of 7ko-pha~ ~. F/ows [in Ressian], Mashinostroenie, Moscow (1974). & V.G. Levich, ehys/co-Chem/c.a/Hycbvdynam/cs [in P.aumian], F'mnatgiz, Moscow (1959).
lq~a ~ .
vat ~#, ~b. 4, Z ~
BUBBLING OF GAS-PARTICLE MIXTURES UDC 532.529.5
IL O. Sabdenov
A formula for the particle passage coefficient, which describes the existing experimental data for Stokes numbers 5 < 2, is obtained.
To remove dust particles or aerosol droplets from air or other gases, foam and centrifugal bubbling apparatus is widely used [1--3]. Their basic principle of operation consists in injecting the air to be purified through small slits or holes into a liquid (usually, water). Foam apparatus has already been around for more than 30 years. The experimental studies of the deposition of a finely dispersed mineral-oil aerosol in a foam apparatus (for example, see [4, 5]) indicate that the passage coefficient (the ratio of the outlet dust concentration to that at the inlet) depends only on the Stokes number S and rapidly decreases with S. However, this has not yet been explained theoretically. Usually, it is assumed that in a foam apparatus dust collection takes place in accordance with the "collision mecbani.~m" [6] in the stage of gas bubble growth. However, so far in the literature no model of such a mochani.~m has been developed. Accordingly, the development of methods of calculatingthe dust removal process could help to formulate clear recommendations for both operating and de~si~ing foam apparatus. In this paper, we perform a theoretical analysis of the dust removal process. L
PARTICI~ DEPOSITION UNDER CENTRIFUGAL INERTIAL FORCES
Consider a single orifice of diameter d (Fig. 1) through which a dusty gas enters a bubble at the constant mean speed Vo. The dust particles can be removed by the centrifugal and inertial forces which develop in the vortex cireulatjng motion of the gas inside the bubble. This may occur both before and after bubble separation. We will estimate the contribution of the above-mentioned forces F. In the first case:
Here, V is a characteristic gas velocity in the growing bubble, Q is the gas flow through the orifice, and R(t) is the bubble radius. In the second case: F2-I4~, where W is the velocity of free ascent of a bubble rising due to the Archimedes force. Then
It is known from experiment that W~03 m/s [8] andd/2Re~O:2 [9], where Re is the bubble radius at the separation instant. For Vo-10 m/s we obtain: F~/F2-102 [5]. It follows that dust deposition typically occurs before bubble separation. This explain~ the experimentally observed slight variation of the passage coefficient with the thickness of the liquid l a i r in foam apparatus [5]. In a centrifugal bubbling apparatus, there is a centrifugal force associated with the rotation of the gas-liquid ring as a whole. If the modulus of this force is at least an order less than F1, then the results of this paper will be valid for this type of apparatus as well. A gas laden with dust or aerosol particles is a two-phase medium. Assuming that the particles are finely dispersed and their concentration is low, we will consider the hydrodynamicproblem of pure-gas motion [7].
Tomsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika ghidkosti i Gaza, No. 4, pp. 113-121, JulyAugust, 1998. Original article submitted May 18, 1996. 0015-4628/98/3304-0559520.00 9 1998 Plenum Publishing Corporation
559
Fig. L Diagram of gas-particle mixture flow into a gas bubble.
2.
THE PROBLEM OF GAS BUBBLE GROWTH AT SMALL REYNOLDS NUMBERS
The experiments show that a growing bubble has a nearly spherical shape [6]. We will consider the orifice through which the gas-particle mixture enters the liquid to be a point source with a given flow rate Q. Then, the spherical bubble radius increases in accordance with the following
(3 t)~ , -~: dR 4~'R O,,~
~(t): ~-Q
The Navier-Stokes equations for the flow under consideration are:
a,,,+v,+.~+;,,a,,, ,,+_~.ap
IA
2v, 20~. 2v~
a,,.+,,+.+++.+,,,~_ :Pt ra0 + +,(A" +.+r2a, ., at ar r 80 r 2 a0 Here, p~ and v are the gas d e ~ variables. In the non,llmensional variables
v,:
" 1
r28inZO
and the kinematic viscosity, and A. is the Laplace operator in the dimensional
4 x R2(t) v
0
,, re:
4xR2(t) 9
O
e
r
9
:~-~,
P : 41tRs(t) p
~r
p,
the transformed equations take the form:
Re- v,+~-=-. +V, -(2
560
+
~] :_av +av, aE
2v, E~
2 ave E2 ~
2 av, ave~ ave+v,av,~ae+v,v,]------~.ael aP+AV~
2v0~o E2
v,
(2.1)
The presence of the variable t in explicit form in Eqs. (2.1) indicates the non-self-similarity of the problem of bubble growth. When Re
