Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P1.77 - Deposition of Solid Particles at Streamlined Surface in Turbulent Flow
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00467
 Material Information
Title: P1.77 - Deposition of Solid Particles at Streamlined Surface in Turbulent Flow Particle-Laden Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kartushinsky, A.
Rudi, Y.
Shcheglov, I.
Tisler, S.
Hussainov, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: grid-generated turbulence
boundary layer
image recording and processing technique
deposition velocity
 Notes
Abstract: Results of experimental investigation of deposition of 12 and 23 μm corundum particles onto horizontal flat plate in moderately turbulent gas flow are presented. The gas flow was formed in a horizontal 200 x 400 mm channel. Turbulence of the flow was generated by the grid of 16 mm mesh size. The free stream velocity was 5.1 ms-1. Particles were ejected into the flow by means of 5 mm tubule. The particles concentration in a free stream and amount of the deposited particles were carried out by applying of the laser visualization, the image-recording acquisition technique and image-processing method. The obtained results show that the deposition velocity of 12 μm particles is larger as compared with 23 μm particles. It was revealed that the deposition of particles of the both sizes increases along the plate surface downstream. The character of dependence of the dimensionless deposition velocity demonstrates its attenuation with an augmentation of the dimensionless particle relaxation time.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00467
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P177-Kartushinsky-2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



Deposition of Solid Particles at Streamlined Surface in Turbulent Flow

Alexander Kartushinskyl, Ylo Rudil, Igor Shcheglovl, Sergei Tislerl and Medhat Hussainov2

'Research Laboratory of Multiphase Media Physics, Faculty of Science, Tallinn University of Technology,
Akadeemia tee 15, Tallinn, 12618 Estonia
sergei.tisler a tt.ee

2Laboratory of Physics of Nano Structures, Institute of Physics, Faculty of Science and Technology, University of Tartu,
Riia 142, Tartu, 51014 Estonia
medhat.hussainovi a tth.ee


Keywords: grid-generated turbulence, boundary layer, image recording and processing technique, deposition velocity

Abstract

Results of experimental investigation of deposition of 12 and 23 Cpm corundum particles onto horizontal flat plate in
moderately turbulent gas flow are presented. The gas flow was formed in a horizontal 200 x 400 mm channel. Turbulence of
the flow was generated by the grid of 16 mm mesh size. The free stream velocity was 5.1 ms '. Particles were ejected into the
flow by means of 5 mm tubule. The particles concentration in a free stream and amount of the deposited particles were carried
out by applying of the laser visualization, the image-recording acquisition technique and image-processing method.
The obtained results show that the deposition velocity of 12 Cpm particles is larger as compared with 23 Cpm particles. It was
revealed that the deposition of particles of the both sizes increases along the plate surface downstream. The character of
dependence of the dimensionless deposition velocity demonstrates its attenuation with an augmentation of the dimensionless
particle relaxation time.


Introduction

The turbulent gas flows loaded with solid particles are of
high relevance in various natural phenomena and very
important in many engineering applications. These flows are
specially generated for industrial processes taken place in
power engineering, chemical, pharmaceutical, food and
other branches of industry. The problem of the predicting of
the deposition amount of solid particles suspended in such
flows remains to be of great interest for the researchers in
many countries. The investigations of the particles
deposition at various surfaces have undoubtedly been
stimulated by its practical relevance to many areas of
technology and science, but the interest has also been
aroused by the intellectual challenge of the problem and the
inability of any theory to provide a truly satisfying physical
explanation of the observed facts. The numerous theoretical
and experimental researches are dedicated to the study of
deposition of solid particles at various surfaces and the
influence of hydrodynamics of the two-phase flows on the
peculiarities of these phenomena. But, unfortunately, most
of them mainly deal with the theoretical aspects. The
existing few experimental ones do not consider the particles
deposition as the complex phenomenon, involving various
physical processes that occur during the deposition.
Extensive experimental and computational studies related to
the particles transport in the gas-solid particles two-phase
flows and reported, for example, by Soo (1967), Liu &
Agarwal (1974), Hinze (1975), Osiptsov (1980, 1985),
Wood (1981), Papavergos & Hedley (1984), Asmolov
(1992) and others, have revealed the presence of the


boundary layer, which formed close to the surface,
streamlined by the flow, and in many respects determined
the particles deposition at the surface. Osiptsov (1985),
neglecting an inertial sedimentation, showed that the
particles accumulated close to a body surface, and even for
the insignificant values of the particles mass concentration
the velocity field of a gas flow was distorted due to the
accumulation of the particles near the surface. Soo (1967)
and Asmolov (1992) also observed the increase of the
particles mass concentration in vicinity of the surface of a
flat plate in the laminar boundary layer.
Numerous studies show that the deposition process at the
obstacles streamlined by two-phase flows is determined
substantially by the interrelationship between the properties
of the carrier gas flow and the particles. The main
parameters that characterize this relation and determine
finally the deposition rate are the particle relaxation time
r, and the Stokes number St. The theoretical study of
deposition of fine particles on the vertical surface by
Johansen (1991) revealed that there is different regimes of
deposition depending on the particle relaxation time z .
For a short relaxation time, the Brownian deposition regime
dominates, while the turbulent deposition occurs for the
long and medium relaxation times. It was found that for the
Brownian diffusion of particles in vicinity of the surface the
distribution of concentration has a maximum at the wall and
the concentration value decreases with the increasing of the
particle relaxation time. Spokoinij & Gorbis (1981) have
shown that there is the critical value of the particle Stokes
number Star which determines the condition of the






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

particles solely determines deposition of the particles. When
the particle material density is much more than the gas
plwsical density, that implies the particles to be highly
massive, the particles are not entrained by the gradient flow,
but continue coasting at the constant velocity and direction,
and the deposition is carried out exclusively by the inertial
mechanism. Actually, the motion of the particles close to the
surface is conditioned by the interaction of all the above
mentioned mechanisms, but in every specific case,
depending on the relation between the parameters of a
carrier flow and the particles, one mechanism predominates.
Based on different assumptions, several models have been
proposed to describe the deposition mechanisms in the
turbulent flows. Friedlander & Johnstone (1957) were the
pioneers introducing the model where the particles are
carried towards the vicinity of the wall by the turbulent
diffusion and then reach the wall by free flight. Last two
decades opened up the possibilities for more intensive study
of near-wall particle-turbulence interactions by the direct
numerical simulations (DNS). These studies suggest that the
particles deposition is mainly caused by the interactions
between particles and coherent turbulent structures located
in the near-wall region of the flow. This supports the
lwpothesis, first proposed by Cleaver & Yates (1975), that
particles are convected to the wall if they are entrained by a
fluid downwash toward the wall. This lwpothesis is also
found in the models developed by other authors, for
example, Fan & Ahmadi (2000). Marchioli & Soldati (2002)
and Marchioli et al. (2003) using DNS for the study of the
particles deposition in a fully developed turbulent open
channel flow also revealed the strong accumulation of the
particles very close to the wall in the form of the streamwise
oriented streaks. This was attributed to the effect of
turbophoresis, that is the preferential accumulation of
particles at the regions of low turbulence (Michaelides,
2006).
The recent investigations being pertinent to various aspects
of the particles deposition in turbulent flows solely deal
with the computational study of the given phenomenon.
Here it should mention the numerical researches by Arcen et
al. (2006), Tian & Ahmadi (2007), Guingo & Minier (2008),
Soldati & Marchioli (2009) considered the influence of
various forces as well as the near-wall turbulent structures
on deposition.
Thus, based on the short review of the state of the art of the
particles deposition in various flows it can draw the
conclusion about the lack of the experimental data,
especially related to the deposition on various obstacles
streamlined by gas-solid particles two-phase flows and
embracing a wide range of the flow parameters and shapes.
The unified models that would allow to cover the deposition
for a wide range of the two-phase flow regimes are not
available, except for some special efforts aimed at patching
together available models of the individual regimes. Efforts
to elaborate such models are continuing, and there is a need
for experimental data that can be applied for the validation
of such models.
In this paper, the solid particles deposition at the horizontal
flat plate surface under the conditions of the turbulent
grid-generated flow is studied.
The flows with grid-generated turbulence have the
following advantages compared to flows of other types,
since turbulence of this type has been quite well studied


Paper No


particles deposition at the obstacle installed within the
two-phase flow. As Star is larger for the other equal status,
the worse conditions for the deposition take place.
Many experimental and numerical studies were devoted to
the influence of various parameters of a carrier flow and
particles on the deposition. One of the scanty experimental
data pertaining to the deposition of particles at the surfaces
was reported by Lane & Stukel (1978). They studied fully
turbulent particle deposition of the micron size droplets of
the water solution of fluorescein at the surface of the
horizontal flat plate. It was revealed that for the turbulent
boundary layer conditions the deposition velocity increases
with the particles diameter.
The systematic investigations of influence of the boundary
layer on the dynamics, the flow structure and the properties
of the inertial sedimentation were carried out by Tsirkunor
(1993), who has analysed the influence of tl e boundary
layer on a motion of particles near the streamlined blunt
body surface and drawn the following conclusions: 1) it is
necessary to take into account the impact of the boundary
layer on the particle trajectories in vicinity of the
streamlined surface together with the influence of the
viscous drag force and the lift Magnus and Saffman forces:
2) it should take into account that inside the boundary layer
the particles of different sizes behave in different ways,
namely, large particles move through the boundary layer
keeping their velocities and direction, whereas fine particles
decelerate in the boundary layer and drift along the surface;
3) the density of the particle mass flux in each point at the
forehead of the streamlined surface is definitely determined
by the trajectories of particles: 4) the boundary layer
obstructs the particles deposition, rejecting the particles out.
Here it should note that along with the Magnus and Saffman
lift forces the gravity is also one of the main factors that
determine the behaviour of particles within the boundary
layer and their deposition.
The experimental and theoretical investigations by
Hussainov et al. (1995) and Kartushinsky et al. (2009)
reported about the presence of a maximum in the
distribution of particles mass concentration within the
laminar boundary layer near vertical flat plate. These studies
showed that the amount of the deposited particles depends
significantly on the value and location of this maximum.
The mathematical model of the two-phase laminar flat-plate
boundary elaborated by Hussainov et al. (1995) considered
the inter-particle collision mechanism that further was
developed by Kartushinsky & Michaelides (21***4). Similar
results were obtained by Wang & Levy (2006) for a
turbulent flow over a flat plate and were attributed to the
Saffman force and the particle-wall interactions.
Tsai & Lin (1999) proposed the numerical description of the
particles deposition in a thermally driven natural convection
for a vertical flat plate streamlined by the laminar flow,
which demonstrated the attenuation of the deposition
velocity with the particle size.
One can distinguish the next mechanisms of the particles
transport to the surface that take place in the isothermal
two-phase flows: the inertia, the convection and the
turbulent and Brownian diffusion. The transport of the
particles in the non-gradient laminar flows is realized only
by the Brownian diffusion. In case of the gradient flows.
when the particle material density approximately equals to
the gas plwsical density, the convective transport of the




















































240 340 440 540 640 740 840 940 1040 1140
x, mm

Figure: Single-phase flow velocity and its turbulence
along the test section. Here X is the distance from the grid.

The manufactured corundum powders with the particle
number average size 6, =12 and 23 Cpm were applied in the
experiments. The number distributions of the particles size
determined by the microscopical analysis are shown in
Figure 3. The particles properties are presented in Table 1.
The particles were ejected into the flow by means of
L-shape tubule of inner diameter of 5 mm. The discharge
outlet of the tubule was located at 20 mm from the grid
downstream and at 100 mm from the top wall of the channel.
The constant mass flux of the particles was obtained by
means of the feeding device (s. Figure 1) and verified by the
single-component LDA system (Albrecht et al., 1993) for
every test run.
Table 1. The narticlesnretis

Pp ,kgm3 3950
Sp Cpm 12 23
Z s 0.0018 0.0064
St 0.045 0.164


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

stream velocity U, =5.1 ms' is presented in Figure 2. The
gas flow was traced by means of the fog generator with the
drops of 2 3 Cpm in size.

Pc terumuna


LDA ormteiv


syste cuo amera
Flatplate 405x205



Camera
Pardicle feeding devicervre system
Laser and srnmittung

Figure 1: Experimental set-up.

The smooth stainless flat plate of 500 mm length, 100 mm
width and 2 mm thickness was installed horizontally in the
test section under the zero incidence. Distance from the grid
to the leading edge of the plate was 1 m, i.e. along the
whole length of the flat plate turbulence of the gas flow was
3.5% (s. Figure 2).


Paper No


both theoretically and experimentally for the single-phase
case; such flows are not complicated by the presence of
radial gradients and the scale of turbulence is readily
variable by varying the grid parameters.
The choice of a flat plate was based on a simplicity of its
surface shape, and that the lwdrodynamic characteristics of
the boundary layer, which was generated near a flat surface
in case of the pure gas flow, had been already well studied.
Measurements of the particles concentration in a free stream
and amount of the deposited particles were carried out by
applying of the laser visualization, image-recording
acquisition technique and image-processing method.
specially designed for the two-phase flows investigations.

Nomenclature

C, number concentration of particles (m )
ANdep number of the deposited particles
Rex Reynolds number defined for current
cross-section of flat plate
U gas axial velocity (ms')
urm root-mean-square value of fluctuating velocity of
gas (ms')
u, friction velocity of gas (ms')
St particles Stokes number
Stbl p8TtiClCS Stokes number calculated by thickness
of boundary laver
VdeI, dimensionless deposition velocity

Greek letters
6bl thickness of boundary layer (mm)
6, particle number average size (Cpm)
v kinematic viscosity of gas (m~s')
p plwsical density of gas (kgm )
p, material density of particles (kgm )
z, particle relaxation time (s)
z,, dimensionless particle relaxation time
r, wall shear stress (Nm )
Subsripts
00 conditions in a free stream

Experimental Facility

Experimental rig for investigations of the particles
deposition in a horizontal flow under the conditions of a
grid-generated turbulence is shown in Figure 1. It included
contractor, grid, 2.5 m long horizontal test section, an outlet
section as well as contraction, the outlet pipes, a cyclone
separator and a suction centrifugal fan. The test section
consisted of the metal carcass and window glass sidewalls.
The initial cross-section had dimensions of 200 x 400 mm,
and it increased gradually downstream up to 205 x 405 mm
at the exit of the test section. The geometry of the test
section partially allowed to compensate the growth of a
boundary layer along the walls.
Turbulence of gas flow was generated by the grid of 16 mm
mesh size and solidity of 0.34. The single-phase flow axial
velocity and modification of the gas turbulence intensity
along the test section measured with the LDA for the free


6
58
57

5 4


65
65


45

4 3
3 5
3


U.
x u'm,$U.























1 3 5 7 9 11 13 1517 1921 2325 2729 3133 3537 3941 4345 4749 51
6,, pm
b)

7
6


4
3
2


1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
6,, pm


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


25
N,, %
20

15

10


DPSS 500 mW laser light sheet
laser


Figure 4: Particles concentration and deposition
measuring systems.

The frame rate of the camera was chosen to allow the
one-time registration of all the particles occurred in the
camera field of view. Based on the particles velocity that
taken place in the free stream equalled 5.1 ms-' and the
Streamwise dimension of the field of view of 16.5 mm, the
frame rate was 300 frames per second.
The exposure time of the camera was chosen to resolve the
particles. On the one hand, the length of the particles tracks
had to allow their assured resolution, while on the other
hand, the length of the tracks was limited by the number of
particles that occurred simultaneously in the field of view of
the camera. It means that the lesser exposure time
corresponded to the higher particles concentration. The
experience has shown that the reliable exposure was 0.6 ms
for the given flow conditions. The camera memory capacity
of 3271 frames allowed to record a sequence of 10.9 s for
the given frame rate.
The sequence of the recorded frames was processed by the
handler based on LabView 7.1 software. The stages of the
data processing were as follows. Firstly, each frame was
subtracted by the one, so-called "background" frame,
obtained without particles in the flow. Then, the noise
filtration of the frame-remainder was carried out. Thus, the
derived frame included the images of the particles tracks
with the blank background. Next, the particles tracks were
recognized for each filtered frame. Each recognized track
was characterized by the frame number, the coordinates of
the track origin and terminus, the slope angle and the
number of pixels per track. These attributes were applied for
the additional random-noise filtration. The result of this
processing was the time sequence of the particles number
per each frame. Figure 5 shows the images of the particles
tracks occurred in the free stream in front of the flat plate.
Then, the particles number concentration C, m-3
occurred in the free stream was determined by the
measurement volume of 13.79 x 13.02 x 2 mm for every test
run.
The measurements of the particles deposition were made at
the locations x=65, 180, 300 and 390 mm from the leading
edge of the plate. The amount of particles deposited in every
location was measured by the laser illumination of the
survey surface area with the help of the high-speed
registration system (s. Figure 4).


N,, %


Figure 3: The number distributions of the particles sizes:
a) 6 =12 Cpm, b) 6,=23 pm. Here 6, is the size of the
i-th particles fraction, N, is the portion of the i-th fraction.

Measuring Techniques and Data Processing

The mean longitudinal component of the single-phase flow
velocity, its distributions within the boundary layer near the
flat plate were measured by LDA installed on the traverse
system that enabled to scan the flow in longwise and
crosswise directions. The LDA signals were processed by
the DISA counter processor. The particles axial velocity in
the free stream was measured in front of the flat plate
upstream by the LDA system separately from the main test
runs. These measurements showed that both 12 and 23 pm
particles completely followed the carrier gas flow.
The number concentration of the particles occurred in the
free stream was measured by means of the laser
visualization and high-speed video image-recording
acquisition system (Figure 4) in the (x, y) plane of the flow
and by the analysis of the recorded images.
The laser light sheet of 2 mm thickness, which served for
the visualization of the particles, was generated in the (x, y)
plane of the flow (s. Figure 4) by means of the continuous
wave (CW) diode pumped solid state (DPSS) 500 mW 532
nm laser and the corresponding optic scheme. Mikrotron
GmbH SpeedCam MiniVis-ECO1-3e CMOS camera was
used for the measurements. The camera sensor had a peak
spectral response at 533 nm which matched well with the
532 nm wavelength of the DPSS laser. CMOS camera was
equipped by the Sigma macrolens of 105 mm focal length.
The depth of field was 2 mm. The field of view was 16.5 x
13.2 mm. The images were recorded with the resolution of
640 x 512 pixels. The corresponding spatial resolution was
25.79 Cum per pixel.





-




--


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Vdep+ x
xe St CN,u x
where u~x is the gas friction velocity in the given location
x of the flat plate surface.


Paper No


Figure 6: Example of the surface area coated with the
deposited 23-Cpm particles.

The test runs for the particles deposition were carried out for
different values of the particles mass flux fed from the
tubule. Every test run included the simultaneous high-speed
registration of the particles trajectories that was required for
the calculation of the number particles concentration
occurred in the free stream, the acquisition of images of the
particles deposited at the survey surface area of the flat plate
and the LDA control of the particles mass flux fed from the
tubule.

Results and Discussion

Based on the LDA data of the gas axial velocity obtained for
the single-phase flow close to the surface (Figure 7), one
can see that the generated boundary layer was the laminar.
UU1Z 2


Figure 5: Particles tracks in the free stream: a) initial
picture, b) after "background" subtraction and filtration,
c) after recognition.

The survey surface area was illuminated by the continuous
wave DPSS 50 mW laser and the optic scheme. Mikrotron
GmbH Motion BLITZ Cube2 CMOS camera was used for
the measurements. It was equipped my the Sigma macrolens
of 105 mm focal length. The field of view was 9.3 x 7.5 mm.
The images were recorded with a rate of 1004 frames per
second for the exposure time of 0.9 ms at the resolution of
640 x 512 pixels. The camera memory capacity of 6200
frames allowed to record sequence of 6.2 s for the given
frame rate. The camera sensor had a peak spectral response
at 533 nm which matched well with the 532 nm wavelength
of the DPSS laser. The duration of the image sequence was
t=4.5 s that assured that the particles covered the surface
within the monolayer. Figure 6 demonstrates the example of
the obtained image of the surface area coated with the
23-Cpm deposited particles in 4.5 s.
The obtained sequence of images was processed by the free
version of the Scion Image software by Scion Corporation
that allowed to count the number of particles Ndep
deposited at the survey surface area S, equalled to the field
of view of 9.3 x 7.5 mm, at the location x of the plate
surface. Then, the dimensionless particles deposition
velocity Vdep+x was calculated for the given location x
according to Young & Leeming (1997):


00 5 1 1 5 2 2 5
Y/bl

Figure 7: The gas axial velocity distributions within the
boundary layer at various locations of the flat plate (1 -
Rex = 0.4 -105, 2 Rex = 0.8-105 3 Rex = 10') and
the theoretical velocity profile (4) occurred in the
single-phase flow. Here Y is the transverse coordinate of the
boundary layer.

This is also confirmed by the calculation of the flat plate
Reynolds number Rex According to Schlichting (1979),
for the flat plate at the zero incidence, the critical Reynolds
number Rexci for the transition from the laminar
boundary layer to the turbulent one is as follows:

Re.,= x -3.-5-1 (2)

































.__ . __ 1_ __ _ __ _
x,mm 65 180 300 390

Rex 0.3-105 0.9-105 1.5-105 1.9-105

6bly ,mm 2.2 3.6 4.7 5.4

"*x ,ms-' 0.24 0.19 0.16 0.15

6, ,Cm 12 23 12 23 12 23 12 23

Stblx 4.1 15.0 2.5 9.0 1.9 7.0 1.7 6.1

rPz 6.8 24.9 4.1 15.0 3.2 11.6 2.8 10.2


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Paper No


This study was carried out for Rex equalled about 2-10'
at the location of the plate surface x-500 mm for U,=-5.1
ms '. This indicates that the boundary layer was the laminar
over all the plate length.
According to Schlichting (1979), Blasius's law of friction
can be applied to the single-phase flat-plate laminar
boundary layer, so the wall shear stress ru x occurred in
the x location of the flat plate surface is as follows:

rn x = 0.332 v p U, V. (3)

Ignoring any modification of the wall shear stress due to the
presence of particles in the boundary layer, the friction
velocity occurred in the x location can be calculated as
follows:


"x ;ux (4)
Table 2 presents the parameters of gas and particles
calculated for the survey locations of the flat plate.
Table 2 De position kev narameters


0.003


ydep+x


0.0025

0.002 3

0.0015 ,

0.001

o.ooos


0 0 .5 1 1.5 2
Re~xx10


Figure 8: Dimensionless deposition velocity along the flat
plate: 1, 2 6, =12 m ( C, =1.7 -10', 2.1-10"' m );

3, 4- 6,= 23 pm (C = 0.7 -10'0, 1.1-10"' m).

The subsequent motion of the particles is caused by the
conditions of the boundary layer taken place at the given
location of the plate. According to Hussainov et al. (1995),
the outer region of the boundary layer is characterized by
the inertial transport of the particles, where they decelerate
and accumulate in this region resulting in the increase of the
concentration. The deceleration of 12 Cpm particles is larger
as compared to 23 Cpm particles, therefore, the maximum of
their concentration, as shown by Hussainov et al. (1995), is
substantially larger.
The inertia transport occurred in the outer part of the
boundary layer is balanced by the convective transport,
which takes place in the more interior parts located closer to
the surface of the plate, and this conditions no further
increase of the concentration. The subsequent decrease in
the particles concentration taken place immediately near the
surface is conditioned by the diffusive transport caused by
the interparticle collisions and their collisions with the plate
surface.
Thus, the character of the distribution of the particles
concentration occurred within the boundary laver arise from
the combined effect of inertia, convection and diffusion
along with the effects of the gravity and the Saffman force
as well as the polydispersity of the particles.
Kartushinsky et al. (2009) have revealed that the deposition
velocity is conditioned by the concentration gradient
occurred within the laminar boundary layer at the given
location of the plate. They have got that this gradient is
larger for 12 Cpm particles as compared with 23 Cpm ones.
Therefore, the deposition velocity is greater for 12 Cpm
particles.
The increase of the deposition velocity at the plate surface
downstream can be explained by the growth of the
concentration gradient occurred downstream.
In order to compare the different experimental and
numerical data for the particles deposition obtained for the
different flow conditions, the results of the particles
deposition experiments are usually presented as the plots of
the dimensionless deposition velocity Vdep+ versus the
dimensionless particle relaxation time r ,, which is the
time scale for the particle velocities to adjust to the
surrounding flow velocity. By using the near-wall units,


Figure 8 shows the experimental data and the trendlines for
the distributions of the dimensionless deposition velocity
Ed,, along the flat plate obtained by Eq. (1) for various
number concentrations of 12 and 23 Cum particles.

As it follows from Figure 8, the deposition velocity of 12
Cpm particles is larger as compared with 23 Cpm ones. Also, it
can see that the deposition increases along the plate
downstream. The same results were obtained experimentally
by Kartushinsky et al. (2009) at the vertical arrangement of
the same flat plate for the laminar boundary layer and the
same 12 and 23 Cpm corundum particles, for the free stream
flow velocities of 1.5 and 3 m/s.
Such tendencies in the particles deposition for the flat plate
can be explained based on the analysis of the particles
behaviour occurred in the free stream and, further, within
the laminar boundary layer.
The considered particles are sufficiently low-inertia in the
free stream, since their Stokes number is much less than
unity, as it can see from Table 1. Therefore, they are taken
easily by the turbulent eddies of gas occurred in the free
stream and move towards the plate surface. Here, due to the
substantial difference between the gas and particles physical
density, they penetrate inside the boundary layer.



































u.= 5 ms-
36,=23 m
U.=30O msl *^
Present ^
study
u.=5 i msl ^ a


> 1 1 10 rpx100


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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Paper No


r,, is defined according to Young & Leeming (1997) as
follows.

Zpus


The values of z,, calculated for the given flow
conditions at different locations x of the flat plate are
presented in Table 2.
Figure 9, where the dimensionless deposition velocity is
plotted versus the dimensionless relaxation time of particles-
presents the matching of the present data with the ones
calculated from the experimental data by Kartushinsky et al.
(2009). One can see that all data are fitted into two sets
which correspond to 12 and 23 Cpm particles and do not
depend on the free stream velocity. It is evident that the
increase of the dimensionless particle relaxation time results
in the reduction of the deposition.
o 01 Kartushinsky et al (2009) 1
Vdep+x r 3,=12 pLm


ocol



0 0001



o00001


Figure 9: Dimensionless deposition velocity
dimensionless relaxation time.

Conclusions


versus


The deposition of corundum 12 and 23 Cpm particles onto the
horizontal flat plate occurred under the conditions of the
laminar boundary laver in the moderately turbulent flow
was studied.
The obtained experimental results show that the deposition
velocity of 12 Cpm particles is larger as compared with 23
Cpm particles.
It was revealed that the deposition of particles of the both
sizes increases along the plate surface downstream.
The character of dependence of the dimensionless
deposition velocity demonstrates its attenuation with an
augmentation of the dimensionless particle relaxation time.

Acknowledgements

This study was supported by the Estonian Science Targeted
Project no. SFI In's ~I-ISt and by the Estonian Science
Foundation (grants ETF7571, ETF7620 and JD120).





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