a design method for the dilution zones of

8/12/2019 A Design Method for the Dilution Zones Of

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m,mnm 16 my. mi' ^ N O T E A E R O NO. I 6 9W130 1OOH3S590H l^^ ' i i


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CoA Note Aero. No. 169February, 196i

1 -22S ?JK_^59 y^^ 2DEPARIMENr OF PROPUIBION

'A design method for the dilution zones ofgas turbine combustion chambers'

- by -A.H.Lefebvre,B.Sc.(Eng.).,D.I.C., Ph.D., M.I.Mech.E., F.R.Ae.S.,

andE.R. Norster, D.C.Ae.

The substance of this Note vas contained in a CoA Memo entitled'Aerodynamic influences on dilution zone design', vhich had a limitedcirculation in September, 1965.


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ContentsPage No.

1. List of Symbols 12. Introduction and Summary 55. Dilution Zone Design Procedure 5

MStep 1. Determination of Ratio r:^ kMStep 2 . Determination of flametube pressure .loss factor ^ fStep 5' Determination of 5Step 4. Determination of r ^ 6anStep 5 Determination of dilution hole area and /-drag coefficientStep 6. Determination of dilution hole diameter 7Step 7- Determination of dilution zone length 8

k. Definition of Aerodynamic Performance 105. Conclusions 116. References 12

Figures


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ListofSymbolsA = maximum cross-sectional areaofouter casing, ins^.D = diameterorwidthofouter casing correspondingto A, ins.

i.e.A k - '^ '^^tubular systems, and.A = 2nrD for annu la r and tubo -annu la r sys t em s, wherer i s th e mean ra d i u s of the cham ber.A_ = flametube area, ins^.f 'A = annulus area, ins^.an '

A = compressor outlet area, ins^.D_ = flametube outlet area, ins^.d = dilution hole diameter, ins.X = dilution zone length, ins.M = total chamberairmass flow,Ib/s.M = mass flowofcombustionproducts,lb/s.M = mass flowofannulus air, Ib/s.an ' '

(note:M= M + M )^ g an'V = velocityofcombustion products,ft/s.T = temperatureofcombustion products, **KgV = velocityofannulus air,ft/s.anT s= temperatureofannulus air,KV = dilutionjetvelocity, ft/s.JP2 = chamber inlet pressure, p.s.i.a.P3 = chamber outlet pressure, p.s.i.a.T2 = inlet temperature, ^T3 = mean outlet tonperature,KT = maximum outlet temperature, Kmax ^ '


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^2-3 overall pressureloss,p.s.i.a.^=-^^- pressure loss in diffuser, p.s.i.a.diff 'AP = pressure loss across flametube, p.s.i.a.

(Note:AP^i^^+ AP^ = AP2.3 )q = dynamic head in annulus, p.s.i.a.q = reference dynamic head, based en V .V >= mean velocity at A, ft/s.


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- 5 -Introduction and Summary

Perhaps the most important and, at the same time, most difficultproblem in the design and development of gas turbine combustion chambers,is that of achieving a satisfactory and consistent distribution oftemperature in the efflux gases discharging into the turbine. In thepast,experience has played a major role in the determination of dilution-zone geometry, and trial and error methods have of necessity been employedin developing the temperature-traverse quality of individual combustordesigns to a satisfactory standard. Experimental investigations intodilution-zone performance carried out on actual chambers have led touseful empirical-design data, but very often it has proved difficult orImpossible to distinguish the separate influences of all the variablesinvolved. Thus although it is now generally accepted that a satisfactorytemperature profile is dependent upon adequate penetration of the dilutionjets,coupled with the correct number of jets to form sufficient localizedmixing regions, the manner in which the total dilution-hole area isutilized in terms of number and size of holes is still largely a matterof experience. Unfortunately, more basic studies of jet mixing do notusually yield results that can readily be expressed in the parameterswhich are most familiar to those concerned with combustion-chamber design.How ever, some of these Investigations can provide a useful guide to therelationships involved.

One such investigation^resulted in the accumulation of a large amountof data on the mixing of cold jets when injected into hot streams underconditions where the temperature and velocity of the hot and cold streams,the injection-hole diameter, the angle cf injection, and the mixing lengthcould be accurately controlled and varied over a wide range. These dataare used here, firstly to demonstrate a logical method of dilution zonedesign and, secondly, to provide quantitative data on the rate of exchangebetween temperature traverse quality and the relevant design parameterssuch as dilution zone length, dilution hole diameter and pressure lossfactor. The effects of chamber inlet velocity and inlet velocity profileare also examined.Finally, it is proposed that the aerodynamic performance and stabilityof a combustion chamber may, for most practical purposes, be adequatelydescribed in terms of a parameter P w hich is the ratio of the flametubepressure loss to the overall pressureloss. Evidence is presented insupport of this proposal and its practical Implications are discussed.

Dilution Zone Design ProcedureAt this stage In the design process the overall pressure loss factorhas been established and the cross-sectional area of the outer casingdetermined. A tentative value for the flametube area will also have beenarrivedat,based on considerations of pressure loss and combustion performance,although it may need modification in the light of the results obtained fromthe following calculations.


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- k -

The dilution zone procedure is carried out in a number of stepswhich are described below in turn.Step 1. Determination of ratio /M

This is the ratio of the mass of the hot combustion productsentering the dilution zone to the total chamber mass flow. It dependsprimarily on the chamber inlet and outlet temperatures, T2 and T3respectively, and on the temperature of the combustion products, Tg.The actual relationship is shown graphically in figure 1 for a valueof Tg of 1,800K. It is considered that1 8001crepresents a nearoptimum value of Tg for the following reasons. If temperatures aremuch in excess of 1,800K, the gases will contain a high proportion ofdissociated products which could become chilled' on contact with thecold dilution jets and hence give rise to combustion inefficiency.On the other hand, if Tg is much below 1,800K, this necessarily meansthat too large a proportion of the total airflow has been injectedinto the flametube upstream of the dilution zone. In consequence,the amount of air left for the true'dilution process will be insufficientto achieve adequate penetration and mixing.

M R ,For any given design the relevant ratio of /M is read off figure 1,using the values of T2 and T3 corresponding to the maximum rating of theengine. This is the engine condition at which temperature traversequality is at a premium. It usually corresponds to a value of overallA.F.R. of somewhere between kOand 60. Thus,according to figure 1,/ Mwill normally lie between 0.i

Step 2 . Determination of fleimetube pressure loss factorThe total pressure loss of the chamber is equal to the svim of thepressure loss in the diffuser and the pressure loss in the flametube.Hence:

^Ps-? ^ dif f.. f - (1)


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- 5 -

T he f l a m e t u b e p r e s s u r e l o s s f a c t o r i s t h e n o b t a i n e d by r e - w r i t i n ge q u a t i o n ( l ) a s :^ = - ^ 3 - 3 _ ^ d i f f^ r e f ^ r e f ^ r e f

in which both terms on the right hand side are now known.^ fStep 5' Determination of ^'ân

The path and penetration of the dilution jets is governed largelyAPby the term ^ , which is the ratio of the pressure drop across theânflametube to the dynamic head in the annulus.We have

ân ^ref ân^ fwhere is the familiar flametube pressure loss factor based on the^ e f'reference' dynamic head.

i . e .AP AP /Vf f ^ f ref

h e n c ea n ^ r e f ^ a n

A P^ A P ^ , , ' ' ^ f / . ^ s\ n < l r ef ( l - ^/uf. . . (2 )

T he a b o v e e q u a t i o n i s s h ow n g r a p h i c a l l y i n f i g u r e 3 i n w h i c h c u r v e sAP^ ,, A^ M7aof /q pP ^ are plotted against /A for various values of / M .^refA P^ A^ MS i n c e / q , 7 a n d r ?^ a r e k n ow n , e i t h e r e q u a t i o n ( 2 ) o r f i g u r e 3 ni ay

A P ^b e u s e d t o d e r i v e .qa n


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- 6 -Step h. Determination of ^/V an

This term represents the ratio of the velocity of the hot gasesflawing inside the flametube to the velocity of the air in the surroundingannulus. It may be expressed quite conveniently in terms of S/ M and/ Afrom the continuity equation as shown below.

We have,V M p Ag f f a n . a nV M p A .an an g g1

K ^ V M - ' ' ^ * ( A ' -V A

1 )1 )

or

^f.The left hand side of he above equation is shown plotted against / Afor various values of / M in figure k . The ratio '^an is obtainedfrom this figure by using the appropriate values of / A and /li, andsubstituting T2 for T and 1,800K for Tan ' gStep 5- Determination of dilution hole area and drag coefficient

We have,AP^ V.^q 2g ' V ^ VV^an an ^ ar w

Also,V A_an VV, Aj . an (5)

assuming that the pressure ratio across the dilution holes is close tounity and that all the annulus air subsequently flows through the dilutionholes.


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- 7 -V .Substituting for rp in equations (k ) and (5) gives:-an

^ ) DAan (6)

The above equation contains two unknown variables - the ratio ofthe total dilution hole area to the annulus area, - ând the dischargeâncoefficient of the dilution holes, C^. Fortunately, these variables arenot independent and adequate and reliable experimental data to connectthem has been provided by Dittrich and Graves^. These data have beenIncorporated with equation (6) into figure 5^ which represents a compositeplot of the relevant parameters.

A A^ Aî)/k{l - -r~), K. is obtained by substitution for A and / A .The ratio /A is given in figure 5 and, since this is equal to

Step 6. Determination of dilution hole diameterIn order to achieve a satisfactory temperature profile at the chamberoutlet it is generally recognized that there must be adequate penetrationof the dilution jet coupled with the correct niamber of jets to f omisufficient localized mixing regions. The derivation of the total dilutionhole area is relatively straightforward, as described above. How ever, themanner in which this area is utilized in terms of number and size of holes

is still largely a matter of experience. Penetration studies, however,have produced relationships which allow assessments to be made of the effectsof design variables on the ratio of max . jet penetration/dilution holediameter. According to Cranfield data-S/e have

sin * (7)

being the angle of penetration.Substituting for p, and equating d = /cT . d, gives

D gNow it has been shown'^thatis related to the C_ of a plain hole bythe expression


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C^ = C^ . s i n ^d dQ

Y [T V C-i52 _ _ IA I.

H e n c e

S u b s t i t u t i n g i n e q u a t i o n ( 9 ) f o r C^ = 0.6h a nd r e - w r i t l n g , g i v e so-^ ^ '1-^5J ^ . ^ . C 10)

an '^ an A P /Itwasshown earlier that C-,is afunctionof / q and, since0. V . ' ân 'compressible flow theorymay beusedtoshow that ^ isalsoafunctionAP^ ânof (seefigure 6 , w ehave,ân Y V /T~ / A P A

The actual relationshipisrather cumbersaneand isomitted here,butitisshown graphicallyinfigure7- TheratioYmax/-,isobtained from/< ÂPf Tthis figure usingthepreviously determined valuesof /q . /T2and^p~' If^rnojristhen stipulated,d isknown,as isalsothenumberanof dilution holes,n,since Aj^=O.785. n d^.

On tubularandtubo-anniilar chambers,it isrecommended thatYshouldbemade equalto theflametube radius. Onconventionalannular systemsitshouldbeequatedtohalftheflametube width.Step7. Determinationofdilution zone length

The lengthof thedilution zoneisobtained from figure8 inwhichtamperature traverse q uality, expressedintermsofT^g.^- s/m Q,, isplotted againsttheratioofdilution zone lengthtoflametube diameterfor various levelsofoverall pressure loss factor. Itshouldbeemphasized that figure8 canonly provideanapproximate guide, sinceitis basedon asmall amountofexperimental data and,in anycase,therelevant pressure loss factor should ideallybethatof theflametubeandnottheoverallasplotted. Unfortunatelytheoriginal data employedinconstructing this figuredid notInclude breakdownsof theoverall pressurelossandhence flametube pressure loss factors couldnot bededuced.


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- 9 -

The design of the dilution zone is now complete. If, for anyreason, it is considered unsatisfactory, a different value of ^ / ^should be chosen and the design procedure repeated from step 5 onwards.Dilution Zone Performance - Further Considerations

Experimental investigations into dilution zone performance carriedout on practical systems have resulted in charts, of the type shown infigure 8, which are useful in design but in which it is difficult orimpossible to distinguish the separate influences of all the variablesinvolved. On the other hand more basic studies of jet mi:clng do notusually yield results which can readily be applied to combustion diamberdesign. How ever, some of these investigations can provide a usefulguide to the relationships Involved.Some typical results from one such investigation-'-are presented infigure 9- They are shown as plots of temperature traverse quality

,, V APfX an ^ Iagainst . ~ for various values of /q . It should be noted

' ^g ^ T - T .that in this figure traverse quality is denoted by zf' =^ , T. beingTg - T2 jthe measured local jet temperature. Instead of the more familiar form_ ^max Ttnean mi- ., i-i. T ^ j i. , .^^

of = . This IS because the latter ratio has no significancei3 - 12when applied to the particular conditions of the Cranfield experiments.

For the same reason the traverse qualities shown in figure 9 cannot beapplied directly to practical combustion systems in terms which wouldbe meaningful to the combustion engineer. Nevertheless, the work hasresulted in the accumulation of a large amount of data on the mixingof cold jets when Injected into hot streams under conditions where thetemperature and velocity of the hot and cold streams, the injection holediameter, the angle of injection and the mixing length could be accuratelycontrolled and varied over a wide range. In utilizing this data forpractical purposes, any difficulties arising from the definition oftraverse quality have been eliminated by fixing the traverse quality atvarious representative values and then examining the inter-relationshipof the other important variables. The results of this analysis aresummarized in figures 10 to 12 . In deriving these figures, the overallA.F.R. and the ratio -^ /d.were fixed at 50 and 6 respectively, these beingregarded as representative values.Figure 10 shows the extent to which the overall pressure loss factormust be Increased, if the chamber inlet velocity is increased, in orderto achieve the same traverse quality in the same length. Results areshown for reference velocities of 80 and 120 ft/ s, these being typicalvalues for tuboannular and annular combustion chambers respectively, andalso for two values of diffuser loss coefficient, T . It is apparentfrom this figure that the effect of increased inlet velocity is most pronounced when the diffuser pressure loss is high and the reference velocitylow.


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- 10 -

The influence of inlet velocity is further illustrated in figure11,in which results are presented for two values of reference velocityand a range of overall pressure loss factors. They show that underconditions where an Increase in inlet velocity cannot be acccanmodatedby an increase in pressure loss factor, then the same standard oftraverse quality can be maintained by an Increase in dilution zonelength. The amount of extra length required is greatest when both theoverall pressure loss factor and the reference velocity are low.

The effect of inlet velocity profile on dilution zone performanceis Illustrated in figure 12 . Calculations have been carried out forthree profiles of parabolic fona and having values of Vjj gx/-y ^' mean1.1, 1.2, and 1.3 In these calculations it was assumed that 2 5^ ofthe toteii inlet air entered the primary snout at the peak velocity,and the remainder flowed over the flametube head. The results obtainedwiththe peaklest profile are shown in figure 12 , along with those fora flat profile. As plotted they show that any increase in profilepealclness' must be accompanied by an Increase in dilution zone lengthin order to achieve the same traverse quality. It will be appreciatedthat these results can also be interpreted in terms of extra pressureloss factor or Increase in reference velocity by transposition betweenfigures 10 , 11 and 12 .

The main purpose of figures 10 to 12 is to provide quantitativerelationships between the chamber entry conditions of velocity andvelocity profile and the main dilution zone design parameters. Perhapsthe most striking point brought out by these figures is that the trendtowards combustion chambers of lower pressureloss,which for manyyears has been a primary research and development objective, mustinevitably result in systems whose dilution zone performance and generalaerodynamic stability are more sensitive to increases in inlet velocityand changes in velocity ixrofile.DefinitionofAerodynamic Perfonnance

The overall pressure loss factor of a combustion chamber representsthe sum of two sources of pressure loss (a) the pressure loss in thediffuser and (b) the pressure loss across the flametube.Thus,

AP2-3 = AP^iff + APfEven the most efficient diffuser constitutes wasted pressure lossin the sense that the pressure loss involved makes no contribution tocombustion. It is Important, therefore, to keep AP^^ff to a minimum,although in practice there is little the combustion engineer can doother than to observe the established principles of diffuser design.


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lt is, of course, equally important to keep the flametube pressureloss factor to a minimum, although in this case there is an importantdifference in that all the pressure loss Incurred is beneficial to bothcombustion and dilution processes. A high value of AP^ Implies smallair injection holes in the flametube. These small holes result in highair injection velocities, steep penetration angles, and a high level ofturbulence X'/hich, in turn, promotes good mixing. Thus for any givenvalue of overall pressure loss factor it is important that the ratioof the flametube pressure loss to the overall pressure loss should bemade as large as possible. Defining this ratio as p where

AP6 = ^ AP2_3it can be stated that, in general, any increase in the value of P willpromote more stable flow conditions, with the exit temperature traverseless sensitive to changes in inlet velocity and inlet velocity profile.

The manner in which P varies with changes in inlet velocity, referencevelocity and overall pressure loss factor is Illustrated in figure 13 .It is apparent from this figure that from a purely aerodynamic standpointthe most satisfactory combustion chamber is one having a low inlet velocity,a high reference velocity and not too low an overall pressure loss factor.Some indication of the increase in dilution zone length required tocompensate for a decrease in p is provided in figure Ik.A practical illustration of the significance of P is gained byconsidering how it is affected by a reduction in the overall pressure

loss factor of a chamber, which may be accomplished in practice in oneof twoways. One method is by reduction of ^f, which inevitablydecreases P, by definition. The other method is to increase the chambercasing area which, for constant APf/ , leads to an increase in '^ diff/'ref ^^refThus it is impossible to reduce the overall pressure loss of a combustionchamber without reducing p, and hence without impairing its aerodynamicperfonnance.Conclusions

It is confirmed that combustion chamber traverse quality is adverselyaffected by an increase in inlet velocity, a more peaked velocity profile,a reduction in chamber reference velocity, an Increase in diffuserpressure loss factor, a reduction in flametube pressure loss factor, anda reduction in dilution zone length. Most of these effects have beenrecognised for some time but in this paper a contribution is made towardsexpressing some of the more Important relationships quantitatively. Thepresentation is by no means caaprehenslve but the same methods could, ifrequired, be employed to extend the number and range of the variablesconsidered.


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For many practical purposes the aerodynamic performance of acombustion chamber may be conveniently and adequately defined in termsof the parameter P, where P is the ratio of the flametube pressure lossfactor to the overall pressure loss factor. It is believed that Pcould provide a useful tool in comparing (a) the aerodynamic quality oftwo different designs of combustion chamber, or (b) the same chamberbefore and after one or more design modifications or (c) the same designof chamber subjected to variations in inlet velocity or velocity profile.References1. Norster, E.R. College of Aeronautics Note Aero. No. I7 0.

2 . Dittrlck, R.T. and Graves, C . C , NACATech. Note3663,April,I956.

3. Norster, E.R., College of Aeronautics Report Aero No.(To bepublished).i|-. Cox,M . N . G . T . E .Report No. N.T.28 I, AprilI957.


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0-4

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4 0 0 6 0 0 8 0 0 l OO O I 2 0 0 I 4 0 0 I 6 0 0TURBINE INLET TEMPERATURE T3 " K

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FIG. 1 DILUTION ZONE FLOW PROPORTIONS AS A FUNCTIONOF TURBINE INLET TEMPERATURE FOR T = 1800K.(SHADED AREA REPRESENTS CURRENT DESIGN REGION)

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AR,: - t f ( t J -FIG. 2 VARIATION OF DIFFUSER PRESSURE LOSSFACTOR W ITH DIVERGENCE ANGLE


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