Thermodiffusion chamber with longitudinal temperature gradient

J. Aerosol S c t . , Vol. 20, No. 8, pp. 1513-1515, 1989. Printed

in

0021-8502/89 $3.00 + 0.00

Great B r i t a i n .

Pergamon Press plc

THERMODIFFUSION C ~ E R WITH LONGITUDINAL TEMPERATURE GRADIENT G.N. Lipatov & G.L.Shingaryov Odessa State University, Phys.Dep., 2, Petra Velikogo St.,270000 OdessaCUSSR)

The experiments on homo- and heterogeneous condensations involve the supersaturation production by various methods with the most common ones being utilized for the adiabatic expansion and cooling chambers as well as chemo- and thermodiffusion chambers. Characteristics of the methods specify the fields of their application. Thus, for producing controllable and timestable supersaturations thermodiffusion chambers (TDC) are most frequently used. Meanwhile, the occurence of inhomogeneous temperature and vapour concentration fields in a TDC brings forth thermo- and diffusiophoretic forces which influence appreciably on the behaviour of aerosol particles in chamber channels [I ]. Z "Y=Z/R The authors suggest an original technique _ex ~ o 1~a~ | for supersaturation production in a thermodiffu~s~T~xf/)~_. ~ sion chamber with longitudinal temperature gradient. The process conception will be exemplified T(X,T) ~ by a cylinder chamber of R o radius (Fig. l). A la~(X,Y)\ ' minar vapour-gas flow with vapour average veloI \ ~Lwa )~"'~-- \ 'i' city Ve, temperature T e ~ and vapour concentra~s[T~]~l_ ~ tion C~$(here a concept of the relative numerical concentration is used) is being brought to ~e~% the inlet. Assume the temperature steady increase w~e I along the continuously watered walls of the chamC~lwaU) ~'~e~k~''-~-'__O - - I X~ ber channel T w a ~ = Twa~(Z) . If vapour-in-gas diffusion constant D4~ exceeds the thermal diffusivity of the gas @e (Le-criterion is B~/n>l), Te,%__ c4e,~,~e~ the vapour concentration in the flow ~(R,Z) will V, rise faster than the temperature of the vapourFig. 1. gas flow T(R,Z). This causes the positive supersaturation with magnitude calculated as ~(R,Z)= =~(R,Z)/~s[T(R,Z)]-I and expressed in % (here ~s[T(R,~] is the saturated vapours concentration). In such channels positive supersaturations emerge even in the vapour-gas mixtures with comparable magnitudes of transport coefficients D1a and ~e (Le = I). Here excess vapour accumulation in the flow is accounted for the specific boundary conditions in the system, such as more rapid growth of saturated vapours concentrations close to a wall ~s[T~a~e(z)] compared with the wall temperature Twain(Z) variations. In general whenever in vapour-gas mixture D42 ~ ~e , the supersaturation 20:6-~

1513

1514

G.N. LIPATOV and G. L. SHINGARYOV

occurs both because of mass transfer speed advancing over the speed of temperature field reconstruction, and due to variations in the boundary conditions transformation rate. Considering a problem of heat and mass convective transfer with reference to the above model of a cylinder channel with the wall temperature longitudinal gradient one must suggest the simplifications: a) the vapourgas mixture flow in the channel obeys Poiseuille's law; b) the transport coefficients are independent of T and CI; c) the heat and mass convective transfer is stationary; d) P~clet numbers are as Pe = Pe >> I (Pc = Pe = 2RoV/CL e ). Within the above simplifications and taking the similarity of heat and mass transfer processes into account the process obeys the following equations with suitable boundary conditions:

2RoV/DI;~,

(x:~Y l~(X,O) = ~°(X),

9X z

X

~X

b~(l,Y) = Y(Y),

here

(I)

8X 91~(o,Y)

= 0

(2)

"Y'= Z/Ro

X--R/R o,

(3)

IT(X,Y)

.~Pe('-Xn)

=

(4)

G(X) :

=

_

X2 )

(5)

(6)

Analitical solution of the problem has been obtained for the linearly i n c r e a s i n g temperature of the channel wall T w a ~ = ~ a ~ + Y" In the cases of more complicated boundary conditions (2) the numerical computations have been employed. ~) .$~"(X,Y),% b) Fig.2a depicts (at the left) ~ra~Twat~ = 0,9?'C I _-

T e~

.

25"C

Tw" tJ" t £5" ~e~=0

Twae~ = 15"C

"Y-- 25

the computed supersaturation fields ~(X,Y) for aqueous vapour

Te,,,~ = 4OoC

z0

~e..t= 0 ~f= ~

in the cylinder channel with linearly increasing temperature

I~

~= I Y=5

Twa~T e~ under boundary_ conditions10 -2 : = 25°C' C~e ~ = 3.13" according to 100% relative humidity of the inlet flow at T e~"l: ; Pe = 84.7 (reduced to T e~%);

f2

"Y=10 ~-----v-----X~ . ~

Y--5

I

i ,~

X

X ;

~,0

0,~

-~,' 0,2 02 Fig. 2.

Y--25 0,6

1,0

Te~+, waf~ = 25°c, %ra~Twa~= 0.97°C. The figure evidently shows the supersaturati°n ~(X'Y) being non-zero for any cylinder section at any Y, the plots of ~ ( X , Y ) running quietly in central areas of the channel (X--O). Computatione also demonstrate the positive supersaturations in the channel for vapour-gas mixtures with Le = 1, the values of ~(X.~')

T h e r m o d l f f u s t o n chamber

1515

appearing to be by a factor of 102 greater than those for the vapour-air mixture. The detailed supersaturation fields calculations under the variation of parameters T ~ % , C1e ~ , ~ r a ~ T w a u and Pe show the supersaturation field within the interval of 10 to 20 diameters from the channel inlet forming in such a way, that later on the supersaturation magnitude will always be stabilized and ~ r a 6 T w a ~

(it is essential)

and dependent only on Pe (the flow velocity)

(see Fig.3).

S(o,Y),r,

e

sra~ Twa¢~ =

O,S°C

Te..¼

=

=

Te..'~ = ZS°C wa~

C; ~ = ~,I~. Io~ '

I

/t~t~"~i,

0

0

I,

tO

Fig. 3.

The

gra~Tw~,¢ = o,z'c

'

,

i ,

20

|

,

,

.~0

,

,

~0

,

50

Y

The supersaturation in the center of a cylinder channel upon variation of the wall temperature gradient.

wide variations of T e~%

and

01e~$

are not influential on the

supersaturation magnitude beyond the stabilized area. This implies the possibility of supersaturation in such channels be regulated by variation of thermal or velocity conditions in the chamber. Comparing the above method with conventional practice of supersaturation production in the cooling channels (when T e ~ > T w a ~ = const. ) one findes out the advantage of suggested technique consisting in the much greater uniformity of the supersaturation fields, especially in the channel central area (Pig.2). It is also important to note that under thermo- and diffusiophoretic forces the aerosol particles are "focused" to the channel central area, and the chamber inlet is free of the inherent to a common TDC effects [I].

REFERENCES I. G.N.Lipatov & G.L.Shingaryov. The analyses of the performance of a dynamic thermal diffusion chamber. Pre-print Eleventh International conf. on atmospheric aerosol condensation and ice nuclei, (Hungary, Budupest, 3-8 sept. 1984) - Budupest, 1984. - V.2. - P. 165-170.