J. Eng. Sci., Univ. Riyadh, Vol. 6 (2) pp. 137 - 145 (1980)
Capture of Air Borne Particles
by
V-Shaped and Plane BafflesM.S. EI-Shobokshy* and I.A. Ismail**
*
Col/ege of Engineering, University of Riyadh, Saudi Arabia.**Col/ege of Science, University ofZagazig, Zagazig, Egypt.
The theoretical collection efficiencies of V-shaped and flat-plate baffies have been analysed for the capture of spherical particles, 2 to 80 /lm in diameter, entrained in air streams. Reynolds number values related to the projected width of the baffie were taken to be in range of 103 to 10' units. Theequation of the motion of the particles was solved by the second order Runge-Kutta method in order to compute the particle paths in the vicinity of the collection barrier.
The collection efficiencies were plotted against the Reynolds numbers for different baffles with the particle diameter as a variable parameter. The effect of baffle geometry is presented by three different arrangements, each at a specific value of Re (Reynolds number).
The baffie having enclosed angle (a) of 900 was found to have the highest efficiency for particles greater than 35/lm in diameter when Re value was 104 This baffie arrangement gave 100 per cent collection efficiency for particles above 10/lm when the Re-value was 5 x 103, the baffie with the enclosed angle of 120° gave a higher collection efficiency than those with 90° and 1800 baffies.
Nomenclature vertical components of particle and fluid
velocity m/s.
a constant (see equation 3)
L m p r
t*
Uo
drag coelTicient for the spherical particle collection efficiency
number of guide points baffie projected width,m particle mass, kg
particle parameter (see equation 3) particle radius, flm
time, second
. . . t.Uo
non-dimensiOnal time (- -) L/2
the upstream undisturbed fluid velocity, m/s horizontal components of particle and fluid velocity, m/s.
non-dimensional horizon tal velocity u u
x x*
y y*
oc
non-dimensional u uJ
components (_P ,_).
UoUo
vertical
horizontal distance, m .
velocity
non-dimensional horizontal distance (~) L/2 critical abscissa of a particle (see equation 12) vertical distance
non-dimensional vertical distance
the enclosed angle between the baffie sides, degree
fluid viscosity, kg/m.s.
fluid density, kg/m3
velocity potential (see equation 4)
Capture of Air Borne Particles by V-Shaped and Plane Baffles
Introduction
Current awareness of the need to protect the immediate and remote environment against man-made pollution has required the introduction of stringent measures for gas cleaning in many industrial processes.
A process gas may have a high concentration of potentially toxic particulates, thus constituting a risk of serious health hazard to industrial workers and to the surrounding population. On the other hand, the particulate matter emitted from power station boilers fired with fossil fuels can be transported and deposited over wide areas, and this may cause detrimental consequences on the environment or a national or international scale.
Natural, non man-made, particulate matter when entrained in moving air streams can cause nuisance and damage on a large scale, and it is necessary to consider various possibilities to arrest the moving particles. One particular example of this is the necessity of preventing accumulations of sand entrained in dry winds on roads passing through exposed desert areas.
The momentum separators were first employed in gas filtration. The collector elements used were in the form of fIbres and were based on the mechanism of impingement of particles on fibres. The collection efficiency of the fibre may be estimated once the velocity field around the fibre has been obtained. The latter may be obtained by solving the Navier-Stokes equations.
Several investigators have obtained such solutions [1- 4]. The flow patterns depend on the Reynolds number (Re) relative to fibre geometry. For low Reynolds number (Re=0.2 and 10), Davies [5] and Davies and Peetz [6] calculated the collection efficiency of isolated fibres. Suneja and Lee [7] have estimated the collection efficiency of round fibres at intermediate Reynolds numbers (100). Their results for Re values of 10 were in quite good agreement with those of Davies and Peetz [6]. At high values of Re, the data on the fibre collection efficiencies have been published by several workers [8- 12].
In industrial gas cleaning, bame-type momentum separators are widely used. Muschelknautz [13] has described a modern development of a simple momentum separator with a change in direction as the separation mechanism. More elaborate and also more efficient, is the collector in which the gas is allowed to impinge'on a surface which is shaped in such a way as to retain the particles, while allowing the gas to escape.
DilTerent types have been developed using a
venturi bame [14], U-shaped bame [15J, and curved slotted surface [16].
. A considerable experimental and theoretical work has been conducted on the Inertia air filters· and Louvered type Inertia tilters [17-19].
Among the momentum collectors is also the Calder-Fox Scrubber [20J, which is used for recovery of acid mists. The gas carrying the droplets of acid mist is forced through orifices where agglomeration takes place and then the agglomerates impinge on bames, where agglomerated droplets are deposited. It is essential for the designers of the momentum separator to choose the proper bame shape which has a best collection efficiency under the given working conditions. Simple bames may be flat plates or V- shaped having different angles. When placed transverse to the flow of particle-laden gas, they will separate the particles with different efficiencies, depending on the flow conditions and on the size of particles.
The object of the present work was to present a theoretical analysis for the collection efficiency of different shaped baffles under varying working conditions. The representative bames considered were:
flat plate bame when the flow is normal to it, and V- shaped bames with enclosed angles of 90° and 120°, when the flow is also normal to the axis. The collection efficiencies were calculated fot the Reynolds number values of the flow based on the projected width of the bames, ranging from 103 to 105, and for particle sizes ranging from 2 to 80,um diameter.
Theoretical Analysis
Consider a particle entrained with a fluid stream approaching a bame of enclosed angle (IX) as shown in Fig. 1. For a steady stream, neglecting gravity and assuming that the flow is two-dimensional, non- rotational and incompressible, the equation of motion of a spherical particle of radius r can be written:
dv 1
md/=2Cob(vJ-vpfnr2 (lb) where m is particle mass,
up, v p is particle velocity in x and y-direction, is fluid velocity in x and ycdirection,
Journal of Eng. Sci.- Vol. 6-No. 2-J980-Col/ege of Eng., Univ. of Riyadh.
M.S. EI-Shobokshy and I.A. Ismail
Fig. 1:
and r
y
y
up: UoI I I I I I
\
\/
/
\ / /
"
... .... _---"" / /~---+-~~ X
L
Particle path and the bafne geometry.
is fluid density,
is drag coefficient for the spherical particle
is particle radius.
Equations (la) and (lb) may be translated into the corresponding expressions with dimensionless units:
*
up * v p * _ u, * _ v, u = - v =p Uo" p -Uo" u'-Uo,v'-Uo'where Uo is upstream undisturbed llu.id velocity and L is the projected width of the baffie.
If the Stokes flow is assumed, i.e. CD is equal to
~
Re
P dv* -P=v*-v* dt* ,
p
where the particle parameter (p) is given by,
p m.Uo
6nll.rL/2
(2a)
(2b)
(3)
However, if the particle Reynolds number will be outside the Stokes range, the imperical non-linear drag law suggested by Serafini [21J, his expression is:
CD =-24 (1 +0.158Re2!3).
Re
To obtain the components of the fluid velocity, the flow is constructed on the basis of transforming the flow in the real plane to a flow around the baffie in the complex plane by using the general transformation,
(<p+iljJ)=a(x+iy)"!·O<a<h (4) Where <p is the velocity potential,
IjJ is the stream function
and a is a constant depending on the initial value of Uo.
When the enclosed angle (a) is equal to 120°,
and
When a is equal to 90°,
u j = a(4x*3 -12x*y*2) and vj=a(4y*3-12x*2 y*) When a is equal to 180°,
uj=2ax*
and vj= -2ay*
(5)
(6)
(7) (8)
(9)
(10) The two equations of motion in the x· and y- directions ((2a) and (2b)) are solved using the Runge- K u tta method of the second order. In each case, the area is taken to be a mesh of grid size O.lcm. Thus in each of the three cases, there is rectangle of the size 1/2L x 3L.
Capture of Air Borne Particles by V-Shaped and Plane Baffles
approaching the baffle its velocity is assumed to be the same as that of the fluid. It is also assumed that the particle path coincides with the fluid stream line. The above two assumptions are valid as long as the distance between the particle and the baffle is sufficiently large so that the baffie has no effect on the flow pattern. For the present analysis it is assumed that the minimum distance at which the flow pattern will not be affected by the presence of the baffle is three times the baffle's projected width, that is, 3L.
When the particle is at a distance less than 3L from the inlet plane of the baffie, a deviation is attributable to the inertia of the particle, which is a function of its mass.
Therefore we take the initial value of up equal to Vo at any point at a distance greater than 3L from the inlet plane (Fig. 2).
The central streamline of the flow goes along the central axis without suffering any deflection.
Consequently a particle along the same axis would act similarly. The initial values of up are taken to be equal to the corresponding values of that of the fluid at the
y (Intr.1 •• i5
~
IIp : U.r..
\
\ \
\
\
\ n ': qrid point
\
\
\ Inl.t pllno
y
/ '
V
VV
VV
V VV
V
V
XL
Fig. 2: Boundary condition for the computation.
second grid point from the central axis, where it is assumed that the particle has not started to deflect.
Hence if the grid distance are small enough, the above assumption will not lead to any significant error.
Read initial values of Uo
t
Compute particle parameter, p
t
Compute the values of u f , v
f all over the grid points.
t
Compute:
Kl = H* ( u fi u . - 1) / P.
pl ufi + 1
K2 = H* ( u. + - 1) / P.
l Kl
u. l + 1 = u. l + 0.5 * (Kl + K2)
t
Get values of u. all over the l
grid points.
t
Compute:
*
vfi 1) / P.
Kl = H ( - -
-
v . pl H* (
vfi + 1 1) / P.
K2 = - 1 -
i -
t
Get values r-f v pi
v pi - 1 = v pi + 0.5* (Kl + K2)
v Y. l - 1
=
Y. l + H * u pipi
T
Stop END
Fig. 3: Flow diagram for the computation.
Journal of Eng. Sci.-Vol. 6-No. 2-J980-Col/ege of Eng., Univ. of Riyadh.
M.S. El-Shobokshy and I.A. Ismail
Equations (2a) and (2b) are now solved numerically for the particle velocities up and v p to get the particle path from the equations:
L/2
Xc
Flu'ld streamli ne
Particle path - - - -
Fig. 4: Particle paths and fluid streamlines.
lQO , - - - : ; _ _ . " . . . . - - : : : - - - - : ? ' " " - - - ,
90 80
~ 10 G ~ 60 U
if
~ 50 z o
~ 4V
o )0
~
90'FLOw REYNOLDS NUMBER
Fig. 5: Collection effiCiency dependence on Reynolds number (900 V-
(11)
where i is the number of the grid point starting in a reverse order, and H is the grid size. The second order Runge-Kutta method is used for which purpose it is necessary to have some initial values adopted for both up and vp components. To give a better insight into the computation technique a Oow diagram is shown in Fig.3.
Having obtained the Ouid stream lines and the particle paths for the whole Oow, the collection efficiency could be defined as the abscissa of this particle (xcr) at a distance 3L (Fig. 4) from the inlet plane divided by L/2, that is
Results and Discussion
E=~ L/2 (12)
The velocity field of the Ouid around the baffie has been calculated and the streamlines of the Oow are shown in Fig. 4. Equations (1a) and (2b) were used to obtain the particle paths, rrom which the collection efTiciency is calculated using equation (12). The particle sizes used in the present computations ranged from 2 to 80.um diameter, with a density of 1500kg/m3. The upstream undisturbed Ouid velocities were taken in the range of 1.0m/s to 30m/s. This corresponds to Re values of 3.8 x 103 to 1.6 X 105 based on the baffie projected width. Fig. 5 and 6 show th'e collection efTiciency of the V-bafOes with ex vlllues of 90° and 120° for different particle sizes. Fig. 7 shows the collection efficiency of the Oat plate baflle, that is when ex is equal to 180°.
100,---==-=-:::~:::::_---,
1.105 FLOW REYNOLDS NUH8ER
Fig. 6: Collection efficiency dependence on Reynolds number (1200
Capture of Air Borne Particles by V-Shaped and Plane Baffles
1001,---:::::::::;;;;~---1
90
1
80
10 180'
FLOW REYNOLDS NUMBER
Fig. 7: Collection efficiency dependence on Reynolds number (Flat- plate-baffle).
100,---- -- - - -- - -- - -, 90
80
"!- 70
g
bO~ so
40
10 20 10
Fig. 8:
R. , 5000
10 10 40 so 60 10 80
PARTICLE DIAMETER , 11m
Effect of baffle geometry on the collection efficiency (Re
=5000).
100
i - ---=:::::::==--:========J
Fig. 9:
10 20 10 40 so 60 70 80
PARTICLE DIAMETER , IJm
Effect of baffle geometry on tbe collection efficiency (Re
= 10000).
20 10
a =90
. ,.
a.:1BORII :: 50,(100
OL-_~ _ _ _ _ ~_~ _ _ ~_~ _ _ ~_~
o 10 20 10 40 so 60 10 80
PARTiClE: DIAMETER , \lilt
Fig. 10: Effect of baffle geometry on the collection efficiency (Re
=50000).
In order to show the efTect of the baffle geometry the latter is plotted against the particle diameter with the angle a as parameter (Fig. 8 to 10). The efTect to difTerent parameters on the collection efriciency of the baffles will be discussed separately.
a. The Effect of Particle Size
The collection efTiciency of a baffle is afTected to a great extent by the particle size. This is due to the nature of the mechanism by which particles are collected by the baffles, and it is based on the deviation of the particle from the fluid flow. The particle deviation is expected to become more pronounced as the size of the particle, and hence its momentum, increases.
Particles of 2.um diameter and less are not efTectively collected by the baflles under investigation unless the value of the Reynolds number is greater than 105. When Re is equal to 105 the collection efTiciency is in the range of 60 to 80 per cent for 2.um particles.
Particles of 40 to 80.um diameter can be collected with almost 100 per cent efriciency by the baffle which has a a value of 90° and when Re is equal to 104• These particles are collected with about 80 per cent efficiency by other collectors, that is when a is equal to 1200 or 180°.
Maximum efficiency can be attained for particles of 10 to 80.um diameter with the 90°-baffle, when Re is equal to 105 whilst for the flat plate, Re value of 5 x 104 is sufricient to achieve lOOper cent efTiciency.
b. The Effect of Reynolds Number
The flow velocity as represented by the Reynolds number, significantly afTects the collection efficiency.
The particles acquire their initial velocity from the
Journal of Eng. Sci.-Vol. 6- No. 2-1980-Col/ege of Eng., Univ. of Riyadh.
M.S. EI-Shobokshy and I.A. Ismail
moving fluid. For low fluid velocities the flow streamlines diverge less steeply around the baffie than at high velocities. When the fluid now is deflected slowly this gives the opportunity for the particles to follow the path of the gas flow. This effect is evident in Fig. 5 to 7, for low values of Re below 103 when the collection efficiency for 2 to 20).lm diameter particles is negligible for all baffies used. As Re increases, the fluid flow deviates more rapidly around the baffie and the particles are deflected from the fluid path and strike the baffie. The collection efficiency increases less steeply as Re increases ror the flat plate baffie (Fig. 7). For the 90°- baffie (Fig. 5) the collection efficiency is strongly dependent on the Re values. For the 120o-baffie (Fig. 6) the efficiency increases moderately with Re except for 80).lm particles; for this particle size, the efficiency is nearly constant for all values of Re used in the computations.
c. The Effect of BafJIe Geometry
Figures 8 to 10 show the efficiency/particle size plots for various baffie geometries at given Re values.
For a low Reynolds number, (Fig. 8) the highest efficiency is achieved by using the 120° -baffie for all particle sizes in the 2 to 80).lm range. However, the 90°_
baffie shows a comparable performance only for 70 to 80).lm particles. The nat plate baffie shows a comparable performance only for 70 to 80).lm particles. The flat plate baffie shows a slightly better efficiency than that of the 900-baffie for particles less than 55).lm. As the Reynolds number increases to 104 (Fig. 9), the 1200-baffie still has the highest efficiency for particles less than 35).lm.
Above this size the efficiency of 900-baffie becomes comparable. This is due to the larger deflection experienced by the fluid stream and the deviation of the relatively large particles from the fluid path. Fig. 9 confirms this fact, for a high Re-value of 5 x 104. The efficiency of the 900-bafOe rises more steeply with increased particle size than that of the other two baffies.
The flat plate baffie shows a poorer efficiency than of the two V - shaped baffies. Thus with high Reynolds number values the best collection efficiency is obtained by using the 900-baffie.
Conclusions
The collection efficiencies of spherical particles impacting on V-shaped baffies have been calculated for Reynolds number values between 103 and 105 based on the projected width of the baffles. Two V-shaped baffles with enclosed angles of 90° and 120°, and a flat plate baffie have been investigated. The 900-baffie is most
35).lm diameter, when the Reynolds number of the flow is 104 Particles 40{lm in size and larger can be collected with 100 per cent efficiency by such a baffie. The Re value of 5 x 104 is required to collect 10{lm particles with 100 per cent efficiency. For Reynolds number value of about 5 x 103 it has been proved that the 120° -baffie is more efficient than the 900-baffie or the flat plate in collecting particles in the range 2 to 80).lm diameter.
When Re is increased to 104 the saIpe baffle still has the highest collection efficiency but only for particles less than 35).lm diameter. The collection efficiency of the flat plate bame is generally low especially for Re greater than 104.
It can thus be concluded that the choice of a specific baffie to be used for particle collection has to be made according to the given flow conditions and the existing particle sizes. Figures 8 to 10 provide useful information needed to assist in making such a choice.
References
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Captllre of Air Borne Particles by V-Shaped and Plane Baffles
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Journal of Eng. Sci.- Vol. 6-No. 2-1980-College of Eng., Univ. of Riyadh.
M.S. EI-Shobokshy and I.A. Ismail
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