmien [1] for afree,round, incompressible jet. Tollmien also used themomentum transfer theory and assumed that mixinglength was proportional to the width of the mixingregion. However, the calculations were based on theassumption of a point source, and therefore in prac-tice similarity of profile would not be reached untilaxial distance became large compared to jet size.

Four profiles of temperature are presented infigure 16 to illustrate the shape over the range ofoperating conditions. In some of the runs, tempera-ture of the secondary air, T3tS, was measured just

before the point of mixing, and, as expected it wassomewhat higher than the inlet temperature Txbecause of heat transfer from the primary zone.Two profiles of temperature in figure 16 were cal-culated by using these measured values of T3>5.Effect of this change to TZtS was a slight shift of thedata points to lesser values of the temperature frac-tion and to greater values of the radius fraction.

At high relative velocity of the primary stream,the edge of the mixing region intersects the wall ofthe 6-in. pipe in which mixing takes place at rela-tively small values of axial distance, and conse-quently the profiles are not complete. Also, themixing downstream of the point of intersection is nolonger in free streams, and the validity of comparisonwith mixing in free streams is questionable. How-ever, some information can be gained by a compari-son, and it is presented with this limitation in mind.

At an axial distance of 9 r3tP, the profile of tempera-ture is in good agreement with the cosine curve, butat greater distances there is a tendency to approachthe distribution predicted by Tollmien. The experi-mental velocity profiles of ForstaH and Shapirowere a good match* with the cosine curve at alldistances studied. Ratio of velocity of secondary toprimary streams does not affect the shape of thetemperature profile.

Although the shape of the profile tends to changewith axial distance, the magnitude of the radius ofhalf temperature rm is a good indication of the widthof the mixing region and is plotted versus axialdistance in figure 17. Theoretical results of Squireand Trouncer for velocity are included for compari-son. Experimental findings of Forstall and Shapiroagreed well with the theory and are therefore notincluded in the figure.

At the condition V3,8/V3tP=.125, rm increasesslowly in the region of the potential core, which inthis case extends downstream a distance of 11 r3p,compared to about 8 r3p in the theory. It is to benoted that at the end of the potential core of tem-perature rm, is 1.1 r3tP, and therefore the width of themixing region would be about 2.2 rs>p if it were notcut off by the 6-in. pipe (width=1.7 r3tP)< Beyondthe potential core the experimental data are not asconsistent, but it may be said that rm grows approxi-mately as predicted in the theory. With respectto the two points of largest rm, these also are nom-inally beyond the wall of the 6-in. pipe. However,in these instances the center line of the profile wasoff the center of the pipe enough to measure theseradii on one side of the traverse. This asymmetryhas been one of the major troubles in these experi-ments. Unknown changes in the configuration ofthe burner, possibly due to high prevailing tempera-tures, cause asymmetry and shifts of the centerlines of the traverse. If the curve as drawn repre-sents the data, then the constant of proportionalityC in the analysis would have to be less than 0.0067by about one-third to bring the theoretical resultsin agreement with the present experiments. Therate of mixing on this basis is correspondingly lowerthan in the theory and in the other experiments.

296

2.5

2.0

1.0

0.9

<X8

V3,s/ V 3.P- 1 2 5

^ ^ —V

S.8TC2=.OO6^

•

FIGURE 17. Half-boundary of mixing., Temperature; , velocity.

At the condition VzJVz>p=.375, the extent of thepotential core is also about llr3>p, but rm convergesto a value of about 0.85 rdyp. At this point the mix-ing region extends to the wall of the pipe (1.7 r-6,p)and therefore mixing downstream is influenced bythe pipe. In this downstream region, rm divergesapproximately as predicted by theory but again atgreater values of axial distance. Radius of halfmaximum velocity was compared to that of tem-perature in three runs and was less by about 5percent, which confirms the conclusion that tem-perature is transferred at a greater rate than velocity.

Data are also included in figure 17 on the radiusof half maximum temperature when velocity of theprimary stream was low compared to the secondarystream (VstJV^tP=l.l and 1.5). Convergence inthe region of the potential core is pronounced, anddivergence begins again at an axial distance of about11 r3tP. In all three cases in figure 17, divergencebegins at an axial distance of about 11 rSfP, and thisis considered additional evidence that the chamberhas a characteristic length.

Two runs in which VstS/VztP was 1.1 were made toshow the effect of velocity difference between theprimary and secondary streams, and data from thesetests are also included in figure 17. Curves werenot drawn through the data points in these two runsin which the mass rate of flow differed by 65 percent.

1.0

0.9

0.8

0.7

0.6

»- 0.4

0.3

0.2

0.1

0.0

V / V j e t

(

/jr C

t

%^ o

(

'I/•

Ly/°

/f

o

-2.0 -1.6 -1.2 -0.8 -0.4<Ty/x

0.0 0.8

FIGURE 18. Free jet boundary.O, z/r3(P=4.50; • , x/n,p=6.75; <r = 12.

Because the rate of flow differed by 65 percent,(yz,s—Vz,p) also differed by this amount. Threeout of four comparisons of rm show that the magni-tude of V3iS— V3tP has little affect on the field. Atan axial distance of 18 r3<p, the maximum temperaturewas beyond the range of the temperature recorderin one of the runs, and consequently the radiusplotted (broken circle) is somewhat greater than thetrue value. It is expected that agreement would bebetter than indicated in figure 17 at this axial dis-tance. On the basis that rm is not affected, it isconcluded that velocit}7 ratio, rather than velocitydifference, determines the mixing field. This sameeffect was evident in another comparison in whichVst8 was about 0.1 V3t?. Forstall and Shapiroreached this same conclusion.

In the region of the potential core, it may be saidthat the mixing region approximates that of a two-dimensional region between semiinfinite movingstreams differing in both temperature and velocity.In recent years the problem of mixing in the two-dimensional case, with the mixing region boundedon one side by a quiet body of gas, has received con-siderable attention. Tollmien [1] presented a cal-culation of the velocity profile for incompressibleflow, and much of the experimental work has beenbased on the determination of a scale factor <r tomatch the experimental with the theoretical profile.The magniture of a may be regarded as an inversemeasure of the rate of mixing.

A comparison of the temperature profile in theregion of the potential core with Tollmien's profile

297

of velocity in a free jet boundary is presented infigure 18. A test in which Vz,slVz,v was 0.12 wasselected as it was the nearest approach in the presentseries of experiments to the condition of still gas onone side of the mixing region. The other importantdifference is, of course, the large difference of tem-perature and density between the streams in theseexperiments. It appears that a value of <r=12brings a fair correspondence between the data andthe curve. Liepmann and Laufer [8] report a valueof 12 based on their own and other measurements ofvelocity in a subsonic jet. However, the conditionsdiffer in several respects as mentioned, and no firmconclusions can therefore be drawn about therelative mixing rate, and these data are presentedmerely as information. Values of a were also de-termined when T/73,s/F3,p was larger than unity, andthese ranged as high as 18.

6. Conclusion

The problems of flow, heat release, and mixing inan equivalent gas turbine combustion chamber havebeen examined analytically. A large primary zoneis advantageous, but the area is limited to about 60percent of the total cross-sectional area. Practicalexperience has also led to the use of chambers ofabout this size relationship. Method of controlcurrently used, although no doubt simple, leads topoor mixture quality in the primary zone and there-fore puts a burden on the combustion process, whichexperience shows it cannot always overcome. Re-quirements for and effects of a possible means ofmixture control are determined analytically. Ex-perimental work demonstrates that the analyticalmethod gives a good description of the flow, heatrelease, and mixing in the controlled combustionchamber. Although the control described wouldcomplicate the structure of the chamber, improve-ments in combustion could be a compensation.

Study of the mixing of primary flame gas andsecondary air, and comparison with other studies ofmixing reveals a general similarity. Ratio of veloc-ity ol the streams, not the velocity difference,determines the field of mixing, but the shape of thegeneralized profile of lateral spread of the mixingregion is not affected by velocity. Temperature istransferred at a greater rate than velocity, and thisconclusion also appears to be general in other studies.Some difference is noted, in that the combustion

chamber has a characteristic length that may beregarded as the extent of the undisturbed potentialcore of temperature of the primary stream. In theincompressible case the extent of the core of velocityis variable with velocity ratio. In the region of thepotential core a convergence of the radius of halfmaximum temperature is noted, while under similarconditions in the incompressible case there is adivergence. Beyond this region, the radius of halfmaximum temperature appears to have the normaldivergence. Axial distribution of temperature issimilar to distribution of velocity, and when ex-pressed with reference to the temparature of thesecondary stream, an inverse relationship with axialdistance is obtained. This inverse relationship,which holds without regard to velocity ratio, is ofgeneral utility in the determination of the tempera-ture field, especially when it is noted that thechamber has a characteristic length. On the basisof rate of approach ol axial temperature to averageor "mixed" outlet temperature, the mixing process isleast effective when the velocities of the streams areequal. Comparison of the field in this with that inthe incompressible case leads to the conclusion thatthe effect of the large difference of temperature ordensity between the streams is to retard mixing.

7. References[1] W. Tollmien, Calculation of turbulent expansion pro-

cesses, translation, Natl. Advisory Comm. Aeronaut.Tech. Mem. 1085 (1945).

[2] H. B. Squire and J. Trouncer, Round jets in generalstream, ARC (Gt. Brit.) Report 1974 (Jan. 1944).

[3] F. R. Caldwell, F. W. Ruegg, and L, O. Olsen, Combustionin moving air, SAE Quarterly Transactions 3, 327(1949).

[4] Wright Field Central Air Documents Office, An experi-mental Ir-IrRh thermocouple with cooled support,July 1949, Air Technical Index No. 58661.

[5] F. W. Ruegg and C. Halpern, Gravimetric analysis ofexhaust gas from gas turbine combustion chambers,J. Research NBS 45, 113 (1950) RP2117.

[6] S. I. Pai, Two-dimensional jet mixing of a compressiblefluid, J. Aeronaut. Sci. 16, 463 (1949).

[7] W. Forstall and A. H. Shapiro, Momentum and masstransfer in coaxial gas jets, J. Applied Mech. 17, 399(1950).

[8] H. W. Liepman and J. Laufer, California Institute ofTechnology, Investigations of free turbulent mixing,Natl. Advisory Comm. Aeronaut. Tech. Note 1257(1947).

WASHINGTON, July 2, 1952.

298