Arch. Min. Sci., Vol. 55 (2010), No 3, p. 501–516

Arch. Min. Sci., Vol. 55 (2010), No 3, p. 501–516
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Electronic version (in color) of this paper is available: http://mining.archives.pl
MARIAN BRANNY*, JUSTYNA SWOLKIEŃ*
USAGE OF FLUENT APPLICATION IN THE PROCESS OF NUMERICAL CALCULATION
OF BARIUM SULPHATE DEPOSITS FLOW THROUGH THE JANKOWICE
AND PNIOWEK COAL MINES’ SETTLING TANKS
ZASTOSOWANIE PROGRAMU FLUENT W OBLICZENIACH NUMERYCZNYCH PRZEPŁYWU
CZĄSTEK SIARCZANU BARU PRZEZ OSADNIKI KWK „JANKOWICE” I KWK „PNIÓWEK
The article treats about the process of barium sulphate deposits flow through the Jankowice and
Pniowek coal mines’ settling tanks. The review is mainly focused on the description of the numerical
simulation of deposits flow through the determination of their velocity field and trajectory. These calculations allow to determine the sedimentation efficiency and the time of particles descending in the settling
tanks. This knowledge is very important due to the “Olza” interceptor sewer’s protection. It allows to
protect pipelines from being overgrown with barium sulphate sediment which is important due to their
technical condition.
Keywords: Sedimentation, sedimentation’s efficiency, deposition of barium sulphate, numerical calculation
W artykule podjęto próbę opisania procesu przepływu cząstek siarczanu baru przez osadniki dwóch
kopalń należących do Jastrzębskiej Spółki Węglowej S.A., a mianowicie KWK „Jankowice” i KWK
„Pniówek”. Obie kopalnie odprowadzają silnie zanieczyszczone wody kopalniane do rzeki Odry za
pośrednictwem systemu retencyjno-dozującego „Olza”. Charakter chemiczny wód obu kopalń ściśle
zależy od warunków hydrogeologicznego ukształtowania terenu południowo-zachodniej części Górnośląskiego Zagłębia Węglowego. Odprowadzanie za pośrednictwem kolektora wód o odmiennym składzie
chemicznym jest główną przyczyną wytrącania się w jego rurociągach osadów stałych, co powoduje ich
zarastanie, zwiększenie zużycia energii na przepompowywanie wody, a w konsekwencji konieczność
przeprowadzania kosztownych remontów.
Na przestrzeni lat opracowano szereg metod pozwalających na zmniejszenie ilości jonów baru i jonów siarczanowych w samych kopalniach, czyli u źródła. W przypadku wymienionych kopalń metoda ta
*
AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY, FACULTY OF MINING AND GEOENGINEERING, AL. MICKIEWICZA 30, 30-059 CRACOV, POLAND, email: [email protected]; [email protected]
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opiera się o proces sedymentacji siarczanu baru w osadnikach przykopalnianych. Skuteczność stosowanej
metody jest wysoka, ale aby nie dopuścić do przedostawania się do rurociągów kolektora niestrąconych
jonów baru i jonów siarczanowych, konieczne jest poznanie przebiegu procesu sedymentacji siarczanu
baru, jak również jego efektywności. Przedmiotem poniższego artykułu jest próba opisania przebiegu
zjawiska sedymentacji wytworzonego osadu siarczanu baru w osadnikach wymienionych kopalń, przy
wykorzystaniu metod symulacji numerycznej jego przepływu.
Symulacje trójwymiarowego (3D) przepływu cząstek stałych przez osadniki kopalń Jankowice
i Pniówek wykonano w oparciu o model Eulera-Lagrange’a zakładając, że przepływ jest dwufazowy.
Fazę ciągłą stanowi woda zaś fazę rozproszoną cząstki stałe o rożnych średnicach. Obliczenia wykonano
z wykorzystaniem programu FLUENT 6.1. Wyznaczenie pól prędkości i trajektorii cząstek siarczanu baru,
przedstawionych na rysunkach 1,2,3,4,5, pozwoliło w przybliżeniu określić efektywność ich sedymentacji
(tab. 2) w zależności od przyjętej do obliczeń średnicy oraz czas ich opadania (przebywania cząstek stałych
w osadniku). Do obliczeń przyjęto oba zbiorniki wymienionych kopalń, gdyż zasadnicze różnice w ich
geometrii (tab. 1) sprawiają, iż przebieg procesu w każdym z nich jest nieco inny. Najmniejsza efektywność, a tym samym najdłuższy czas opadania występuje przy średnicy 1×10–6 m. W przypadku osadnika
Jankowice i średnicy cząstek siarczanu baru 1×10–6 m efektywność sedymentacji wynosi 62,5%. Nieco
niższą efektywność otrzymano dla osadnika kopalni Pniówek. W obu omawianych przypadkach wraz ze
wzrostem średnicy cząstek skraca się czas ich opadania i jednocześnie wzrasta efektywność sedymentacji.
Efektywność wynoszącą 100% uzyskano w przypadku osadnika kopalni Pniówek przy średnicy ziaren
1×10–5 m, podczas gdy dla osadnika kopalni Jankowice praktycznie tą samą efektywność uzyskuje się już
przy średnicy cząstek wynoszącej 7×10–6 m. Różnice w efektywnościach i czasach opadania zależą od
geometrii zbiornika, usytuowania miejsc dopływu i odpływu (zasilania i odbioru wody), objętościowego
natężenia przepływającej wody, a także przyjętej do obliczeń wartości średnicy ziaren. Wariantowe obliczenia przepływu przez osadnik zawiesiny o rożnym strumieniu masowym pozwalają zobrazować przebieg
zjawiska sedymentacji, a wiedza ta pozwala ocenić jak długo należy przetrzymywać wodę w osadnikach
wspomnianych kopalń, by zapobiec przedostaniu się niestrąconych jonów baru i siarczanowych do rurociągów kolektora „Olza”. Ma to olbrzymie znaczenie ekonomicznie, gdyż brak osadów w rurociągach
zmniejsza energochłonność systemu, a także wpływa korzystnie na ich stan techniczny.
Słowa kluczowe: sedymentacja, efektywność sedymentacji, osadzanie się siarczanu baru w osadnikach,
symulacja numeryczna
1. Introduction
Jankowice and Pniowek coal mines transport their mine waters through the “Olza” retaining-dose system. The Waters’ chemical character of both mines strongly depends on the hydrological lay of land of the south-western part of Upper Silesia. The different chemical character of
transported waters is a main reason for precipitation of solid sediments in the interceptor-sewer’s
pipe-lines. This leads to their overgrowing with sediment, increasing of water pumping energy
and, in the end, necessity of overhaul repairs. Through the years, in certain mines special water
cleansing methods were introduced. They were focused on removing barium and suphate ions and
most of them were highly effective (Pluta et al., 2006; Pluta & Piotrowski, 2000, 2002; Pluta &
Szczepańska, 2002; Badurski et al., 2001; Orzechowski et al., 1997). As an example, Jankowice
mine, through the medium of one big settling tank, drains off its waters with increased concentration of barium ions, and also waters of increased concentration of sulphate ions coming from
Chwalowice coal mine. The same situation is being proceeded in one of the settling tanks of
Pniowek coal mine. This settler drains off waters of increased concentration of barium ions from
Krupinski coal mine and waters of increased concentration of sulphate ions from Koscielniok
Dumping Ground. In both cases the process of precipitation of barium sulphate is being proceed
at the source, that is in the settling tanks. In order to prevent penetrating the remaining barium
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sulphate into the pipe-lines it is necessary to get to know the process of its sedimentation and
efficiency. The main reason for this article was to describe the process of barium sulphate sedimentation in both settling tanks mentioned above, using the numerical simulation method of its
flow. Calculations were proceeded on both settlers, since the geometrical differences in their
structure cause the sedimentation to proceed a little bit different in each of them.
2. Computational modeling of multiphase flows
The flow of the suspension through the settling tank might be characterised as a two-phase
flow, in which the water is a continuous phase. The second phase consists of spherical mineral
or chemical particles (barium sulphate) dispersed in the continuous phase.
Two-phase flows might be described using the same conservation of mass, energy and
momentum as in the one-phase flows. This description is much more complicated, what is the
consequence of huge differences between these flows. The basic meaning has not only occurring the external interactions from rigid walls and washed bodies on the fluid, but also internal
interactions on the surface of phase separation. The last ones are variable both in place and time.
Difficulties with solving theoretical models account for starting point of working out many methods based on semi-empirical equations describing particular two-phase flows cases (Wacławik,
1993; Bemonowski et al., 1995; Fluent 6.1).
Currently in the computational fluid mechanics there are two approaches for the numerical calculation of multiphase flows: the Euler-Lagrange approach and the Euler-Euler approach
(Fluent 6.1). In the first approach the fluid phase is treated as a continuum by solving the timeaveraged Navier-Stokes equations, while the dispersed phase is solved by tracking a large number
of particles through the calculated flow field. The dispersed phase can exchange momentum,
mass and energy with the fluid phase. A fundamental assumption made in this model is that
the dispersed second phase occupies a low volume fraction, even though high mass loading is
acceptable. The particle trajectories are computed individually at specified intervals during the
fluid phase calculation.
The simulation of three-dimensional solid particles flow through the Jankowice and Pniowek
settling tanks was made based on Euler-Lagrange approach, assuming the two-phase flow, with
water as a fluid phase and solid particles as a dispersed one. Calculations were made based on
FLUENT 6.1.
3. Description of Eulera-Lagrange approach
The foundation of description of fluid phase movement is a set of equations based on
conservation of mass and momentum. When the stationary incompressible fluid flow is being
considered these equations are presented as follows:
• continuum equation:
¶ vi
=0
¶ xi
(1)
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• equation of motion:
é¶ v ¶ (vi vj ) ù
¶p ¶ti , j
rê i +
+
ú = Fi ¶ xi
¶ xj
¶ xj úû
êë ¶t
(2)
where:
v
t
ρ
F
p
τ
x
i, j = 1,2,3
—
—
—
—
—
—
—
—
center’s linear velocity field, [m/s],
time, [s],
center’s local density, [kg/m3],
local not fluctuating body force, [N/m3],
local pressure, [Pa],
local stress deformation tensor (deviator), [Pa],
Cartesian component, [m],
values of index ascribed to certain spatial variables.
In case of Newtonian incompressible fluid, deviator’s components are presented with an
equation (3):
æ ¶v
¶ vj æ
ç
t i, j = r v ç i +
ç ¶ xj
ç
x
¶
i è
è
(3)
Introducing the definition (3) to equation of motion (2) and its transformation leads to Navier-Stokes equations. In case of turbulent flow the Reynolds theorem is being used. Substituting
equation (3) for (2), introducing pro velocity and pressure their medium and fluctuating values
and caring out mathematical transformations we get the equation called Reynolds equation (4).
There is an additional stress tensor which is not present during laminar flows (5).
-
- -
¶ v i ¶ (v i v j ) 1 æ
¶p æ
¶
ç+
+
= çç Fi ¶t
¶x j
¶xi çè ¶xj
rè
- æù
é æ êv ¶ vi + ¶ vj ú - ¶v 'i v 'j
ç ¶x
ê ç ¶x
¶xi èú
j
ë è j
û
(ti )ij = - r v i' v 'j
(4)
(5)
Turbulent stress tensor, called Reynolds stress, present in the turbulent flow, causes the set of
equations not to be closed due to the lack of six completing relations describing tensor’s components (5). It is necessary to form supplementary equations, what in the fluid modelling terminology
is called closing hypothesis. One of the first hypotheses, which introduced the turbulent viscosity coefficient, was proposed by Bousinesqa (1887) (Hinze, 1987). This coefficient was defined
based on the stress tensor (5) through the analogy to the Newtonian formula, describing stresses
in the shear fluid. Turbulent viscosity is not a physical fluid’s feature and therefore it has no clear
physical sense. It is a property arising during turbulent flows and depending on the turbulent
intensity in a specific velocity field point (velocity component’s fluctuation module per its mean
value). Bringing in some simplifications, turbulent viscosity creates the scalar field in the flow
area. In reality, it creates second row tensor field (Tu et al., 2008). Bringing in this magnitude to
the Reynolds equations allows to close the set of equations describing certain flow.
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4. List of differential equations used in the turbulent model
Prandtl mixing length model (1925) was the first turbulent model to use concept of the
turbulent viscosity (Hinze, 1987). Models which use this concept, Reynolds stress tensor’s
components (5) are presented throughout the components of the mean movement’s velocity
deformation tensor (6).
- v 'i v 'j = uT
where:
v–i, v–'i
δij
υT
k
—
—
—
—
æ ¶ v-i
ç ¶x
è
+
j
¶ vj æ 2
- k dij
3
¶xi
è
ç
(6)
as follows: i-direction mean and fluctuating velocity vector’s component,
Kronecer delta function,
turbulent viscosity coefficient,
turbulence kinetic energy.
For the wide rage of researches most practical flow calculations solved by CFD (Computational Fluid Dynamics) were based on the two-equations k-ε model (turbulence kinetic energy
and its dissipation rate) (Fluent 6.1; Hinze, 1987). Turbulent viscosity was calculated either from
the algebraic relations or turbulent kinetic energy transport equation (one-equation model) and
additional differential equation (two-equation model).
The turbulent viscosity in two-equation k-ε model is computed by relation (7):
uT = Cm
k2
e
(7)
where:
Cµ — constant,
ε — dissipation of turbulence kinetic energy.
The turbulence kinetic energy, k, and its rate of dissipation, ε, are obtained from the following transport equations (8) and (9) (Tu et al., 2008):
-
¶(v jk )
¶xj
-
¶ (v j' e )
¶ xj
=
¶
=
¶ xj
¶
¶x j
ìïæ
u T æ ¶k
íççu + çç
d k è ¶ xj
ïîè
üï
¶ vi
-e
ý - v'i v'j
¶ xj
ïþ
ìï æ
¶ vi
u T æ ¶e üï
e
e2
- C2
í ççu + çç
ý - C1 v'i v'j
k
k
¶x j
de è ¶ xj ïþ
ïî è
(8)
(9)
where: C1, C2, δε, δk — constans.
Taking into account fluid incompressibility, equations (6) to (9) account for closed set of
equations.
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There are a few modifications of standard k-ε model known and it is usually hard to choose
the one which reflects the real flow parameters the best. In this specific case the RNG model
(Renormalization Group) was chosen, especially because its recommendation for the low- Reynolds number flows (Fluent 6.1). That kind of low Reynolds number ranges have to be taken
into consideration in these cases.
The main difference between the RNG and standard k-ε models lies in the additional term
in the transport equations for the dissipation rate of turbulence kinetic energy, given by:
h æ
æ
Cm rh 3 ç1 ç 2
è 4.38 è e
Re =
k
1 + 0.012h 3
where: h = S
(10)
k
e
Effective Prandtl number is computed using the formula (11)
m
a - 1.3929
=
mef
a 0 - 1.3929
0.6321
a + 2.3929
a 0 + 2.3929
0.3679
(11)
where:
µ, µef — dynamic viscosity – accordingly laminar and effective,
α — invers effective Prandtl number,
α0 — constant.
Except for solving transport equations for continuous phase, this model requires computing the trajectories of the dispersed phase entities. It is done by integrating the force balance
on the particle, which is written in a Lagrangian reference frame. This force balance equates the
particle inertia with forces acting on the particle, and can be written (12):
dvpi
dt
= FDi (vi - vpi ) +
g i ( rp - r)
rp
(12)
The first term on the right - side hand is the drag force per unit particle mass, and FDi is:
FDi =
where:
vpi
vi
gi
ρp, ρp
µ
dp
—
—
—
—
—
—
18 m CD Re i
r p d p2 24
i-direction particle velocity component,
i-direction fluid phase velocity component,
i-direction gravitational acceleration component,
accordingly: particle and fluid densities,
dynamic viscosity,
particle diameter.
(13)
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The drag coefficient, CD, which is the function of the relative Reynolds number defined as:
Re i =
r dp vp - vi
m
(14)
For sub-micron particles, with diameter lower then 1×10–6 m, FD is defined as (15):
FDi =
18 m
d p2 rp Ce
(15)
Where Ce is the Cunningham correction to Stokes’ drag law.
In the FLUENT the finite difference method is used to resolve equation (12), and the trajectory of a certain particles are computed taking into consideration equation (16)
dxi
= vpi
dt
(16)
5. Boundary conditions
For the continuous phase (water) following conditions were made:
• boundary conditions of the first kind were made in the inflow cavity in the form of constant
flowing in velocity to water area. Turbulence kinetic energy and rate of its dissipation
were computed providing 5% of turbulence intensity on the inlet,
• the constant value of static pressure in the exit section and, for the other variables, zero
value of gradient in the direction of flow were assumed, so called pressure conditions,
• nonskid flow on the rigid walls and classical wall function model on the boundary areas
were assumed,
• free surface was modeled assuming zero values of shear stresses.
Boundary conditions for the dispersed phase are brought in to set the place where the solid
particles are released and to define conditions of their collision via the wall. There were two types
of boundary conditions for the discrete phase assumed:
• particle is being reflected via collision with the wall. This condition is being determined
through the amount of momentum lost via collision and was used for the side walls of
the settling tanks,
• particle after reaching the edge disappears (it is stopped or it flows out of the area). Its
trajectory calculations are being stopped. This condition was set for the bottom surface
of settling tanks and in the inlet and exit section cavities.
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6. Three dimensional numerical calculations of two-phase
flow through the settling tanks and their analysis
Numerical particles flow calculations were made for two geometrically different settling
tanks. The water from Jankowice and Chwałowice coal mine is drained off to Jankowice settling
tank. The situation is almost the same in the Pniowek settling tank, which adopts water from
Krupinski coal mine and Koscielniok Damping Ground. The characterization of the settlers was
presented in the table 1.
TABLE 1
Characterization of settling tanks
Name
Dimensions
[m]
Flow
[m3/24 h]
„Jankowice” settling tank
250×180×1
9670
„Pniówek” settling tank
70×40×1,5
6900
Description
Not structural numerical net with over
800000 knots
Settler in the shape of cuboid. Structural
numerical net with around 400000 knots
Numerical calculations were proceeded assuming homogenous diluted suspension flow
through the settlers. Monodispersed, sub-micron barium sulphate particles are of spherical shape
with diameter of 1×10–5 ÷ 1×10–6 m and density of 4500 kg/m3 (Lebecka, 1994). The sedimentation process is of continuous character which means that different concentration of particles
within the settlers is seen. The flow is stable and three dimensional. Volume and mass flux on
the inlet and outlet is equal (tab. 1). It means that mass of the settling particles due to the inlet
and outlet mass flux balances is negligible.
The numerical calculations brought the three-dimensional (3D) velocity, pressure, turbulence
kinetic energy and its dissipation rate fields for the continuous phase. Moreover, the trajectories
of the discrete phase (barium sulphate) were calculated. It all allowed to define the sedimentation efficiency as a ratio of the number of particles settled on the bottom of the settler per total
number of released particles. Solutions’ independency of the numerical net density was checked
out through its densification.
In the figures 1, 2, 3, 4 and 5 stream lines coming out from the surface of inlet, velocity
fields in the plane of water table and path lines of barium sulphate deposits of different diameter
were presented. In both cases barium sulphate is released from the point of inlet streams mixing. In the Pniowek settler this point is about 8-10 m away from the inlet, which was presented
in the figure 3a.
Additionally in the table 2 the list of particles’ diameter dependency of sedimentation efficiency was presented.
There are differences between stream lines and velocity fields presented in the figures 1, 3a
and b. It results from different settlers’ shape and inlet and exit cavities position. Still, in both
settlers there are two zones with recirculation flow to be marked out. The difference is both in
range and intensity of flow.
Figures and data (tab. 2) analysis illustrate the sedimentation efficiency dependency of the
particle diameter. The lowest efficiency, and the longest descending time is characteristic for the
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a)
b)
Fig. 1. a) Stream lines coming out from the surface of inlet of Jankowice settler
b) Velocity field – plane of water table in the Jankowice settler
diameter of 1×10–6 m. This diameter in the Jankowice settler allows to attain efficiency of the
magnitude of 62,5%. A little bit lower efficiency was reached in the Pniowek settler. It is important
to remember that Jankowice settler has a much bigger surface and volume fluxes on the inlets.
The colour scale presented in the figures 2, 4a, b and 5 corresponds to the time of particles’ abiding in the settler. According to the boundary conditions the particle either settles on the bottom
or flows out through the exit cavity. The abiding time is a function of many variables, among
which geometry of the settler, mass flux of the flowing suspension as well as physical features
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a)
b)
Fig. 2. Path lines of barium sulphate deposits (ρ = 4500 kg/m3) released from the point
of inlet streams mixing in Jankowice settler a) diameter d = 1×10–6 m, b) diameter d = 7×10–6 m
of particles themselves, have an essential meaning. Knowledge of particles’ abiding time might
be useful during the settlers’ modernization. Not only does it concern the optimization of the
settlers’ shape and arranging inlet and exit cavities but also designing new objects.
In both cases, along with increasing particles’ diameter, sedimentation efficiency is increasing whereas descending time is decreasing. 100% efficiency was achieved in Pniowek settler at
1×10–5 m diameter, whereas in the Jankowice settler practically the same efficiency was achieved
already at 7×10–6 m diameter.
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a)
b)
Fig. 3. a) Stream lines coming out from the surface of inlet of Pniowek settler
b) Velocity field – plane of water table in the Pniowek settler
TABLE 2
List of diameters and efficiency of sedimentation in settling tanks
Name
diameter
[m]
efficiency
[%]
diameter
[m]
„Jankowice’ settling tank
1×10–6
62,5
7×10–6
99
–
–
–6
57,7
7×10–6
84,4
1×10–5
100
„Pniówek” settling tank
1×10
efficiency
[%]
diameter
[m]
efficiency
[%]
Difficulties with clear specification of the barium sulphate particles’ diameter reflect on the
appraising their free descending velocity and in the end on the sedimentation efficiency. Pinpointing the real particles’ diameter is quite difficult and literature data publicize only its range
(Majcherek, 2006). According to those data, continuous steering would allow to obtain crystals
of diameter around 6 µm to 8 µm, whereas, intensive, mechanic steering crystals of diameter
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a)
b)
Fig. 4. Path lines of barium sulphate deposits (ρ = 4500 kg/m3) released from the point
of inlet streams mixing in Pniowek settler a) diameter d = 1×10–6 m , b) diameter d = 7×10–6 m
around 3 µm to 1 µm. It is quite important to know that barium sulphate has an ability to occlude,
adsorb and create mixing crystals, what all the more, obstructs setting its diameter.
Analysis of numerical calculations data (tab. 2) and assumption of the most probable barium
sulphate particles’ diameter (Lebecka, 1994), around 7×10–6 m, would bring us to the statement,
that during the water flow regulation it is necessary to lengthen the contact time of the chemically
different waters. It would surely have a large effect on the protection of the interceptor-sewer’s
pipe-lines from being overgrown with barium sulphate sediment. This specific particles’ diameter
allows to gain, in the Pniowek coal mine, sedimentation efficiency around 84,4%.
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Fig. 5. Path lines of barium sulphate deposits (ρ = 4500 kg/m3) released from the point
of inlet streams mixing in Pniowek settler, diameter d = 1×10–5 m
7. Test of the Eulera-Lagrange approach’s verification
The verification of the applied two-phase flow model was based on the classical method of
apprising free solid particle’s descending velocity in the liquid. This velocity is a result of the
force of gravity, lift force, and the drag center force action:
vc =
4 d ( rc - r )g
3l (Re) r
(17)
where:
d — particle’s diameter, [m],
ρc and ρ — accordingly: particle and liquid densities, [kg/m3],
λ(Re) — pipe friction factor.
Pipe friction factor is being determined through Stokes, Allen and Newtonian equations.
Classical Hazen’s sedimentation theorem concerns free descending particles in the oblong settler,
and it is based on (Majcherek, 2006) an assumption of non-agglomerating, spherical particles
descending with constant velocity. Water inflow and outflow is being proceeded throughout
the entire cross-section of the settler (ideal settler). The flow is stable, and the velocity field is
homogenous. Particles which have descended on the bottom are not raised again. Sedimentation
efficiency is pinpointed with Hazen number as follows:
E=
tp
tc
100
(18)
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where:
tp — theoretical water flow through the settler,
tc — particles’ descending time from water surface on the bottom of the settler.
Verification of Euler-Lagrange approach was made for the oblong settler of 30 m long
and 2 m high (2D-two dimensional). Fulfilling the limitation accepted by Hazen forced certain
assumptions to be adopted while describing boundary conditions. On the side of inlet, along
the edge, the constant water inflow velocity was assumed (0,002 m/s). On the upper and lower
edge (water table and the bottom of the settler) zero value of shear stresses were assumed. This
assumption (the edge of the bottom) is non-physical, but allows to obtain requested velocity
field. Setting up so called pressures conditions on the outlet is analogical as in the boundary
conditions. The velocity field of the continuous phase (water), obtained during the simulation,
is humongous. It means that velocity layout in the cross sections along the settler is identical
(fig. 6). The trajectories of particles were computed assuming that they had been realised from
equally distant points, placed along the inflow edge. Particles which trajectories ended on the
bottom of the settler were treated as vanishing ones.
Fig. 6. Image of water velocity field in the ideal settler (using stream lines)
Calculations data carried out for spherical particles with density of 1800 kg/m3 and diameter of 8×10–6 m to 2×10–6 m were presented in the table 3. Free particles’ descending velocities
calculated from the equation (17) were placed in the second column and the responsive Hazen’s
sedimentation efficiencies (18) were placed in the fourth column. Data of the sedimentation
efficiencies for the ideal settler, fulfilling Hazen’s assumptions, but calculated through the E-L
approach, were presented in the fifth column. Moreover, calculations for the model of the settler
more similar to the real object than the mentioned above, but still 2D, were made. Keeping the
geometric dimension of the settler and the flowing water volume flux not changed, water inflow
and outflow is being proceeded through the cavities 0,05 m high, placed under the water table.
The identical boundary conditions for the inlet (velocity of 0,08 m/s), outlet and water table
were made. During the description of the boundary condition on the bottom edge (the settler’s
bottom), the classic wall function model was used. The image of water velocity was presented
in the figure 7. Calculated sedimentation efficiencies for the particles released from the edge of
the inlet cavity were presented in the sixth column of the table 3.
The maximum error made in the calculated sedimentation efficiencies values is about 9%
and it refers to the particles of the lowest diameter. It is worth to notice that for this diameter
Reynolds number reaches the value around the lower boundary of the Stokes’ formula validity
(Orzechowski et al., 1997). In other cases this error does not exceed 4%. Despite the important
differences in the velocities field images, computed through CDF simulation, in the first example
velocity field is homogeneous (fig. 6), and in the second one (fig. 7) almost 1/3 of its length is
involved with recirculation flow. In both cases the sedimentation process, on account of its efficiency, is being proceeded similarly.
515
It might be conceded that on the account of this one parameter (sedimentation efficiency)
calculations of the two-phase flow made by the Euler-Lagrange approach reflect the real flow. It
is necessary to remember that the proceeded verification is fragmentary and it does not provide
for series of parameters of great importance, as for example velocity field verification.
TABLE 3
List of calculations results of Euler-Lagrange approach’s verification
Deposit’s
diameter
[m]
Velocity of
deposit’s free
descending
[m/s]
Reynolds
number
Efficiency of
sedimentation
according to Hazen
[%]
Efficiency of sedimentation
in the ideal settler
[%]
Efficiency of sedimentation in the
oblong settler 2D
[%]
1
8×10–6
1×10–5
1.5×10–5
1.55×10–5
1.8×10–5
2×10–5
2
2.15×10–5
3.35×10–5
7.55×10–5
8.06×10–5
1.09×10–4
1.34×10–4
3
1.32×10–4
2.58×10–4
8.71×10–4
9.61×10–4
1.50×10–3
2.06×10–3
4
16.1
25.1
56.6
60.4
81.5
100
5
17.5
25.0
57.5
62.5
82.5
100
6
15.0
25.0
55.1
60.2
80.4
100
Fig. 7. Image of water velocity field in the oblong settler with dimensions of 30 m x 2 m
8. Conclusion
Numerical simulation of the solid particles flow (barium sulphate) proceeded in this article
throughout Fluent 6.1, was the way of describing the sedimentation process. Usage of the twophase model flow throughout the calculations of the velocity field and trajectory of barium sulphate
particles, allowed to pinpoint the sedimentation efficiency and the particles’ descending time
(time of particles being in the settler). The calculated sedimentation efficiency for the particles
of 7×10–6 m diameter for the Jankwice settler was 99% and for Pniowek 84%. The Differences
in the sedimentation efficiency and descending time depend on the settler geometry, inlet and
outlet placing (water inflow and outflow), flowing water volume flux and in the end on particles
diameter. Numerical calculations of the different mass flux suspension flow through the settler
allow to demonstrate the process of sedimentation. This knowledge is very important due to the
“Olza” interceptor sewer’s protection. It has a great economic value because the lack of sediments
in the pipe-lines decreases power-consuming and is beneficial for their technical condition.
This paper was carried out as a part of Scientific Research (AGH) nr 11.11.100.497 financed
from the means of Ministry of Science and Higher Education
516
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Received: 30 March 2010