Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity
Improvement of the efficiency of the cleaning of flue gases of coal-fired boilers from ash particles is an important environmental problem. In the power engineering of Ukraine, apparatus for the wet cleaning of flue gases are widely spread, especially Venturi scrubbers. Their characteristics often d...
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| Дата: | 2014 |
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General Energy Institute of the National Academy of Sciences of Ukraine
2014
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Репозитарії
System Research in Energy| _version_ | 1871103998568693760 |
|---|---|
| author | Shraiber O.A. Antonets I.V. |
| author_facet | Shraiber O.A. Antonets I.V. |
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"author": "Shraiber O.A.",
"institution": null
},
{
"author": "Antonets I.V.",
"institution": null
}
] |
| author_sort | Shraiber O.A. |
| baseUrl_str | https://systemre.org/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T12:57:41Z |
| description | Improvement of the efficiency of the cleaning of flue gases of coal-fired boilers from ash particles is an important environmental problem. In the power engineering of Ukraine, apparatus for the wet cleaning of flue gases are widely spread, especially Venturi scrubbers. Their characteristics often do not meet the present-day requirements, although the possibilities of improvement of their work are far from being exhausted. The most reasonable way of solution of this problem is connected with mathematical modeling. Earlier, the authors have built such a model. In the present work, we describe the generalization of this model with regard for the effect of turbulence of gas flow.The work consists of two parts. First, approximating the distribution of fluctuation velocities of gas moles and particles by Maxwellian functions, we determine the average velocity of fluctuation slip between two fractions. Second, we find relations for calculating the effective slip velocity of particles with regard for their both averaged and fluctuation motion. We determine the domain where the proposed method of calculating the effective slip velocity enables one to obtain more exact data as compared with the known, approximate approach. |
| first_indexed | 2026-03-24T02:02:07Z |
| format | Article |
| fulltext |
57ISSN 1562-8965. Проблеми загальної енергетики, 2014, вип. 3 (38)
Various technological processes in many branches
of industry are connected with the formation of
exhaust gases, which contain solid particles and are
thrown out to the atmosphere. Power engineering
based on coal makes its substantial contribution to
the contamination of atmospheric air. Numerous
power units are equipped with apparatus for the wet
cleaning of gases from ash particles, among which
Venturi scrubbers should be considered as the most
efficient and promising [1]. Nevertheless, in many
cases, such apparatus do not provide the necessary
purity of gases thrown out to the atmosphere, and,
hence, the search for ways of enhancing the effi-
ciency of gas cleaning from solid particles in Venturi
scrubbers represents an important ecological prob-
lem. The most real way of the solution of this prob-
lem is connected with mathematical modeling. We
have constructed such a model [2, 3], but one quite
significant factor is here not taken into account.
It is customary to think that, under usual condi-
tions, fluctuation velocities (caused by turbulence)
are much lower than averaged ones. However, as
shown in [4], this is correct for absolute velocities of
suspended particles, but not for their relative veloc-
ities. Even in the case of a channel of constant
cross-section, the fluctuation velocities of slip
between two fractions of particles can have the same
order of magnitude as the averaged slip velocities
[4]. This feature is still more clearly pronounced for
channels of variable cross-section (e.g., Venturi
tubes): at some domains of the flow, the curves of
averaged velocities of two fractions can intersect,
and fluctuation slip velocities can here be much
more than averaged ones. Therefore, the aim of this
paper is to generalize model [2, 3] with regard for
turbulent motion of particles.
First, we give a short characteristic of model [2,
3]. It is based on the continuous approach to the
description of particle interaction (coalescence and
breakup). Here, collisions of a given fraction i with
smaller and greater particles are described in differ-
ent ways: in the first case, particle i preserves its
individuality (the substance continues to belong to
the same fraction) and loses it in the second. Two
polydisperse ensembles are considered: drops with
small solid inclusions and solid particles (SP) with
(possible) liquid shells. The state of each fraction is
described by five quantities: particle mass (m, M),
specific mass flow rate (g, G), velocity (u, U; small
letters refer to drops, and capital to SP), tempera-
ture, and the mass content of «foreign» phase.
According to the continuous approach, four types
of interaction are considered: two fractions of
drops, small drop – large SP, small SP – large drop,
two SP.
As an example, we present equations for drop
mass mi and SP specific flow rate Gj. The first con-
sists of four terms taking into account phase transi-
UDC 532.529
MODELING OF THE PROCESS OF ASH REMOVAL FROM GAS IN A VENTURI SCRUBBER
WITH REGARD FOR THE TURBULENT FLUCTUATIONS OF PARTICLE VELOCITY
We generalize our model of gas cleaning from suspended solid particles in a Venturi scrub-
ber with regard for the influence of turbulent fluctuations of gas flow. We develop a method
for calculating the effective velocity of slip between two fractions of particles, including their
averaged and fluctuation motion.
K e y w o r d s: drops, solid particles, interaction, turbulence, kinetic energy of turbulent fluc-
tuations, Venturi scrubber, gas cleaning.
© A.A. SHRAIBER, I.V. ANTONETS, 2014
A.A. SHRAIBER, Doctor of Science (Eng.), Professor, I.V. ANTONETS
Institute of General Energy National Academy of Sciences of Ukraine,
03680, Ukraine, Kyiv, Antonovycha st., 172
58 ISSN 1562-8965. Проблеми загальної енергетики, 2014, вип. 3 (38)
tion, interaction of drops i with smaller ones, coa-
lescence with smaller SP, and liquid sticking onto
SP that do not coagulate with our drops:
where δ, Δ are the sizes of drops and SP, V is the
intensity of phase transition, E is the collision effi-
ciency, K, L are the interaction constants, Φ, Ψ are
the parameters of coalescence (and breakup), and β
is the coefficient of liquid sticking.
Equation for Gj has the form
(Qij can be obtained from Nji by substitution of Eij
instead of Eji, X is the parameter of coalescence and
breakup for interaction small drop – large SP).
We now calculate the velocity of slip between
two fractions with regard for turbulence. According
to [5], the root-wean-square fluctuation velocity of
a particle is equal to
where γ-1 is the particle relaxation time, and ψ-1 is
the integral time scale of turbulence. For calculat-
ing the average velocity of fluctuation slip between
two fractions of particles, it is reasonable to use the
approach [6], where only monodisperse particles
are considered. The function of joint distribution of
the particles of two fractions (i and p) by fluctuation
velocities is
where vector quantities are denoted by bold letters,
and fgip is the function of joint distribution of gas
moles and two fractions (integration is performed
over the entire space of fluctuation velocities):
Here, two first multipliers characterize the con-
ditional probability that the particle velocity takes a
certain value if the gas velocity is equal to Vg, and
the third represents the distribution function of gas
velocities. As follows from the definition of condi-
tional probabilities, we may write
where fgn is the function of joint distribution of gas
moles and particles n by fluctuation velocities.
Hence, using (5) and (6), we obtain
Further, following [6], we approximate the
velocity distributions of particles and gas by
Maxwellian functions:
where vn is the number of particles per unit volume.
The simplest variant of joint distribution of gas and
particles, corresponding to (8), is
A.A. SHRAIBER, I.V. ANTONETS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
59ISSN 1562-8965. Проблеми загальної енергетики, 2014, вип. 3 (38)
Modeling of the process of ash removal from gas in a venturi scrubber with regard for the turbulent fluctuations of particle velocity
where
We now substitute functions (8) and (9) in (7)
and obtain
The integration of function (10) over the space
of fluctuation velocities gives
Obviously, the average velocity of fluctuation slip
between particles i and p is equal to
For calculating the integrals in (12), it is conven-
ient to pass to new variables G and g:
Then we obtain instead of (11):
(9)
(10)
(11)
(12)
(13)
(14)
It is easy to verify that the corresponding
Jacobian is . Further, we pass
to spherical coordinates G, ψ°, θ°, g, ψ, θ and cal-
culate the distribution function for pairs of particles
by the modulus of vector g:
(15)
60 ISSN 1562-8965. Проблеми загальної енергетики, 2014, вип. 3 (38)
A.A. SHRAIBER, I.V. ANTONETS
(here, the vector G is first fixed so that ψ = (G, g),
and then integration by its direction and modulus is
performed). Having calculated the integrals in (15),
we arrive at the following result:
Finally, calculating
carrying out the corresponding transformations, we
obtain
The last part of our study is connected with com-
bining average and fluctuation slip velocities. This
problem was first solved in [7] for the case of
isotropic pseudoturbulence. Here, for simplifica-
tion, the actual distribution of the moduli of fluctu-
ation velocities (e.g., (16)) was replaced by delta
function
which led to the following result for effective slip
velocity:
where u is the averaged slip velocity between parti-
cles i and p.
Let us now take, instead of (18), a more actual distri-
bution of pairs of particles by fluctuation slip velocities
(16). For brevity, we denote the coefficients of this distri-
bution by D (pre-exponential multiplier) and B. Then,
using, as earlier, spherical coordinates g, ψ, θ, we write
The way of calculating the internal integral in
(20) (we denote it by I) depends on the relation
between u and g, and, hence, we must divide the
second integral in (20) into two:
calculations give
(cf. (19)). Substituting (21) in (20) and carrying out
remaining integration, we finally obtain
where
Calculations show that the new approach
enables one to refine the average slip velocity and,
hence, the intensity of catching of solid particles by
drops (see (2)). In Table, we present the values
of wpi calculated according to (19) and (22) for the
interaction of water drops (δi =0.25 mm) with ash
particles (Δj = 5 μm) at a gas velocity of 60 m/s
(here, gpi = 9.22 m/s).
It is seen that, in the case where averaged and
fluctuation slip velocities are comparable, the
refined method (22) give results different from the
approximate approach [7] by 15–18%. At the same
(16)
and
(17)
(18)
(19)
(20)
(21)
(22)
is the error function.
Table – Effective slip velocities (m/s)
Simple
61ISSN 1562-8965. Проблеми загальної енергетики, 2014, вип. 3 (38)
Modeling of the process of ash removal from gas in a venturi scrubber with regard for the turbulent fluctuations of particle velocity
time, for very low of very high u, this difference
becomes not so important.
Note that the described results form a tool for
the search for the optimal conditions of gas clean-
ing from SP in Venturi scrubbers.
CONCLUSIONS
In three-phase mixtures flowing in channels of
variable cross-section (e.g., Venturi tubes), the fluc-
tuation velocities of slip between two fractions of
particles can be not only comparable with the aver-
aged slip velocities, but also exceed them substan-
tially. Therefore, we have generalized our model of
three-phase polydisperse flow in apparatus for the
wet cleaning of combustion products from ash par-
ticles with regard for turbulent fluctuations. First,
approximating the distribution of fluctuation veloc-
ities of gas and particles by Maxwellian functions,
we determine the average velocity of fluctuation slip
between two fractions. Second, based on the same
approximation, we find the effective slip velocity of
particles, taking into account their average and
fluctuation motion. We determine the domain
where the proposed method of calculating the
effective slip velocity between two fractions enables
one to obtain more exact data as compared with the
known, approximate approach.
1. Kropp L.I., Akbrut A.I. Ash catchers with
Venturi tubes at thermal power plants [in
Russian]. – Moscow, Energiya, 1977. – 160 p.
2. Shraiber A.A., Fedinchyk I.V. Modeling of
the process of the wet cleaning of exhaust gases
from flue ash //Prom. Teplotekhnika. – 2012. –
Vol. 34, No. 3. – P. 86–92.
3. Shraiber A.A. Modeling of gas cleaning from
solid particles in a Venturi scrubber // Prom.
Teplotekhnika. – 2013. – Vol. 35, No. 3. –
P. 87–93.
4. Shraiber A. A. Effect of the turbulent fluctua-
tions of slip velocity on the motion, heat trans-
fer, and coalescence of particles in a gas suspen-
sion flow // Prom. Teplotekhnika. – 2003. –
Vol. 25, No. 2. – P. 15–21.
5. Shraiber A. A., Yatsenko V. P. Gavin L. B.,
Naumov V. A. Turbulent flows in gas suspen-
sion. – Hemisphere, New York, 1990. – 262 p.
6. Lavieville J., Deutsch E., Simonin O. Large
eddy simulation of interaction between colliding
particles and a homogeneous isotropic turbu-
lence field // ASME FED, Gas-Solid Flows. –
1995. – Vol. 228. – P. 347–358.
7. Rokhman B. B., Shraiber A. A. Mathematical
modeling of the aerodynamics and physico-
chemical processe s in the free-board of a fur-
nace with fast fluidized bed. II. Particle interac-
tion (pseudoturbulence) // Inzh.-Fiz. Zh. –
1994. – Vol. 66, No. 2. – P. 159–167.
Надійшла до редколегії 29.05.2014
|
| id | systemreorg-article-531 |
| institution | System Research in Energy |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-07-19T01:17:06Z |
| publishDate | 2014 |
| publisher | General Energy Institute of the National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | systemreorg/91/5968353724d925081a4bcad49ffea691.pdf |
| spelling | systemreorg-article-5312026-07-18T12:57:41Z Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity Моделювання процесу видалення золи із газу в скрубері Вентурі з урахуванням турбулентних пульсацій швидкості частинок Shraiber O.A. Antonets I.V. drops, solid particles, interaction, turbulence, kinetic energy of turbulent fluctuations, Venturi scrubber, gas cleaning. краплі, тверді частинки, взаємодія, турбулентність, кінетична енергія турбулентних пульсацій, скрубер Вентурі, очищення газу. Improvement of the efficiency of the cleaning of flue gases of coal-fired boilers from ash particles is an important environmental problem. In the power engineering of Ukraine, apparatus for the wet cleaning of flue gases are widely spread, especially Venturi scrubbers. Their characteristics often do not meet the present-day requirements, although the possibilities of improvement of their work are far from being exhausted. The most reasonable way of solution of this problem is connected with mathematical modeling. Earlier, the authors have built such a model. In the present work, we describe the generalization of this model with regard for the effect of turbulence of gas flow.The work consists of two parts. First, approximating the distribution of fluctuation velocities of gas moles and particles by Maxwellian functions, we determine the average velocity of fluctuation slip between two fractions. Second, we find relations for calculating the effective slip velocity of particles with regard for their both averaged and fluctuation motion. We determine the domain where the proposed method of calculating the effective slip velocity enables one to obtain more exact data as compared with the known, approximate approach. Поліпшення ефективності очистки димових газів пиловугільних котлів від леткої золи є важливою екологічною задачею. В енергетиці України значне розповсюдження знайшли апарати для мокрої очистки димових газів, найпоширенішими з яких є скрубери Вентурі. Їх ефективність часто не відповідає сучасним вимогам, хоча можливості покращення їх роботи ще далеко не вичерпані. Найбільш раціональний шлях розв’язання цієї задачі пов’язаний із математичним моделюванням. Раніше авторами було побудовано таку модель для скрубера Вентурі. В роботі описано узагальнення цієї моделі із врахуванням впливу турбулентності газового потоку.Робота складається із двох частин. У першій з використанням апроксимації розподілу пульсаційних швидкостей молів газу і частинок максвеллівськими функціями визначається швидкість пульсаційного ковзання між двома фракціями частинок. У другій частині отримано формули для обчислення середньої ефективної швидкості ковзання із врахуванням як пульсаційного, так і осередненого руху. Визначено область, де запропонований метод обчислення ефективної швидкості ковзання дозволяє отримати точніші дані порівняно з відомим, досить наближеним підходом. General Energy Institute of the National Academy of Sciences of Ukraine 2014-11-03 Article Article application/pdf https://systemre.org/index.php/journal/article/view/531 System Research in Energy; No. 3 (38) (2014): The Problems of General Energy; 57-61 Системні дослідження в енергетиці; № 3 (38) (2014): Проблеми загальної енергетики; 57-61 2786-7102 2786-7633 uk https://systemre.org/index.php/journal/article/view/531/467 Copyright (c) 2014 Shraiber O.A., Antonets I.V. https://creativecommons.org/publicdomain/zero/1.0 |
| spellingShingle | drops solid particles interaction turbulence kinetic energy of turbulent fluctuations Venturi scrubber gas cleaning. Shraiber O.A. Antonets I.V. Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| title | Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| title_alt | Моделювання процесу видалення золи із газу в скрубері Вентурі з урахуванням турбулентних пульсацій швидкості частинок |
| title_full | Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| title_fullStr | Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| title_full_unstemmed | Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| title_short | Modeling of the process of ash removal from gas in a Venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| title_sort | modeling of the process of ash removal from gas in a venturi scrubber with regard for the turbulent fluctuations of particle velocity |
| topic | drops solid particles interaction turbulence kinetic energy of turbulent fluctuations Venturi scrubber gas cleaning. |
| topic_facet | drops solid particles interaction turbulence kinetic energy of turbulent fluctuations Venturi scrubber gas cleaning. краплі тверді частинки взаємодія турбулентність кінетична енергія турбулентних пульсацій скрубер Вентурі очищення газу. |
| url | https://systemre.org/index.php/journal/article/view/531 |
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