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74-WA- GT-10

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' Discussion is printed only if the paper is published in an ASMEjournal or Proceedings.Released for general publication upon presentation.Full credit should be given to ASME, the Professional Division,

$3.00 PER COPY and the author (s).

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A NOx Correlation Method for Gas TurbineCombustors Based on NOx FormationAssumptions

GEZA VERMES

Fellow Engineer,Gas Turbine SystemsEngineering Department,Westinghouse Electric Corp.,Lester, Pa.Mem. ASME

Based on a simplified description of the combustion process in the primary zone of a cantype gas turbine combustor, a generalized NOx versus fuel flow relationship is proposed.Using this relationship and considerations based on chemical kinetics, the effect of com-bustor inlet pressure, inlet temperature and air residence time on NOx formation is inves-tigated in industrial and automotive type combustion chambers. Data reported in the litera-ture and original test work is cited to substantiate the validity of the assumptions. Based onthe findings, a simple method is presented to predict NOx emissions of a gas turbinecombustor under conditions which differ substantially from those of the test run. The as-sumptions may be used to assemble a model for a priori prediction of NOx emissions in agiven combustion geometry.

Contributed by the Gas Turbine Division of The American Society of Mechanical Engineers for presenta-tion at the Winter Annual Meeting, New York, N. V., November 17-22, 1974. Manuscript received atASME Headquarters August 2, 1974.

Copies will be available until September 1, 1975.

AMERICAN SOCIETY OF MECHANICAL ENGINEERS, UNITED ENGINEERING CENTER, 345 EAST 47th STREET, NEW YORK, N.Y. 10017

Copyright © 1974 by ASME

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A NOx Correlation Method for Gas TurbineCombustors Based on NOx FormationAssumptions

GEZA VERMES

INTRODUCTION AND OBJECTIVE

The rapid increase in gas turbine pressure

ratios and temperature levels during the last

few years has the consequence (among many other

things) that gas turbine combustor chambers underdevelopment will have to operate very soon undercombustor ambient conditions different from those

presently in practice. It is of practicalinterest to know what NOx levels can be expected

from a given combustor geometry in these advanced

machines, Another question of practical signifi-cance is the influence of regeneration on NOxformation. It is also of interest to compare the

NOx emissions of different gas turbines: this is

not meaningful when the available test data must

refer to different combustor ambients,

It is the objective of this paper to proposea method which provides answers to the foregoingquestions,

VARIABLES CONSIDERED

The influence of the following variableson NOx will be considered:

• Fuel flow (or fuel/air ratio)• Residence time

• Combustor inlet pressure

• Combustor inlet temperature,

ASSUMPTIONS

It will be assumed that the fuel has onlynegligible nitrogen content. It will be further

assumed that at one point, NOx measurement was

performed under known operating conditions. It

will be assumed that the influence of air humidityon NOx formation can be assessed (1).

It will be further assumed that NOx forma-tion in a gas turbine combustor follows a

1Numbers in parentheses designate Refer-

ences at end of paper,

qualitative model as described below,

THE RICH-LEAN MODEL OF NOx FORMATION IN THE GAS

TURBINE COMBUSTOR

The type of gas turbine combustor discussedin this paper is the can type, This combustorcan be considered to be a cylinder, wide open on

one end discharging the exhaust gases; the fuel

injection takes place at the opposite end in theform of a shallow cone spray at the centerline

of the cylinder, the spray emerging from a

pressure atomizing nozzle,For the purposes of this paper, the absolutr

pressure and temperature of the air around the

combustor basket will be considered as "combustor

inlet pressure (temperature)"; it will be assumed

that the difference between total pressure and

static pressure is negligible around the combustor

basket.Note that the combustor inlet temperature

is close to the compressor exit temperature in a

non-regenerative machine, but it is much higher

in the regenerative turbine,The other important temperature is the

combustor exit temperature, usually close to the

turbine inlet temperature.The third temperature level which has a

bearing on NOx formation is the temperature of

the gas mixture in the primary zone; this level

is on the order of the flame temperature.It was shown in Reference (2) that the

combustion reactions are at least one order ofmagnitude faster than the NOx formation mechanism,

which may be described by the often-quotedZeldovich mechanism (3)a It follows from theZeldovich mechanism that in the fuel rich areas

of the combustor, NOx formation is negligible.As the spray itself is, quite obviously, extremely

fuel rich, the central cylindrical zone of thecombustor upstream end containing the spray can

be excluded from the NOx producing areas. As

N


>ST ATOMIZER

BASED ON NORSTERLEFEBVRE (2), FIG.21

60 80 100 120 140

OVERALL AIR- FUEL RATIO

NO XPPM(VOL)

NODE I I MODE II I MODE III(RICH) (LEAN) ("UPSWING')

pT=TCOMB. IN -TCOMB.OUT —ÔR FUEL FLOWOR FUEL/AIR RATIO — '

Fig. 1 Three modes of NOx generation in the gasturbine combustor

this cylinder does not contain much oxygen, itis only a vapor generator for the outer, annular

shaped portions of the combustor, where there is

plenty of oxygen; in general, this is the zoneof recirculation.

Considering the aforementioned, one mightconsider the conventional gas turbine combustor

a "rich-lean" device: In the center, it isrich; around the center core, it is lean. It

should be pointed out, however, that "leanness"

might not be an appropriate expression to useas mixing is quite incomplete in the primaryzone; therefore, reactions may proceed in richpockets surrounded by lean volume elements. Theabove described primary zone will now be

considered in its implications on NOx generation,

assuming the combustor pressure and combustor

inlet temperature (i.e., compressor exit condi-tions) do not change.

FUEL FLOW

It will be now postulated that with

increasing load (fuel flow), the combustor will

have three modes of operation, as far as NOxproduction is considered (Fig. 1).

At low fuel flow (idle operating conditions

or below), the fuel flow might be so little that

most of the combustion takes place in the central

core and very little fuel vapor gets into therecirculation zone. This first mode of operation

will not result in significant NOx production due

to its short time at temperature and is shown as

INLET AIR TEMP=600°K(1080°R)

280®,ZDUAL ORIFICE (PRESSURE ATOM.)

Z 240 ,p 0 -200PSIA03.6ATM)

x- 135PSIA(9.2ATM)200 O

zwZ 1600U

N 120

80

w00 40U

oZ 40

Fig. 2 Influence of fuel flow, combustor pressure

and fuel injector design on NOx formation

producing essentially zero NOx in Fig. 1.As the fuel flow increases, significant

amounts of fuel vapor will burn in the recircula-

tion zone and NOx production will start. The

rate of NOx production will be defined by the

aerodynamics of the head end of the combustor.As the fuel flow increases, new streamlines ofairflow will be involved in NOx production;

however, the time-temperature history of the new

streamlines will be similar to the previous ones;

i.e., the additional quantity of fuel willproduce as much NOx as the previous quantity:the NOx versus fuel flow function will be astraight line. This is the second mode ofoperation of a gas turbine combustion chamber

as a NOx producer.

As the fuel flow further increases, either

the oxygen available in the head end will not be

sufficient to consume all the fuel there or drop-lets will escape from the primary zone into thesecondary zone because of the high droplet

velocity, due to the large fuel flow. The fuel

in the secondary zone will have a time-at-tempera-

ture history different from the fuel in the

primary zone; generally, more time at hightemperature will be available in the secondaryzone. Therefore, the fuel which creates peakload temperature will cause — relatively

speaking — more NOx than the first batches.

This operation is the third mode of NOx production

in the gas turbine combustor: It is character-

ized with an "upswing" in the NOx production(Fig. 1).

It is of importance that the variable

controlling, the NOx formation process is really

3


NO, PPM (VOL)

28(

26(

24(

18(

16(

14(

12(

101

81

61

4

21

• ri:•1■•■■•■■■■

■11C■1l■■■■■■

■■ ■■■

N =. N ■■■■■■■■■■■ ■■■ ■■•ONE•■■■■■NOON ■■■■■■■■■so•OMEN

■■■■■■■ r

/a►. .

■•■■■■■■

■■■■■

■■■C■■■■■■■■■■■MEMO

'■■.■.■..■■■■■■■■■■■A.

■■■.

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■■■■■■■■■■OMEN■■■■■■■

■■NESS.■■■■!■ ■■■■■■■NONE••■■■■^■■'•■■

■• ■••••••■■■■■■■■■■■■■■■■ • ■■■■■■■•••••••

' ■■■■■■■f'// ■N■■■■■■■■■•■■■■■■V4U ■■■■■■■■■■•■.

■■■■■■UI ■■■■■■■■■■■■■■ - ■■

•

SELECTED NORMALIZING CONDITIONSCOMBUSTOR INLET PRESSURE 100 PSIG (6 8OATM)COMBUSTOR INLET TEMPERATURE:673°F(374°C)

HUMIDITY - 0.017 LB WATER/LB DRY AIRFUEL: NO.2-GT

+ LABORATORY DATAo TURBINE DATA

NOx PPM(VOL.)

AT = TCOMB OUT

-TCOMB. IN

20

60

0 0.2 0.4 0.6 0.8 1.0V L Y V V IV IL I1 1 V iv Iv -

FUEL/AIR RATIO

Fig, 3 Linearity, pressure effect and atomizerinfluence on NOx

--0-

A MAX.

Fig, 4 Linear dependence of NOx on AT

not the fuel flow but the combustion airinvolved with the fuel in the combustion process.

The fuel flow is proportional to this combustion

airflow, Therefore, a plot of NOx versus any

variable which is proportional to the airflow

involved in the combustion process should give

a plot similar to Fig, 1. One of these variables

is the overall fuel-air ratio, It is obviousthat fuel-air ratio and combustor temperature

rise are also interrelated (for all practical

purposes they have linear relationships); there-

fore, NOx versus AT = Tcomb,out - Tcomb,in should

also be a straightline relationship,A recent paper by Breton, Koblish, and

Marshall (4) sheds interesting light on the

problem of linearity of NOx versus fuel flow,

Probing the primary zone of a combustor, they

found that the local NOx level was a linear

function of the local CO 2 level (which they

considered proportional to the local air/fuel

ratio), up to about 10 percent CO 2 . Above 10

percent CO 2 , deviations from linearity in NOx

generation become more frequent,The implication of these measurements is

that as long as the fuel/air ratio in the primaryzone changes uniformly with increasing fuel flow,

the NOx versus fuel flow curve will be linear.Note that the level of the fuel/air ratio can bedifferent in the different parts of the primary

zone for a given fuel flow condition; linearity

of the NOx versus fuel flow curve only requires

that the rate of change of the fuel/air ratio

should be constant at a given location inside the

combustor,Such a linear relationship of NOx versus

fuel flow can be deduced, for example, from Fig,

21 of Reference (5), The original is shown in

Fig. 2 and replotted as Fig, 3, The latter

figure demonstrates two facts: (a) when NOx

is plotted against the appropriate variable (in

this case, against fuel/air ratio instead of

air/fuel ratio), it becomes clear that NOx gener-ation proceeds in accordance with the scheme

shown in Fig. 1; (b) it is demonstrated that the

mode III operation shown in Fig, 1 can beeliminated — at least under certain conditions

— by changing the pressure-atomizing nozzle toan air blast type nozzle, A similar plot is

shown in Fig. 4 from the combustion experience

of the author's company; there the NOx is plotted

against AT = Tcomb,out - Tcomb,in, i,e,, combustor

temperature rise,For comparison, field performance of the

same combustor is also shown in Fig, 4, All theNOx data of the figure were normalized for a

selected common combustor inlet pressure andtemperature in accordance with methods described

later in this paper.

4


NORMALIZED TO

COMBUSTOR INLET PRESSURE: 60PSIG (4.OATM)

COMBUSTOR INLET TEMPERATURE 600`F(315 °C)

TCOMB.OUT-TCOMB.IN=LT NCM=1050'F(570 C)

NOXPPM(VOL)..■■■■■■■NR■■moil. • ■■■■■■■■■

_ ■

_ /.' ■

..■■■■■■■M■■■.J■■ ■■• ■■■■■■■ ■■■■^^^■■■NEON ■■■■■■■■oso'■■ ■ ■■■■■ ■N

•AIR FLOW

Fig, 5 Influence of residence time on NOx

As the correlation of different operating

conditions usually does not involve large changesin AT (or fuel-air ratio), the presented straight-line relationship is usually sufficient to obtaininformation on future performance, Having

obtained the dependence of NOx on fuel flow (fuel /air ratio or AT), we may now proceed with the

next variable: residence time.

RESIDENCE TIME

Changing airflow will usually provide

different resident times for the unreacted

nitrogen and oxygen to combine. Other conditions

being equal, the residence time will be inversely

proportional to the mass flow. We have only fewmeasurements on this relationship; they are shown

in Fig. 5. Before plotting the test points, theywere normalized in respect to combustor inletpressure and temperature and AT, to preselected

conditions indicated in the figure, using the

relationships described later in this paper and

the NOx versus fuel flow (or AT) law establishedin the previous section. Then, one of the testpoints was, arbitrarily, selected as the basisof calculation ("anchor point") and the solidline was calculated. The validity of the

assumption that residence time is inverselyproportional to mass flow (other conditions being

equal) is indicated by the agreement between the

calculated line and the other test points.

PRESSURE LEVEL

As indicated in the description of the

model, each streamline in the combustor defines

its NOx generating level, observing the general

■■■■■■■■■■■■■■■ ■■■■■■■■■■■■■■N■■■■■■■■. ■C•■■. ■■■■■■■■ ■N■■■■■^ ■^ •■•■■■■■■■•• : • •■■ _

■.•.••...••..

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•• ■■■■//■■■ ■■■C■•■■■■►..•■•■•••■■•■••••••••••••••••••■m •■■■■•■■■■•■•■■ ••■M■■■■u■• ■■■■■

I■■ ■■ ■■■■■■■■■■■■■■■■■■ u■■u■■■■■■N■■■ii ■MMFAMM U•IUUUU•iiiiii

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• r1■■N■■■■■■■■■■■■■■■■■■• ■■■■■■■■■■■■■I■■N■M■N■■N■■

■■.. ^C■■■■■NI^■■■■N■■■ •••■■isu muuuuurnuuuuuu•uuu•u•■L•••■•■•■■•■■•••■••■•■■■•■•i1•■■■■■■■•■•■•■■■■■■■■■■■•a■■■•■■■■■■■■■■■■■■■■■•■■

. ■%NNNNN■■■■■■■■■■■■

U■■■■■■■■■■■■■■■■■■■■ urn■■■■UFig, 6 Influence of combustor inlet temperature

increments on NO

mechanism of the Zeldovich equations, As thepressure level influences the generation of NOxin proportion to the square root of the absolute

pressure, the entire combustor will be considered

to respond to changing pressures in proportion

to the square root of the ratio of the pressure

change. Test results of Reference (5) are shown

in Fig. 3. Using the square root law, the testpoints of the lower pressure level (line 1) wererecalculated for the higher pressure level (line

2), It can be seen that the NOx data calculated

from the low-pressure points fall on the same

line as the NOx data obtained at high pressure.It should be noted here that changing the

absolute pressure, the specific volume of the airwill also change. Therefore, when the mass flow

is kept constant, the residence time has to be

recalculated for changed pressure operation.

Consequently, the changing pressure will have adouble effect on NOx; one effect, the residencetime effect, however, can be counteracted (eitherby changing the mass flow per combustor ordecreasing the size of the combustor), whereas

influence of pressure on the chemical kinetics

(the square root relationship) cannot be changed.

CURVELCULATEDOM ANCH.POINT

G/SECB/SEC

5


CULATEDANCHOR POINT

ISTEP AND'EBVRE(5)

R

POINT

0.7 0.8 0.9 1.0

EASURED

ALCULATED FROMNCHOR POINT

PCOMB. IN= COMBUSTOR INLETPRESSURE

PCOMB. IN(PCOMB IN)

ANCH. P

Fig, 8 Combustor airflow, fuel flow, inletpressure and temperature effect on NOx during

field test of a turbine

NOx PPM (VOL.) NOx PPM (VOL.)

TCOMB. IN —^

Fig, 7 Inlet temperature and residence time

influence on NOx

No recalculation of residence time had to be done

for Fig. 3 because the mass flow was adjusted

for the pressure change (7),It is concluded that the simple relationship

to describe the effect of pressure on NOx forma-tion, as suggested by the Zeldovich mechanism,

can be used to describe the behavior of a gas

turbine combustor:

(NOx),,' p 0.

(NOx) Pt

This relationship between cycle pressure change

and change in NOx formation will hold as long as

other variables do not change; along with pressure,the "other variables" include residence time andthe performance of the fuel atomizer,

THE INFLUENCE OF COMBUSTOR INLET TEMPERATURE

The last variable to be considered is the

combustor inlet temperature, As it was explainedin the section on the NOx model, the formationof NOx is mostly, though not completely, influenced

by the history of the high-temperature pockets inthe primary zone, These pockets exist even in

generally lean areas for awhile; therefore, the

effect of change in combustor inlet temperature

on NOx formation should be investigated firstin respect to these high-temperature regions, Therate at which NOx is being formed is (6)

as Ndx,, =1j4

1 QXN XOc—bx0idt + XN0

x01

In the foregoing formula, the rate is expressedin ppm NO/ms, the concentrations (X) are expressed

in mol fractions and the pressure in atmospheres.

The rate constants will be approximately

16• e-6 =T exp.(-134000/RT)

2.9 X 10b

15 exp(-90800/RT)^ TTJZ

c w 8.5 exp(7400/R7)

where

R = 1,98 cal/mole, deg K and T is in deg K

The temperature, T, is on the order of the

temperature level of the gas mixture in the flame

zone; T can be considered as a characteristic

NOx formation temperature, It will be shown in

the Appendix how the ratio of the NOx generationrates at different combustor inlet temperaturescan be obtained from the foregoing formula, Thisratio, derived in the Appendix, 15:

r(dN0„ ldt)T^^,+e.,^^1 r ^^ N^ *^rs. ,^^s

6


Table 1 NO Generation in a Small Regenerative

Car Turbine (8)

1 2 3 4 5 6 7 9 10 ,

Fuel flow Comb.Prez. Airflow Rel.res. (Tcomb.out) Comb.In.Tem. y "Str.Line"c

IT0. (NOx) NOx% om r. ar . time -(Tcomb.in) -Des.In.Tem. Fig.6 NOx-NOs

calc4 . Test(From(8)) D(8) IT °F/°C (8) (From Fi .9) NO.S )" (8)

TT I 0=^ AT OF i7) ^CFig. 9

100* 1.0 1.0 1.0 609/320 0 0 1.0 128 1.0 128 128

75.2 0.835 0.835 1.0 546/285 63 35 1.14 114 0.915 119 120

52.5 0.681 0.681 1.0 467/241 142 79 1.36 96 0.825 108 109

35.1 0.565 0.545 1.03 386/196 223 124 1.64 81 0.75 102.5 99

17.1 0.460 0.488 0.95 229/109 -188 -104 (1.51) 47 0.68 20.1 19

10.3 0.392 0.375 1.05 176/80 -127 - 71 (1.32) 37.5 0.626 18.7 19

* Design Load Condition

NOTE: Subscript D means Design Load Condition, i.e. the inlet conditions of the "anchor point".

The foregoing expression of y versus A(Tin ) isshown in Fig. 6 where

i.e. the change in combustor

inlet temperature.Throughout the paper, it was emphasized

that the simple relationships used to describe

the change in the rate of NOx formation only hold

when the change in one variable does not cause

a simultaneous change in another variable. Sucha consideration was followed in the discussion

of the influence of the change in pressure onthe residence time. As the changing inlet

temperature changes the specific volume of the

gas flow and thereby the residence time, thisside effect of the inlet temperature change on

residence time will now be investigated the sameway as it was done before in the section on thepressure effect.

RESIDENCE TIME AND INLET TEMPERATURE

In general, higher inlet temperature will

increase the volume flow of air, thereby decreas-ing the residence time, which means that theincrease in NOx formation due to higher tempera-

ture will not completely materialize: There will

be less time available to form NOx - albeit athigher rates. It will be seen, however, that the

residence time of the high-temperature stream-

lines, which form the bulk of the NOx, will de-

crease only very modestly under the influence of

changing combustor inlet temperature. For

example, when the combustor inlet temperature

changes from 600 F (59 0 K) to 700 F (645 K), the

change in the residence time of the low-temperaturezones will be on the order of 590/645 = 0,914, i,

e., 8.6 percent, but the high-temperature stream-

lines will change their time, for the same 100 F

(55 .5 K) temperature change only, say, in the

ratio 2500/(2500 + 55.5) = 0.98, i.e., by 2 per-cent. The actual difference is even less, as

100 F (55 .5 K) change at the combustor inlettemperature level does not translate into thesame amount of change for the high-temperature

streamlines (see Appendix),

It is concluded, therefore, that the typeof residence time adjustment, which was necessarywhen the pressure effect was calculated, isinsignificant when the influence of combustor

inlet temperature change on NOx formation is

considered. For example, Norster and Lefebvre's

results on the influence of inlet temperature

(5) are shown in Fig. 7. Norster and Lefebvre

adjusted the massflow to keep the customary flow

parameter, m/P, constant (7); T and P arecombustor inlet pressure and temperature. Con-

sidering one of the test points as the "anchor,"

a curve will now be calculated. The calculated

curve, using Fig. 6 and compensating for the

changing residence time because of changing m,agrees fairly well with the test results except

at the highest inlet temperature. Note that atthis point both the airflow and the fuel flow are

minimum, and secondary effects not accounted for

by this simplified theory may increase the NOx

level.

7


SOLID LINES CALCULATEDFROM BASELINE.ZERO °C ON AT SCALE

NO MADE TO MATCH ZERO ° FPPM(VOL)200 ■■■■■■■■

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■N

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■■■• • =

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Vv1 v 1 VVIv II.A 11•

Fig, 9 NOx formation in a regenerative turbine

U ouu ww r eAT= TCOMB.OUT-TCOMB IN

Fig, 10 Influence of combustor inlet temperatureon NOx in an experimental combustor

pressure, Pis the relative airflow, and O is

the relative residence time. Using the inlet

temperature correction factor, y, of Fig, 6, the

straight line nitrogen oxide value NO s will become

NOx data at the changed inlet conditions as

follows:

SUMMARY OF THE METHOD OF ADJUSTMENT

The previous sections discussed influence

of the different variables on NOx production;the several methods of correction will now be

assembled into a procedure.

First, a relationship between NOx and fuelflow (or AT, fuel/air ratio) has to be established,according to the scheme shown in Fig. 1. If

there are not enough consistent measured points,

the line has to be established using other infor-mation available, as will be shown on an example.

The NOx values of this NOx versus AT linewill be referred to as "straight line NOx" (NO S ),and they will be characteristic to the combustor

as long as the inlet pressure, temperature, andmassflow (Po , To , m o ) do not change. When theychange to P 1 , T1 , ml , the following relationshipshave to be established:

Tr F

m,

In the foregoing expressions, II is the relative

(NOx) p' , T^ (NOS) YTr {8

APPLICATION OF THE METHOD

Small, Regenerative Car TurbineIt will now be shown how the results of

the preceding sections can be applied in the

analysis of an actual turbine, when fuel flow,

combustor inlet pressure and temperature andairflow are changing simultaneously. The selected

example is a small, regenerative automotiveturbine, reported by Wade and Cornelium (8),

Operational and test data based on Reference (8)

and calculations are shown in Table 1. The

design load point will be chosen as the logical

"anchor point" (AT = Tcomb.out - Tcomb,in =609 F/321 C). Note that the procedure would workif any other operational point would be selectedas the base. The objective of the calculation

will be first to establish the NOx versus AT =

(Tcomb,out - Tcomb.in) line for the subjectcombustor as if the inlet conditions were those

of the "anchor" point; then, the NOx output ofthe combustor will be calculated for the real

8


inlet conditions and compared with the test data.

The line containing the "anchor point"

will be obtained as follows:

As a first approximation, we assume that

the reference velocity, i.e., the residence time

in the combustor, does not change significantlyfor the various load points. (This assumptionwill have to be verified later.) If we adjustthe test data of Reference (8) for pressure

(using the square root law), we obtain approximate

NOx values which would be comparable with the

"anchor point" data except for the inlet tempera-ture effect, These pressure adjusted NOx data areshown in Fig. 9. The figure also shows the inlettemperatures for the test points (8). The

straight line containing the "anchor point" will

have to run below the points that have a higher

inlet temperature than the "anchor point" andabove those points which have a lower inlet

temperature. We also know that the line through

the anchor point cannot have a positive intercept

with the vertical axis because this would mean

NOx production at zero AT (i.e., zero fuel flow).

Inspection of Fig. 9 indicates that to satisfy

the aforementioned restrictions, the NOx versusAT line for the "anchor point" conditions has torun across the origin. Now we can turn to thetask of calculating the actual test data from the

straight line established in the foregoing and

the operational conditions of Table 1 and compare

the results with the NOx data of Reference (8),

shown in Table 1, Column 11.Consider, for example, the 35.1 percent fuel

flow point in Table 1. According to Reference

(8), the speed of the turbine is 70 percent of

the design speed at this point, and the airflowdrops to 54.5 percent of the airflow at design

load conditions (anchor point): enter IF = 0.545

in column 3. The cycle pressure also decreases,from 3.68 atm-abs (54 psia) to 2.06 atm-abs(30.6 psia): enter II = 0 .565 in column 2. Theratio 0.565/0.545 yields the relative residence

time, 0 =11/F= 1.03 (column 4). (Note that the

numbers in column 4 substantiate the assumption

made before [when the straight line NOx versus

AT going through the "anchor point" was estab-lished) that the residence time does not change

significantly at different points of operation

of the turbine.)

We next establish the temperature rise in

the combustor, from data in Reference (8): 386

F/196 C and enter this in column 5. Operationaldata (8) yield the combustor inlet temperature

for AT = 386 F/196 C: Tcombustor in = 1314 F/710 C, which yields A(Tin) = 1314 - 1091 = 223 F

(124 C) to be entered in column 6.

The next step is to obtain y from 6, at

A(Tin) = 223 F (124 C). The figure was not

calculated beyond 150 F where y = 1.38. We maywrite, however,

Therefore, Y223 F = Y150 F ` y73 F = 1 .38 x 1.18= 1.64 (column 7). We now read the "straight

line NOx" from Fig. 9 (81 ppm), enter it in

column 8, then calculate IIz from column 2 (0.75),

enter it in column 9 and now we can calculate theNOx for the changed conditions:

(NUX) p! • Tj • m^ • NUS

$1 x 0.7$ z 1.64 x 1.03 • 102.5 pp.

This calculated value compares quite well with

the test value from Reference (8) in column 11:

99 ppm.

ANALYSIS OF FIELD TEST

The results of the previous sections were

applied to an industrial gas turbine of the

author's company. The turbine is equipped with

compressor inlet guide vanes; closing of the

vanes reduces the mass flow and decreases thecombustor pressure and temperature. The turbineinlet temperature was kept constant; therefore,

the temperature rise across the combustor changed.

NOx was measured for the nominal opening ofthe guide vanes ("anchor point") and at fourdifferent pressure levels as shown in Fig. 8.

NOx was calculated for these operating conditionsas in Table 1 (Fig. 8, solid line). It can be

seen that the measured NOx values compare fairly

well with the calculated curve.

INLET TEMPERATURE EFFECT IN AN EXPERIMENTAL

COMBUSTOR

The NOx performance of an experimental

combustor is shown in Fig. 10. The family of

straight lines was calculated on the basis of

the 750 F (399 C) line, using the method shownin Fig. 6. It can be seen that the "third modeof operation" (upswing) is most pronounced atlow combustor inlet temperature, then gradually

disappears as the inlet temperature increases.

It is believed that the increasing temperature

level at the entry of the spray promotes fastervaporization of the droplets resulting in fewerdroplets escaping from the primary zone into the

downstream end of the combustor where there isless mixing; therefore, more time at high tempera-

9


ture is available for the gas mixture to produce

NOx than in the primary zone proper.

CONCLUSIONS

1 The NOx level of a gas turbine combustorcan be calculated at different pressures,

temperatures, and fuel flows if NOx at one opera-

tional point is known, provided there is no over-

loading of the primary zone.2 The calculation is based on model con-

siderations. The concepts of the model wouldsuggest that the assembly of a calculation method

to obtain NOx data a priori, from the geometry

and flow data of a combustor, is a distinct

possibility.

APPENDIX

THE INFLUENCE OF COMBUSTOR INLET TEMPERATURE ON

THE RATE OF NOx GENERATION

The rate equation quoted in the body of

the paper may be re-written [using the approximatevalues of Reference (6)] as follows:

will be approximately

Pxp /_ '34000 + i 34000 1^ XNO%Il)To ` xT PT, /

Furthermore, one can re-write the exponent asfollows:

PY ^ r 131,000 134030

` 7 t — )°exp(134000/RT,T,1YT,-)0

In the foregoing expression, the right-hand side

will be considered as exp (134,000/RT OT1 ) raisedto the T1 - TO power. For the temperature range

2400 < T < 2600 K, the expression, exp (134,000/

R TOT1 ), can be considered constant: consideringT1T0 =2500 2 , exp (134,000/R 25002 ) = 1.0108871and 1.0108871200 = 8.7207; exp (134,000/R 2400X 2600 = 1.010904 and 1.010904200 = 8.7494. It

can be seen that even for the limits of the range

in T considered (2400 and 2600 K), the ratio of

the NOx formation rates only depends on T 1 -T0 .

Consequently, we may write

` X,a p 4- 4̂ 0 'd 410K Pns (_ 134o0fl1 X '^ X4

-0046 X êx ' K' ^dX ^/?1 170

^xî^13ti000/RlSoos)^^-T^^êxp 0.00^8(^" ^^

eX \ Jdt ra P Rr

I1+&5exp(7400âT)X 1

In the foregoing equation, the influence of the

change in combustor inlet temperature from (Tin) 0

to a new value of (Tin),, will make itself felt

through a change in T, where T is the high-

temperature level of NOx formation (in the order

of the flame temperature). Therefore, two

calculations will be performed in this Appendix:(a) the effect of a change in T, T 1 - TO on

dXNO/dt will be estimated, and (b) the relation-

ship between T1 - TO and (Tin) 1 -(Tin) 0 will be

assessed. The quantity, T, occurs at four loca-

tions in the foregoing expression of dX NO/dt:

twice in the lengthy expression In brackets anO

twice in the term preceding the bracket: 6.3 x1016 P0.5/T0.5 exp (-134,000/RT). Considering

realistic high levels for NOx formation tempera-

ture, 2400 K < T < 2600 K, one can show that the

value of the expression in brackets will change

only insignificantly when T changes between 2400and 2600 K (4320 and 4690 R). It can also be

seen that within the quoted temperature range,

TO ° 5 will also contribute only a few percent toa change in dX NO/dt.

One can, therefore, write the change in

the NOx formation rate (dXNO/dt), due to a change,T1 - TO in the temperature, T, of the gas mixture,

The foregoing expression accomplishes the first

task of this Appendix, namely the calculation of

the change in the rate of NOx formation, due to

a change in the NOx formation temperature, T 1 -T0 .We shall assess now the relationship between the

changing combustor inlet temperature (Tc,in) 1 -(Tc.in) 0 and T1 - T0 .

Standard curves show that at or near

stoichiometric conditions, a 200 F change in in-

let temperature to the combustor will cause 90 F

change in the adiabatic flame temperature; i.e.,

T1 -TO = 0.45 (Tcomb.in) 1 - (Tcomb.in) 0 = A(Tcomb.in ) X 0.45

We may write

(/X df)TO exr Q45)( .olod a(T-o , e p(aoo4s5)o(r0, ,,.)

Converting from deg K to deg R (or deg F) forthe change in the combustor inlet temperature

0(Tcomb.in), the constant c = 0.00485 will change

to 0.0027

As not all the NOx is generated at flametemperature, the exact calculation would have toconsider all temperature levels with theirweighted influence on the rate — which is not

10


the purpose of the approximate method described

here. Analysis of test results showed that using

an "effective" Ceff <C = 0.0027, one should use

0.00224 instead of 0.0027:

(d XN0 ^()(rrcw,e . in )^ ^^NJ^r ôr,•b. l„)d

('Ci AM, ,d! )( 7ra , i. . (X NO )(Tron^b. ")o

where Tcom.in is in deg F. The function, y,

is shown in Fig. 6.

ACKNOWLEDGMENTS

The writer would like to thank for the

help, encouragement and constructive criticism

of his colleagues, especially M. J. Ambrose, S.

M. DeCorso, W. S. Y. Hung, C. E. Hussey, andS. S. Lin,

REFERENCES

1 Carl, D. E., "The Influence of Ambient

Humidity on Nitric Oxide Generation,” Gas Turbine

International, Vol. 15, No. 3, May-June 1974,pp. 28-32.

2 Marteney, P. J., "Analytical Study ofthe Kinetics of Formation of Nitrogen Oxide inHydrocarbon-Air Combustion," Combustion Science

and Technology, Vol. 1, 1970, pp. 461-469.

3 Zeldovich, Ya, B., Sadornikov, P. Ya.

and Frank-Kamenetskii, D. A., "Oxidation of

Nitrogen in Combustion," Academy of Sciences ofthe USSR, Institute of Chemical Physics, Moscow-Leningrad, 1947 (translations by M. Shelef),

4 Breton, R. A., Koblish, T. R., and

Marshall, R. L., "Design and Test Limitations on

Reducing NOx in Gas Turbine Combustors," SAE

Paper 740182, Society of Automotive Engineers,Inc., New York, 1974.

5 Norster, E. R. and Lefebvre, A. H.,"Effects of Fuel Injection Method on Gas Turbine

Combustor Emissions," Proceedings of the Symposium

on Emissions from Continuous Combustion Systems,General Motors Research Laboratories, Warren,

Mich., Sept. 1971, Plenum Press, 1 97 2 , pp. 2 55-278.

6(a) Wolfrum, J., Chemie Ing, Technik,

Vol. 44, 1972 , p. 656 ; (b) Stull, D. K., ed.,

JANAF Thermochemical Tables, Dow Chemical

Company, Midland, Mich., 1971.

7 Norster, E. R., verbal communication to

G. Vermes, 1974.8 Wade, W. R. and Cornelius, W., "Emission

Characteristics of Continuous Combustion Systemsof Vehicular Powerplants," Proceedings of the

Symposium on Emissions from Continuous Combustion

Systems, General Motors Research Laboratories,

Warren, Mich., Sept. 1971, Plenum Press, 1972,

pp . 375-445.

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