Investigation of admixture sedimentation in the horizontal settler Текст научной статьи по специальности «Строительство и архитектура»

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ЕКОЛОГ1Я НА ТРАНСПОРТ!

UDC 628.334.5:519.6

V. A. KOZACHYNA1*

1 Dep. «Hydraulics and Water Supply», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 15 09, e-mail kozachynav@yandex.ua, ORCID 0000-0002-6894-5532

INVESTIGATION OF ADMIXTURE SEDIMENTATION IN THE HORIZONTAL SETTLER

Purpose. Sedimentation by gravity is the most common and extensively applied treatment process for the removal of solids from water and wastewater and it has been used for over one hundred years. Sedimentation tanks are one of the major parts of a treatment plant especially in purification of turbid flows. Horizontal settlers are mainly used for purification of high quantity of water. In these tanks, the low speed turbid water will flow through the length of the tank and suspended particle have enough time to settle. Finding new and useful methods for calculating and increasing hydraulic efficiency of horizontal settlers is the objective of many theoretical, experimental and numerical studies. But currently used models and methods in Ukraine do not allow taking into account geometrical form and various design features. In this paper the numerical model was developed to evaluate the effectiveness of horizontal settler with modified structure. Methodology. Numerical model is based on: 1) equation of viscous fluid dynamics; 2) mass transfer equation. For numerical simulation the finite difference schemes are used. The numerical calculation is carried out on a rectangular grid. For the formation of the computational domain markers are used. Findings. The model allows obtaining the purification process in the settler with different form and different configuration of baffles. Originality. A new approach to investigate the mass transfer process in horizontal settler was proposed. This approach is based on the developed CFD model. The fluid dynamics model was used for the numerical investigation of flows and waste waters purification. To investigate influence of baffles on settler efficiency physical experiment was carried out. Practical value. The developed model has more capacity than the existing models in Ukraine. The developed model allows computing quickly the efficiency of water purification in settlers. The model is not computationally expensive. Calculation time of one variant of the problem takes few minutes. Keywords: CFD model; settlers; mass transfer; water purification; physical experiment

Introduction

Horizontal settlers are essential hydraulic structures which have to be engineered, designed and constructed at all water treatment plants to remove most of suspended solids which enters the intake by polluted water. The bigger the settler, the best the settlement of pollutants, but the expenses are higher. Therefore, improvement of performance and increasing of removal efficiency of horizontal settlers by alternative method is necessary. Finding new and useful methods for calculating and increasing hydraulic efficiency of horizontal settlers

is the objective of many theoretical, experimental and numerical studies [1, 6, 8, 10, 11, 12, 13, 14]. An approach in present paper for increasing horizontal settler performance is to use system of baffles and plates.

To obtain the horizontal settler efficiency the empirical models are used in Ukraine [2, 3]. But these models don't allow calculating horizontal settlers with comprehensive geometrical form and different systems of baffles and plates. That's why it is important to develop CFD models having more capabilities to simulate the process of the

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waste waters treatment in settlers and which do not need much computational time for running and allow taking into account the geometrical form of settlers [1, 8, 9].

Purpose

The objective of this paper consists of two parts. The first part is the experimental investigation of flow in horizontal settlers. The second part is development of the effective computer model (CFD model) which is more effective than the employed in Ukraine models and which can be used for prediction of the horizontal settler efficiency.

Methodology

Experimental investigation. The experiment was carried out in the hydraulics water channel, where the plates were established to form geometry of horizontal settler (Fig. 1). The main objective of the experiment was confirmation that plates influence on increasing of horizontal settler efficiency.

Physical experiments were carried out in horizontal settler (Fig. 1, Fig. 2) with dimensions 1:100 to real settler (height - 2 cm; length - 24 cm; width - 8 cm), which is in operating now at the coal mine «Stepova», Pavlograd region.

Щ к

Fig. 1. Experimental model of horizontal settler without plates:

1 - distribution of the sludge inside the horizontal settler;

2 - distribution of the sludge outside the horizontal settler

Fig. 2. Experimental model of horizontal settler with plates (r-shaped, vertical and horizontal):

1 - distribution of the sludge inside the horizontal settler

in the first zone (in front of the r-shaped plate);

2 - distribution of the sludge inside the horizontal settler

in the second zone (in front of the vertical plate); 3 - distribution of the sludge inside the horizontal settler in the third zone

Froude number was chosen as criterion

V

Fr = — = idem

Fig. 3. Sludge (1) on the bottom of the classical horizontal settler (top view)

Fig. 4. Sludge on the bottom of the modified horizontal settler (top view): 1 - zone before r - shaped plate; 2 - zone before vertical plate; 3 - zone after vertical plate

At Fig. 3, Fig. 4 results of physical experiments are shown. Table 1 presents mass of sludge, which was settled at the bottom of each horizontal settler. As we can see, mass of sludge at the bottom of modified settler is higher, than in classical one.

Table 1

Results of the experimental investigation

Model of settler settling velocity, cm/sec

0,75 0,90 1,05

classical horizontal settler, g 1,1 1,9 4,2

modified horizontal settler, g 1,8 2,5 5,1

2

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CFD model. For numerical modeling of mass transfer process in horizontal settler CFD model was developed. It consists of two models: mass transfer model and model of viscous fluid flow.

Mass transfer model. To simulate the process of water purification in the horizontal settler the transport equation (1) is used [1, 5, 7, 9]:

dC duC d(v- w)C

dt dx

dy

cC =

dC

I M —

dx I x dx

д f dC ^

— M —

dy \ y dy

(1)

д2у d2y dx2 + ~д/

= -ю

[4]:

1

2

дю дю

дю дию ду ю — +-+- 2

дt дx ду Re I дг ду

2

(3)

where C is the concentration; u, v are the velocity components in x, y direction respectively; w - is the settling velocity; a - is the parameter taking into account the process of flocculation and decay; ¡¡x, ¡y are the coefficients of turbulent diffusion in x, y direction respectively; xi, yi are the Cartesian coordinates;

The transport equation is used with the following boundary conditions [1, 5, 8, 9]:

- inlet boundary: Cjnlet = Ce , where C^ is

the known concentration (in the case study of this paper it is dimensionless and equal to Ce = 100 );

- outlet boundary: in numerical model the condition C (i +1, j ) = C ( i, j ) is used. Here, C(i+1,j)

is the concentration at the outlet boundary cell (this boundary condition means that we neglect the process of diffusion at this plane). C (i, j ) is the

concentration in the previous cell.

Initial Condition:

C=0, for t=0 [12].

Fluid Dynamics Model. To simulate the flow in the horizontal settler fluid dynamics model of viscous flow was used.

The governing equations of fluid dynamics model are equation (2) and equation (3).

Equation (2) is Poisson equation for flow function [4]:

where Re = is Reynolds number. v

Boundary and initial conditions of this fluid dynamics model are discussed in [7].

Computation of settling velocity. To compute the settling velocity the following model is used [11, 13]

w = w0(e~K1(C-Cm'n) - e~K2(C-Cm'°))

where Kh K2 are experimental constants [11, 13].

Numerical solver. Numerical integration of governing equations is carried out using rectangular grid. The geometrical form of the horizontal settler in the numerical model is created using porosity technique (markers method) [5, 7].

To solve Poisson equation (2) the following difference scheme of splitting is used [7]:

- at the first step of splitting the difference equation is

At 2

- at the second step of splitting the difference equation is

1 1111

n+— n+— n+— n+— n+—

Vi,j2 - vlj = Vi,j2 - Vi-12j Vi,j2 - Vi,j-21 .

At

Ax'

.2

Ay

2

- at the third step of splitting the difference equation is

3 1 3 3 3 3

n+— n+— n+— n+— n+— n+—

Vt.j4 -Vi,j2 Vi+1J-Vi,j4 , Vi.j4 -Vi,j4 .

At

Ax'

2

Ay

2

- at the last step the difference equation is

3

1 — vj1 -V.,4 ю

у Tij =_j

At 2

(2) where

Equation (3) describes vorticity transfer in fluid

= 4 , j + ю -1,j+1юг'-1, j-1 +ю,, j-

1 ).

Velocity components are calculated using the following expressions_

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= Vj+1 -V.j . v = vi+1,j j

Ay ' Ar

or

Ay

To solve equation (3) the change triangle difference scheme is used [7]. First of all velocity components are written in the following form

u + u u - u

u = u + u = -

v+v v—V

V = V + V = -

du+ю dx

du ~ю дх

dv+ю dy

dv-®

dy

< л+ ю = (+1,j - ui>,-1,j )) ,

< л-ю = (u-+1, jю,+1,j -u,-j®i,j )) , ;Л+ю = (+1® -v+/0,j-1 )), !Л-ю=(- j+1®, j+1 -v-j )).

d 2ю

dx

2 "LxxL-x® =

d 2ю

dy

= (-ю,, j -

L,„, ю - Lyy ю =

1, j Vax2+(

®i+1, j-®i, j )lAx

< )/A

2 yy yy

= (ю, v-1 -ю,

Ji, j-1 VJi,l

)lAy2 + (® j+1 )/аУ2

n+1 n ,j -®i,j

Ai

(л+ + Л- + Л+ + Л- )(юп+^ + (1 Ч)юп )

U

Re

( + L-xx + L+yy + L-y )( + (1 -^)юп )

(E + Аф(

Л х +л- + Л+ + Л- )юп+1 -

п+1

(11)

After that the convective derivatives are approximated using the following expressions:

- Re Ф+х + L-x + L+y + L-y ) =

:( E-At (1 Ч)(л+ +Л- +Л+ +Л- ))юп +

At^-*)(( + L-x + iLyy + L№

+Re (1 -*))■

)юп.

where is parameter.

If ^ = 1/2 we have the difference scheme which has the second order of accuracy in time.

The change triangle difference scheme for equation of vorticity transfer is written as follows

( E

л X +Л+ )-

= ' E-f(л- +л-

At (

2Re(( '

(LXx + L+y ))юп+2 =

)+^Ate (L-x+L )п.

2Re

E + "'Л X + Л )-2R- (( + L-y H®" =

At I

л y> 2 Re

)

The second order derivatives are written as following:

= fe-A(a+ +a;)+-al( + n ))n+2.

^ 2 1 x y' 2Rel ™ yy})

Using these expressions the unknown meaning of vorticity is computed using «running calculation» [7].

To solve the mass conservation equation (1) the implicit difference scheme of splitting is used [1, 7]. At first step the physical splitting of equation (1) is carried out:

d c d uc d( v - w)c

The difference approximation of the equation (3) can be written as follows

d t d x d c d

d x

c c = 0

^ X

d c

d t d x I d x

^ V

d c

d y 1 V d y

At the second step the following approximation of the first order derivatives are used [5]:

d_ dt

_п +1 - _п _j

At

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диС ди+С ди С -=-+-

дт дx дт дуС ду+С ду~С

дy дy дy

+ и + Сп +1 - и + Сп +1 ди С ~ ' +1, j 'j 'j ' -1, j = L+ en +1

x

дx

Ax

ди С „ и'+1.j e"+ï. j -u'j = L- СП+1

д x

Ax

x '

difference equation is:

с k cc

+1 (l7Ck + L-Ck) C^ = 0; A i Л x .V /2 4

3 1

- at the third step k = n + —; с = n + — the dif-

4 2

ference equation is:

Ск - Cc 4 V _

At

д +C v4" . C +1 -v+Cn + *

ду C „ j +1 j 'j i, j -1 = L+ Cn +1

дy

Ay

y

f

M- Cc + M + Ck + M- Cc + M + Ck xx

xx yy yy

д -C v" _ C + 11 -v~.Cn. +1 ^ C „ j +1 j +1 'j 'j = L-Cn +1

ду

Ay

y

д f дC

& lM x «

y^n+1 y^n+1 +1,j - Cij

-M x

ÖC_

дy У y дУ

Ax

CC n+1_cc n+1

u - 2 j = Mxcn+1 + MC1.

a 2 ЛА ЛЛ

Ax

ci, j+1 - Cj

M» Ay2

y2

cn+1 cc n+1

j ^ 2 i,j-1 = MyCn+1 + My+yCn + 1

is:

Сn + к - Cn

"" j +1 (lL+Ck + L+ Ck ) + C Cn = 0:

'j

At

2\ x

y

2 'j

- at the second step к = n + -1; c = n +1 the

2 4

- at the fourth step к = n +1; c = n + — the dif-

The second order derivatives are approximated as following:

ference equation is:

Ск - Cc 4 V _

At

f

M Ck + M + Cc + M Ck + M + Cc

xx

xx

yy

yy

The developed numerical models where coded using FORTRAN.

Findings

The developed computer model was used to compute water purification in the horizontal settler with two vertical plates (Fig. 5)

Here we use notation v=v-w. In these formulas L+, L-, L+, L-, L+, L-, M+, M-, etc. are the notations of the difference operators [7].

After the approximation the solution of the difference equation is splitted in 4 steps [1, 7]:

- at the first step k = 4 the difference equation

Fig. 5. Concentration field in the horizontal settler with two vertical plates

In Fig. 5 the concentration field in the settler is shown. The concentration is presented using «Integer» form of number. Every number shows the percentage of the concentration in the computa-

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tional cell. The maximum concentration is at the inlet cell (it's equal to «99») and the smallest concentration is in the outlet cell. This concentration shows the efficiency of the settler.

The computational time was 5 min to solve the fluid dynamics problem and mass transfer using the developed numerical model.

Originality and practical value

Results of physical experiments are presented in the paper. These results show the peculiarities of sludge sedimentation in horizontal settler with additional plates.

A new approach to investigate the mass transfer process in horizontal settler was proposed. This approach is based on the developed CFD model. The fluid dynamics model was used for the numerical investigation of flows in the settler. These models use the rectangular grid and porosity technique to create the form of the settler in the numerical model. The developed models have more capacity than the existing models in Ukraine. The developed models allow to compute quickly the efficiency of water purification in settlers. The models are not computationally expensive.

Conclusions

The experiments which were carried out in hydraulic laboratory confirm the idea that the additional plates in the horizontal settler can increase the efficiency of water purification.

The CFD model was developed to compute the flow field in horizontal settler. This model is based on the equations of viscous flow. The process of mass transfer in the horizontal settlers is simulated using convection-diffusing equation. Numerical study based on the developed models was carried out. Results illustrate that the developed models can be used to simulate the process of water purification for settlers having comprehensive geometrical form.

LIST OF REFERENCE LINKS

1. Беляев, Н. Н. Математическое моделирование массопереноса в отстойниках систем водоотве-дения / Н. Н. Беляев, Е. К. Нагорная. - Дншро-петровськ : Нова вдеолопя, 2012. - 112 с.

2. Василенко, О. А. Водоввдведення та очистка спчних вод мюта. Курсове i дипломне проек-тування. Приклади та розрахунки : навч. поаб.

/ О. А. Василенко, С. М. Епоян. - Кив ; Харшв : КНУБА : ХНУБА : ТО Ексклюзив, 2012. -540 с.

3. Ласков, Ю. М. Примеры расчетов канализационных сооружений : учеб. пособие для вузов / Ю. М. Ласков, Ю. В. Воронов, В. И. Калицун.

- Москва : Высш. шк., 1981. - 232 с.

4. Лойцянский, Л. Г. Механика жидкости и газа / Л. Г. Лойцянский. - Москва : Наука, 1978. -735 с.

5. Марчук, Г. И. Математическое моделирование в проблеме окружающей среды / Г. И. Марчук.

- Москва : Наука, 1982. - 320 с.

6. Нагорная, Е. К. CFD-модель процесса массопе-реноса в вертикальном отстойнике / Е. К. Нагорная // Наука та прогрес транспорту. - 2013.

- № 1 (43). - С. 39-50. doi: 10.15802/stp20-13/9578.

7. Численное моделирование распространения загрязнения в окружающей среде / М. З. Згуров-ский, В. В. Скопецкий, В. К. Хрущ, Н. Н. Беляев. - Киев : Наук. думка, 1997. - 368 с.

8. Biliaiev, M. M. New codes for the CFD simulation of the water purification in the horizontal settler / M. M. Biliaiev, V. A. Kozachyna // Проблеми водопостачання, водовщведення та пдравлши. - 2014. - Вип. 24. - С. 16-23.

9. Biliaiev, M. M. Numerical determination of horizontal settlers performance / M. M. Bi-liaiev, V. A. Kozachyna // Наука та прогрес транспорту. - 2015. - № 4. - С. 34-43. doi: 10.15802/stp2015/49201.

10. Critical modeling parameters identified for 3D CFD modeling of rectangular final settling tanks for New York City wastewater treatment plants / K. Ramalingam, S. Xanthos, M. Gong [et al.] // Water Science & Technology. - 2012. - Vol. 65. -Iss. 6. - P. 1087-1094. doi: 10.2166/wst.2012.944.

11. Griborio, A. Secondary Clarifier Modeling: A Multi-Process Approach / A. Griborio // Dissertation and Theses (for the degree of Doctor of Philosophy in The Engineering and Applied Sciences Program). - University of New Orleans : USA, 2004. - 440 p.

12. Kleine, D. Finite Element Analysis of Flows in Secondary Settling Tanks / D. Kleine, B. Reddy // Intern. J. for Numerical Methods in Engineering. -2005. - Vol. 64. - Iss. 7. - P. 849-876. doi: 10.1002/nme.1373.

13. Takacs, I. Experiments in Activated Sludge Modelling / I. Takacs // PhD Thesis (for the degree of Doctor (Ph.D.) in Applied Biological Sciences), Ghent University : Belgium, 2008. -267 p.

Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2016, № 4 (64)

14. Tamayol, A. Determination of Settling Tanks // J. of Applied Fluid Mechanics. - 2008. - Vol. 1,

Performance Using an Eulerian-Lagrangian № 1. - P. 43-54.

Method / A. Tamayol, B. Firoozabadi, G. Ahmadi

В. А. КОЗАЧИНА1*

1 Каф. «Пдравлжа та водопостачання», Днiпропетровський нацюнальний ушверситет залiзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дшпро, Украгна, 49010, тел. +38 (056) 373 15 09, ел. пошта kozachynav@yandex.ua, ORCID 0000-0002-6894-5532

ДОСЛ1ДЖЕННЯ ОСАДЖЕННЯ ДОМ1ШОК У ГОРИЗОНТАЛЬНОМУ В1ДСТ1ЙНИКУ

Мета. Осадження домгшок е найбшьш простим та широковживаним методом мехашчно! очистки природних або спчних вод. Цей процес реалiзуегься, зокрема, в горизонтальних вщстшниках, як е одним iз найважливiших елеменпв у технолопчнш схемi очищення води. 1х застосування пов'язано з можливiстю пропуску досить великих обсяпв води. В цих спорудах вода, що очищуеться, рухаеться з невеликою швидюстю, що дозволяе домiшцi осiсти. Пошук нових метода для розрахунку горизонтальних ввдстшнишв та пдвищення !х ефективностi е метою багатьох теоретичних, експериментальних та чисельних дослвджень. Проте моделi та методики, як в даний час використовуються для розв'язання поставлено! задач^ не дозволяють врахувати форму вщстшника i рiзнi конс-труктивнi особливосп. Метою роботи е побудова чисельно! моделi для оцшки ефективностi горизонтального вщстшника з вертикальними пластинами i проведення експерименту для вiзуалiзацii процесу осадження домгшки в горизонтальному ввдстшнику з набором пластин. Методика. Основою моделi е: 1) вихровий рух реально! рвди-ни (рiвняння Нав'е-Стокса); 2) ргвняння масопереносу. Для чисельного розв'язку рiвнянь використовуються р!з-ницевi схеми. Чисельний розрахунок здiйснюеться на прямокутнш рiзницевiй сiтцi. Для формування виду розра-хунково! областi та видшення i! особливостей застосовуеться метод маркування. Результата. Розроблена чисель-на модель дозволяе розрахувати процес освгтлення води в горизонтальних ввдстшниках рiзноi' форми i з рiзними конфцуращями пластин. Наукова новизна. Автором представлено новий тдхщ у дослiдженнi та розрахунку роботи горизонтальних ввдстшниюв рiзноi конфiгурацii. Даний щдх1д грунтуеться на чисельному iнгегруваннi ргвнянь руху рщини i масопереносу домгшки. Практична значимость. Розроблена чисельна модель розрахунку роботи горизонтальних ввдстшнишв пред'являе невелик! вимоги до потужносп комп'ютерно! техники. Час розрахунку одного варiанта завдання становить калька хвилин.

Ключовi слова: чисельна модель; горизонтальний вщстшник; очистка води; ф!зичний експеримент

В. А. КОЗАЧИНА1*

1 Каф. «Гидравлика и водоснабжение», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днипро, Украина, 49010, тел. +38 (056) 373 15 09, эл. почта kozachynav@yandex.ua, ORCID 0000-0002-6894-5532

ИССЛЕДОВАНИЕ ОСАЖДЕНИЯ ПРИМЕСЕЙ В ГОРИЗОНТАЛЬНОМ ОТСТОЙНИКЕ

Цель. Осаждение примесей является наиболее простым и широкоиспользуемым методом механической очистки природных или сточных вод. Этот процесс реализуется, в частности, в горизонтальных отстойниках, которые являются одним из важнейших элементов в технологической схеме очистки воды. Их использование связано с пропуском достаточно большого количества воды. В этих сооружениях очищаемая вода движется с небольшой скоростью, что позволяет примесям осесть. Поиск новых методов для расчета горизонтальных отстойников и повышения эффективности их работы является целью многих теоретических, экспериментальных и численных исследований. Но модели и методики, которые сейчас используются для решения поставленной задачи, не позволяют учесть форму отстойника и различные конструктивные особенности. Целью работы является построение численной модели для оценки эффективности горизонтального отстойника с вертикальными пластинами и проведение эксперимента для визуализации процесса осаждения примесей в горизонтальном отстойнике с набором пластин. Методика. В основу модели положено:

Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 4 (64)

1) вихревое движение реальной жидкости (уравнения Навье-Стокса); 2) уравнение массопереноса. Для численного моделирования моделирующих уравнений используются разностные схемы. Численный расчет осуществляется на прямоугольной разностной сетке. Для формирования вида расчетной области и выделения ее особенностей применяется метод маркирования. Результаты. Разработанная численная модель позволяет рассчитать процесс осветления воды в горизонтальных отстойниках различной формы и с различными конфигурациями пластин. Научная новизна. Автором представлен новый подход в исследовании и расчете работы горизонтальных отстойников различной конфигурации. Данный подход основывается на численном интегрировании уравнений движения жидкости и массопереноса примеси. Практическая ценность. Разработанная численная модель расчета работы горизонтальных отстойников предъявляет небольшие требования к мощности компьютерной техники. Время расчета одного варианта задачи составляет несколько минут.

Ключевые слова: численная модель; горизонтальный отстойник; очистка воды; физический эксперимент

REFERENCES

1. Belyaev N.N., Nagornaya Ye.K. Matematicheskoye modelirovaniye massoperenosa v otstoynikakh sistem vodootvedeniya [Mathematical modeling of mass transfer in settlers of waste water treatment plants]. Dni-propetrovsk, Nova ideolohiya Publ., 2012. 112 p.

2. Vasylenko O.A., Epoian S.M. Vodovidvedennia ta ochystka stichnykh vod mista. Kursove i dyplomne proektu-vannia. Pryklady ta rozrakhunky [Sewage and wastewater treatment. Course and diploma design. Examples and calculations]. Kyiv, Kharkiv, KNUBA, KhNUBA, TO Ekskliuzyv Publ., 2012. 540 p.

3. Laskov Yu.M., Voronov Yu.V., Kalitsun V.I. Primery raschetov kanalizatsionnykh sooruzheniy [Examples of calculation of sewer plants]. Moscow, Vysshaya Shkola Publ., 1981. 232 p.

4. Loytsyanskiy L.G. Mekhanika zhidkosti igaza [Mechanics of liquid and gas]. Moscow, Nauka Publ., 1978. 735 p.

5. Marchuk G.I. Matematicheskoye modelirovaniye v probleme okruzhayushchey sredy [Mathematical modeling in problem of environment]. Moscow, Nauka Publ., 1982. 320 p.

6. Nagornaya Ye.K. CFD-model protsessa massoperenosa v vertikalnom otstoynike [CFD-model of the mass transfer in the vertical settler]. Nauka taprohres transportu - Science and Transport Progress, 2013, no. 1, pp. 39-50. doi: 10.15802/stp20-13/9578.

7. Zgurovskiy M.Z., Skopetskiy V.V., Khrushch V.K., Belyayev N.N. Chislennoye modelirovaniye rasprostraneniya zagryazneniya v okruzhayushchey srede [Numerical modeling pollutant transfer in environment]. Kyiv, Naukova dumka Publ., 1997. 368 p.

8. Biliaiev M.M., Kozachyna V.A. New codes for the CFD simulation of the water purification in the horizontal settler. Problemy vodopostachannya, vodovidvedennya ta hidravliky [The problems of water supply, drainage and hydraulics], 2014, issue 24, pp. 16-23.

9. Biliaiev M.M., Kozachyna V.A. Numerical determination of horizontal settlers performance. Nauka ta prohres transportu - Science and Transport Progress, 2015, no. 5, pp. 34-43. doi: 10.15802/STP2015/49201.

10. Ramalingam K., Xanthos S., Gong M., Fillos J., Beckmann K., Deur A., McCorquodale J. A. Critical modeling modeling parameters identified for 3D CFD modeling of rectangular final settling tanks for New York City wastewater treatment plants. Water Science & Technology, 2012, vol. 65, issue 6, pp. 1087-1094.

11. Griborio A. Secondary Clarifier Modeling: A Multi-Process Approach. Dissertation and Theses. USA, University of New Orleans Publ., 2004. 440 p.

12. Kleine D., Reddy B. Finite Element Analysis of Flows in Secondary Settling Tanks. Intern. Journal for Numerical Methods in Engineering, 2005, vol. 64, issue 7, pp. 849-876. doi: 10.1002/nme.1373.

13. Takacs I. Experiments in Activated Sludge Modelling. PhD Thesis. Belgium, 2010. 267 p.

14. Tamayol A., Firoozabadi B., Ahmadi G. Determination of Settling Tanks Performance Using an Eulerian-Lagrangian Method. Journal of Applied Fluid Mechanics, 2008, vol. 1, no. 1, pp. 43-54.

Prof. S. A. Pichugov, D. Sc. (Phys. and Math.) (Ukraine); Prof. S. Z. Polyshchuk D. Sc. (Tech.) (Ukraine) recommended this article to be published

Accessed: May 9, 2016

Received: July 7, 2016