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NASA TECHNICAL NOTE NASA TN D-7382

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" DISPERSION COP TURBOJET

' ENGINE EXHAUST IN FLIGHT - --- I

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NASA TN D-7382

DISPERSION OF TURROIET ENGINE EXHAUST IN FUCHT 4 T # i h and SUM l i e

AUhWSt 1973

I O W a k Ihl

o ~ ~ a m n ~ ~ ~ x l t m i o n NJ- ~ ~ t t 50 1 -?4 11 Contract o( Cum: ka

Lcwh Research Center Ndtional Aeronautlca and Space MministrAtip '

13 T y p d R g o n M d kd CavUed ClWCldnd, Ohio 4413s

I S I M u a n p Aqm-~t h m ma *ddrnr j Technical Note Ndtioml Aerondutirs and Space Administratism Washing?$on. D.C. 20546

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The dispersion or the exhaust of turbojet engines into the atmosphere is estimated by using a model developed f o r the mixiw of a round jet with a parallel flow. The analysis is appropriate for determinlrg the -read and dilrtion of the jet exhaust from the engine exit until it is cn- trained in the aircraft trailing vortices. Chemical reactions are not expected to be importat and a r e not lncluded in the flow model. Calculations of the dispersion of the exhaust plumes of three aircraft turbojet enpines with and without alterburning at typical flight conditions ;L-e presented. Calculated average concentrations for the exhaust plume from a single ewine jet

.fighter are s h o m to be in good agreement rlth measurements made in the aircr& vake during flight.

Dl SPERSION OFTURBOJET ENGINE EXHAUST IN FLIGHT

by James D. Holdeman Lewis Research Center

SUMMARY

The dlqmrsim of the czhnust of turbojet engines into the atmosphere is modeled as a round jet mixing with a parallel flow. The analysis is appropriate f o r determinlng the spread and dilution of the exhaust plume in the region of the aircraft rake from the en- gine exit plane until the exhaust is entrained into the aircraft trailing vortices. Chemical reacttons are not considered since residence times in this region are too short for photo- chemical reactions and engine exhaust static temperatures m d pressures at altitude flight conditions are below levels required for m y other significant reactions. An eddy viscosity model appropriate for the jet engine exhaust problem was formulated. It is used in an integral momentum method to calculate the dispersion of the exhaust plumes of both large and small aircraft turbojet engines with and without afterburning a t typical flight conditions.

Measurements of carbar monoxide, oxides of nitrogen, and ozone obtained in the wake of an F-104 aircraft flying at Mach 0.8 at M altitude of 11 kilometers are compared with exhaust plume concentrations’calculated by using the turbuled diffusion model, es- timated concentrations at the engine exhaust plane, and experimentally determined am- btent concentrations. The caiculated average concentrations are shown to be in good agreement with values measured in the wake of the source aircraft.

I NTRODUCTION

A method for estimatiqg the dispersion of turbojet exine sxh.uet hh flight i8 we- ~ n t e d . The method Is appropriate for determinlng the dildion of crhnust products ond the plume sire in the reglora of the aircraft wake from the engine exit plane udll the ex- hauat is entrained in the aircraft trailing vortices.

Public concern about the possible adverse impact of Y fleet of hfgh-altihxie airctaft O(I the en*ironment ha8 motivated Merest in aircraft rakes and stratospheric chemical kinetics. The aignLiiculce of chemlcal reactbas in *craft wakes is expected to be

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dependent on atmospheric cond'tfona and nn t h e concentrations of possible reactants. The latter, of course, are determincd by the engine exhaust emissions and their disper- sion into the atmosphere.

scribed in reference l. These a r e (1) the jet reRion, which extends from the engine ex- haust plane to the downstream location where the exhaust is entrained in the aircraft trailing vortices; (21 the vortex region, which extends from the jet region to vortex breakup; .and (3) the wake dissipation rexion, which extends bevond \ortex breakup. The extent of the jet reRion is drgendent on aircraft configuration 2nd flight speed. For the aircraft and conditions examined isf'rcference 1, t h i s region was reported to extend to distances of the order of 2 kilometers behind the aircraft.

Chemicd reactions are not considered to be important XI the jet reqion. Residence times are too short for a n y significant photochemical reactions. And static temperatures and pressures at the engine exhaust at altitude flight conditions, even with afterburning, are low enough to preclude any 9 h e r significant chemical reactions in the jet. This as- sumption is supported by chemical kinetics calculations presented in reference 1 for the constant-property je t core of the GE4 turbojet engine at Mach 2.7 and 19.8 kilometers altitude with maximum afterburning. Similar unpublished calculations made at NASA Lewis Research Center for various altitudes, flight speeds, and power levels typical of the 585 afterhurnhg turbojet engine also support this assumption.

The model considered in reference 1 for the dilution and spreading of the exhaust in the jet region is an empirical formulation from experiments on low-speed, incompress- ible jets mixiw with an annular coaxial stream at nearly common density and temper - ature (ref. 2). Since the turbojet engine exhaust is (at least) sonic and jet temperatrires are of the order of 5 limes the ambient temperature with afterburning, the relations of reference 2 are not appropriate. Furthermore, these relations do not reduce to the cor- rect asymptotic jet spreading and decay relations for distances from the jet exit wherc the free-stream velocity is large with respect to the difference between the j e t centerline velocity and the free-etream velocity (ref. 3).

To overcome some of the shortcomings of previous methods, the present investiga- tion w;u undertaken to develop a model which would be appropriate for the initial condi- tions presented by the turbojet engine exhaust and which would yield the known asymptotic spreading ud decay relations at large distances from the jet exhaust. The analysis is an integrg momentum method for which the dimensionless velocity difference profile shape and the shear stress relation must be spcciflcd. The eddy viscosity model used in the shear stress relation waa formulated by assuming that the eddy viscosity is directly pro- portional to the jet mass flow rate plus the absolute d u e of the entrainment mass flow rate and that it is inversely proportional to the jet width.

Calculations of exhaust plume dispersim for both large and small afterburning tur- bojet engines at typical night wndltions are presented. Finally, measurements of oxides

2

The jet wake behind an aircraft in flight may be considered in three regions as de-

,

of nitrogen (NOx), carbon monoxide (CO), and ozone (Os) obtained in the wake of an F-104 aircraft flying at Mach 0.8 at an altitude of 11 kilometers are presented and winpared with concentrations calculated by using the diffusion mocfel, estimated exhaust concentra- tions, and experimentally determined ambient concentrations.

ANALYSIS

The exhaust of a turbojet engine is modeled as a round jet mixing with a parallel flow. This flow is shown schematically in figure 1. Free mixing of ideal gases is as- sumed to occur between M axially symmetric jet (subscript j) and an ambied gas stream (subscript 4. The two s t reams are assumed to be chemically inert. The Prandtl and Schmidt numbers througliout the flow are assumed to be equal to 1; thus, the conservation equations for momentum, total enthalpy, and species concentration are identical. This permits the problem to be solved by considering only the continuity d momentum equa- tions. The integral momentum method of Donaldaon and Gray (ref. 4) for the mixing of an axisymmetric jet with a quiescent ambient gar, of a different density has been extended to the cas3 where the ambient gas may be moving at a velocity u,.

I ntegral Relations

The integral momentum equation evaluated at the half -value radius is

where rs is the radius at which the velocity is one-half the sum of the centerline and 8mbleat velocities. A second relation, abt;rlned by anluating the integral momentum equation .cmsa the entire width of the flow, requires that the net thrust remains constant at all domstream lucations. That is,

I Velocity Profiles

To provide a relation between # and I, velocity profiles a re aesumed. Those used in reference 4 are adopted here, except that now the exponential relation8 apply to the velocity difference ratio rather than to a velocity ratio. For the core region (see fig. I),

where ri is the radius of the constult-prophrty core, rs is the half-value radius, ud X - h 3. For the developed region,

where uc in the velocity on the jet centerline at the s t reamrisa location of iderest . B e c a w the Prsuxitl and Schmidt number. a r e assumed to be equal to 1, the concentra- tion difference, total enthalpy difference, and velocity difference ratios are identical. Thus, equation (0 provides the r e l a o n for (c - c,)/(c, - c,) and bo - h",/'hp - hz) in a d i t f a to - u,)/(u~ - uJ.

Density f

Tb. denmity can be exprosred in terms of the velocity difiarewe ratio8 through the perfect-gu Lor and the as"gM0n of identical velocity difference, total enthalpy differ- once, ud coacentrPllon difference distributions. For economy, let U - (r5t - uJ/ ("1 - u-1. The density axpression ia then

4

The Priutdtl model has been very successful in predicting the mean flow in nearly- conshnt-density cases where u, # 0 and in variable-density cases where u, = 0. Huwever, this model predicts decreased shear and hence decreased mixing with decreas- ing uj/ua for all density ratios. This result is consistent with the experimental data of reference 2 for mixing of a jet and an ambient stzeam at nearly common density, but it is contrary ta the experimental results of Chriss (ref. 6) for the mixing of low-density (hy- drogen) jets in air.

The Ferr i model attempts to account for the density ratio effects and does predict the correct mixing trends for both the hydrogenair and air -air experimental results. However, t h i s model predicts segregation of the two streams (no mixing) when (pu$ = bu), near this condition; hence, the Ferri model is not appropriate.

The Zelazny model is one of the more recent models and has been shown to be effec- tive for predicting the experimental results of most of the jet t ed cases considered dur- ing the Langley Working Conference OR Free Turbulent Shear Flows (ref. ?1. This model is based on the displacement thickness concept previously used in boundary layer anal- ysis. However, tllis model, like the Ferri model, is inappropriate for (pull % (pu),. The Zelazny model includes an empirical factor for compressibility and an empirical function for variatlon of z with radial position. This latter factor 1s not included here since only the eddy viscosity at the half-value radius is of Merest. Compressibility cor- rections have been applied by others also; for example, the eddy viscosity model used successfully by DQnaldson and Gray (ref. 4) is the Prandtl model with an empirical com- pressibility correction applied.

Because of the inapplicability of previoua models to the engine exhaust problem, a new eddy viscosity model was developed. The displacement thickness concept (cq. (9)) suggests that the eddy viscosity is proportional to the entrainment or detrainment of am- bied fluid. Since segregation of the streams is not expected even for cases with zero net entrainment, it is postulated in thls report that the eddy viscosity should be directly p r o p o r t i d to the Jet mass flow rate plus tie absolute value of the entrainment mass flow rate and inversely proportional to ths half-value radiue. Ln addition, Zelazny's compresalbility factor (eq. (9)) is adopted. The resultant eddy viscosity relation is

Unfortunately, the init id conditions posed by turbojet engine4 in flight are often

6

I , :. 2. The expression analogous to equation (IO), which is appropriate to the core region, is

4

% The relations given provide a clmed set of equations for the solution of the spreading ** and dilution of the jet from a uniform (slug profile) condition 3t the jet exit plane to any

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1 desired downstream location. The solution parallels that given by Donaldson and Gray (ref. 4) except that, because of the inclusion of a moving ambient stream, additional in- tegral terms appear and many of the constants are different.

The integrals in equations (1) and (2) can be evaluated in closed form at any stream- wise location. For the constant-prqerty core region, r5 is obtained in terms of ri with equation (21, whence the streamwise distance corresponding to ri is obtained with equation (1). The entire solution for the core reglon is obtainable in closed form. For the developed region, r5 is obtained in terms of uc with equation (2). The i n c r e m e d l Changes in streamwise distance corresponding to aelected incremedal changes in center- line velocity are obtained wlth equation (1). The streamwise distance corresponding to any desired uc must then be obtained by numerical irtegration.

reference 7. , For all canen where the jet dynamic pressure was greater than the free- stream d}mamic p r e r w * e , the agreement bet qeen calculated and experimental results wan very good.

The method descrlbtd h a s been used to calculate the mixing for the jet test cases in

RESULTS AND DISCUSSION

DispeNion of Jet Exhaust Plumes

Calculations 0i nrhaumt plume dinperaim have been made for both rmall aad large aircraft turbojet ongines at typical flight conditioru. ExhPrut conditloru for the JOS-GE- 13 were chosen to reprerent a small afterburning turbojet cnglne. The es t imatd exhauat comlitionn for the GE4 engine which viu proponed for the Boeing-2707 89T were wed to represent a large afterburn!ng turbojet e-ine. CP~CUI&~OM were also made for the &a- per@* of the exhaud plume of a J798 engine for comparison rlth flight data obtained La the wake of an F-104 aircraft, Both maJslmum afterburntag 2nd IzI;uL1mwn power without afterburnlng were considered for each engine and each flight condition. The following

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starting conditions were usad: flight Mach number, ambient temperature, jet exhaust pressure ratio, jet tot& temperature, and primary nozzle diameter. An isentropic ex- pansion ms assumed from the sonic primary nozzle to obtain the pressure-matched con- dition which was a s k e d to exist at the engine exit. This expansion yielded the jet- to free-stream density and velocity ratios ud the exJuust jet diameter which provided the required initial conditions for the plume dispersion calculation. These initial conditicns for each of the engines and flight conditions examined are shown in table f .

Since the shipe of the radial distribution is assumed to be invariant downstream of the core region and because the velocity difference and concentration difference ratios are !assumed to be identical, the exhaust dispersion is completely defined by relations for the centerline concentration difference ratio and the half-value radius as a function of streamwise distance from the engine exhaust plane. Because Gaussian profiles are as- sumed for the radio1 distributions, an ub i t r a rp choice for the radial extent of the plume region must be made in order to define an average concentration. The jet edge radius re is defined as the radius to the point where the concentration dfflerence ratio is 0.001 times the centerline value. Thus,

and

re = 3. 157rg

, For most turbojet engines. engine airflow remains nearly constant from maximum power without aftmburn!ng through maximum afterburning. Thus, equation ( 14) provides the result that the half-value radius corresponding to a chosen centcrlinc dilution does not vary signtftcantly with power level, although the downstream distance to the specified dilution ratio decreases as power level increases.

and the average and centarline concentration difference ratlos feq. (13)), the relation be- tween re and (caV - e,)/(~~ - c-1 in the downstream region becomes

From the relatlons between the jet edge radius and the half-value radius (eq. (121)

,/

2 5 = 0.999 (15)

The plume radii correspondlng to 1OOO:l average dilution and thu half-value radii corre- sponding to 1OO:l centerline dllution for the engines and night conditions examined are given in table I.

Estimated range of plume concentratlons for NO , CO, and Ox - Table II compares estimated plume and background concentrations for afterburning a d nortatterburning con- dltiom for 1000: 1 dilutlon I e the plume. The engine exhaust concentrations expressed In parts per mllllon by volume (ppmv) represent the range of values obtained from tests of varlous engine6 at simulated altltude flight conditions (refs. 8 to 11). The ambient at- motrpheric cmcentrationar (ref. 12) and diluted concentrations b the plume are expre68ed in parts per billlon by volume (ppbvl. Amblent ozcne levels near the lower end of the range shown would be expected in t\e troposphere, while the higher concentrations wouid be expcctcd In the strrtoaphere.

Calculated and Measured Pollution Levels in a n Aircraft Jet Wake

A8 @Ut Of 8 .hrdy baiw COndU&& to a8M88 the feasiblllty Of 1oCltlIIg ?nd 8rmp1hg m([in8 exhaust productr I n an .kcraft wake, a rendezvous fllght between the NASA h" Rasearch Center's CV-$00 and the NASA Fllght Rerearch Ceder ' s F-101 was conduct&. The fllght experiment wan performed at an altltude of approximately 11 ;.llomrterr at mmlrul fllgM speeds of Mach 0.8. Th8 F-104 as it rcndezvwsed with the CV-9.3 is ahown in IlgUre 5(aL Bceaure of favorable weather conditionr, a clearly vlaible contra11 was produced by the 8ouree aircraft. as shown in figure 5b). Thla vislble contra11 war wed to poaltlon the serulng aircraft (CV-990) ln the F-104 wake. The separation

10

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* between the two aircraft was varied from approximately 2 to 10 klltuncterri duriN: cdch

of two encounters, as shown in figure 61a). For the firfit encounter, the F-104 was flt,wn

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without afterbaning of the 579 encine. Duriw the second encounter, aftrr turn.troun<!. the J79 afterburner wia4 operated.

board the CV-990 are shown in figures 6(b) to (d\. The decrease kn h) th CO and NO, levels as aircraft separation distance was increased shows thc relative nlixinc: and d is - persion of the engine exhaust products wlth distance. The CO data clearly show the higher conccntrition of this specles expccted dcring afterburner operation. The m u - imum measured NOx during the afterburning encounter wa9 approxtmatcly equal to that measured with no afterburning. This result would also be ry>cctcd, since en.$nc altitude emission tests have shown that afterburnin(: has only a small cffcct on the NOx conccntra- tlon (ref. IO). The ozone data do not show any variations whlch can be related to the F-IO4 wake.

sltivlty of 10 ppbv. Carbon monoxide was measured wIth a fluorescent NDIR Instrument with 8 scnsitlvlty of 200 ppbv. Ozone was measured with b d h a n electrochemical total oxidant meter and an ultravfolet absorbtion monitor, The senaitivitics of the ozme in- struments were, respectively, 5 and 3 p p h . From manufacturers' specifications, the response ttmc of the CO monttor to 90 percent of a step input is about 30 seconds, while the response time of the NO, monitor to 90 percent of J step Input is less than 2 minutes. However, because of the turbulence in the F-104 wake, the CV-990 was intermittently pitched in and out of the vleible contrail, and the sanipling instrumcntatlon waq subject to a constantty varylnu input signal. Because of this, the time response of the Instruments can only be approxlmated. And since a correction is not required for lnterprctation of the data obtalned in the wake, no correction has been applied to the data shown in flgure 6.

N'"'

out afterburning are shown It: figure 4. In addition to the centcrllne dllution and half- value radius relations, the average dllWon and the corresponding jet edge radlus re are shown. Also the half-riwspan of the F-104 and the CV-990 are 1ndic;ltcd in fig- ure 4@) for comparlson with the plume radius. The concentration of any nonreacting species in the p1un.e at any deslred downstream illdance can bc calculated from the dilu- tlon relation (fig. 1(.i)) and known or cstlmatcd concentrations al'thc engine exhaust and in the ambient atmosphere.

For the scparatlon distances b d e n the CV-990 and F- 104 during the fllght exper- iment (fig. 6CN. averakc NO, concentrations were calculated for englm exhaust concen- trations of 10 and 40 ppmv without afterburning and 40 and 80 ppmv wlth nfte.-burnlng.

11

The CO, KO,, and O3 data obtained during the rendezvous flight with instruments on

\

Tho oxides of nitrogen were measurepi with a chemiluminescence nronltor with a sen-

The tnstrumentation usc'd was on board the CV-990 for night evnluatlon as part of the 'ob01 Air Sampling Program (GASP). This progtam la dlscussr?d in reference 12.

Jculated dilution and plume spreading for the J79 englne at Mach 0 .8 with and with-

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The ambient NOx level was assumed to be 1 ppbv. Carbon monoxide average concentra- tions were calculated for engine exhaust concentraiions of 100 and 300 ppmv without afterburning and 1000 ;urd 3000 ppmv with afterburning. An ambient CO level of 50 ppbv was assumed. The enginelexhaust was assumed to contain no ozone. A mean ambient O3 level of 32 ppbv was assumed, based an experimental data obtained preceding and follow- ing t h e rendezvous flight elrperiment. The average concentrations of CO, NO,, and O3 calculated for the conditio& of the experiment are shown in figures 6(b) to (d). The sep- aration distance - night time relition has been used to present the calculated concentra- tions as a function ob time for comparison with the measured emission levels in the plume. Because the CV-990 was traversing the plume in an unknown pattern, the gas sampling probe was exposed tn a constantly varying input. Also, as discussed pre- viously, the sampling instrumentation does not have instantaneous response. Conse- quently, concentrations of the order of the centerline concentrations were not expected and not observed. The good agreement between the measured emissions and the cat- culated average concentrations should not be interpreted as a calibratfm of the J79 tail- pipe emissions, which were not known; nor should the interpretation be made that the sample probe yielded an integrated emission level as defined by equation (13). Rather, the comparison is intended to show that concentrations estimated by assuming that the exhaust diffuses as a round jet i n a parallel flow with no chemical kinetics are of the same order of magnitude as the measured concentration levels.

SUMMARY OF RESULTS

The dispersion of the exhaust of turbojet engines into the atmosphere was estimated by usirg a model developed for the mMng of a round jet with a parallel flow. The anal- ysis is appropriate for determining the spread and dilution of the engine exhaust from the engine exit until it is completely entrained in the aircraft trailing vortex pair. In this region, chemica! reactions are not expected to be important and were not considered in the flow model.

The analysis is an integrzl momentum method f o r which the dimensionless local velocity difference profile shapes and the shear stress relation must be specified. The eddy viscosity model used in the shear dress relation was formulated by assuming that the eddy viscosity is directiy proportional to the jet mass nor rate plus the absolute value of the entrainm,ent mass flow rate and inversely proportfonal to the jet vidth.

CalcuIations of tlu dilution of the exhaust for large and small aircraft turbojet en- gines with and without afterbutnilg at typical flight conditions are presented. These re- sults indicate that a 1OOO:l average dilrtion may be expected in less than 15 xconds after aircraft passage. This dilution corresponds to distvlces from 0. S to 7 kilometers

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APPENDIX - SYMBOLS

specific heat at constant pressure

concentration

enthalpy

total enthalpy

Mach number

molecular weight

radius '

jet edge radius jet core radius

jet exit ratliw

half-vdue radius, whru (a - a,)/(ue - ti-) = 0.5

radius where [p' - b.),Mb.& - @),I = 0.5

streamwise rclocity

7 -uo streamrise distance

eddy riscosity

Ln2

gas density

ahear stress Bubscripts:

pt average

c centerline

I jet exit

0 free dream

5 -n?ttdat r5

14

REFERENCES

1. Hoshizaki, H.; Conti, R. J.; Anderson, L. B.; Redler, K. 0.; ud Meyer, J. W.: I Rudy of High-Altitude Aircraft Wake Dynamics. Rep. DOT-TST-90-3, Lockheed

Missiles and Space Co. (AD-754918), Dec. 1972.

Coaxial Gas Jets. J, Appl. Mecli., vol. 17, no. 4, Dec. 1950, pp. 399-408.

3. Hinze, J. 0. : Turbulence. McGraw-Hill Book Co., Inc., 1959, pp. 404-409,

4. Domldson, C. DuP. ; and Gray, K. E. : Theoretical Experimental lnvestigatioa of

2. Forstail, Walton, Jr. ; and ShapLro, Ascher H. : Momentum and M a s s Transfer in

the Compressible Free Mixing of Two Mssimilar Cases. AIAA 3. , V O ~ . 4, no. 11, NOV. 1966, p ~ . 2017-2025.

5. Zelazny, Stephen W. : Modeling of Turbulent Msymmet r i c Coflowhg Streams and Quiescient Jets: A Review and Extension. Ph. D. Thesis, State Unh. of New York at Buffalo, 1972.

ric Gas Streams. Rq,. AEDC-TR-68-333, ARO, Inc. (AD-672975), 1968.

7. Anon. : Langley Workiqg Conference on Free Turbulent Shear Flovs. NASA SP-321, 1973.

6. Chriss, D. E. : Experimental 9Mp of the Turbulent Mixing of Subsonic Axisymmet-

8. Mehl, Larry A. : Preliminary Investigation of Gaseous Emissions from Jet Engine Afterburners. NASA TM X-2323, 1971.

9. Palcza, J. Lawrence: ghdy of Altitude and Mach Number Effects on Fxhaust Gas Emissions of an Afterburning Turbofan Engine. Rep. FM-RD-72-31, Federal Aviation Mmtnistration (AD-74 12491, Dec. 197 1.

je t Engine at SimtAated Altitude Conditions. NASA TM X-2726, 1973. 10. Mehl, Larry A. : Measurement of Gaseous Emissions from an Afterburniag Turbo-

11. Forncy, A. K.: Engine Exhaust Emissions Levels. Paper 73-98, AUA, Jan. 1975.

12. Rudey, Richard A. ; and Perktns, Porter J. : Measuremeut of High-Altitude Air Quality Using Aircraft. NASA TM X-68223, 1973.

15

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TABLE E. - P L F E AND AMBIENT CQNCENTRATK)NS OF OXIDES OF

IJITROCEN. CARBON MONOXIDE. A N 3 OZONE

Condttucd

Wklhout .tfterhurning With afterburning

1 IO 3 20 to 100 20 to 100 40 to 200 40 to 200 10 to 200 50 to 300 e4 to 500 500 to 50qO 500 to 5000 I 1 O I O M o I 0 I 1 o t o m I 0 I lot0200 I

'Parts par bllllon by volume. bPartr gor mllllon by volume.

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