Numerical analysis of dust particles motion inside gas bubbles for flue gas desulfurization in a jet bubbling reactor

Computers Fluids Vol. 21, No. 2, pp. 211-219, 1992 Printed in Great Britain. All rights reserved

0045-7930/92 $5.00 + 0.00 Copyright © 1992 Pergamon Press plc

NUMERICAL ANALYSIS OF DUST PARTICLES MOTION INSIDE GAS BUBBLES FOR FLUE GAS DESULFURIZATION IN A JET BUBBLING REACTORt Y. HOZUMIL~and Y. YOSHIZAWA 2 *Chiyoda Corporation, P.O. Box 10, Tsurumi, Yokohama 230, Japan 2Institute of Engineering Mechanics, University of Tsukuba, Tsukuba 305, Japan (Received 31 March 1991; received for publication 8 November 1991) Almtraet--The motion of dust particles in a rising air bubble is governed by the inertial force due to the internal flow inside the bubble and the diffusion process due to the nonuniform distribution of the dust particles concentration. The circulating flow inside a bubble has a considerable effect on both phenomena. The dust removal efficiency under the influence of the circulating flow is analyzed numerically. Comparison of the calculated results with the experimental data in a pilot plant with respect to the removal efficiency shows that the phenomena are well described by this analysis, and that inertial motion and diffusion play important roles in determining the motion of particles inside a bubble in a jet bubbling reactor.

INTRODUCTION Environmental pollution has recently become an object of public attention. Acid rain due to sulfur dioxide has caused serious damage to the forest in industrialized countries. Flue gas, including sulfur dioxide and dust particles, is exhausted by burning coal and fuel oil in the boilers of thermal power plants. Several flue gas desulfurization (FGD) processes for coal-burning power plants have been developed in Japan, and have made great contributions to solving the acid rain problem. Dust particles in the flue gas are also a very severe problem for people near the power plants. Dusts in flue gas are initially removed to some extent by the electrostatic precipitator (EP), and secondly by a liquid medium in the FGD process. High removal efficiency is one of the most important characteristics of the FGD process. There are two scrubbing methods as a typical dust removal system in the FGD process: one is a spray method spouting absorbent liquid into the flue gas, where dusts are removed by liquid droplets; the other is a bubbling method where flue gas bubbles are sparged into absorbent liquid, and the dusts in the bubbles are removed by the surrounding liquid. The JBR (jet bubbling reactor), the main equipment of Chiyoda's FGD (CT-121), shows a high efficiency in dust removal in experiments by pilot and commercial plants. The bubbling flow in a JBR is a turbulent two-phase flow of flue gas and absorbent liquid, and consequently the actual mechanism of removal is quite complicated. However, it is important to analyze the mechanism for removing dust particles from a microscopic point of view, taking into account the shape of the bubbles and the flow fields [1, 2]. Many fundamental studies have focused on the spray method [3, 4]. For the falling droplet, the particle removal mechanism is evaluated by the inertial impact and diffusion process. Langmuir [5] estimated the inertial impact efficiency for potential flow and low-speed viscous flow. The diffusion of the droplets is evaluated with the help of the Reynolds number and the particle diffusion theory of Kerker and Hampl [6]. These investigations are concerned with a spherical droplet. On the other hand, few studies on the bubbling method have been reported. In the case of removal by inertial motion, Takahashi [7] estimated the capture of particles during bubble formation using a few simple bubble formation models, and rising bubbles by simple flow pattern [8]. There is no study of the removal phenomena with deformation of the bubble's shape and diffusion process under the internal circulating flow. This paper reports the path and concentration profiles of dust particles inside a spherical gas bubble through the numerical transient tPresented at the 2nd Japan-Soviet Union Joint Syrup. on Computational Fluid Dynamics, Tsukuba, Japan, 27-31 August 1990. :~To whom all correspondence should be addressed. 211

212

Y. HOZUMIand Y. YOSHIZAWA

analysis of the circulating flow inside the bubble under JBR operating conditions, and compares the removal efficiency expected from the calculated results with the experimental results from the pilot plants. Figure 1 shows an outline of the F G D system. Flue gas is exhausted from a boiler and passes through an EP and a heat exchanger before it reaches the JBR. The gas is injected violently through sparger pipes into an absorbent slurry. Then the sparged gas bubbles rise in the slurry. While the flue gas bubbles are rising, the flue gas contacts the absorbent slurry, the sulfur dioxide is dissolved due to diffusion into the slurry and the dust particles are removed from the surface of the bubbles into the slurry. Clean gas is finally exhausted from the JBR. The flow pattern in the JBR is bubble flow, which is closely related to the discharge pressure and exhaust hole diameter of the sparger pipes. Although the motion of the bubbles becomes unsteady, and the shape and size of the bubbles become nonuniform, it is assumed for this article that a single spherical bubble rises at a constant velocity due to buoyancy. The representative diameter of the bubbles, from experimental observations in pilot plants, is assumed to be about 3 mm. The principal ingredient of the dust exhausted from coal-burning boilers is fly ash. The diameters of the dust particles considered are assumed to be from 0.1 to I0.0/~m, which is the range generally found in actual plants. Generally speaking, it is difficult to remove the dust particles in the micron and submicron ranges, because the removal phenomena is inefficient in those ranges. Based on the sizes of the dust particles and observations by electron microscope, the shape of the dust particles is treated as a sphere. The removal mechanism for dust particles at the bubble surface is classified into two categories: one is the inertial motion caused by the circulating flow inside a bubble; the other is the diffusion process. The diffusion is caused by the gradient of the particle concentration due to absorption of the dust particles at the bubble surface. Thus, it is necessary to solve the internal flow of the gas to evaluate the motion of the dust particles. I N T E R N A L FLOW IN THE BUBBLE If a gas bubble rises at a constant velocity, the tangential shear stress due to the outer viscous flow produces circulation of the gas flow inside the bubble. The basic equations for both the inner and outer flow fields are expressed using the well-known vorticity transport equation: 8to -rot(u x to)= LAto c~t Ke

(1)

®

®

,

Itadust ialwater ) (D (~) @ (~)

Chimney Heat exchanger G~fan Mist eliminator

(~) JBR (~) Pump (~) EP

Fig. 1. Outline of the FGD process (Chiyoda CT-121).

®

Flue gas desulfurization in a jet bubbling reactor

213

to = rot u.

(2)

and Equations (1) and (2) are rewritten using spherical coordinates (r, 0, ~b), and derivatives with respect to ~b can be neglected due to the symmetry of the flow field: Ot + -

r ~

(ruco) +

co

; I ~ 1[ ~r(0o) ~-r +sinO (Vco)

=

_ _

r2

=

-

sin 0

-ffd

--

~

'

[ ( 1 d~k) 1 d_~( 1 0~k)] 1r ~rr c~ sin 0 drr + ~ s i - ~ ~-0

(3) (4)

and u

r 2sin030'

v=

r s i n 0 0r"

(5)

Here Re is the Reynolds number, defined differently in the inner and outer flow fields. The above two equations are solved by a numerical analysis with boundary conditions that satisfy the continuity of the shear stresses of the gas and the liquid at the bubble surface: i o "Cs = T s ,

"~s

=

# ~0u0 ; -r

(6)

where rs is the shear stress at the bubble surface and # is the viscosity. A body-fitted grid ~ = ~ (r) is used for spatial meshes. The delta form is applied to the vorticity co to obtain the steady flows: A"CO = co" + l _ co,;

(7)

n is the time step. The Beam-Warming method is applied to equation (3): FAt

3

At

0

A"co - 1 + ~ dt (A~co) + 1 + ~ 0t (co") + ~

E

(A"-~co) + 0(At2),

(8)

with F = 1 and E = 1/2. The calculating procedures are as follows: (1) Potential flows are assumed at the initial condition. (2) The internal flow is induced to satisfy the continuity of the shear stress caused by the external flow. (3) The shear stress is reevaluated by the internal flow. (4) The external flow is reanalyzed using the shear stress evaluated in step (3). Steps (2)-(4) are repeated until steady flows are obtained for both flow fields. The ADI method is applied for solving equation (3) and the SOR method for equation (4). Figure 2 shows a typical streamline pattern of the internal and external flow for a gas bubble rising in a liquid. Velocity vector distributions are shown in Figs 3 and 4. M O T I O N OF D U S T P A R T I C L E S BY AN I N T E R N A L F O R C E The motion of dust particles is induced by a force in proportion to the relative velocity between the particle motion and the internal circulating gas flow. Since the sizes of the particles are quite small, the force is assumed to be the Stokes drag force: f = 6n#~ ~ (u - v),

(9)

where u is the velocity vector of the internal flow, v is the velocity vector of the dust particle, d v is the diameter of the particle and #s is the viscosity of the flue gas. Equation (9) is modified by the use of the Cunningham constant C¢, because particles are too small to treat the flow field as a continuum. The particle motion is expressed as follows: dv m~=

3r~#~dp(u - v) + m s ,

Cc

(10)

214

Y. HOZUMI and Y. YOSHIZAWA

Fig. 2. Streamlines; Re = 1.

Fig. 3. Velocity vectors in the bubble.

where Cc = 1/[1 + 0.42(l/dp)] + 1.67(l/dp), l is the apparent mean free path of the gas molecules, m is the mass of the particle and g is the gravity acceleration. Equation (10) is reduced to the x and z directions. The effect of the gravity force is considered in the z direction only: dw St ~ (It

= u ~. - v ~

(11)

and dr.

St~ - =u.-v:+G,

(12)

where St is the Stokes number, St = Ccppd~u/(18 #gdb), and G is the nondimensional gravity force, G = Ccppd~g/(18 I~gu). pp Is the density of the particle,/~g is the viscosity of the flue gas and db is the bubble diameter. The particles move with the internal circulating flow inside a bubble and all the particles which reach the bubble surface are completely removed into the slurry. Equations (11) and (12) are integrated in parallel with respect to time. The centrifugal force due to circulation extends the radius of the particle path itself. The particle finally reaches the surface of the bubble, and is removed into the slurry. Figure 5 shows a comparison of a streamline with a particle path. Figure 6 indicates the calculated paths of the different sized particles. Large particles are affected by inertial force than small ones, and reach the surface more rapidly. In Fig. 7 the calculated relationship between particle removal efficiency and particle diameters is plotted. The flow field inside the bubble is divided into cells for numerical analysis. Although small particles are abundant in actual cells, it is assumed that all particles are placed on the grid points at the initial time in the analysis. The removed volume of particles is calculated such that particles in a cell are assumed to be completely removed, when the four particles at the grid points surrounding one cell reach the surface. The removal efficiency is defined as a ratio of the removed volume to the bubble volume. The calculation is executed over the

Flue gas desulfurization in a jet bubbling reactor I

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t i I • l l

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Fig. 4. Velocity vectors outside the bubble.

Fig. 5. Comparison of a streamline ( path (. . . . ).

) with a particle

bubble's residence time in the absorbent liquid in the JBR. The method of solution is Runge-Kutta method for equations (l l) and (12). From the calculated results, dust particles are perfectly removed when the diameter of particles is >2.0 #m. On the other hand, particles of <0.1 #m dia are neither affected by inertial motion nor removed. Experimental results, however, indicate that particles of < 0.1/zm are also removed. To explain this phenomena, the diffusion process is taken into account in next section.

the the the dia the

P R O F I L E S OF C O N C E N T R A T I O N BY THE D I F F U S I O N PROCESS Since the size of a small particle, of approx. 0.1 # m d i a , becomes almost comparable with the apparent mean free path for the gas molecules, the approach for analyzing its motion should be considered to be different from those for large particles. Therefore, the diffusion effect is investigated to analyze the motion of small particles. If the particles are too small, they are hardly affected by the centrifugal force caused by circulation. Such particles are considered to move, approximately, with the internal gas flow, and the equation of diffusion is expressed as follows: ~C ~ t -- - ( u , grad C) + ~AC,

(13)

where C is the concentration of the small dust particles, and ~ is the diffusion coefficient. Equation (12) is rewritten using (r, 0) coordinates, in the same way as the vortex transportation equation: ~C ( aC U0 aC'x f2 ~C c3---t = -- \U'~r+--'~)+~r-~r+-~r2-tr

~2C

1 aC 1 ~2C~ r2 tan 0 d0 + ~ ~-~Tj.

(14)

The change in the concentration distribution is analyzed with respect to time. A uniform distribution of concentration is assumed as the initial condition. The boundary condition is CAF 21/2--F

216

Y. HOZUM~and Y. YOSmZAWA

I%

SS

t

/" ~sSo 6B

~

~li~oolo

0

°

Fig. 6. Particle paths: . . . . . , Dp=0.2/~m;

, D p - 1.0/~m.

assumed to be C = 0 at the bubble surface. The method of analysis is essentially the same as the method for the vortex transport equation. Figure 8 shows the concentration profile with respect to time. The gradient of the particle concentration develops from the bubble surface to its center. If there is no internal flow, the concentration becomes the same at all points which are at the same distance from the surface. However, the convection in the bubble makes that concentration different at the front and the back of the bubble. Symmetrical circulating flow occurs inside a bubble due to the shear stress by the external flow. The internal flow circulates from the front to the back of the bubble along the surface, and rises from the back to the front of the bubble along the centerline. Since the particles are i00 a~ ~,

N0

80 60

~ ~ . - . ~ . . . . _ ~ . _ - L ~ L . ~ _ L ~

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(Dp) ~m

Fig. 7. Removal ef~ciency due to inertia and diffusion.

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Y. HOZUMIand Y. YOSHIZAWA

218 Sweep Time N

=

. . . . :~/" :I /l / / :~ m l

5

[ , 0 --

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Fig. 8, Profiles of concentration. removed at the bubble surface, the particle concentration at the back of the bubble becomes less than that at the front. RESULTS AND

DISCUSSION

The efficiency of dust removal due to diffusion is obtained by integrating the concentration of individual cells at the instant when the bubble reaches the slurry surface. Figure 7 shows the relationship of the particle sizes and the efficiency of dust removal. Although the motion of the actual particles in a JBR is dependent on the coupled effect of the inertial force and the diffusion process, the total efficiency of dust removal in a JBR is expected to become slightly greater than the sum of the efficiencies of the inertial motion and the diffusion. Figure 9 shows a comparison of the total efficiency, which is evaluated as the sum of both the calculated efficiencies, with the actual data in a pilot plant. Overall agreement is fairly good. The calculated total removal efficiency is overestimated by treating the bubble surface as a perfect sink i00 80

~

~o

~

4o

20

..... i ................... i

i l

....

,,

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0.I

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i

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il N

Iill l lil_l

........... l . I

Calculated Resul

!tlzll

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i I liiil i _1....1 I i l

j l'llliil I

1.0

Diameter of particles (Dp) ~,n Fig. 9. Comparison of calculated results and experimental data.

III

il i0.0

Flue gas desulfurization in a jet bubbling reactor

219

for the dust particles, however, on the other hand, it is underestimated since particle removal during the initial bubble formation and the horizontal bubble motion are neglected. It is concluded that the dust removal mechanism is well described in this analysis by offsetting the above-mentioned underestimation against the overestimation. The process of dust removal in a JBR is simulated on the basis of the microscopic motion of the dust particles. The phenomena of dust removal is classified into three regimes dependent on the particle sizes. The removal is governed by diffusion for dust particles between 0.01-0.1 #m dia. For dust particles between 0.1-1.0/~ m dia, the removal is governed by the coupled effects of inertia and diffusion. Above 1.0/~m dia, inertial motion becomes dominant. It becomes clear that particle concentration decreases more rapidly at the bubble back than at its front since particles at the bubble surface are removed into the absorbent slurry by the internal flow circulation inside a bubble. REFERENCES 1. Y. Yoshizawa and Y. Hozumi, Numerical calculation of viscous flow in and around a liquid droplet. In Proc. 3rd Numerical Fluid Dynamics Syrup., Nagoya, pp. 275-280 (1989). 2. R. Clift, J. R. Grace and M. E. Weber, Bubbles, Drops, Particles. Academic Press, New York (1973). 3. K. Takahashi, Kiso Aerosol Kougaku, Chaps 3 & 4. Youkendou, Tokyo (1982). In Japanese. 4. A. K. Postma and R. K. Hilliard, Nucleation and capture of condensible airborne contaminates in an aqueous scrubbing system. HEDL-TME 78-82 (1978). 5. I. Langmuir, J. Met. 5, 175 (1948). 6. M. Kerker and V. Hampl, Scavenging of aerosol particles by a falling water drop and calculation of washout coefficient. J. Atmos. Sci. 31, 1368 (1974). 7. T. Takahashi, T. Matumoto and S. Kanekawa, Internal capture of particles during bubble formation. Aerosol Kennkyu 1, 48 (1989). 8. T. Takahashi, T, Matumoto and S. Kanekawa, Internal capture of aerosol particles in a rising bubble. In Proc. 4th Syrup. on Aerosol Science & Technology, Nagoya, pp. ~ 6 (1986).