JOURNAL OF APPLIED ENGINEERING SCIENCES
ISSN: 2247-3769 / e-ISSN: 2284-7197
VOL. 4(17), ISSUE 2/2014
ART.NO. 157, pp. 19-26
STUDY ON MECHANICAL SEPARATION OF DUST USING
LOUVER TYPE INERTIAL SEPARATOR
F. Domniţa a, *, C. Bacoţiu a, Anca Hoţupan a, T. Popovici a, P. Kapalo b
a
Technical University of Cluj-Napoca, Romania – *e-mails: [email protected],
[email protected], [email protected], [email protected],
b
Technical University of Kosice, Slovakia, e-mail: [email protected]
Received: 05.09.2014 / Accepted: 15.09.2014
Revised: 13 .10.2014 / Available online: 15.12.2014
KEY WORDS: louver type separator, powder, dust, mechanical separation, inertial separator, purification, air movement
ABSTRACT:
Since louver type collector has reduced dimensions, it can be used as a pre-separator in addition to a filtering installation, in order to
increase the degree of mechanical separation of dust particles. The use of the louver type collector in a filtering installation requires a
description of the particle movement inside the device and also a method for determining the rate of particles separation.
1. INTRODUCTION
The separation of dust particles from gases has been a
concern for researchers since the development of
industrial processes. The necessity to approach such an
issue was imposed because the solid particles
circulation together with technological gases through
installations leads to high energy consumption and low
reliability of technological equipment. Equally, the
fight against dust from the industrial environment is of
special importance for health and social hygiene.
One of the areas where environmental quality can be
significantly improved is dealing with the removal of
dust particles in suspension in gas streams. This
favourable evolution is due to industrial processes
based on mechanical, electrical, hydraulic separation
techniques and also on porous layer hydraulic
separation (Lăzăroiu, 2006).
degree of particles removal, physical and chemical
characteristics of dust particles, and also temperature,
pressure and flow rate of polluted air or gas.
This paper presents a new method of separation of solid
particles from gases using louver type inertial
separator.
Inertial separators are devices working on the principle
of inertia. If suddenly the movement direction of the
carrier gas is changed due to inertial forces, the
particles are separated from the deflected stream. Thus,
the gas comes out through device side openings, having
a much reduced concentration of particles. Due to this,
as the carrier gas passes through the device, the particle
concentration will increase, reaching its maximum at
the main exit from the device (Popovici et al., 2011).
When a gas stream changes direction as it flows around
an object in its path, suspended particles tend to keep
moving in their original direction due to their inertia.
Particulate collector devices based on this principle
include cyclones, scrubbers, louver type separators and
filters.
The gas cleaned by the inertial separator has a much
lesser concentration of particles than the carrier gas
before the entrance to the collector. Therefore, these
devices can be used in industrial installations as preseparators. As a result, the required degree of particles
removal is much lower for the next steps of dust
collectors (located downstream the louver type inertial
separator), which represents a big advantage.
The main elements required for choosing the method
and separation equipment are: particles concentration
in the gas stream, particles size analysis, required
Design features associated with louver separators have
been evaluated by a number of researchers. They
investigated design features such as louver length,
* Corresponding author
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JOURNAL OF APPLIED ENGINEERING SCIENCES
ISSN: 2247-3769 / e-ISSN: 2284-7197
louver angle, louver spacing, louver overlap, scavenge
flow rate, and Reynolds number. Further studies
showed effects of these parameters on particle
separation and pressure losses.
Zverev (1946) has performed one of the earliest studies
of a louver separator. He experimentally measured
separation efficiency and found that increased
scavenge flow rate, increased Reynolds number and
decreased louver spacing led to an increased
efficiency.
VOL. 4(17), ISSUE 2/2014
ART.NO. 157, pp. 19-26
After passing through the last louver of the device, the
undeflected carrier gas, enriched with dust particles,
enters a duct leading to a cyclone collector, in which
concentrated particles are removed with high efficiency
(Bancea, 2009). The cleaned air comes out of the
separator and is discharged outside, together with the
cleaned air from the cyclone.
Smith and Goglia (2006) found that particle separation
was highly dependent upon the location of the
particle’s impact on the louver. They found that
separation efficiency could be increased by modifying
the louver array to eliminate the louver overlap and to
include a louver anchor. Their findings, confirmed by
Gee and Cole (2009), concluded that for obtaining
good collection efficiency, equal flow rates through
each louver passage were necessary.
This paper studies the two-phase flow in inertial
separators by first solving for the flow field in the
separator, and then calculating particle trajectories by
solving a force balance on each particle. This method
assumes that the particle concentration in the fluid is
small enough that particle interactions are negligible.
This method also assumes that there is no effect of the
particles on the flow field (Jones et al., 2011)
(Ghenaiet and Tan, 2004).
2. MATERIALS AND METHODS
2.1. Principle of operation
Louver type inertial separators consist of a series of
truncated cone-shaped louvers, whose diameter
decreases in the direction of flow of the mixture of dust
and gas. Thereby, about 90% of carrier gas comes out
clean through the device side openings, and the
remaining 10% of the gas, together with all of the dust
particles, maintain their direction until reaching the exit
of the collector (Figure 1). The first fraction will be
called deflected clean gas and the second, undeflected
carrier gas.
Figure 1 presents the principle of operation of a louver
type inertial collector. The carrier gas enters along the
longitudinal axis of the separator and the cleaned gas
comes out on the sides (through the openings between
truncated cone-shaped louvers). The louvers have very
narrow spacing, which cause a very abrupt change in
direction for the carrier gas. The dust particles are
thrown against the flat surfaces; they agglomerate and
concentrate while approaching the exit of the collector
(Popovici et al., 2011).
20
Figure 1. Louver type inertial separator
Louver type inertial separators may operate in good
condition in any position because the influence of
gravity is negligible compared to the separation inertial
forces of particles from the gas stream.
Because these devices have relatively small
dimensions, they can be used to improve a classic
cyclone mechanical separation installation, when the
available space is limited and the required degree of
particles removal is high.
2.2. Forces acting on the particles
The particle removal into an inertial separator is
influenced mostly by the trajectories that particles
follow under the action of the separation forces (Fs)
and resistance forces (Fr). The percentage of particles
that follow the stream of undeflected carrier gas is
calculated based on theoretically determined
trajectories of the particles (Jones et al., 2011)
(Ghenaiet and Tan, 2004). Thus, the degree of
fractional separation of inertial collector is theoretically
estimated.
Resistance force:
For determining trajectories that particles take, it is
necessary to know the magnitude of the resistance
force Fr opposed by the carrier gas due to deformation
and friction, caused by the relative movement of the
particles.
The resistance force is calculated with the Newton
relationship:
JOURNAL OF APPLIED ENGINEERING SCIENCES
ISSN: 2247-3769 / e-ISSN: 2284-7197
VOL. 4(17), ISSUE 2/2014
ART.NO. 157, pp. 19-26
v2
Fr = C R ⋅ ρ a ⋅ A ⋅ rel
2
• particle diameter is sufficiently large compared to
the free path of the carrier gas molecules;
• particles do not influence the trajectory and the
velocity field of the carrier gas;
• particles do not gather or crumble along the
stream.
(1)
where: CR – resistance coefficient of particle
movement, relative to carrier gas
(calculated with relationships summarized
in Table 1);
ρa – carrier gas density;
A – projection area of the particle in carrier gas
movement direction;
vrel – relative velocity of the particle with respect to
carrier gas.
Mathematical relationships presented in Table 1 are
valid under the following assumptions:
Taking into account these simplifying hypotheses, the
resistance coefficient of particle movement relative to
carrier gas depends only on Reynolds:
Re =
vrel ⋅ d p
(2)
ν
where: dp – particle diameter;
ν – kinematic viscosity of the carrier gas.
• the particles have a spherical shape;
• bounding walls influence on the flow is absent;
No.
1
2
3
Relationship
24
Re
24
CR =
+2
Re
21
6
CR =
+
+ 0 ,28
Re
Re
CR =
4
CR = 0 ,4
5
C R = 0 ,44
6
21
CR =
+
Re
4
Re
Validity domain
Maximum deviation
Relationship
no.
Re≤0.2
-
(3)
Re<1
Re<10
<2%
±4%
(4)
0.1≤Re≤4000
±4%
(5)
2000≤Re≤104
±4%
(6)
+10%;-12%
(7)
±6%
(8)
2000≤Re≤10
+ 0 ,4
Re≤2·105
5
Table 1.Calculation relationships of particle movement resistance coefficient relative to carrier gas CR
(Smith and Goglia, 2004)
Resistance forces always oppose separating forces of
the particles. When the separation forces are equal to
the resistance forces, the relative velocity between
particle and carrier gas remains constant and will be
equal to:
• Sedimentation velocity vs, when only the separation
force due to gravity Gp and the resistance force Fr act
on the particle;
• Floating velocity vp, when more separation forces Fs
and resistance forces Fr act on the particle.
Separation forces:
Separation forces may have a value that exceeds
several times the weight of the particle GP. Thus, there
is the possibility that through the action of separation
forces Fs, the gravity force will increase by a factor n.
With the help of the multiplication factor n, the
separation force can be calculated:
Fs = n ⋅ G p
(9)
For n=1, particle velocity is equal to the sedimentation
velocity. The value of sedimentation velocity results
from the condition: Fs = Fr . Substituting the
expressions of the two forces based on relationships
(1), (2), (3), (9) and taking into consideration that
Gp=m·g, gives:
3 ⋅ π ⋅ ν ⋅ ρ a ⋅ d p ⋅ vs = m ⋅ g ⎫
⎪
⎪
( ρ p − ρ a ) ⋅ g ⋅ d 2p ⎬⎪
⇒ vs =
⎪
18 ⋅ μ
⎭
(10)
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ISSN: 2247-3769 / e-ISSN: 2284-7197
VOL. 4(17), ISSUE 1/2014
GUIDE FOR AUTHORS
Gas streams having velocities that exceed the
sedimentation velocity vs will cause the particles to
float in the gas.
Figure 2 presents the variation of floating velocity vp
with respect to particle diameter dp and multiplication
factor n.
where: ar – radial acceleration along the pole radius r;
at – tangential acceleration.
Each of these two accelerations has also two
components, a linear one and a centrifugal one (Kurten
et al., 1996):
• Linear acceleration component is
radius direction, respectively r
dr 2
along the pole
dt 2
d 2ϕ
along the tangent
dt 2
direction (they result from the variation of radial and
tangential velocities);
• Centrifugal
acceleration
component
is
v2
⎛ dϕ ⎞
r⎜ ⎟ = ω2 ⋅ r = t along the pole radius direction,
r
⎝ dt ⎠
2
respectively
the
Coriolis
acceleration
dr
2dϕ dr
along the tangent direction (they
⋅
= 2⋅ω⋅
dt
dt dt
result from the change in direction of particle motion).
Scalar values of these accelerations are given by the
relations:
Figure 2. Variation of floating velocity vp with respect to
particle diameter dp and multiplication factor n
ar =
d 2r
− ω2 ⋅ r
2
dt
(15)
Inertial forces:
The inertial force occurs in accelerated or delayed
movement of a particle:
at =
r ⋅ d 2ϕ
dr
+ 2 ⋅ω
2
dt
dt
(16)
r
r
Fi = m p ⋅ a
(11)
When the particle movement is flat and is related to a
rectangular coordinate system, the acceleration is given
by:
r r
r
a = ax + a y
(12)
Acceleration components ax and ay result from the
variation of velocity components vx and vy, according
to a rectangular 0xy coordinate system:
r
r
d2y
d 2x
and a y =
ax =
dt 2
dt 2
(13)
Reporting the flat particle movement to a polar
coordinate system gives:
r r
r
a = a r + at
22
(14)
The inertial force may be determined using Newton's
law, according to which the inertial force is equal to
the sum of all forces acting on the particle:
r
r
r
Fi = Fs + Fr
2.1. Particles motion
separators
equations
(17)
in
inertial
Particles motion equations in carrier gas of an inertial
separator were determined according to the
relationship (17). This vectorial relationship expresses
the equilibrium between external forces acting on the
particle and the inertial forces.
In the case of inertial separators, only resistance and
inertial forces are acting on the particles.
r
r
r
r
dv
Fi = m p ⋅ a p = m p ⋅
= Fr
dt
(18)
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Between relative velocity vrel, carrier gas velocity va
and particle velocity vp exists the following
relationship:
r
r
r
v rel = v a − v p
(19)
Taking into account the Fr formula and relationship
(19), we obtain:
(
)(
r
r r
r
va − v p va − v p
r
m p ⋅ a p = CR ⋅ ρa ⋅ A
2
)
(20)
For relatively low velocities of small spherical particles
(Re≤0,2), based on the relationship (3), we have:
(
r
r
r
m p ⋅ a p = 3 ⋅ π ⋅ μ ⋅ d p ⋅ va − v p
)
(21)
Replacing the particle mass mp and considering
relationships (10), (4) and (16), we obtain:
r
r
r
r ⎫
dv
18 ⋅ μ
=
⋅ va − v p ⎪
ap =
2
dt
d p ρ p − ρa
⎪⎪
⎬
⎪
r
r
g r
⋅ va − v p
ap =
⎪
vs
⎪⎭
(
(
(
)
)
)
(22)
Forces acting on the particle are situated in the same
plane; therefore particle motion in inertial separators
will be planar. As a result, the flat trajectory of the
particle can be bounded to a rectangular or polar
coordinate system.
⎫
dv pt
v pt
rd 2ϕ
dr
+ 2ω
=
+2
v pr ⎪
2
dt
dt
r
dt
⎪⎪
⎬
⎪
g
at =
⋅ v at − v pt
⎪
vs
⎭⎪
at =
(
Differential equations of particle motion (23), (24),
(25) and (26) can be integrated only in specific cases,
namely when the carrier gas velocity components vax,
vay, var and vat are constant, or the variation laws of
these components are known.
The paper presents the integration of the particle
motion equations, when the size and direction of
velocity va are constant.
2.4. Integration of the particle motion equations,
when the size and direction of velocity va are
constant
In order to facilitate the integration, the relationship
(19) was considered, and because the size and the
direction of carrier gas velocity are constant, the
following equation was obtained (by derivation relative
to time):
dv
dv
= − rel
dt
dt
a py =
dv px
dt
dv py
dt
=
=
(
g
⋅ v ax − v px
vs
(
g
⋅ v ay − v py
vs
)
)
− mp ⋅
v2
dv rel
= Fr = C R (Re) ⋅ ρ a ⋅ A ⋅ rel (28)
2
dt
(23)
Considering the particle shape as a sphere, A =
(24)
(27)
Taking into account that CR=CR(Re), the differential
equation (18) becomes:
In rectangular coordinates, the differential equation
(22) is expressed by the relationships:
a px =
)
(26)
π ⋅ d 2p
4
3
π ⋅ dp
and m p =
ρ p − ρa . Because the value of ρa is
6
(
)
much smaller that ρp, ρa is not taken into consideration.
Using polar coordinates and considering the
relationships (15) and (16), the differential equation
(22) becomes:
dv pr
v 2pt ⎫
d 2r
⎪
ar =
− ω2 ⋅ r =
−
dt
r ⎪⎪
dt 2
⎬
⎪
g
⎪
ar =
⋅ v ar − v pr
vs
⎪⎭
(
)
Finally, the equation becomes:
−
dv rel
3 ⋅ ρa
=
⋅ C R (Re) ⋅ v 2
rel
dt
4⋅ρp ⋅dp
(29)
(25)
Considering Re given by relationship (2), equation (29)
becomes:
−
d Re
C R (Re) ⋅ Re 2
=
3 ⋅ ρa ⋅ν
dt
4 ⋅ ρ p ⋅ d 2p
(30)
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VOL. 4(17), ISSUE 1/2014
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It is important to emphasize that both terms of the
equation are dimensionless.
There are two separation degrees of particles from
gases, carried out by inertial separators:
By integrating the right side of equation (30) between
the boundaries t=0 and t=t1, the corresponding
boundary values for Reynolds numbers to the left side
of the equation will be Re0 and Re1:
• fractional separation degree, ηf;
• total separation degree, ηt.
(31)
The fractional separation degree is the ratio between
the number of particles of a certain diameter dp
collected in the separator and the number of particles
of the same diameter entered in the separator per unit
of time.
This integral was determined by Lapple and Shepherd
(1940), but in the end it has not been used for the
determination of particle trajectories under the action
of the carrier gas flow. For these purposes, it was used
another relationship, that gives the elementary time dt,
depending on the elementary relative distance dsrel:
The total separation degree is determined by reporting
the weight of all separated particles, regardless of their
diameter, to the total weight of all the particles existing
in carrier gas at separator inlet.
Re1
3 ⋅ ρa ⋅ν
− d Re
=
⋅ t1
∫
2
⋅
⋅ ρ p ⋅ d 2p
C
(Re)
Re
4
Re0 R
ds rel = v rel dt
=> dt =
ds rel
v rel
(32)
By introducing this value in equation (30), we obtain:
−
3 ⋅ ρa
d Re
ds rel
=
C R (Re) ⋅ Re 4 ⋅ ρ ⋅ d
p
p
(33)
By integrating between boundaries Re = Re0, for srel =
0 and Re = Re1 for srel = srel1, we have:
Re1
3 ⋅ ρa
− d Re
=
⋅ s rel1
∫
⋅
C
(Re)
Re
4⋅ρp ⋅dp
Re0 R
(34)
In order to determine the relative distance srel within
the validity limits of the Stokes's law, relationship (3)
was used. Together with equation (33) gives:
s rel =
ρp ⋅dp
18 ⋅ ρ a
⋅ (Re0 − Re1 )
(35)
If movement takes place in a field in which the
Reynolds number of the particle is between 0.1 and
4000, by taking into consideration the equation (5), the
relationship (34) becomes:
s rel 1 =
4ρ p d p
3ρ a
Re0
d Re
∫
Re1 21 + 6 Re + 0 ,28 Re
2.5. Determination of separation
particles from the gas stream
24
degrees
(36)
of
The total separation degree can be also determined if
one knows the granulometric structure of powder at
separator inlet and the fractional separation degree
accomplished by the separator.
The fractional separation degree can be determined in
several ways:
• theoretically, by the means of the mathematical
relationships determined on the basis of the differential
equations of the particles;
• by tracing the appropriate trajectories, both for each
particle diameter dp (from powder granulometry at the
entrance in separator), and for the position held by
each particle (at the beginning of the movement);
• by laboratory tests carried out by the means of
pattern/template separators.
The paper only presents the determination of fractional
separation degree through the theoretic method.
When the particles are uniformly spread in the carrier
gas (Musgrove et al., 2009), the separation degree is
determined by the relationship:
r − r0
η 'fs = a
ra − ri
(37)
where: ra - radius of the duct outer wall or of the outer
gas stream;
ri – radius of the duct inner wall or of the inner
gas stream;
ro – radius corresponding to the position held by
the particle at the beginning of the movement.
Relation (37) was established on the assumption that
all particles that reach during their movement the
outside of the pipe wall are separated (r≥ra for ϕ=π/2).
Consequently, particles whose polar radius r<ra, for
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VOL. 4(17), ISSUE 1/2014
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ϕ=π/2, are not separated, being taken further away
along the deflected carrier gas stream.
In order to determine the separation degree η′fs, it is
necessary to provide the polar radius of the particle
trajectory, based on the polar angle ϕ, r=f(ϕ). Schetz
and Fuhs (1996) determined the mathematical
relationship of the separation degree in the following
hypotheses:
• deflected carrier gas streams are circular, symmetric;
• tangential velocities of the carrier gas and tangential
velocities of the particles are equal and have constant
values vat=vpt=ct. within the whole area of the gas
flow;
• radial velocity of the deflected carrier gas var=0
(consequently, a relative movement between the
particle and gaseous environment exists only in the
radial direction);
• in the separation zone, particle concentration in the
carrier gas is homogeneous;
• particles movement takes place within the validity
limits of the Stokes's law (Re≤0.2).
Starting from the trajectory equation in polar
coordinates:
r = f (ϕ ) =
( ρ p − ρ a ) ⋅ d 2p ⋅ v at ⋅ ϕ
18 ⋅ μ
− r0
(38)
It results:
η 'fs =
( ρ p − ρ a ) ⋅ d 2p ⋅ v at ⋅ ϕ
18 ⋅ μ ⋅ ( ra − ri )
(39)
Which is valid to apply for ηfs<1.
The above relationship indicates the possibility to
improve the separation degree η′fs by increasing the
deflected carrier gas velocity vat or by decreasing the
separation section width, S=ra-ri
Figure 3. Fractional separation degree variation curves
depending on dp and vat
Figure 3 presents the variation curves of fractional
separation degree η'fs depending on particle diameter
dp and radial velocity of the deflected carrier gas vat for
an inertial separator, calculated with relationship (39).
In the same hypotheses, the fractional separation
degree can be calculated using the equation:
η 'fs =
ΔS
S
(40)
S is the distance covered by a particle in the radial
direction under the inertial forces action.
3. CONCLUSIONS
Tests and experiments performed during the operation
showed, that under certain conditions, cyclones can be
replaced by inertial separators in a dust extraction
installation. In case of cyclones, the particles removal
is selective because only especially heavy and large
granulated particles are retained with high efficiency.
Introducing a louver type inertial collector as preseparator in a cyclone de-dusting system leads to
increased efficiency of the separation process for the
whole spectrum of particles. Also, this solution has the
advantage of reducing investment costs and required
installation space.
In order to use an inertial collector as pre-separator, it
is necessary to know:
• the movement of gas inside the collector;
• the type and size of the forces acting on the particles;
• the particles movement equations;
• the values of separation degrees.
These aspects are needed for determining the
characteristic parameters of the gas at the outlet of the
inertial separator and the inlet of the cyclone. These
parameters are required as initial data for dimensioning
the cyclone, in the second stage of particle separation.
4. REFERENCES
Bancea, O., 2009. Sisteme de ventilare industrială (Industrial
ventilation systems). Timişoara, Ed. Politehnica, ISBN 978973-625-800-8, Chapter 8, pp. 90-122, (in Romanian).
Gee, D.E., Cole, B.N., 2009. A Study of the Performance of
Inertia Air Filters, Inst. Mech. Engineers - Symposium on
Fluid Mechanics and Measurements in Two-Phase Systems,
University of Leeds, pp. 167-176.
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Ghenaiet, A., Tan, S.C., 2004. “Numerical Study of an Inlet
Particle Separator,” GT2004-54168.
Jones, G.J., Mobbs, F.R., Cole, B.N., 2011. “Development of
a Theoretical Model for an Inertial Filter,” Pneumotransport
1 – 1st Int’l. Conf. on Pneumatic Transport of Solids in
Pipes, Paper B1.
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eines kugelfˆrmigen Feststoffteilchens im Strumungsfall
konstanter Geschwindigkeit (Acceleration of a solid spherical
particle in the case of constant velocity flow). Chem-Ing.
Tech 9. ISBN 978-3-642-24967-9, pp 941-948, (in German).
Lapple C.E., Shepherd C.B., 1940. Calculation of particle
trajectories, Ind. Eng. Chem. 32 (5), pp. 605–617.
Lăzaroiu, G., 2006. Soluţii moderne de depoluare a aerului
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Romanian).
Musgrove, G. O., Barringer, M. D., Thole, K. A., Gover, E.,
Barker, J., 2009. Computational design of a louver particle
separator
for
gas
turbine
engines.
http://www2.mne.psu.edu/psuexccl/Pubs/2009-Musgrove IGTACE.pdf, viewed at 13 June 2014.
Popovici, T., Domnita, F., Hoţupan, A., 2011. Instalaţii de
ventilare si condiţionare (Ventilation and air conditioning).
Volume II, Cluj-Napoca, Ed. U.T.PRESS, ISBN 978-973662-7, Chapter 5, pp. 149-172, (in Romanian).
Schetz, J., Fuhs, A., 1996. Handbook of Fluid Dynamics and
Fluid Machinery, Vol 1, John Wiley & Sons, Inc., New
York, pp 905-906, Chap. 14.
Smith, Jr., J.L., Goglia, M.J., 2006. Mechanism of Separation
in Louver-Type Dust Separator, ASME Transactions, 78 (2),
pp. 389-399.
Zverev, N.I., 1946, Shutter-Type Dust Collector of Small
Dimensions, Engineer’s Digest, 7 (11), pp. 353-355.
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