nenes et al-2001-journal of geophysical research solid earth (1978-2012)

7/25/2019 Nenes Et Al-2001-Journal of Geophysical Research Solid Earth (1978-2012)

1/26

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. D4, PAGES 3449-3474, FEBRUARY 27, 2001

A theoretical analysis of cloud condensationnucleus

(C CN) instruments

Athanasios Nenes

California Institute of Technology,Pasadena,California

Patrick Y. Chuang

National Center for AtmosphericResearch,Boulder, Colorado

Richard C. Flagan and JohnH. Seinfeld

California nstituteof Technology,Pasadena,California

Abstract. The behaviorand performance f four cloud condensation ucleus nstruments re

theoreticallyanalyzed.They include he staticdiffusioncloud chamber SDCC), the Fukuta

continuouslow spectrometerFCNS), the Hudsoncontinuouslow spectrometerHCNS),

and the California nstituteof Technology ontinuouslow spectrometerCCNS). A numeri-

cal model of each nstrument s constructed n the basisof a general luid dynamicscodecou-

pled to an aerosolgrowth/activationmodel. nstrument erformances exploredby simulating

instrument esponsewhen sampling monodispersemmoniumsulfateaerosol.The uncer-

tainty n the wall temperature oundary ondition s estimated or all the instruments nd s

found o be appreciable nly for the CCNS. The CCNS andHCNS models easonablyepro-

ducedexperimental ata, while reported imits were alsoverified by the FCNS model. Re-

garding he performance f each nstrument, imulations how hat the SDCC produces rop-

lets hat are monodisperseo within 10% of the particlediameter for particlesof a constant

critical supersaturation).he FCNS can potentiallyactivateparticlesover a wide rangeof

critical supersaturations,ut the prevailingdesignexhibits ow sensitivity o particleswith

criticalsupersaturationselow 0.1% as a resultof the short ime available or dropletgrowth

under ow supersaturations.he resolution apabilityof bothHCNS and CCNS with respect

to critical supersaturations shown o be particularlysensitive o operational arameters. his

is a consequence f the stronglynonlinearnatureof dropletgrowth;dropletsize cannotalways

be used o distinguish articleswith differentcritical supersaturationecause f the growing

droplets' rend owardmonodispersity. f the two instruments,he HCNS generallydisplays

higher esolution apability.This is attributed o the smoother nd monotonicsupersaturation

profilesestablishedn the HCNS. While differentdesignparameters r operating onditions

may lead to modestshifts n the performancerom thatpredicted ere or any of the four in-

struments,he essentialeatures escribedn this paperare nherent o their designs.

1. Introduction

In theory, the cloud droplet activationspectrumof atmos-

pheric aerosols an be inferred on the basis of composition.

Measuring he completechemicalcomposition f atmospheric

aerosolas a function of particle size in real time, however, s

not yet possible.Thereforea direct measurement f the parti-

cles hat activate o form dropletsunder supersaturationsypi-

cal of atmospheric louds s the acceptedway to experimen-

tally measurecloud condensation uclei (CCN). Existing in-

struments o determine he CCN distributionexposean aero-

sol sample o a controlledenvironmentwith known water su-

persaturation rofiles; he activationspectrums then obtained

by measuringhe number or sizedistribution) f particles hat

activate.

Copyright 001 by theAmericanGeophysical nion.

Papernumber 000JD900614.

0148-0227/01/2000JD900614509.00

This studyanalyzes he performance f four existingCCN

instrument esigns. he main focusof this work is to deter-

mine he capability f each nstrumentor, moreprecisely, f

the methodology mbodied y each nstrument)o resolvea

CCN activation pectrum. he resolution omputeds solelya

resultof the process f CCN activation nd growthwithin

each nstrument; ncertaintyntroduced y the dropletdetec-

tion systems not considered. urthermore,he modelscon-

structed ererepresentdealized nstruments.his abstraction

allows one to calculate he best possible theoretical imit)

resolution or an actual nstrument;secondary ffects not con-

sidered n thesemodelswill further degrade he resolution.

In addition o assumingdealized nstruments,t is also as-

sumed hat a perfectlymonodisperseerosol s introduced,

composedf pure NH4)2SO4.n reality,atmosphericerosol

is polydispersendwith a nonuniform omposition. s a con-

sequence,articles ith he same otentialor activation eed

different imes or growth; his shouldhave a deleterious f-

fect on the instrument erformance ut will not be addressed

in the current study.

3449


2/26

3450 NENES ET AL.' ANALYSIS OF CCN INSTRUMENTS

An important uncertaintyarises rom the water film tem-

peratures hat are used to generatesupersaturationn each n-

strument. Typically, CCN instrumentsmeasureand control

temperatures y using thermocouples or thermistors) hat are

embeddedn thechamberall atherhan t hegas-wetur-

face interface.The actual emperature ifferencebetween he

cold ndhotwaterilms s lowerhan hemeasuredalue

owingo he hermalesistancesf he latendilms,eading

to a lower supersaturationhan intended.As a result, the in-

ferred ctivationpectrumsbiasedowardmallerizes.

In the sections that follow, the CCN instruments are de-

scribed;henhemathematicalodelssedosimulatehem

arepresented.n estimatef uncertaintyn thewaterilm

temperatureoundaryonditionshenollows.heesponse

to a monodisperse erosol nput is simulated or each nstru-

ment. Finally, the performanceof each (idealized) nstrument

is assessed on the basis of these simulations.

2. Description of CCN Instruments

Of the CCN instrumentscurrently available, we will focus

upon four: (1) the staticdiffusion cloud chamber SDCC); (2)

the continuous low parallel plate chamber,specifically, he

designof Fukuta and Saxena [1979] (FCNS); (3) the CCN

spectrometer f Hudson [1989] (HCNS) and; (4) the Califor-

nia Institute of Technology (Caltech) CCN spectrometer

(CCNS) [Chuang et al., 2000]. Other instruments,or exam-

ple, isothermalhaze chambers IHC) [Laktionov,1972], have

been used to measure CCN but will not be discussed here.

IHC instrumentsdo not actually activate the particles nto

dropletsbut rather measure he diametersof particles n equi-

librium with an ambient relative humidity of 100%, from

which the critical supersaturation, , can be inferred. In the-

gl

wall

"' Coldwall

, Hot wall

,,"'*l view VOlume l

symmetryxis - . .......

side-wall

origin ........................................................................................................................................

i Cold wall

Figure 1. Staticdiffusioncloudchamber SDCC).

H

0.01

t Coldlate

- -- 273

- " 283

-- 290

_

[ i i

0 1 2 3 4 5 6 7 8 9 10

Temperature ifference etweenplates K)

Figure 2. Maximum supersaturationpercent)n the SDCC

as a function of hot and cold plate temperatures. inear

temperature nd water vapor concentration rofiles are

assumed. ater vaporsaturation ressures calculatedrom a

correlation ivenby Seinfeld nd Pandis 1998].

ory, this s not a limitation f the particles re composed f in-

organicsalts, but ambiguitycould arise if slightly soluble

compounds r surfactants re present n the particles Alofs,

1978; Shulman et al., 1996].

2.1. Static Thermal Diffusion Cloud Chamber

These nstruments re among he oldest or measuringCCN

concentrations.he original static hermal diffusionchamber

design Twomey,1963] consists f two parallelmetal plates,

held at different emperatures, ith their facing surfaceswet-

ted (Figure 1). Assuming uiescent onditionshroughouthe

chamber, inear emperature nd nearlyparabolic upersatura-

tion profilesdevelopbetween he plates,with the maximum

supersaturationocatedmidway.Figure2 shows he maximum

supersaturationeneratedn the SDCC for a varietyof hot and

cold plate emperatures.he CCN that are able o activate t

the prescribedmaximum supersaturation row to become

large dropletsand in this way are distinguishedrom those

that do not activate. The concentration of CCN that activate at

thisprescribed upersaturations determined y measuringhe

droplet number concentration.n order to obtain the CCN

spectrum,he numberof activated ropletsmustbe measured

at severalsupersaturations,hich s achieved y changing he

temperature ifferencebetween he plates.This processypi-

callyrequires everalminutes er spectrumLala and Jiusto,

1977]. The lowest critical supersaturationhat can be meas-

ured in the SDCC is around 0.2% [Sinnarwalla and Alofs,

1973].

One of the primary challenges egardingSDCC measure-

ments nvolves he methodused or counting he particles hat

activatewithin the region close o the maximumsupersatura-

tion. Initially, direct countingof the activateddropletswas

used but has been almost abandoned wing to the difficulty


3/26

NENES ET AL.' ANALYSIS OF CCN INSTRUMENTS 3451

Outlet

Metalnvelope ............................................

.....:::::::::...

Insulation

Inlet

Hott s

H

,/

Cold tip

It__A_erosoj_egi_on__.1

origin

state, eliminating transients hat complicate data analysis.

Furthermore, sefuldata can be obtained ontinuously,ather

than in the sampling ntervalsof batchcycle operation.When

the sample s confined o the region close o the centerlineof

the instrument,all CCN are exposed o essentially he same

supersaturation.FDC measurementsre imited o supersatu-

rations arger han about0.1%, owing to the long growth ime

requiredat low supersaturations. hen the two platesare ori-

ented horizontally,gravitationalsedimentationimits the time

during which dropletsexperience uniform supersaturation

and can causesignificantparticle loss within the instrument.

For vertically orientedplates, he maximum emperature if-

ference hat can be imposed s limited by buoyancy-induced

flows. Of the two configurations, owever, he vertical seems

to be more effective and s normallyused.

An improvementof the CFDC was proposed y Fukuta

and Saxena [ 1979] (FCNS). In this design,a gradient n tem-

perature s imposed perpendicular o the flow direction, so

that particleswith the same esidence ime experience iffer-

ent supersaturations long different streamlines Figure 3).

This instrument hereforecan be regarded s a seriesof CFDC

instruments perating imultaneouslyt different emperature

differences. igure4 showsqualitative emperaturend super-

saturationprofiles perpendicular o the flow for fully devel-

Figure 3. Fukutacontinuouslow spectrometerFCNS).

associated with such measurements. Photometric estimation is

now the method of choice; concentration is inferred from the

light scatteredoff the growing dropletscontainedwithin a

view volume n the proximityof the instrument's enter.Re-

gardless f the scatteringmetricused suchas peak ntensity,

rate of signal growth, etc.), each introducesuncertainties hat

affect the resolution that can be obtained with SDCCs, be-

cause ight scatterings a strong unctionof concentration nd

particle size (both of which vary considerably uring the

measurement).

One could make the simplifying assumption hat all acti-

vating particles, egardless f their critical supersaturation,

have approximatelyhe samegrowthbehavior.This approxi-

mation s reasonablewhen the critical supersaturation,c, s

much smaller than the maximum supersaturation, maxbe-

cause hen he driving orce or growth s approximately qual

to the supersaturation).or S,close o Smax,articleswith dif-

ferentcriticalsupersaturationseeddifferent imes o grow up

to a given size. Furthermore, he parabolic supersaturation

profile within the instrument xposes articles o differentsu-

persaturations ithin the view volume; so dropletswith the

samecritical supersaturationo not grow unifo__rm_ yhrough-

out the view volume.The combination f a nonuniform uper-

saturationprofile and different growth rates among he acti-

vating particles generatesa droplet distribution within the

view volume that contributes o the uncertainty n the aerosol

measurement. As was mentioned in the introduction, addi-

tional uncertainty ould arise rom the differencebetween he

imposedand effective emperature ifferences.

2.2. Continuous Flow Parallel Plate Diffusion Chamber

The continuouslow parallelplate hermaldiffusioncham-

ber (CFDC) [SinnarwallandAlofs,1973]wasdevelopedo

overcome some of the limitations of the SDCC. Because the

samplelow is continuous,he nstrumentperatest steady

wall

wall

Hot

:::::::::;:::::::::;:;:;:;:;:;::;:;:;:;:::;:;:;:::;::;:::;:;:;:;:;:;:::::::::::::::::::::::::;:;:;::;:;:;::::;:;::::::;:;:;::;:;::;:;:;:::::::;:;::;:?:::;:;:;::::::::;:;:;:;:;:

s x

I ....... z..l

E:: :i::i:i:5:5:5:: :::: ::::E: :5: ::: :::5:: : :::i:: : ::i:: :::i:5::5:i: :5:i:::i::i:i:i:i: :i:i:i:i:i:i:i:i::i:i:i::::::::::

Cold

wall

wall

Supersaturation

Figure 4. Typical temperatureand supersaturation rofiles

for the FCNS along a flow section, for developed inlet

conditions.


4/26

3452 NENES ET AL.: ANALYSIS OF CCN INSTRUMENTS

autlet

Inlet

y x

Non-heated

section (top view)

Warmide ThlTh2 h3 h4

........................................................................................................:'"':'::'.'.'.'..'iii

Cold side

Tc1 Tc1 Tc2 Tc3 Tc4

Figure 5. Hudsoncontinuouslow spectrometerHCNS).

oped aminar flow (neglectingsidewalland buoyancy ffects).

The profiles for a given streamlineare similar o thoseattained

in the SDCC at steadystate;so diagramssuchas Figure 2 can

be used for predictingSmaxt different positions n the instru-

ment. It should be noted that Smaxs attained toward the exit of

the instrument, fter the concentration nd temperatureields

develop. A significant portion of the instrument s used to

"precondition" he aerosol low, by developing he velocity

and temperature rofiles before exposing he flow to the wet-

ted hot wall. If this is not done, incoming air that mixes with

saturatedhot air in the entrance egion of the instrument an

generate much higher supersaturationshan intended. This

may bias he measurement y activatingaerosol orresponding

to a different supersaturationhan prescribed.Strictly speak-

ing, the FCNS is a particle counter, since each streamline s

exposed o only one supersaturationafter the flow completely

develops).f all streamlinesre simultaneouslyrobed, CCN

spectrum anbe obtainedn real ime.

2.3. Dynamic CCN Spectrometers

The underlying dea behind hese nstrumentss to expose

an aerosolsample o a variablesupersaturationield and nfer

the CCN spectrum rom the outlet droplet size distribution.

CCN with low Scare expected o activatenear he entrance f

the instrument, nd so they have more time to grow than do

particleswith higherSc; he atteractivateartherdown he n-

strument.Therefore the outlet droplet size is expected o de-

creasewith increasingcritical supersaturation.urthermore,

the initial size of the particlesentering he instrument being

in equilibrium with the inlet RH) decreaseswith increasing

critical supersaturation,hus enhancing he size differences

betweenparticlesof different critical supersaturation,c.The

sensitivity of the instrumentdependscritically on how the

outlet droplet size varies with particle dry size, and henceSc.

Because he rate of dropletgrowth varies nverselywith parti-

cle diameter, the droplet size distribution considerablynar-

rowsas particles row, mplying hat a veryprecise izemeas-

urementmay be neededat the outlet of the instrument.Com-

paredwith SDCCs and CFDCs, dynamicspectrometerstilize

a completelydifferentconcept n instrument esign, n both

the activation and size measurement omponents.

Hudson [1989] developed a dynamic spectrometerby

modifying a continuous low thermal diffusion chamber

(HCNS) (Figure5). This instrument xposeshe sampleair to

a supersaturationrofile that increasesn the streamwise i-

rection,as shown n Plate 1. The flow field is preconditioned

beforea supersaturations imposed, n a similar ashion o the

FCNS. Because he HCNS design measuresparticles over a

large range of S,.simultaneously, CN spectra an potentially

be determined apidly.The reported angeof measurable riti-

cal supersaturationsn the HCNS is considerablyarger han

that for thermal diffusion chambers,0.01 to 1%, covering

much of the range of interest or climatically mportantwarm

clouds.The supersaturationange s extendedbecauseow Sc

particles re exposed o very high supersaturations,huscon-

siderablyacceleratingheir growth.This instrument lso uses

white ight sizedetection, liminating ny sizeambiguity rom

Mie scatteringesonanceseen n lasersizedetection.Because

I nlet

Warm Cold

section section Insulation

Sheathir

Aerosol ir

Symmetryaxis

Figure 6. Caltechcontinuouslow spectrometerCCNS).


5/26

NENES ET AL.' ANALYSIS OF CCN INSUMENTS 3453

3.0

2.0

1.0

0.0

-1.0

-2.0

Non-heated

section

Warmide

Th Th Th Th

I -1 / m m i

Centerline -,- ................................

--'l .X

, Tc Tc Tc Tca Tc

Cold ide (topiew)

m mm mm mm mmmm m mmmm m m mmmm mmm m mmmm mmm m mm m

m

Max. AT (K)

4

......... 0

-12

mmmmm m i

-3.0

0.0 0.1 0.2 0.3

Position (m)

Plate 1. Typicalsupersaturationpercent) rofiles or the HCNS alonga flow section,or various

maximumemperatureifferences,TmaxtheAT at the astsegment).he temperatureifferenceetween

each egments assumedo ncreaseitha constanttep "linearamp") nboth oldandwarm ides. he

profiles recomputedyusingheHCNSnumerical odeln thispaper.

of the speedand wide range of supersaturationshat can be

covered, his instrumenthas been used frequently on airborne

measurements McMur, 2000].

The Caltech CCN spectrometer CCNS) [Chuang et al.,

2000] (Figure 6) implements Hudson's streamwisegradient

method n tube flow. A method originally developedby Hop-

pel et al. [ 1979] is employed o produce upersaturationn the

flow in a wet-walled cylindrical ube; he tube s divided along

its length nto sectionshat are alternately eatedor cooled.As

the air flows through he tube, it is saturated n the warm sec-

tions and then cooled to produce supersaturation ear the

center of the tube. The supersaturation rofile that develops

depends n the geometryof the segments,he flow rates, he

temperature ifference,and the operatingpressure. he super-

saturation s increased along the length of the tube by in-

creasing he temperaturedifferencebetween successiveube

segments,eading o a centerline upersaturationrofile such

as that shown n Figure 7. The first sectioncan be used o pre-

condition the inlet flow.

Another mportant ssue s to estimate he uncertainty hat

would arise when calibration curves producedby using pure

salt aerosol are used to infer ambient CCN spectra. Both

spectrometersperate n the assumptionhat particleswith

the same S. (but different composition)will have the same

growth ehavior henexposedo an dentical upersaturation

field. In reality,an even stricter onstraintmustbe satisfied:

the KOhler curves need to be similar, which is not the case for

aerosol-containingurfactant nd slightly solublematerial.

Furthermore, he inlet air may also containcondensable ases

that can also have a large mpacton the activationproperties

of the aerosol; his may not be correctlyaccountedor in the

instrument. These issues are to be addressed in future studies.

3. Mathematical Models of CCN Instruments

To evaluate he performance f the different CCN instru-

ments, flow, heat, and mass transfer have been numerically

modeled within each instrument o determine the temperature,

watervapor,andsupersaturationistributionss a functionof

position nd, or unsteadynstrumentperation,ime.Particle

activation nd growthare simultaneouslyimulated y track-

ing individualparticles s they flow through he instrument.


6/26


84 Warmold

1

, Centerline

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Axial position (m)

Figure 7. Indicative supersaturationpercent)profile for the CCNS along a flow section.The volumetric

flow ates0.7L rain.TheprofilescomputedyusingheCCNS umericalodel f his aper.

The equations sed o describe erosolparticlegrowthare first

given n the next section, ollowed by the general orm of the

gas phaseequations sed for all the instruments. inally, the

appropriate boundary conditions and specific relations for

each nstrumentare given.

3.1. Aerosol Growth

The rate of changeof droplet size for eachof the particles

is calculated rom the diffusionalgrowth equation Seinfeld

and Pandis, 1998]'

dD

D P

P dt

S -Seq (1)

P '

RTAHvapPwlAHvapM

w + w 1

4p*D'M 4k'T TR

p w a

whereDp s the particle iameter, ' is thesaturationapor

pressuret he ocalemperature, & = p,,/p* 1 is the ocal

supersaturation, , s the equilibrium supersaturationf the

droplet,p}, s the waterdensity,AHvaps the enthalpy f va-

porization of water, Mw is the molar massof water, and R is

the universal asconstant.DT. s the diffusivityof watervapor

in air modified for noncontinuum effects [Fukuta and Walter,

1970]:

mv

1+ 2D,, 2zcM

acD RT

where D,. is the diffusivity of water vapor n air, ac s the

condensationcoefficient. The thermal conductivity of air

modified or noncontinuumffects,k, s givenby

2k,2zcM

rDppc RT

where Ma is the mean molar massof air, k,, s the thermal

conductivityf air, p is theair density, ps theheatcapacity

of air, and a is the thermalaccommodationoefficient.The

equilibriumsupersaturationf the droplet, S,. is givenby the

K6hler equation:

S qexp[M.,o',,,6n.MwV.,_

RTp..D,,

1 ,

where o-w s watersurface ension,ns s the numberof moles

of solute erparticle, nddp s thedrydiameter f theparticle.

3.2. Gas Phase Equations

Differential momentum, energy, and mass conservation

balances are written for the gas phase, assuming a two-

dimensional Cartesian or axisymmetric coordinate system.

This results in a system of differential equations,each of

which s of the general orm


7/26

NENES ET AL.' ANALYSIS OF CCN INSUMENTS 3455

ox2F - x2F---

(2)

where ,,x2are hespatial oordinatesnd is thedependent

variablee.g.,T). SO s a sourceerm,andF0 s a transporto-

efficient,both of which dependon the form of . Table 1

lists heexpressionsf So, 0 for each ypeof . ForCarte-

siangeometry,heexponent = 0 and hecoordinates,x2

can be replacedwith the moreconventional, y. For axi-

symmetriceometry, = 1 and hecoordinates,x2 canbe

replaced ith themoreconventional, r.

The rateof condensationf liquid water in molesper vol-

umeof airpersecond)n heaerosol articles,cond,s needed

in the watervaporand energy onservationquations.his

quantity s givenby

:

1 d%

M,. dt

where L s the ocaliquidwater ontentkgm3air).Fora

populationf waterdropletsonsistingf Ni dropletsf di-

ameter pipervolume f air,

w--p.6,=, ' "

Furthermore, a source term in the momentum equations,

Jbuoy,epresentshemomentumeneratedrom hermal uoy-

ancyeffects.For ideal gasest is givenby

1

buoy T.u,kx2)

(5)

whereT is the temperaturend g,: is the componentf

gravity n the x2 direction.TbukX2) s the x average em-

perature t position x2 and is computed ifferently or each

instrument. inally, ,o is gasphasedensity,calculated t Tbuk

(x2).

3.3. Static Diffusion Cloud Chamber

The geometry nd characteristic arameters f the SDCC

are shown n Figure 1. The following assumptionsre made o

simulate the instrument: (1) there is a two-dimensionalaxi-

symmetric hambergeometry; 2) the air is quiescent;3) par-

ticles fall by gravitationalsedimentation nd attain terminal

velocity instantaneously s they grow; (4) coagulationand

Brownian diffusion of particles are neglected;and (5) wet

wallsact as a perfectsink/source f watervapor, .e., the air is

saturatedwith water vaporat the walls.

At the top and bottomwalls, a constantemperature ound-

aryconditions imposed, hileat thesymmetryxis,3T/Or=

0. At the sidewall, a compositeheat conduction-natural on-

vectionheat flux boundarycondition s used,

wheren is the numberof dropletsizes ound n the distribu-

tionandp,.s thedensityf water. n hebasis f thisdefini-

tionof wL, he ateof change f liquidwater ontent f the

particles s

dwL N.D..

t dt

;z ,. dD,,

(3)

wheredDpi/dts calculatedrom heaerosol rowth quations.

Substituting quation 3) into the definition or Jcondives

J ... .7T.. D2 D,iNi pi

m,,,: dt

(4)

= u (Ln. Tr , (6)

where is the heat lux per unit area,Tam s the ambient em-

perature utside f the cell, Tf is the air temperaturet the

computational ell adjacent o the sidewall,and U is the ap-

propriate eat ransfer oefficient etween he outside mbient

and chamber fluid,

1C,

= + In 1+ (7a)

U h kwall T '

whereCp s thewallheat apacity,w:,Us thesidewallhermal

conductivity, nd h is the naturalconvection eat ransfer o-

efficient, calculatedby the following correlation Incropera

and DeWitt, 1985]:

Table 1. TransferCoefficientsand SourceTerms or the Gas PhaseEquations

Conservationaw p F S

Continuity 1 0 0

P__.lluh( 8v

xy +

x,momentumu /1 -x-x_+x''x._J'-x2LJ Juoy

x,

=momentum v - 8x= - _

Heat T 'PJco.d

Cp Cp

Water vapor C pD, --PJco.d


8/26


hL

= NuL = 0.68 +

k

0.670Ra}/4

1 0.492/Pr)9"614/9

(7b)

where

Rs

CpP2gLV -Tanlb

is the Rayleigh number for an ideal gas, Pr =///pk(, is the

Prandtlnumber, is the average emperature f the SDCC

Plexiglaswall, and Tam is the ambient emperature. he first

term on the right-handside of equation 7a) is the heat con-

duction resistance between the outer sidewall and the envi-

ronment, and the second term is the resistance within the

sidewall.At the sidewall and the symmetry xis, OC/Or= O.

Particles are assumed nitially to occupy the entire chamber,

with a uniform concentration nd size distribution hroughout.

The droplet sedimentation elocity s given by the Stokes

equation Seinfeld nd Pandis, 1998],

2

DpPpgCc

, (8)

18//

where

C =1 2/Dp[1.2570.4exp-1.1Dp/1,)1

is theslipcorrectionactor,pp is theparticle ensity,//is he

air viscosity, is the gravityconstant, nd ,;[ s the mean ree

path of air.

3.4. Fukuta Continuous Flow Spectrometer

Using scalingarguments,t can be shown hat sidewallef-

fects in the velocity field become significant when the dis-

tance from the sidewalls s of order H. The FCNS geometry

examinedhasan aspect atio of W/H = 20; so more han90%

of the total width of the instrument emainsunaffectedby the

presenceof walls. Thus the FCNS (Figure 3) can be reasona-

bly simulatedby solving a seriesof two-dimensional rob-

lems, each of which is for a fixed value of the z coordinate. A

vertical flow configuration s assumed. n addition, he fol-

lowing assumptions re made: (1) conditions re steadystate;

(2) aerosol particles follow the air flow streamlines, t the

same velocity as the surroundingair; (3) coagulationand

Brownian diffusion of particlesare neglected; 4) walls act as

a perfect sink/source f water vapor; and (5) the temperature

profile along he wall (in the z direction) s linear.

Two typesof inlet velocity conditions re considered,ully

developed i.e., parabolic) or plug flow. The other variables

(T, C) are assumed o have a uniform profile at the inlet. At

the walls, a no-slip boundarycondition s assumed,u = v = 0,

and for the outlet, 0u 0x = 0; v = 0. At the outlet, 0T / 0x = 0.

A constant emperature ondition s used for the walls; this is

a function of the z position of the sectionexamined and is

computedby using assumption 5). Given that the temperature

at the two tips Th (for any x, y = H and z = W) and Tc (for any

x, y = 0 and z = W) are known, the temperatures t the top

wall T, and the bottom wall Tb at a given coordinate are

r,(z) ,, (W- ) r,,(z) + (W-z),

where s is a coordinate hat runs along the heatedwall, with

its origin locatedat the hot tip (Figure 3) and endsat the cold

tip;

ar r,,-rc

ds 2W +H

is the temperaturegradient along the s coordinate. At the

walls, the air is assumed o be saturatedwith water vapor at

the local temperature. t the outlet, 0C/Ox = 0. Basedon the

sheath/aerosol flow ratio, the section of the flow field occu-

pied by the aerosol s calculated rom a massbalance.Finally,

the mean emperature

H

IT(x, )dx

Tbu,Y) =

H

0

is used n calculating he buoyancy erm in the u momentum

equation.

3.5. Hudson Continuous Flow Spectrometer

In simulating he HCNS (Figure 5), the following assump-

tions are invoked: 1) conditions re steadystate; 2) geometry

is two-dimensionalCartesian; 3) aerosolparticles ollow the

air flow streamlines ith the samevelocityas the surrounding

air; (4) sedimentation, oagulation,and Brownian diffusion of

particlesare neglected; 5) walls act as a perfectsink/source f

water vapor, i.e., the air is saturatedwith water vapor right

adjacent o the walls; and (6) buoyancy s neglected.The two-

dimensionalassumption eglects op and bottom wall effects.

This can be shown through scaling arguments o be a good

approximationwhen the aspect atio H/W is largeand breaks

down only when the distance rom the sidewalls s of order W.

In addition o the constant emperature onditionposedat the

controlled emperaturesections,a zero-heat lux condition s

assumed at the insulated areas.

3.6. Caltech Continuous Flow Spectrometer

In formulating the conservationequations or the CCNS,

the sameassumptions s those or the HCNS are made, except

that an axisymmetriccoordinate system s used. Although

buoyancy s not expected o be significant, t is included n the

model for completeness.Tbun(Z)n this case is the radial-

average emperature t axial position :

R

I 2IrrT(r,)dr

=

2;rrdr

0

Boundary nlet conditions sedare similar o thoseof section

3.4. In addition to those, 0u Or = Ov Or = 0C / Or = 0T / Or = 0

at the symmetry xis.


9/26


4. Numerical Solution of Conservation Equa-

tions

The conservation quations or the four instruments annot

be solvedanalytically;so a numericalsolution s obtainedby

the finite volume method [Patankar, 1980]. A hybrid upwind-

central differencing scheme s used for calculating he con-

vective-diffusive fluxes over the finite control volumes. The

schemeused employsa staggered rid, in which each velocity

grid node lies between two scalar volumes,ensuring hat the

numericalsolution s consistentwith respect o pressure. he

Semi-Implicit Method for Pressure-Linked Equations

(SIMPLE) iterative solution method [Patankar, 1980] is used

to solve the hydrodynamiccycle of the finite volume equa-

tions, while the particle growth equationsare solved numeri-

cally integratedwith the LSODE solverof Hindmarsh 1983].

The computercode used for the numericalsimulationswas

based on the TEACH-2E CFD code [Gosman and Ideriah,

1976] coupled ogetherwith an aerosolgrowth module. The

computational rid and time stepusedensure hat the numeri-

cal solution s within a few percentof the asymptotic with re-

spect o grid density) imit. The numericalsolutionwas ob-

tained by using 100 cells for each spatialcoordinate. or the

unsteady tatesimulationsof the SDCC, a time stepof 0.025 s

is taken for the gas phase equations, or a total integration

time of 30 s. The aerosolgrowthequations se a variable ime

step, which is scaleddependingon the instrumentsimulated.

For the SDCC simulations, t is scaledon the gas phase ime

step, while the othersuse the transit ime througha computa-

tional cell.

5. Uncertainty Analysis or Wall Temperature

of CCN Instruments

In order o assesshe effect of wall temperature ncertainty,

simple heat transfermodelswill be constructedor all of the

instruments.n thesemodels, he nner water ilm temperature,

Tf, s estimatedrom he heat lux throughhe walls.The tem-

perature ifference etweenTf and the controlledwall tem-

perature,T,,., s then computedand expressed s a fraction of

the "nominal" difference, Th -T,., for various values of water

film thickness, ilter paper thickness,and flow rates.Realistic

valuesorboth aper ndwaterilm hicknessre10 3m; he

wall is assumedo be of order 10 2m.

5.1. SDCC Uncertainty Analysis

With respect to wall heat transfer in the SDCC, the fol-

lowing can be assumed: 1) steady state conditionsand (2)

one-dimensional onductiveheat transfer stagnant low field)

along the axial direction of the instrument see Figure 8a).

With theseassumptions,he heat flux betweenpoints 1 and 2,

Q,2, s equal to the heat flux between he top and bottomwall,

Qt,;,.Expressinghese luxes as a functionof the temperature

differences, T,-T,. and T-T2, we have Q,2 = Qt.b,which

leads to

wall Tt

W

114-1---- ' -- ---

(a) waterilrn+ilteraper L

w2

wall T/,

Before proceedingwith the numericalsimulationof the in-

struments,t is instructive o perform an analysisof the un-

certainty n one of the most critical parameters f CCN in-

struments, amely, he temperature oundary ondition or the

instrumentwall. When operatinghe nstruments, ne controls

the temperature f the metal supportingwall (or plates),

whereashe boundary ondition hat actuallygoverns he per-

formanceof the nstruments the temperature f the inner face

of the water film on the wall. Differences between these two

temperatures ould bias the predictions, ince he supersatu-

ration is a strong function of temperaturedifference. One

could include heat transfer hrough he walls and film in the

simulations, ut the analysisof constantwall temperatures

adequateor the purpose f estimating he relativemagnitude

of the uncertainty rising rom a temperature ifference.Fur-

thermore, uchan analysiss useful n that t is independent f

any specificgeometryor configuration.

When estimating the wall temperatureuncertainty,one

mustconsider ll the factors hatcontributeo the temperature

drop between the controlled emperatureside and the water

film. Apart from the metal walls and the water film, there is

also a material that helps keep the walls wet. The material

conventionallyused for the SDCC, FCNS, and CCNS is filter

paper, while the HCNS uses a steel matrix. The material will

be shown o have a larger mpacton the wall temperature n-

certainty in the continuous flow instruments han on the

SDCC. The results or the SDCC may be consideredntuitive,

but the analysiss included or completeness.

(b)

wall Tt

-.....-m-....-.'--ir.4

_

15+1 __ -

waterilm ilter aper /

..............

(c)

hot ide T

Wl ' ' "' .........

waterilmilteraper fl

1+2 .....

w:

coldide T

Figure 8. Geometriesused n the simple modelsdeveloped

for determining he uncertainty n the temperature oundary

conditions for (a) the SDCC; (b) the CCNS, and (c) the

HCNS.


10/26


Sl,2rl - T2 '-St,b(rh-rc),

(9)

where Ui,2 and Ut.bare the total heat transfer oefficients e-

tweenpoints1, 2 and , b, respectively.heseheat ransfer o-

efficientsanbe evaluatedy the esistanceethodInctop-

era and DeWitt, 1985] to lead to

1 L-(ll+12)-(4+2)

UI,2 ka

(10)

1 (Wl w2)

St,b kst.steel

L-(1,+12)-(l+2)

4 + R, + R,2, (11a)

k,

wherekst.s,eel15, kwater0.58 and :p.p,0.1 are he hermal

conductivitiesin W m l K l) of stainlessteel, ater, nd il-

ter paper,respectively.Also, wi, li, and . are the thickness f

thewall, filter paper, ndwater ilm, respectivelyi = 1 corre-

spondso thehotplate,while = 2 refers o thecoldplate). n

equation11a), the esistancesf thewall,soakedilterpaper,

and air are assumed to be in series. The resistance of the

soakedilter paper,R,i, is

g$i=

kwater kpaper

+

min Si,1,) min 8,,li)

8-min (8,li) /,-min (t,,1,)

+ . (11b)

kwater kpaper

The irst erm n theabove quationssumeshatanequal

segment f waterand filter paperare combinedn parallel

(which orrespondso thewell-soakedortion f the ilterpa-

per), and he remaining aper or water) s connectedn series.

Allowing for the excess f filter paperand waterconsiders

situations here he filter paper s partially ry or when oo

muchwater s provided n the ilterpaper. hesensitivityf

theuncertaintyo these onditionss an mportantperating

parameterof these nstruments.

Substitutingquations11a), (l lb), and 10) into (9) and

solvingor (r - T2)/(Th Tc)yield

r ka l

+ R,lk, + R,lk

r r2 (Wl- 2)sttee'

= .

-(1,+12)-((51+(52)

(12)

The uncertainty ould herefore e definedas

practically equal to the nominal. For example, for

T,-T c = 2 K, then, depending on the thicknessof the water

film, T- is about 1.99 K, the uncertaintyhus being at

most0.01 K. This result s not surprising, ince he gap be-

tween the plates is occupied mostly by air, which has low

thermal conductivity compared with conductivities of the

other materials. The resistance therefore to heat conduction is

mainly owing to the air and is relatively nsensitive o the

presenceof water and filter paper. In addition, variations n

water film or changesn wall thickness o not have a large

impact on the uncertainty. t can be concluded hat once the

steady state temperatureprofile has been achieved, he tem-

perature ncertaintyn the nstruments negligible.

5.2. CCNS Uncertainty Analysis

In our presentation f the two spectrometers,sually he

HCNS precedes the CCNS. For convenience,however, we

shall begin now with the CCNS, for which we assume he

following: 1) conditions re steady tate; 2) there s one-

dimensionalonductiveeat ransfer long he adialdirection

and convective eat transferalong he axial directionof the

instrument;3) on theentry o each otandcoldsegment,he

temperaturerofile s uniform ndequal o thewall empera-

tureof thepreviousection;4) the low field s fully devel-

oped and laminar;and (5) the latent heat flux from water con-

densationhroughhe wall is small n comparisonith the

sensible heat transfer, which is reasonable or near-atmos-

pheric ressuresndsmall emperatureifferences.heap-

prophategeometrys defined n Figure8b. With theseas-

sumptions,he problemeduceso a developingemperature

profilen theentry egion f a pipe,witha fullydeveloped

hydrodynamiclow field. The heat lux throughhe wall for

thegivensegmenthereforeanbe calculatedy

O= hAaT ,

whereA is the otalsurface xchangerea,AT s the empera-

ture changeof the bulk fluid betweenentry and exit of the

pipe segment, nd h is the mean heat transfercoefficient,

which s calculatedy the following orrelationIncropera

and DeWitt, 1985]:

hD 0.0668Gz

= NuD = 3.66 q- (14)

k 1+ O.04Gz / '

where Gz = Re Pr (D / L) is the Graetz number,

Re= (4pVDrD/)is the Reynoldsnumber,Pr = lt/pk, is the

Prandtl number,L and D are the length and diameterof the

segment,nd1) is thevolumetriclow ate hroughhepipe.

Using assumption , the bulk temperaturesn and out of the

section re equal o eitherThor T..The temperatureifference

AT then n (13) is approximatedwith Th T.

Furthermore,he heat lux canbe expressed sa functionof

the nner ilm Tf and heouterwall temperature,, s

T-T2>


11/26


where,as n equation 11b),

kwaer kpaper

+

min &/) rain &/)

- rain &l) I - rain

+

k,mer kpaper

Equatingquations13)and 15)andsolvingor (T,.- Tf)/(Th

- Tc)yield

(17)

The uncertaintycould thereforebe defined as

>< 100%.

Equation 17) depends n the thickness f the materials nd

on the Reynoldsnumber.The validity of assumption de-

creases s Re increases ut can be used n our analysis, ince

the instruments operated suallyat low Re and provides n

upper imit estimate f the uncertainty. he appropriatenessf

assumption can be assessedrom the numericalsolutions.

Figure shows ontoursf (T.- T.r)/(ThTc) asa function

of water film and paper hickness. he wall thickness s as-

sumedo be 1 cm,and he low ate s equalo 10L min.As

can be seen, he uncertainty s a somewhatstrong unction of

filter paper thicknessand has a weaker dependence n water

film thickness.Everything else remaining constant, he mini-

mum uncertainty s encounteredwhen the water film and filter

paper have the same thickness;under this condition the un-

certainty rangesbetween 4 and 6%. However, when the water

thickness ecomes maller han the filter paper i.e., the paper

partially dries), the magnitudeof the uncertainty ncreases nd

can approach 10%, or higher. The reason or this behavior,

which differs from the SDCC, lies in the fact that forced con-

vection in the CCNS increases he heat transfer efficiency

through the bulk of the fluid, and so the resistancesn the

water film and filter paper have a larger effect on the tem-

peraturedrop across he wall than in the SDCC. Furthermore,

the temperaturedifferencesbetweensegments eeded o gen-

erate supersaturationslong the centerlineare increased, om-

paredwith the SDCC; so the absolute alueof the uncertainty

increases long with it. For .......... for Th -T. = 10 K

Xalllpl, , UlU:11,

depending n the thickness f the water film, T,.- T.rcan

rangebetween0.5 and 1 K.

Given that heat transfer efficiency increaseswith the flow

rate,onewouldexpect hat (T.- Tf)/(Th - Tc)depends n the

flow rate. ndeed, his is the case,assuminghat wall and pa-

per thicknessdo not change,a tenfold increase n flow rate

addsan additional 10% to the uncertainty; his would translate

to a T,.- T.r shighas2 K if Th Tc= 10 K. As wasstated e-

fore, assumption is not as appropriate t high flow rates;so

the uncertaintymay not increaseby as much as 10%, but still

one would expectan appreciable hange n film temperature.

In any case, especiallywhen condensational eat flux is

considered (which further increases he temperatureuncer-

20

18

16

12

10

" 8

6

4

0 2 4 6 8 10 12 14 16 18 20

Water film thickness % of gap)

Figure9. Contoursf (T,. T.r)/(Th TO or theCCNSasa function f paper ndwater ilm thickness.he

thickness of the metal wall is assumed to be 1 cm.


12/26

3460 NENES ET AL.' ANALYSIS OF CCN INSUMENTS

tainty), one would expect hat the effective temperaturen the

instrumentwould be appreciablysmaller han that posedon

the walls. Therefore any simulationsor experimental alibra-

tions shouldbe adjusted or this difference.

5.3. HCNS and FCNS Uncertainty Analysis

Both the HCNS and FCNS employ laminar flow between

parallelplates.The two systems iffer in the choiceof the po-

rous wetted ayer; the FCNS uses ilter paper as in the SDCC

and CCNS) while the HCNS usesporousmetal. The thermal

conductivityof the latter material s much higher han that of

the paper, leading to much smaller temperaturedifferences

between the measuredand surface emperatures. general

model that accounts or the resistancen the porousmaterial

will enableevaluationof the uncertaintiesn both systems.

In the following analysis,we assume s follows: (1) condi-

tions are steady state; (2) one-dimensionalconductive heat

transfer is perpendicular o the flow, and convectiveheat

transfer s along the flow axis; (3) the fluid reaches he devel-

oped inear temperature rofile at the exit of eachsegment; 4)

the sectional verage emperature oesnot vary throughouthe

instrument which is true in the HCNS for a symmetrically

cold-hot emperature rofile); (5) the flow field is fully devel-

oped and laminar; and (6) the latent heat flux owing to water

condensation s small in comparisonwith the sensibleheat

transfer,which is reasonableor near-atmosphericressures

and small temperature ifferences. he geometrys defined n

Figure 8c. Resistance hrough he steel matrix of the HCNS is

neglected.With theseassumptions,he problemreduces o a

developing emperatureprofile in the entry region of an en-

closedplate geometry,with the hydrodynamiclow field fully

developed.Assumption ensures hat the bulk enthalpyof the

fluid doesnot changeas it passes hrough he instrument; hus

any heat exchangebetween the plates s perpendicularo the

flow. For a given segment, he heat flux through he hot wall,

'", canbe expresseds a function f the nner ilm Tf and

the outerwall temperature ' as

where h s theheat ransferoefficienthroughhecombined

metalwall, ilterpaper, ndwaterilm equation16)),andAh

is the exchange urfaceon the hot wall side.A similarexpres-

sioncan be written or the cold plate side:

=UA(T., Tf), (19)

where T c and T,5 are the inner film and outer wall tempera-

tures t thecoldwall, respectively,ndAc s theexchangeur-

face on the cold wall side. Furthermore,because he system s

in steadystate and the fluid does not experience ny overall

increasen enthalpy, 4,= 4c; so

UhA T.jTh UCA c .

,) -

(2O)

Assuming hat the surfaceareasand heat transfercoefficients

are alsoequal, we get that

=r c c,

which means hat the temperature rop across he film is the

samemagnitudeor both cold and hot walls.After furtherma-

nipulations f equation 21) we obtain

The heat flux from the fluid to the cold film, 4c, can also

be expressed s

c=hAC(Tbu,k_T), (23)

where Tbuns the bulk temperature f the fluid (which is the

samealong a segment) nd h is the meanheat transfercoeffi-

cient.Since he systems in steady tate, his heat lux is equal

to the flux that passes hrough he cold wall (equation 19)).

By equatinghe wo fluxesandsolving or Tf, we obtain

Tf hTbukUcT"'c (24)

+U c

By substituting quation 24) into equation 22), we finally get

.r 1- 2 . (25)

rd: c, h+ V - E

The uncertainty ould hereforebe definedas

T c

- .r-T x 100%.

The heat transfercoefficient h is calculated rom equation

(14) by using the hydraulic diameter. To incorporate he

noncircular section effects, the heat transfer coefficient calcu-

lated from (14) is then multipliedby a factorof 2, which s the

limiting factor for an aspect atio approachingnfinity [In-

croperaand DeW#t, 1985]. This approximations reasonable,

given hat the HCNS examinedherehasan aspect atio W/H =

20.

Equation 25) depends n the thickness f the materials nd

on the Reynoldsnumber.However, f Tbu emains he same

between segments, hen the uncertainty emains the same

throughouthe instrument.Given that heat transferefficiency

increases with the flow rate, one would expect that

(T -T/)/(T,'.'- T7) depends n the low rate. ndeed his s the

case,as shownby Figure 10. The wall thicknesss 1.0 cm, and

the paper hicknessn this plot is assumedo be zero (there-

fore this plot shows he uncertaintyor the HCNS). As canbe

seen, or a film thickness hat is 5% of the gap, a tenfold n-

crease n the flow rate almostdoubles he uncertainty, rom 11

to 18% (or a ratio of 0.89 to 0.82). However, for film thick-

nesses round1% of the gap (or around1 mm in our case), he

flow rate has little effect on the uncertainty and remains

around 3-5% (or a ratio of 0.97 to 0.95). For example, or

T,'.'-T7= 5 K, depending n the thickness f the water ilm,

T -T/ can ange etween.85and4.75 K, or theuncertainty

is at most 0.25 K. Thus the temperature ncertaintys ex-

pected o havea minoreffecton the nstrumenterformance

and is thereforeneglected.


13/26

20

NENES ET AL.: ANALYSIS OF CCN INSTRUMENTS

,

3461

18

0 1 2 3 4 5 6 7 8 9 10

Water film thickness % of gap)

Figure10. Contoursf (T,, Tr)/(Th Tc) or heHCNSasa functionf flow ate ndwaterilm hickness.

The thickness f the metalwall is assumedo be 1 cm, andno filter paper s used.

The presence f the filter paper n the FCNS is expected o

increase he temperatureuncertainty, elative to the HCNS.

For a paper hickness f 1 mm, which s well wetted,and wall

thicknessof I cm, the uncertainty s around5%. A tenfold in-

crease n the flow rate almostdoubles he uncertainty, rom 5

to 9% (or 0.95 to 0.91 ratio). For example, or T,"-T5 5 K,

dependingon the thicknessof the water film, T]'-T; can

rangebetween4.75 and 4.55 K, or the uncertainty angesbe-

tween 0.25 and 0.45 K. Thus although he uncertainty s in-

creasedwith respect o the HCNS, it is still smallenough o be

considered minor.

6. Operating Conditions

After assessing he uncertainty n the wall temperature

boundarycondition or each device, the geometricdimen-

sions,operating onditions, nd aerosolused or simulating

the performancef the nstrumentseed o be specified. he

dimensionsand operating conditions of each instrument,

which are summarized n Tables 2 to 5, are thosereported n

the literature. The SDCC dimensions were taken from an ex-

isting nstrumentP. Chuang, nternalcommunication,ali-

fornia nstituteof Technology, 999). The FCNS, HCNS, and

Table 2. OperatingConditionsand Parametersor the SDCC (P. Chang,

internal communication, 1999)

Parameter Value/Range

Distancebetweenplates,m

Radius of plates,m

Thickness of view volume, m

Radius of view volume, m

Initial pressure, a

Initial relative humidity, %

Bottom plate temperature constant),K

Top plate temperaturevariable), K

Sidewall thickness, m

Thermalonductivityf sidewall, m 2K 1

Ambient temperature,K

lxlO -2

0.1

lxlO -3

lxlO -3

1.013 x 105

1 O0

290

292 to 297

2x 10 3

1.4 (Plexiglas)

290


14/26

3462 NENES ET AL.: ANALYSIS OF CCN INSUMENTS

Table 3. OperatingConditions nd Parametersor the FCNS [Fukutaand

Saxena, 1979]


Length, width, and height,m

Orientation

Distance from entrance where wall becomes

wet on top and bottom plates, m

Inlet pressure,Pa

Inlet relative humidity, %

Volumetriclow ate,m s

Inlet temperature constant),K

Cold tip temperature constant),K

Hot tip temperature variable), K

Ambient temperature,K

0.838, 0.191, 0.018

vertical

0.168, 0.168

1.013 x 105

100

1.6667 x 10 4

283

283

284 to 293

290

CCNS dimensionswere on the basisof thosegiven n the lit-

erature [Fukuta and Saxena, 1979; Hudson et al., 1981; Hud-

son, 1989, Yumand Hudson,2000; Chuanget al., 2000]. The

dimensionsused for the HCNS simulations Yum and Hudson,

2000] are different from those eportedby [1989] and reflect

changesn the instrument hat improve ts resolution. low

ratesandwall temperaturesre allowed o varybut, again, e-

flect reportedoperating onditions.

To determine the behavior of the instrument,we simulate

theresponsef each nstrumentsa function f initialparticle

diameter;he inlet aerosoln all the simulationsresenteds

assumed o be monodisperse nd composed f ammonium

sulfate. The number concentration in each instrument is as-

sumed to be low, in order to minimize their effect on the su-

persaturationnd emperatureields rom the depletion f gas

phase water vapor. This is particularly mportant or the

SDCC, since biases n the supersaturationnd temperature

fields from the presence f the aerosolcomplicate rowth

history.

7. Simulation of Instrument Performance

7.1. SDCC

First, it is useful to determine the extent of wall effects, the

time needed o attain he steadystateprofiles,and the concen-

tration below which depletioneffects in the water vapor and

temperatureields) are negligible.Simulationseveal hat wall

effects extend inward of the order of the gap between he

plates, which coversroughly one seventhof the total radius.

Thus wall effectsare not expected o influencemeasurements

made near the center of the instrument. The maximum con-

centration f the aerosolwithin the instrument, eforedeple-

tion effectsare seen,dependson both S,.and Smax;imulations

indicate hatconcentrationselow 1000 cm 3 nside he SDCC

ensure that the supersaturationield is uninfluencedby the

aerosol.When depletioneffects are not important, he time

needed o achievesteady tate anges etween3 s (for 7-K dif-

ference) o 5 s (for 2-K difference).An interesting eature s

that the supersaturationrofiles approach he steadystate n a

Table 4. OperatingConditions nd Parametersor the HCNS [Hudsonet al.,

1981; Hudson, 1989; Yum and Hudson, 2000]

Pm'ameter Value/Range

Length, width, height,m

Height of aerosol njector

Length of wetted wall on hot and cold

side, m

Total numberof heatedsegments

Insulator length, m

Orientation

Sheath/aerosol volumetric flow ratio

Totalvolumetriclow ate,m s

Inlet pressure,Pa

Aerosol, sheath low inlet temperature

(constant), K

Aerosol, sheath flow inlet relative

humidity, %

Minimum cold side temperature,K

Maximum hot side temperature,K

0.38, 0.3, 0.015

0.0015

0.28, 0.38

9

0.001

vertical

10 to 20

3.3 x 10 4 o 5.0 x 10 5

3.09 x 104

295,295

100, 90

295-289

295-301


15/26

NENES ET AL.: ANALYSIS OF CCN INSTRUMENTS 3463

Table 5. Operating onditions ndParametersor theCCNS [Chuang t al., 2000]


Length, adius f tube,m 0.7, 9.27x 10

Radius f aerosolnjector 2.29x 10 3

Total numberof hot-coldpairs 7

Insulator ength, m 0.01

Orientation of instrument vertical

Sheath/aerosol volumetric flow ratio 0.7 to 20.0

Totalvolumetriclowrate,ms s 1.166 10 s

Inletpressure,a 1.013x 10

Inlet relative humidity, % 100

Aerosol, sheath low inlet temperature 295, 295

(constant), K

Aerosol, sheath low inlet relative 100, 90

humidity, %

at, ac

Wall segment emperature rofiles, K

1.0, 1.0 (case 1)

0.98, 0.041 cases2-4)

295,290, 295, 290, 295,290, 295, 285,295, 285, 295,283, 295,283 (case1)

295, 290, 295, 290, 295,290, 295,285,295, 285,295,283, 295,283 (case2)

294, 291,294, 291,294, 291,294, 287,294, 287,294, 285, 297,285 (case3)

294, 292, 294, 292, 294, 292, 294, 289,294, 289, 294, 287, 297,287 (case4)

nonsymmetricashion, rom the bottomplate to the top. Al-

though he direction from bottom o top or vice versa)could

change depending n the initial conditionsn the instrument),

the asymmetric pproach o a steadystateprofile would tend

to bias the particles on one side of the view volume toward

larger sizes.The strengthof this bias dependson the duration

of the transientselative o the total growth ime.

Plate 2a presents he simulatedeffective radius (defined as

the third momentover the secondmomentof the dropletsize

distribution) within the view volume as a function of time for

differentdry aerosolsizes.Plate 3a representshe normalized

aerosol concentration in the view volume as a function of

time. In both plots, the initial aerosol concentration s uni-

form, and the temperature ifferencebetween he plates s

kept at 2 K. This temperature ifferencegenerates maximum

supersaturationf about0.15%. Under hese onditions, arti-

cles with dry diameter arger han 0.1 gm shouldactivate. n-

deed, his s what s seen.Simulationsor 0.05- and 0.09-gm

particles yield constant effective radius and concentration,

meaning that the particles grow to their equilibrium size,

which is not large enough o experience ignificantsedimen-

tationon the timescale f the simulations. argerparticlesdo

show variability, and they are the ones that activate.The be-

haviorof particleswith a dry diameter f 0.50 gm differs rom

those of the other sizes examined, because sedimentation ve-

locity of such particles s appreciable ven for subsaturated

conditions. As a result, the concentration in the view volume

increases ecauseaerosol rom above falls through t more

rapidly than the aerosolwithin the view volume falls out. The

concentrationf particles f smaller nitial sizestays elatively

constant,as particles that fall out of the view volume are re-

placed by those from above. This behavior asts roughly

around 7 s, during which the slope of the effective radius

curve is approximately he same for all particle sizes.After

most of the aerosol above the view volume has passed

through, he aerosol oncentrationtarts ropping.

The behaviorof the SDCC depends n the supersaturation

profile, which can be characterizedy the maximumsuper-

saturation,Sin:x, nd the critical supersaturation f the ob-

served articles. articleswith S,--Stoaactivate nly midway

between he plates and are observed s they grow and sedi-

ment out of that small region.Their growthrate is initially

slow' so concentrationeaks ate. On the otherhand,particles

with S.


16/26


3.0

2.5

2.0

1.0

0.5

0.0

- 0.09 0.12

-

0.20 0.25

_

_

- 0.30 0.50

_

_

- (a)

_

0 2 4 6 8 10

TllTI e

1.25 :

o 1.00

o

z

0.75

0.09 0.12

0.20 ' 0.25

(a)

0.30 .50

''1 i J t I

0 2 4 6 8 10

Time

5.0 '

(b)

0.09

0.12

'' 0.20

' 0.25

0.30

0.50

0 1 2 3 4

Time

1.25

o 1.00

t'q -

(b)

0.09 "0.12

0.20 0.25

0.75 .......

0 1 2 3 4

Plate . Simulatedffectiveadiusn theSDCCiew Time

windowsa functionf imeorvariousnitial articlesizes Plate . Simulatedarticleoncentrationn theSDCC iew

(drydiameter,icrometers).he temperatureifference indows unctionf imeorvariousnitial articlesizes

betweenhe woplatess assumedo be a)2 K (Srnax (drydiameter,icrometers).hetemperatureifference

0.15%)nd(b)7 (Srn,,x1.81%). betweenhe woplatess assumedobe a)2 K (Srn,,x-

0.15%) and b) 7 K (Srn,, 1.81%).


17/26


1000

0 2 4 6 8 10

Time

100

& 10

0.09 ' ' 0.12

0.20 0.25

(b)

0 1 2 3 4

Time

Plate 4. Simulated particle size resolution n the SDCC view

window as a functionof time for various nitial particlessizes

(dry diameter, micrometers). The temperature difference

between he two plates s assumedo be (a) 2 K (Sm,,x

0.15%)and b) 7 K (Sm,,x 1.81%).

fectly monodisperse,he resolution n both plots startsoff

from nfinity.As the supersaturationrofilesdevelop nd the

particles row, R,. drops nd fluctuatesround he valueof

10; this means hat the dropletsizes angewithin 10% of their

mean diameter,regardless f temperature ifferenceor initial

particle size (Table 6).

7.2. FCNS

The continuous flow in the FCNS eliminates some of the

limitations that arise from the transient nature of SDCC meas-

urements. However, buoyancy forces develop that limit the

maximum temperaturedifference that can be imposed at a

given flow rate. Simulations ndicate that the maximum tem-

peraturedifference hat can be imposed or the reported low

rate is about 6 K, a value that agreeswith the experimentally

reported difference [Fukuta and Saxena, 1979]. Larger tem-

peraturedifferences ead to flow reversal.The simulationsare

relatively nsensitive o the specific ype of inlet velocity pro-

file; so the resultspresented pply to both nlet velocity ypes.

The supersaturation ields that develop within the instru-

ment control the growth of aerosol particles.Although the

maximum value of the supersaturation an be estimated rom

the local temperature difference between the hot and cold

walls and Figure 2, the supersaturation rofile has to develop

first before this maximum value is attained. Plate 5 shows su-

persaturationprofiles for different streamlinesalong the cen-

terline of the FCNS. As can be seen, half (or more) of the flow

path is subsaturated, xposing particles to the maximum su-

persaturation or only a fraction of their residence ime in the

instrument.Moreover, the time in the supersaturatedegion

decreaseswith decreasingS .... Therefore particles with low

S,. may not have sufficient time to activate by the time they

reach the outlet. This difficulty is compounded by slow

growth once activatedat low S ....

Buoyancy effects on the velocity field tend to distort the

supersaturationprofiles from being symmetric around the

centerline; his deviation becomesstrongeras the temperature

difference between the plates increases.The position of the

maximum supersaturations also shiftedslightly.Furtheraway

from the tips, the temperaturegradient between the walls de-

creases,buoyancyeffects become ess mportant,and symmet-

ric supersaturationand temperature)profiles are attained.The

centerline egion, however, particularly or the low S,.stream-

lines, s relatively unaffectedby buoyancy.

Plate 6 shows he simulated esponse urves or the FCNS.

The horizontal axis represents he critical supersaturation f

the inlet aerosol, and the vertical axis is the outlet wet diame-

ter of the aerosol. Each curve represents different centerline

streamlinewith its own supersaturation. he particle outlet di-

ameter is relatively insensitive to the inlet aerosol size, for

particles or which Sc< Stoa,. articlesof S.> Smaxo not acti-

vate: so there is a dramatic decrease in outlet size. The result-

ing "elbow" in the curve enablesdetectionof particleswith S

< Smx f the specific streamline,since here is a clear distinc-

tion between particles hat activate and those that do not. The

sharper his "elbow" is, the better resolved he CCN concen-

tration is at the given supersaturation. arther away from the

heated tips, the maximum supersaturation ecreases, nd the

positionof the "elbow" shifts toward lower critical supersatu-

rations. However, becausegrowth at lower supersaturationss

slower and because he particle exposure o the maximum su-

persaturation s briefer, droplets do not grow as much (in

comparison with larger supersaturationstreamlines). As a

consequence,he elbow becomes ess pronounced, ventually

vanishingcompletely.The elbow more or lessdisappears t Sc

= 0.1%, in agreementwith the value reportedby Fukuta and

Saxena [1979]. In its CUlTentconfiguration, the FCNS can

probeeffectivelyCCN with S,.between0.1 and 1.0%.

7.3. CCNS

At first glance, this instrumentseems o avoid many of the

problems encountered n the FCNS. Buoyancy effects are not


18/26


1.5

1.0

O.S

o.o

Acresole;ion z

[ .......... Z.,

Cold

/

/ --0:140

/ --0.065

--- 0.015

i i i ] i j I i I i i

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

y-position m)

Plate 5. Supersaturationpercent) rofiles or differentstreamlineslong he centerline f the FCNS

lOO

lO

--0.190

--0.140

--0.115

0.090

-- 0.065

--0.040

--0.015

Critical curve

Hot

I

Cold

Aerosolegion z

o.1 i i i I l i i I i i i i I ill I

0.001 0.01 0.1 1

Criticalsupersaturation%)

Plate 6. Simulated rowthcurves or selected treamlinesf theFCNS.The temperatureifference etween

the ips s 5 K, and hevolumetriclow ate s20L min.


19/26


Table 6. Summaryof SDCC Simulations

AT, K Smax,%

Dry Diameter of Smallest

(NH4)2SO4 Particle

Activated, gm

D,/AD nViewVolume

Mean Minimum Maximum

2 0.15 0.101

3 0.34 0.059

4 0.60 0.040

5 0.93 0.030

6 1.34 0.024

7 1.81 0.019

14.8 12.6 21.0

10.0 8.3 13.7

10.2 5.0 12.7

8.9 4.0 11.4

9.3 0.2 13.4

10.5 8.7 13.0

significant,and most of the instrument s utilized for exposing

the particles o supersaturationsFigure7). The supersatura-

tion profile is, however, considerablymore complex, making

it more difficult to assess instrument behavior on the basis of

the temperature nd supersaturationrofiles alone. t is, there-

fore important o evaluate he sensitivityof the predictedout-

let droplet distribution o the parameters hat affect particle

growth. Two very important parameters ffecting the simula-

tions are the film temperatureat the wall (which determines

the supersaturation) nd the mass accommodation oefficient

(which affects he particle growth).

Figure 11 showspredictedand measured alibrationcurves

for the CCNS. Details about the experimental data can be

found in the work of Chuang et al. [2000]. Curves corre-

sponding o cases1 to 4 in Figure 11 represent he temperature

boundaryconditionsand accommodation oefficientsspeci-

fied in Table 5. Case 1 represents n accommodationcoeffi-

cient of unity and the nominal wall temperatures s the wall

boundaryconditions. he predictedsize is larger (by about a

factor of 2) than the measured ata. When lowering he tem-

perature oundary ondition y around2-3 K (which, ac-

cording o section .2, is a reasonable rop,especially ince

latent heat flux through he film can further ncrease he un-

certainty),he predicted urves case3, case ) lie close o the

experimental ata. Changing he accommodationoefficient

from 1.0 to 0.041 further improves he predictions. n all

cases, hough, he qualitativebehaviorof the curvedoesnot

change:he outletdiameter f dropletss relativelynsensitive

to critical supersaturationparticularlywhen the dropletsare

activated).Thus the model captures he essential eaturesof

the instrument espite he complexgrowthbehavior mposed

by the supersaturationrofile hat developsn the instrument.

For subsequentimulations, ase3 conditions reused.

From both simulationsand experimentaldata, it is clear

that the dropletsize at the outletof the CCNS is relatively n-

sensitive o the initial particlesize. For a rangeof critical su-

100

Experiment

--- Case 1

Case 2

........................................ase 3

.................ase 4

0.01 0.1 1

Critical supersaturation%)

Figure 11. Experimental nd simulated alibration urves or the CCNS. The differentsimulation ases

correspondo differentvaluesof effectivewall temperature nd accommodationoefficients,he valuesof

which are given n Table 5.


20/26


persaturation panning2 orders of magnitude, he outlet di-

ameter changesat most by a factor of 2. This low sensitivity

arises rom the particle growth kinetics.At the late stagesof

growth, when the particle s in the continuumsize region and

soluteand surface ensioneffects are minor, equation 1) can

be integrated o yield

2=D2

D, po

t

I S,,dt

tact

(26)

AHvpPwAHvpM'

1

4k,T TR

The particlesize at activation, po, s relatively mall;so at

sufficiently ong growth ime,

resolvinghe CCN spectrum. ince he aerosol ccupies fi-

nite regionof the flow field, not all particles re exposedo

the samesupersaturationr have he same esidenceime.As

a consequence, monodispersenlet aerosolwill produce

droplet istribution ith initespread;hiseffectmay nterfere

with the ability o resolve CCN spectrum,incedroplets f a

givensizeat theoutlet renotunambiguouslyelatedo criti-

cal supersaturation.his spread t the outlet s a functionof

the sheath o aerosol low rate ratio (because hat determines

the uniformityof the supersaturationield andresidenceime

to which he particles re exposed) ndwill decrease ith in-

creasing atio.

In determininghe precision f the dropletdiametermeas-

urement eeded, e use he droplet iameteresolution, ,,

and the criticalsupersaturationesolution,RscS,./AS,. Di-

viding these wo quantities,we get the "resolutionatio,"

R,c/R,,,.,hich an hen e elatedo he nstrumentesponse:

t

ISdt

v

D2= t't (27)

-- 4- "-1

4p'D,M, 4k,,T TR

i.e., all particlesapproach he same size, regardless f initial

size (or &). This asymptoticapproachof all particles o the

samesize also explains he uniform response f the SDCC for

S,


21/26


1ooo

lOO

lO

O.Ol o. 1 1


Figure 13. Relative critical supersaturationncertainty s a

function of critical supersaturation,or the CCNS. Each curve

represents ifferentvaluesof Phe,h/l...... The uncertainty

was predicted by using the curves of Figure 12, and the

variability of the outlet droplet diameter (calculatedby the

model results).

reveal that the droplet growth kinetics, like those for the

CCNS, lead to a restricted angeof final dropletsize for parti-

cles with a wide range of critical supersaturations.or exam-

ple, when the maximum plate temperatures set to more than

6 K, the outlet droplet diameter changesby a factor of 2 for

critical supersaturationshat span 2 ordersof magnitude be-

tween 0.01 and 1%). This variation does not seem to be

strongly nfluenced by the volumetric flow rate (although he

outlet droplet diameter s) but dependsstronglyon the tem-

peratureprofile in the instrument. mprovement s seen only

when the maximum temperaturedifference drops to 4 K; in

this case, the variation in droplet diameter increasesconsid-

erably but has the drawback hat particleswith St.> 0.4% do

not activate. As can be seen, the resolution of the instrument

increasesas the outlet droplet size gets closer to the critical

curve; he drawback o this is that the S. ange or which parti-

cles are activated becomes more restricted.

Calibration data available in the literature [Yum and Hud-

son, 2000] do not preciselyspecify he maximum temperature

difference (or the total volumetric flow rate) used in the

HCNS, making it difficult to precisely assess he performance

of the HCNS model. In addition, the data provide the mean

channel number (as opposed o particle diameter) as a func-

tion of critical supersaturation.However, since mean channel

numberscales inearly with particle size, the nondimensional-

ized mean channel number and mean particle diameter are

equivalentquantities:

F(S,)-F(S,hlgh) mp(s)-mp(S,lgh)

F(Xrlou,)--F(Xrhtgh

CCNS outlet is, on average,between 15 and 20% (Table 7).

Therefore he aerosol/sheathlow rate ratio used or the op-

eration of this instruments very influential or obtaininga

CCN spectrum.While increasing his ratio to 10 or 20 consid-

erably reduces the uncertainty, he uncertainty still exceeds

50% for S,. > 0.04%. Further ncreasing he flow ratio might

decreasehe uncertainty, ut obtaininggood dropletcounting

statistics hen becomesa problem.

7.4. HCNS

The HCNS exposes articles o supersaturationrofiles hat

vary smoothlyand monotonically n the streamwisedirection.

Simulationswere performed or severaldifferent temperature

profilest ow 6 L min)and igh 20L min) otal olumet-

ric flow rates (Plates7a and 7b, respectively). he sheath o

aerosol flow ratio was assumed to be 10. These simulations

where F is the mean channel corresponding o critical super-

saturationS,..Using these non-dimensionalized uantities,we

compare measurementso the model predictions Plate 8). As

can be seen, he measurements re very close o model predic-

tions for a volumetric low rate of 20 L min and a maximum

temperaturedifference of 6 K. Given that thesevaluesof flow

ratesand maximum emperature ifferenceare within reported

operatingconditions,we can assume hat the model captures

the behavior of the HCNS.

Plate 9 displayshe predictedesolutionatio, R&/Rn,,,or

the HCNS, for different temperatureprofiles and total volu-

metriclow ates f: (Plate a)6 L min, and Plate b)20 L

min . The sheath o aerosol low ratio was assumedo be 10.

Here the instrument sensitivity s increased n relation to that

of the CCNS, particularly or low temperature ifferencesand

critical supersaturationsetween0.1 and 1%. For a maximum

Table 7. PredictedOutletDropletDiameterVariabilityandResultingCritical Supersaturation

............ .y ............... q... ret,,,-tirnRanger,txx,,,mi fil and 1 n)

Psheath ZDp, AS,%

Q..... Dp S,

Mean Minimum Maximum Mean Minimum Maximum

0.7 28.9 9.7 57.4 303.0 25.1 1326.2

10.0 5.5 1.1 36.5 53.7 2.7 755.3

20.0 4.0 0.6 19.3 38.6 1.5 388.3


22/26


lOO

lO

1

Ol

O.Ol

4

6

....... 10

12

(a)

Critical curve

lOO

0.1


(b)

0.1

O.Ol

4

6

8

10

12

Critical curve

0.1


Plate 7. Simulated calibration curves for the HCNS, for

various maximum temperaturedifferences,ATmaxthe AT at

the astsegment),nd volumetriclow ateof (a) 6 L min

and b) 20 L min. The emperatureifferenceetweenach

segment s assumed o increasewith a constantstep ("linear

ramp") on both cold and warm sides.

temperaturedifference of 4 and 6 K, the resolution ncreases

dramatically or Sc> 0.1%. This happens ecause he super-

saturationgenerated n thesecases s not sufficient to activate

particleswith Scclose o 1%; so an "elbow" similar to those n

Plate 6 develops.Consequently,he calibrationcurve slope

becomesmuch steeperaround the region of this elbow. Be-

causeof this, it is expected hat the uncertainty n the critical

supersaturations considerablyower than that for the CCNS.

Indeed, this is the case,as is shownby Plate 10. The uncer-

tainty was computed y usingequation 28) and the calculated

variabilityof the outlet dropletdiameter.Plate 10a refers o a

volumetriclow rateof 6 L min I, andPlate 10b hasa flow

rateof 20 L minl (sheatho aerosolatio s 10) For these

conditions, the relative variation in droplet diameter at the

HCNS outlet is on averageonly between2 and 3% (Table 8).

However, his is enough o generate ubstantial ncertaintyn

S,..Minor fluctuations n this variability account or the large

fluctuationsseen in the computeduncertainty.For example,

for a maximum emperature ifferenceof 8 K (which s an op-

erationalvalue reportedby Hudson 1989]), the Scuncertainty

ranges etween30 and 100% and can reachas high as 390%.

When the maximum temperature ifference s around4 K, the

resolution mprovesby an order of magnitudeand averages

around 10%. The simulations ndicate that a spectrumcan be

obtained or critical supersaturationsetween0.08 and 0.8%.

Particlesoutsideof this range do not activate,either because

the supersaturations lower than the criticalvalue or simply

because there are kinetic limitations that inhibit low-

supersaturationarticlesrom activating.

Comparedwith the CCNS, the HCNS seems o exhibit ess

uncertainty;his is attributed o the smoother nd monotonic

supersaturationrofilesgeneratedn the HCNS. The oscilla-

tions in the flow direction seen for CCNS slow down (or even

reverse)particlegrowth;so lessof the instruments utilized

for particlegrowth.Because f this,particles f differentcriti-

cal supersaturationsssentially row to the samesize by the

time theyreach he outletof the nstrument.

8. Summary and Conclusions

The behavior and performanceof four cloud condensation

nucleus nstrumentsare theoretically analyzed. These include

the static diffusion cloud chamber (SDCC), the Fukuta con-

tinuous flow spectrometer FCNS), the Hudson continuous

flow spectrometerHCNS), and the Caltech continuous low

spectrometerCCNS). A numericalmodel of each nstrument

on the basisof reported nstrumentdimensions nd operating

conditions s constructedon the basis of a general fluid dy-

namics code coupled to a description of aerosol

growth/activationmicrophysics. nstrument performance s

exploredby simulating nstrumentesponseo a monodisperse

ammonium sulfate aerosol. The CCNS and HCNS models

were comparedwith experimentalmeasurementsnd found to

be in good agreement.The FCNS model predictions greed

with instrument imitationsreported n the literature.

Uncertainties n the wall temperatureboundary condition

vary with instrumentconstruction nd arise mainly from the

presenceof filter paper (used for wetting instrumentwalls).

Using a simple heat transfermodel for each nstrument, his

uncertainty s found to be negligible for the SDCC (of the or-

der of 0.01 K) and very small for the HCNS and FCNS (rang-

ing between0.25 and 0.45 K). It can be appreciable or the

CCNS (ranging between 0.5 and 2 K); so the wall boundary

condition in the instrument simulations must be adjusted to

account for this. The numerical model for the CCNS repro-

ducesexperimentalmeasurements, hen the wall temperature

boundary conditions is adjusted by a factor slightly higher

than hat predictedby this simpleuncertainty nalysis.

SDCC exhibit the least uncertainty n the wall temperature

boundary onditions nd producedroplets hat are (for a given

critical supersaturation)monodisperseo within 10% of the

dropletdiameter, hroughout he durationof the measurement.

The FCNS is an instrument hat can be used as a CCN spec-


23/26


1.0

0.9

0.2

0.1

0.0

Experiment

V=6, AT=4

--V=6 AT=6

V=20 AT=4

V=20 AT=6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8


Plate8. Experimentalndsimulatedalibrationurvesor theHCNS.Non-dimensionalizedroplet iameter

is plottedas a functionof critical supersaturation. is the total volumetric low rate, and AT is the maximum

temperatureifference etweenhe plates. p.,he.,,hlpc,....= 10 in the simulations.

Table 8. PredictedOutlet Droplet DiameterVariability and ResultingCritical Supersaturation ncertainty

for heHCNS P,he.,t/P,.o,o,10,Critical upersaturationange etween.01and1.0%)

Maximum?, ADp ASc,

AT,K Lmin Dp S,.

Mean Minimum Maximum Mean Minimum Maximum

4 6 2.6 0.5 9.0 14.1 1.2 30.9

6 6 2.7 0.6 8.6 35.5 7.5 67.2

8 6 3.2 0.5 9.2 102.5 15.8 393.2

10 6 3.6 0.6 12.8 163.2 16.0 670.2

12 6 3.0 0.4 10.1 203.8 20.2 723.8

4 20 2.4 0.6 10.0 11.4 0.9 26.3

6 20 2.8 0.4 8.8 22.4 7.3 47.9

8 20 3.1 0.4 7.4 31.5 5.6 61.6

10 20 2.6 0.5 7.2 76.7 14.2 259.6

12 20 3.2 0.3 11.6 108.3 7.8 423.4


24/26


10

1

0.1

0.01

0.01

0.1

Critical Supersaturation%)

1000

4 6 ....... 8

....... 10 12

113 VV/, , .vl ....

0.01 0.1 1


10.

01

4

6

8

10

12

0.01

0.01

CriticalSupersaturation%)

1000

4

6

>, .... 10

' ' 12

0.01 0.1 1


Plate9. PredictedesolutionatioRs,./R,,,,or heHCNS, or

differentATm:,x,nda volumetriclow rateof (a) 6 L min

and b)20L min. pshc,/p:e,.oso,=0 n theseimulations.

Plate 10. Relativecritical supersaturationncertainty s a

function of critical supersaturation,or the HCNS. The

uncertaintywas predictedby using he curvesof Plate 9 and

thevariability f the outletdroplet iametercalculatedy the

modelesults).olumetriclow ates f (a) 6 L min[ and b)

20L minl. shealh/Pae,.osol10 n heseimulations.


25/26


trometer,sincedifferentstreamlines ttaindifferentsupersatu- kw,,

rations,allowing particles o activateover a rangeof critical kwa

supersaturations.he range of critical supersaturationshat 1

can be measureds limited because 1) the temperature iffer- L

encemustbe kept smallenough o avoid buoyancy-inducedM,,

flow reversalor secondarylows and (2) the instrumentoses

its sensitivity or particles of critical supersaturationower n

than0.1% becausehe particles o not haveenough ime for

growth. The first issue s not a serious imitation, since he su- N

persaturation n the high temperaturedifference side is suffi- P

ciently high to include all the climatically mportantaerosol. Pr

The secondimitation,however,constrainshe ability o probe p,

the climatically ritical ow supersaturationCN. Both HCNS p,

and CCNS have inherent imitations n the ability to resolve

the distributionof particleswith respect o critical supersatu- r

ration. The most mportantparameters ffecting he perform- R

ance of dynamic spectrometersre the maximum temperature Ra

differenceetweenhewalls,he otal olumetriclow ate,

and the sheath o aerosolvolumetric flow ratio. For the mono- Re

dispersemmoniumulfateerosolonsideredere, ondi-

tionscan be found or the HCNS for whichan activation R,

spectrum an be resolved or critical supersaturationsetween s

0.08 and0.8%. Simulationsor the HCNS ndicatehat he

calculated uncertainty in critical supersaturationexceeds

100% when the maximum emperature ifferenceexceeds K

for 20 L min total flow rate or 8 K for 6 L min total flow.

The sameuncertaintycan decreaseo 10% (on average)when

the temperature ifference s reduced o 4 K. The uncertainty,

however, s not uniform and dependsstronglyon the initial

size of the particle. The predicteduncertain

nenes et al-2001-journal of geophysical research solid earth (1978-2012)

Documents