3. PUBLICATIONS/PRESENTATIONS
Menon, S. and Chen, J.-Y. (1995) "A Numerical Processes during Interactions between an Aircraft's Vortices," NASA Conference on The Atmospheric 1995, Virginia Beach, Virginia.

Study Engine Effects

of Mixing and Chemical Jet Plume and its Wingtip of Aviation, April 23-29,
Menon, S. and Wu, J. (1997a) "Large-Eddy Simulations of Interaction between Engine Exhaust Plume and Aircraft Wingtip Vortices," NASA Conference on The Atmospheric Effects of Aviation, Virginia Beach, VA, March 10-14, 1997. Menon, S. and Wu, J. (1998) "Effects of Micro- and Macro-scale Turbulent the Chemical Processes in Engine Exhaust Plumes," J. Applied Meteorology, 639-654, 1998.

Mixing on Vol. 37, pp.

J. and Menon, S. (1998a) "Numerical Studies of Near-Field Plume-Vortex Interactions," AIAA Paper No. 98-2902, 29th AIAA Fluid Dynamics Conference, 15-18, Albuquerque, NM. J. and Menon, S. (1998b) "Large-Eddy Simulations Interactions," J. Geophysics Research (submitted).

of Near

field Plume-Vortex
Wang, Z. and Chen, J.-Y. (1997) "Numerical Near-Field Engine Exhaust Plumes," J. Geophys.
Modeling of Mixing and Res., 102, 12871-12883.

Chemistry

References

Beck, J.,

Emissions
Reeves, C., de Leeuw, on Tropospheric Ozone
F., and Penkett, S. (1992) in the Northern Hemisphere,

"The "Atm.

Effect of Aircraft Env., 26A, 17-19. in Stratospheric
Brasseur, G. P., Granier, C., and Waiters, S. (1990) "Future Changes Ozone and the Role of Heterogeneous Chemistry, "Nature, 348, 626-628. Brown, R. C., Miake-Lye, R. C., Anderson, "Aerosol Dynamics in Near Field Aircraft 22,953. Brown, R. C., Miake-Lye, M. R., Anderson, Aircraft Exhaust Sulfur Emissions on Near 24, 3607-3610. Brown, Buriko, 3606.
M. R., Kolb, C. E., and Resch, Plumes," J. Geophys. Res.,
T. J. (1996a) 101, 22,939-

M. R., and Field Plume

Kolb, C. E., (1996b) Aerosol, "Geophys.
"Effect of Res. Lett.,
R. C., Anderson, M. R., Miake-Lye, R. C., Kolb, Y. Y. (1996c) "Aircraft Exhaust Sulfur Emissions,"

(R52) NOS+O

M---E--*NOS HNOS
(R53) NO2 + OH _ (RM) NO2+NOs _N=Os
(R55) N_Os _ (R56) (R57) HNO_ _ H'NOS_
NOS + NOS OH + NO OH + NOS

(RSg) (R59)

SOS + O_ SO: + OH _

SOs HSOS

1.49 10J2cxp(-601:r) !.97 x 10"_:exp(867.3/T)
1.19 x I0 ") 2.0 x 10"t2

(R60) co+o_U

2.49 x 10 "s3cx.p(-1550/T)
2.66 x i0 "l' cxp(-1459/T)
The effective second-order reaction rate constant is [Demor et aL, 1992]

k(M,T) = (.

ko(T)[M]
_n*_is'_k(r>{ul/k'_r)))2_''
Forlhird-,ordcr low-pressure second-ordcr and high-pressure limits, thcunits cm6 mol_cu]c s"I am "2 and cm 3 mol_uJ "is"Imspc_ctivly. Forsecond.ordcr low-pressure firsl-ordcr and high-pressure limits, thcunits src cm _s"s and s", respectively.
Although the species in the quasi-steady state do not appear explicitly in the global reactions, their kinetics effects are included in the elementary reaction rates. The concentrations of quasi-steady state species following expressions: [HSO3] are computed by iteration using the
[O] --k_[O_l[SO] + k_[H][OH] + kdIHl[HO2] + k_o[OHI[OH] D O = k_,_[SO2]

4- ]'16[H202

+ k_s[SO3l + k_iH][M]
] 4- ]60[CO] 4- k]I[HNO3]

+ k42[Ol[M]

4- ]2_[HNO2 ]
+ k_s[NO_] + k_[HO21 + kss[SO21+ k_[O_ kv[OH] 1+
= k59[OH][SO2] k40[O2] A [NO3] = k26[O1+ k2s[NO_] + k2_[OH] + ks4[NO2] + k2_[NO] ' d = h[[OI[HNO_] + h_IN2Os] + k_2[O][NO2] + kz_[NO2][O_ ]+ k3:[OH][HNO_ ]; B E [H2I = _" ko[OH] ' E = ke[H][H] + k3[H][OH] + k_,[H][H202] + k2_[H][HNO2 ]+ ks[HI[HOwl , [SOl = k,._[O]tSO21 /q4[O3] +R_s[OH] +/q6[NO2] +k3_[O2]. ' ' + ksz[NO2 ] + kso[ NO] + kz_[NO2 ] + k43[O2 ],

[H] C' =

B = k3s[OH][SO] + k[OH][O] + ]o[OH][H2 ]
+_,_[OHI[CO], C = k_[H] +k_[OH] +k_[O][M] +k_s[H_O2] +k2_[HNO2]
+ kl'_ [H202 ]+ ks[ HO21 + ks[HO2 ]+ k47[OH] + k,,[H02 ] + k2[O3]+ k24[NO2] +k45[O2], [H202 ] = k4[HO2 ][1"[O2 k_[HO2 ]+ ][HO2 ]+ k_[OH'][OH]
t_s[H] +k_dO] +ki_[H] +kt2[OH]
WANG AND CHEN: MODELING F

12,877

triO21 = E, F = k_,[H][H:O:I + k_dOl[H_O21 + k27[OH][NO31
+ kI2[OH][H202 ] + k${OH][O31 + k40[O2][HS%I + _45[H][O2 ], G = ks[H] + ks[H] + k4[H] + k|310] + k49[HO2 ] + k15 [HO21
action (30) becomes less important free-stream/exl'must ratios. Reaction
for mixtures (19) becomes

with high the domi-

nant mute for NCh production for mixtures with large free-stream/exhaust ratios as more O3 is present in the system Reaction (51) has positive sensitivity with respective to NOz as it produces FINCh which then forms NO2 via reacdon (30). Figure 6 shows the sensitivity information of O3 over all mixtures. As expected, reaction (19) NO + 03 _ NO2 + O_ is the most irnportam siep in controlling Ch. For mixtures with low free-stream/exhaust ratios, O3 is produced via reaction (43) O + O2 + M _ O3 + NL and NO2 is converted to NO via reaction (22) NO2 + O --* NO + 02. When free-slnaun airis increased, the importance of these two reactions diminishes due to the consumption of the O radical. Evaluation of Reduced Chemistry

earlier, streamwise

nearly
all previously The formation
employed to determine (lest ruction Before inflow inflow decay

periodic the

direction). on the

objective

of turbulence

transport

of SOw. and
of ozone. discussing tile details flow field scalar of the plume-vortex summarized. concentration phune-vortex employed interaction, Figure is used region. the while the effect of different the effect marker) inflow of
turbulence turbulence with

on the on the

is briefly S02

2 shows

as a scalar Three

increasing conditions

plume are

age in a B747 Two

different
turbulence but same after in the in the with

same the

energy third into

sl)eclruln used the

a 5c7_ and isotropic

10% turbulent spectrum

intensity, as the other
respectively, two but with a final realistic was

case the

initial evolving third frst

introduced

flow field
for a certain case. the inflow the

length evolved

of time

turbulent turbulent

intensity isotropic turbulence. yield
of.5_7_. Thus. state whereas igure ahnost identical at 2.

to a more but

two cases, that

field is isotropic with

is not realistic turbulent of the that
It can be seen results. least here). field. This for the means global

the cases the

the same

intensity

that measure

effect used

of evolving here. (Note

inflow

turbulent measures have

field are

is small, of interest on tile

global does must with

However, This implies

it can that

be seen the
turbulent turbulent and jet

intensity intensity

an effect

flow The

inflow vortex

be carefully flight

chosen. such

turbulence climate,

intensity altitude and

in the ambient

varies

conditions 5{7_ and

flow field.

10_/, is

common
in tile typical with 5% and species the results.

of interest

[Ragab may
and Sreedhar, to quanti_,

199413]. an upper

Thus. and

simulations lower bound

10% inflow distributions
turbulence in actual velocity

be used

flights. computed from these the three cases vortex turbulence by

computed plume).

to varying comparison It can structures role

age of the and can

Thus, in this

experimental that the

is expected accurate prediction 15NIWAKE the
be observed of the turbulent diffusion ignore of average of the

figure.

be argued in the LES

resolution since

small-scale plays small a large scale

improves

in scalar effects. decay. Figures

mixing. This may

In contrast. contribute to

predictions

under-prediction 4.2.2. Detrainment two the

scalar the

concentration plume magnitude two jet plumes the

6a and plot.s in the

show. at
respectively, v=0 in the entrained vortex. from first
instantaneous simulation. After

vorticity The

contour develop

x-z plane

almost jet plume
independently starts the to get wing-tip This
4 semi-spans. into the wing-tip
4 semi-spans, and two jet the jet plumes

outboard

vortex, the

plume break

is deflected up into

towards smaller

Further

downstream, by patches

structures.
is characterized much lower The

of concentrated

vorticity

are surrounded

by flow with Figure 6.
vorticity. level of intermittency seen in the flow field makes Reynolds averaged
approach portions Oil the the
inapplicable of tile outboard contrary, due

it cannot

capture are deflected turbulent inboard
this effect. and motion jet plume planes that it. As

It can

be seen into the

tile broken vortex. of

jet plmne to the strong of the

entrained and gets such

wing-tip influence the show core
relatively delrai_ed as the

weak from B747, vortex

vortex,
a portion of contrails behind

wing-tip that contrail

vortex. there and out, are
Observation two contrails that

from the

widebody one from

aircraft;

is the Gel':

normal and

another irregular

is distinctly of the and

separated wing-tip

or parabolic to the

discrepancy we need

numerical including and

However, binary

to confirm and near

to carry

these This

sinmlations, effort

nucleation in the

coagulation

aerosol

models.

is underway

will be reported Some into larger relative the
future. are also analyzed. shown in Figure 12. than The mass of entrained simulation simulation be used the ,VO and shows does. that Since 5'03, a the the

integrated wing-tip

quantities vortex are
Temporal the spatial can and

amount reaction

of NO rate
is entrained is small, NO between

for NO The

entrainment the spatial plume.

to represent

entrainment may be due

process. to the

difference velocity begins
simulations between engine into the plume two part to I Figure 12

deficit around

of the jet

The most

deviation
two types is entrained parts. becomes the ,\'O One
of simulations into part the
z = 12s, where and the inboard

of outboard plume splits

wing-tip gets the

engine

eventually from

into the The

wing-tip chemical

while that

second result due

detrained concentration

vortex. in these

will be different

two regions.

Tile spatial

mass case.
entraiument Tile discrepancy earlier. and S03 the

of S03

wing-tip concentration number in the

for tile

in the The
in the of aerosol condensed

vortex measured sulfuric

is particularly in tile acid wake to been

bothersome [Faheg the

as noted

increased increase

et al., 1995] between as one Tile can high affect

potential and

(due have
condensed could spatial impact

water) long again

forming term

on these global

particles
identified balance. conditions

process peak the

that for the
atmosphere that simulation plume. and

chemical boundary Figure

H2.qO4 oil

suggests

especially

near-field

In order plunm also 502 mass

to study

tile effect and the
of heterogeneous spatial simulations reactions

reactions without have

of H:VO3 heterogeneous negligible

evolution, carried out.

temporal Since

reactions on.\O

were and of.c,'0:3 and the in

agreement shows
experimental agreement axial data.
plume-vortex data and shows the

for the of average

qualitative with availal)le vortex The indicate (especially were impact that iz_ for the

LIDAR for the

concentration with wing-til) analyzed. Results exists

distance The

B747 and in the

quantitative plumes

agreement into the

entrainment captured

detrainment spatial

numerically of fluid

simulation process and
(for the has been temporal has
13747) and estimated. simulation an important partly of the

mechanics

a significant the predicted
difference SO3 of sulfuric

spatial This in the the

concentration). acid aerosols studies suitable and
difference wake data. near and

implication the also

prediction between spatial it was using
explain results process. was

discrepancy shows that

Analysis
simulation determined the spatial

is more that model.

field interaction in the B747
For example, only captured

(observed

contrail)
Acknowledgments. Cez_ter and

This work

was supported

in part

by NASA

Langley Research

Research hfitiative
tile Air Force Office of Sciez_tific Research

uz_der tile Focused

(monitored were carried Huntsville.

by General

Electric

Aircraft

Engine

Company. NAVO,

Cincinnati. Stennis

Ohio). Space

Computations and ARC.
out at the DoD HPC center

at MSRC

Center
Arnold, F., J. Scheneider, van Velthoven, potential 24, 57-60, Brown, K. Gollinger, H. Schlager, P. Schulte. sulfur D. Hagen, dioxideformation, P. Whitefield. and

Observation

of upper

tropospheric radical

and acetone-pollution: Geophgs. Re._. Lett.

implications 1997.

for hydroxyl

and aerosol

R., R. Miake-Lye, plumes, J. Geophgs.

temperature with squares) mechanisms. major species

and Subgrid

major and the

species reduced

distributions (lines with by

with modified with are

detri-

reversed

is modeled by pdfjet Lines lines
Curl's 44 differresults are model. 45
model.. distribution mixing and simulation, with squares Curl's reversed of subgrid mixing subgrid model.
Centerline ent with results treatment subgrid with

well-mixed, mixing

triangles mixing

modeled

by modified
Comparison of the ratios of various chemical over the ambient background levels from the km to UNIWAKE results at 20.2 km and km..
species concentrations present predictions at 1 values at 126.0 46

to measured

4.1 4.2
Schematic _1 and Schematic the curve saturation TLc is the

of the partial

molar molar

volume, volume

9, of a two-component of component 1 and formation. Ps,_t,tiq(T) and the
mixture. 2, respectively. It shows and ice lines. 82

_2 are the partial

showing threshold condition for contrail of the liquid water saturation pressure pressure threshold Psat,ice(T) ambient versus temperature temperature

for contrail

formation

4.3 4.4

Spatial distribution The radial distance, Spatial the flow distribution field distance, densities with coagulation
of temperature in the flow field of a B747jet engine. r, and the downstream distance, x, are in unit m. of the jet x, are total number The rates density radial along droplets, downstream and sulfate nucleation of soot distance, the jet soot particles r, and plume particles, with in the engine. in unit nucleation versus

of a B747 H2SO4-H20

downstream 4.5 4.6 Homogeneous Number soot 4.7 without Mixing stream ppmv/sec H2SO4 lution 4.8 Average plume 4.9 coated

m. axis. and and

of volatile H2SOa-H20

H2SO4-H20

effects. sulfur species homogeneous Dashed aerosols versus downrate ,/horn in unit of the evolution of gaseous pure dito the for a soot of gaseous
ratio of gaseous distance. The is also shown. species (solid age. surface when
line represents is included sulfur

nucleation

as compared species
line).. coverage of oxidized of coverage versus H2SO4 It is composed by adsorption
and by scavenging of volatile H2SO4-H20 Maximum conversion efficiency of emitted percentage of fuel sulfur conversion
aerosols. SOx to H2SO4 at axis engine.

89 versus ra2%, 91

to SO3 in the

Subscript with that

involved

Thermodynamic

Database.

output

3.1: Reaction

Reaction Rate

Mechanism: Constant

Reactions -1 sec- 1)

(cm 3 molecule
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 Rll R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28 R29 R30 R31 R32 R33 R34 R35 R36 R37 R38 R39 R40 R41

O + 03 --+

1.21 x 10-11exp(-2125/T) 1.15 x 10-1exp(-436/T) 8.10 x 10-21T2-Sexp(-1950/T) 2.8 x 10-1exp(-440/T) 6.9 x 10-nexp(-636.9/T) 2.8 x 10-12T4%xp(-677.9/T) 1.83 x 10-nexp(173.3/T) 1.9 x 10-12exp(-1000/T) 1.11 x 10-16Tl'64exp(-1589/T) 8.34 x 10-17Tl'54exp(355/T) 5.09 x 10-11exp(72.6/T) 2.13 x 10-13T47exp(-179.8/T) 2.71 x 10-nexp(-224/T) 1.4 x 10-14exp(-600/T)
H + O2 -----+OH + 02 H + OH ----+ O + H2 H + HO2 _ H + HO2 --_ OH + OH H2 + 02
H +HO2 _ H20 + O OH + O -----+H + O2 OH + 03 -'-+ HO2 + 02 OH + H2 _ H20+ H OH + OH -----+H20 + O OH + HO2 ----+20 + 02 H OH + H202 _ H20 + HO2 HO2 + O -----+OH + 02 HO2 + 03 -----+OH + 202 HO2 + HO2 _ H202 + H202 + O -----+OH + HO2 H202 +H _ OH +H20 H202 + H -----+HO2 + H2 NO + Oa -----+NO2 + O2 NO + HO2 --+ NO_ + OH NO + NO3 ---+NO2 + NO2 NO2 + 0 _ NO + 02 NO2 + 03 ---+NO3 + 02 H + NO2 _ OH + NO NO2 + NO3 ---+NO + NO2 + 02 NO3 + O ---+NO2 + 02 OH + NO3 --_ H02 + NO2 HNO2 + O --+ OH + NO2 HNO2 HNO2 HNO3 HNO3 + H _ NO2 + H2 + OH --+ H20 + NO2 + O ---+ OH + NO3 + OH --_ H20 + NO3
2.2 x 10-13exp(600/T) 2.33 x 10-11exp(-2814/T) 1.7 x 10-nexp(-1800/T) 1.77 x 10-11exp(-2890/T) 2.14 x 10-12exp(-1408/T) 3.7 x 10-12exp(240/T) 1.8 x 10-11exp(ll0/T) 6.5 x 10-12exp(120/T) 1.2 x 10-13exp(-2450/T) 1.4 x 10 -1 1.91 x 10-13exp(-1696/T) 1.0 x 10 -11 2.3 x 10-11 2.0x 10-nexp(-3000/T) 2.0 x 10-nexp(-3700/T) 1.8x 10-11exp(-390/T) 3.0 x 10 -17 4.02 x 10-14exp(317.7/T) 1.55 x 10-13exp(-2288/T) 4.3 x 10-12exp(-l148/T) 8.59 x 10-11 1.4 x 10 -11 3.0 x 10-12exp(-7000/T) 3.17 x 10-nexp(-4455/T) 1.2 x 10 -15 1.23 x 10-1_exp(-316.8/T) 4.44 x 10-16T'98exp(94/T)
SO + 02 ---+SO2 + O SO + 02 --_ SO_ + 02 SO + OH --+ SO2 + H SO + NO2 ---+SO2 + NO SO_ + 02 --.-+ 02 + SO3 SOs + O ---+ 02 + SO2 SO3 + H20 _ H2804 HSO3 + 02 _ HO2 + SO3 CO + OH --+ CO2 + H
Table 3.2: Gas Phase Thermal Decombination
Chemical Reaction Reactions

mechanism:

Three-Body
Reaction R42 R43 R44 R45 R46 R47 R48 R49 R50 R51 R52 R53 R54 R55 R56 R57 R58 R59 R60 O + O _ 02

Consequently, in terms as there addition, the species

of major is no need

by a set of algebraic ordinary differential with are the

computing species.

for these

the stiffness in the

of the ODEs

derived The

is reduced Newton

fast-reacting.

iteration

Y*(k) h*(k) _

Residence Time,
Temperature, Enthalpy, h(k) T

rn Y(k) h(k)

Figure reactor
Schematic where inlet the
of a Perfectly-Stirred rh is the mass The key condition.
Reactor flow rate, parameter

(PSR). is the

The species
characteristics k, and time,

is shown,

k denotes
superscript 7" = pV/rh.

* indicates

residence

is used

to solve state

coupled species.

nonlinear

algebraic

equations

for concentrations

Sensitivity
information influence on the as
is useful for identifying the controlling of a certain chemical The steps that

Sensitivity have strong

creation/destruction

species.

sensitivity

are displayed

OXk _z,k = OAi' (3.4)

f_,,k is the change

of change

of the A,,

species, i-th

due rate

to a small
in temperature-independent

pre-factor,

k, = AiT n exp(-Ea/T).
27 The transient well-mixed reactor (WMR) model enablesone
evolution air. of chemical model kinetics of the engine here exhaust gas subject the WMR

to injection

of ambient with 3.3.

is employed A schematic

to investigate for the can
sensitivity is sketched as

of species in Figure

respect Similar

to reaction to the PSR,

diagram time

be defined

TR = rh'--a'

where Using written

of gas inside conservation

reactor equations

rha is the

entrainment and energy

rate. can be

As more

is entrained

(R19) the
becomes sensitivity by with due
important. with respect to different + + 02 steps. M, and The the
Figure buildup product SO3 (not nally
3.8 shows of H2SO4 HSO3 shown

of H2SO4 (R59) 02

is initiated reacts plot

SO2 + OH reaction H2SO4

+ M --4 H2SO3 (R40) sensitivity

H2804.

further on the

via fast small

--+ HO2 + Fi-

to the (R39)

to this Since OH

reaction).

is generated

SO3 + H20

2.0xl 0.o7
10. 2OH-=.H=OO 11. OHHOt==.H=OO, 20. NOHO=a)NO,+OH 30. HNO,OH==.H,ONO_ 31. SO,+HIO=:_H, SO. 48.2OH(.M).=.H,O=(M) Sl, OH+NO(+M).=.HNO,(+M) S3, OHNOt(M)==_HNO=(+M ) 59. $O=_OH(M)=_.HSO=(+M)

1.5xl 0.o7

/j_ _'=

1.0xl 0.o7

_ _ _ B B m _ _

4)-- _.[3--.

5.0xl 0.o8

-5.0xl 0.08

- 1.0x 10 _

"1.5x107 10.4

, ,,,,,,I 10.3
E_'R--]-E_ -B- B -_- G- E3--E]_

i , , ,

i i iiiii

i i liill

10 "1
Figure 3.8: Sensitivities of H2804 to reaction steps predicted by WMR model.

mainly sumption

NO2 via (R10) and

three-body (R48)

reactions as depicted

(R51) in Figure

by self
reactions is expected section

3.4, the

conversion

of SO2

to H2SO4 later

to be low. from the

low conversion of major species of these

fraction species. along

will be demonstrated

in this Figure

distribution the major top

sulfur evolution figures

3.9 to 3.11 is also The

depict plotted

second plume

x-axis age.

to show
corresponding in Figure 3.9.

centerline

evolution

of major

nitrogen

is shown

35 At about 5 m past the nozzleexit plane, the turbulent stirring (macroscalemixing) becomesimportant and the correspondingplume ageis about 3 ms. The primary exhaustproductsNO andNO_stay nearly constantup to this point and then decrease slowly. In the early jet regime, small amountsof NO and NO2 are oxidized by OH (not discernibleon this logarithmic scale)via three-body reactions (RS1) and (R53). However, these reactions lead to significant amounts of nitrous acid, HNO2, and nitric acid, HNO3, as comparedto their backgroundabundances. A small fraction of HNO: is consumedthrough (R30) when the OH level is high. After OH becomes depleted(compareFigure 3.11), the chemicalbuildup of HNO2 and HNO3 ceases and thesesecondaryexhaustproducts are diluted like tracers,similar to the fate of NOx in the late jet regime. At later stagesof plume dispersion these acids may either becomephotolyzedunder daytime conditions, or depletedby heterogeneous removal processes. In the earlyjet regime,the nitrate radicals,NO3,aregeneratedvia (R52)NO: O + M -_ NO3 + M and (R32) HNO3 + OH _ H20 NO3. The chemicalproduction of NO3 ceasesas soon as O and OH becomedepleted and its further evolution is governedby plume dilution. In the early jet phase,dinitrogen pentoxide, N205, is producedvia (R54) NO2+ NO3+ M --_N205 + M in contrast to the strong thermal decayreaction (R55) N205 + M _ NO2 + NO3 + M. Hereafter the N205 abundance increasesquickly by entrainment, and at the endof jet regime,N205 already attains its ambient level. The NO3level at the end of the jet regimeis much lower compared

by doubling

volume

consecutive
52 The typical sizedistributions of nascentprimary soot particles are assumedto be log-normal, with median radii of 15-30 nm, modal widths of 1.4-1.6, and number densities of 10_-10 cm-3 [Hagen et al., 1992; Petzold and SchrSder, 1998]. _ log-normal distribution for the sizeof soot particles can be expressedas (lnr- lnfg) 2] _ia _ j
per cm a of air in the size range of all sizes deviation. radius per The cm a of air, number by The
n(lnr)= where n(ln r)d In r is the number total

V/_ngt

a 9 exp-

(4.10)

from In r
to In r d In r, Nt is the median particles radius, in the dN and jth

number geometric

of particles standard around the

fg is the density of

a 9 is the size

bin centered

ry is given

= n(ln r)d In r -

exp v_r In ag

(4.11)

Nucleation

The liquid

classical droplets, rate
nucleation or embryos, in the form

theory

is based with

on the their

equilibrium vapors.

state The

of critical-sized theory gives the

in contact of

parent

J = Aexp(-AG'/(P_T)),

(4.12)

where prefactor, the

J is the AG*

nucleation is the of an

with of the and
of embryos/(cma-sec), free energy during constant. the
A is the phase The calculated.

kinetic for

change embryo,

Gibbs /_,

change exponential

is the AG*

universal

dependence

of J on AG*

be accurately

53 The changeof the Gibbsfreeenergyfor the formation of a liquid embryoin contact with a binary vapor mixture can be written as [Flood, 1934;Reiss,1950;Doyle, 1961]
AG = n,(/_ - #_) + n2(#_ - #_) + 4rrr'2a, (4.13)

conversion fuel sulfur

(SO3+H2SO4) is lower

for higher

4.5.4 Threshold temperature for contrail formation

Jet-A and craft

1 fuel is a standard combustion kerosene heat with

aviation

kerosene

with hydrogen [Schumann,

of mH =0.14 air-

specific burning

of Q = 43 x 106 J/kg a thrust and

1996]. engine

For a B747
F = 31.1 x 103 N per the air velocity are estimated
[Schumann, the and propulsion EIH_o
1996], effi-- 1.25, humidity K.
a fuel flow rate ciency and the

rh = 0.785 H20 With

V = 237 m/s, to be rl = 0.216 atm and

emission the

respectively. RH, For = 30%, a higher

ambient the

pressure threshold humidity humidity K which

P_ = 0.2361 ambient RHa

we compute ambient higher
TLC to be 221.51 K. As expected, For situation

relative relative

= 50%,

TLC=222.48 contrail

ambient and RH

air with = 50%, Hence,

facilitates is about would

formation. than the

rl = 0 with
TLC is 220.19 the Appleman's the
2 K smaller give lower heat
= 0.216. since wake it did vortex

criterion

threshold kinetic
temperatures energy in the

not consider regime.

Given threshold pressure the
the overall temperature (altitude),
propulsion turns as seen out from

of an aircraft

the type relative (4.68).
of fuel burnt, humidity In Figure versus

the and 4.15,

to be a function equations (4.65),
of ambient (4.66), formation 100%. value and
temperature humidities is the

is plotted The

ambient efficiency jet or

for ambient

of 0, 50, and approximate tend

rl is specified engines.

to be 0.3,

which that

for modern

commercial pressure

It clearly

indicates

to form

at higher

81 higher relative humidity. The threshold temperature is seensensitive to the aircraft propulsion efficiency,and contrails tend to form at a higher propulsion efficiency.

mole fraction

Figure _1 and 4.1: Schematic partial of the molar

of the second

partial volume molar

component,

mixture.

volume,

_, of a two-component 1 and 2, respectively.

_2 are the

result conden-

embryos H20 engine

also enhance Consequently, number

of H2SO4 from area

onto the nozzle

SO3 and

increases aerosols.

cumulative

SO3 emission

also promotes

99 activation of soot particles with enhancedacid coating. This suggeststhe need for measurements the partitioning of sulfur species(SO2and SO3)at the exhaustexit. of The threshold condition for ice contrail formation behind an aircraft dependson the ambient pressure,the ambient relative humidity, the overall propulsion efficiency of the aircraft, and the fuel properties such as the fuel hydrogen massfraction and the specificcombustionheat. Higher valuesof ambient relative humidity or pressure facilitate contrail formation. The threshold temperature is found sensitive to the overall propulsion efficiencyof the aircraft. The prediction of particle and speciesdistribution in the near-field plume can serveas input for the follow-onlarger-scalemodel. The presentwork alsoprovides an estimateof the aerosolsurfaceareadensityfor subsequent valuationof heterogeneous e oxidation mechanisms the wake. in

American ation

Society fuels,

for Testing

and Annual

Materials Book

(ASTM) of ASTM

Standard Standards,

specification Philadelphia,

aviPa.,

D 1655-93a,

555-563,

Anderson, exhaust Geophys.

M.R., plume Res.,

Miake-Lye, structure 101, and

Brown,

R.C., ER2

C.E., in the

Calculation stratosphere,

emission 1996.

4025-4032,

Appleman, Amer.

H., Meterol.

The formation Soc., 34,

of exhaust 1953.

trails

by jet

14-20,

Arnold, jet

F., Scheid, aircraft

J., Stilp,

Schlager, altitude,

H., and

Reinhardt,

M.E., gases
Measurements NO, NO2, HN02,

emissions Geophys.

at cruise Res. Lett.,
I. the odd-nitrogen 1992.

and HNOz,

19, 2421-2424,