Modelling and simulation of the multicomponent aerosols

J. Aerosol Sci., Vol, 26. Suppl 1, pp. SI51-S152, 1995 Elsevier Science Ltd Printed in Great Britain 0021-8502/95 $9.50 + 0.00

g°eramon ~

Modelling

and Simulation

of the Multicomponent

Aerosols

Naouma Kourti Institute of Nuclear Technology and Energy Systems (IKE), University of Stuttgart, Pfaffenwaldring 31,70550 Stuttgart, Germany INTRODUCTION Multicomponent aerosols gain in significance, because of the toxic, radioactive and other harmfull substances, they may carry. They play a growing rolle to the material processing and they seem to affect the global climate. The mathematical description of all the physical properties of a multicomponent aerosol is a very complicated issue and still a topic of research. The most usual description, the singlecomponent description, is the one known from the classical aerosol theory. Thereby all the particles have the same chemical composition. Although this method is CPU friendly, is totaly insufficient for the treatment of multicomponent aerosols. If the treatment occurs in terms of the particle mass inspite of the volume, then the description is named multispecies description, nevertheless the particle have still the same chemical composition and density. Recently some efforts have been undertaken to extend the multispecies description by allowing the different particle sizes to own different chemical compositions, As every size is allowed to have only one chemical composition, a mean chemical composition of the particles is defined in dependance of the mass of the species in this size bin. This method is named variant multispecies description of the aerosol. THE MULTICOMPONENT DESCRIPTION Real multicomponent description means to allow to each existing chemical composition in the aerosol to have its own size distribution density and thus a separate treatment in the GDE. The size distribution density of the aerosol is then: k k k

n(k,t) = E T~ ...~ n(k/.~,,v=,...,%,t) vI-0 v==0 vI =0 In this formula the particle volume steps are marked with the latin letter k and the chemical composition volume steps of the s species are marked with the greek letters el, ½ .... v,. The expression k/v1, % .... v. means, that only these combinations are used, of which the sum is equal to k (k= el, v 2.... %). The discrete muiticomponent GDE for each chemical composition is:

~ n(klvl,...,v,,t ) = 1 k

~

k

i

I

J

J

I

I

~ ¢'1=0 E "'E E "E K(k/i,p,j,pj)n(i/t;1,..,t:,,t)n(j/X,,..,X,,t)8(x) (;,=0Xl-0 ;q-O

-n(klvl,--,v,,t)~ ~E~ ..~ K(k, pk,i,p#n(i/t:l,..l~,,t) + q,~l "~vq(l(k, Pk) n ( k / " 1,..,v,,t))

+ R(k, Pk) n(kl v 1,..,v,,t) + S(k,t) The delta function indicates all the chemical reactions, mixtures or solutions may occur, when two particles collide with each other.The p= indicates the variability of the density of the particles. Considering

p~ _ Pr,

M~,p~,

mit Pr, = P0=+RTIn=~,•

where/J= is the chemical potential of the ith- specie, the delta function may be written: S151

S152

N . KOURTI

x= : Lie

- o

8(x)= .

-

.

if x = ~[,Lle ~'a~p=, +~iep, iej[~- v~=p~= ~,o and it is valid only if the particle is in chemical equilibrium. Equation Eq. 2 is implemented in the code MOSAIC, which uses the Monte Carlo method to solving it, under the assumption, that the particles are solid and thus no reactions or mixing processes between the species take place. THE SIMULATION The method is tested on a variaty of conditions. Here an application from the reactor safety research is presented. Particles of Cs, I and Ag and gaseous I are transported through a 0,7 m long tube with a velocity of 4m/s. The gas temperature is 423 K and the surface temperature is 298 K. The simulation time equals the time, that the carrier gas needs to cross once the tube, since no sources are considered. Deposition only due to thermophoresis can occure. The figures below show the change of the volume distribution density of the particles of pure J and Ag for the MOSAIC calculation and a hypothetical muitispecies calculation.

30,10"

....

t0.O*

"/\\

o

Z0mto., u. o

i

c,i g ~'lr'

:

g0.t0* .J O>(10=to*

/

40,'IY'

i

/ l~to ~

/

&0,,to" t0~O" 10.to4

,

~t~to 4,

20.O' PAKIIOL,EDIkMETI~ IN m

~0,to" I S0.to" ~0,10"10.1F'

aC,~'

Z0,t~ pARTICLE ~AMETm IN m

30,10'

hW

Fig. 2

Fig. 1 Volume distribution density of I

Volume distribution density of Ag

Condensation of specie 2 may occur on every particle speciation. Since the condensation is due to diffusion, mainly small particles of silver grow through it. The muitispecie discription let the particle of all the size spectrum grow in order to maintain a uniform chemical composition.The main deposition mechanism is the thermophoresis. The muitispecies description allows iodine to condense also on the big particles, in order to maintain a uniform chemical composition. Hence it overestimates the iodine deposition, whilst the muiticomponent description calculates the iodine to be contained only in the smalt particles. The table below shows the difference between muitispecie and muiticomponent discription for the deposited particles. Specie

Initial mass [/Jg]

deposits [ / J g ] /muitispecie

deposited ~g] /muiticomponent

relative difference

Ag

387

9,8

10,4

6%

I

2,69

0,056

0,016

250%

Cs

41,7

0,86

1,06

20%

N. Kourti [1994]: Solution of the combined Coagulation and Condensation Processes of the Aerosols with the Monte Carlo Method, Abstract Int. Aerosol Conf., Los Angeles, U.S.A