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ISSN 222Б-3780
технологический аудит
6. Слесаренко, А. П. Моделирование нелинейных тепловых процессов на базе совместного применения метода возмущений, регионально-структурного и вариационного методов [Текст] / А. П. Слесаренко, Т. В. Бутенко // 1нформацшш технологи. Автоматизоваш системи управлшня. Серiя «Математичне моделювання». — 2008. — Вип. 10, № 833. — С. 89-96.
7. Слесаренко, А. П. Идентификация нелинейной нестационарной зависимости мощности источника энергии от температуры на базе вариационно-структурного и проекционных методов [Текст] / А. П. Слесаренко, Н. А. Сафонов // Проблемы машиностроения. — 2010. — Т. 13, № 6. — С. 58-63.
8. Слесаренко, А. П. S-функции в обратных задачах аналитической геометрии и моделировании тепловых процессов [Текст] / А. П. Слесаренко // Восточно-Европейский журнал передовых технологий. — 2011. — № 3/4(51). — С. 41-46.
9. Слесаренко, А. П. S-функции в построении консервативных структур решения геометрических обратных краевых задач [Текст] / А. П. Слесаренко // Восточно-Европейский журнал передовых технологий. — 2012. — № 2/4(56). — С. 60-66.
10. Choi, I. G. Mathematical modeling of radioactive waste glass melter [Electronic resource] / I. G. Choi // Conference: Symposium on nuclear waste management, Cincinnati, OH (United States), 28 Apr — 2 May 1991. — United States: DOE; USDOE, Washington, DC, 1990. — Available at: \www/URL: http:// www.osti.gov/scitech/servlets/purl/5637005.
11. Бребия, К. Методы граничных элементов [Текст] / К. Бре-бия. Ж. Теллес, Л. Вроубел. — М.: Мир, 1987. — 524 с.
РОЗРОБКА МЕТОДОЛОГИ МОДЕЛЮВАННЯ ФОРМОУТВОРЕННЯ ПОВЕРХОНЬ ТА ТЕПЛОВИХ ПРОЦЕС1В ЗА ДОПОМОГОЮ S-ФУНКЦЖ
Розроблена методолопя моделювання формоутворення по-верхонь, описуваних ваговими функщями, побудованими на баз1 ршень зворотних завдань диференщйно! геометри за допомогою ^-функцш. Результати виршень зворотних завдань диферен-щально! геометри використаш при побудов1 консервативних структур виршення завдань теплопровщност1, що точно задо-вольняють граничним умовам третього роду. Структура ршення
враховуе вплив граничних дш лише в граничному поясочку обласп ршення задача
Kлючoвi слова: моделювання теплових процеав, структура ршення, S-функщя, формоутворення поверхонь.
Слесаренко Анатолий Павлович, доктор физико-математических наук, профессор, ведущий научный сотрудник, лауреат Государственной премии Украины, отдел моделирования и идентификации тепловых процессов, Институт проблем машиностроения им. А. Н. Подгорного НАН Украины, Харьков, Украина. Журавлёв Юрий Владимирович, кандидат технических наук, доцент, профессор кафедры автоматизации производственных процессов, Харьковский национальный университет строительства и архитектуры, Украина.
Жиленко Владимир Борисович, инженер, ассистент, заведующий лабораторией электротехники, кафедра автоматизации производственных процессов, Харьковский национальный университет строительства и архитектуры, Украина.
Слесаренко Анатолт Павлович, доктор фiзико-математич-них наук, професор, провГдний науковий ствробтник, лауреат Державноi премп Украти, eiddu моделювання та iдентифi-кацп теплових процеав, 1нститут проблем машинобудування ж. А. М. Пдгорного НАН Украти, Хартв, Украта. Журавльов Юрш Володимирович, кандидат техшчних наук, доцент, професор кафедри автоматизацп будiвничих процеыв, Хартвський нащональний утверситет будiвництва та архi-тектури, Украта.
Жиленко Володимир Борисович, тженер, асистент, завгдувач лабораторп електротехтки, кафедра автоматизацп будiвничих процеыв, Хартвський нащональний утверситет будiвництва та архтектури, Украта.
Slesarenko Anatoliy, A. N. Podgorny Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
Ghuravlev Yuriy, Kharkiv National University of Civil Engineering and Architecture, Ukraine.
Ghilenko Vladimir, Kharkiv National University of Civil Engineering and Architecture, Ukraine
UDK ББ.14.Б83
РОЗРАХУНОК СТАБ1ЛЬНО1 РОБОТИ ВИХРОВОГО РОЗПИЛЮЮЧОГО ПРОТИТОЧНОГО МАСООБМ1ННОГО АПАРАТУ (ВРПМА) В ЗАЛЕЖНОСТ1 В1Д Г1ДРОДИНАМ1ЧНИХ ХАРАКТЕРИСТИК ГАЗОКРАПЕЛЬНОГО ПОТОКУ
У данш роботг наведено методику вибору стшких режимгв роботи вихрового розпилюючого протиточного масообмтного апарату (ВРПМА), яка включаерозрахунок польоту крапель зура-хуванням одноргдностг потоку i гх взаемного впливу один на одного. В результатi теоретичних i практичних долджень вдалося визначити швидкють потоку газу i крапель, ствв^дношення в^дцентрових сил i сил аеродинамiчного опору.
Клпчов1 слова: масоперенос, швидтсть, пристрш, вихор, крапля, апарат, розрахунок.
1. Introduction low-waste and highly-effective technological processes with
minimal losses, full heat recovery, purification of wastewater
Lately, the world faces an acute lack of energy and and gases. Their creation is impossible without devices raw material resources. This causes the need for using new, with high specific indicators. Therefore, developing a new
Абдуллах Джалал Мохаммед, Ал Xайят Мохаммед №дим Касим
TECHNOLOGY AUDiT AND PRODUCTiON RESERVES — № 4/1(18), 2014, © Абдуллах Джалал Мохаммед,
Ал Хайят Мохаммед Надим Касим
с
технологическим аудит
ISSN 222B-37B0
type of mass-exchange equipment and solving the problem intensifying vortex spray countercurrent mass exchange devices (VSCMED) is relevant.
Based on the analysis of intensification methods of mass exchange processes in vortex spray countercurrent mass exchange devices, promising directions for organizing the motion of gas-drop flow were revealed. A physical model of the motion of gas and drop flows in the VSCMED cavity, and the mathematical model of calculation of hydro-dynamic, structural indicators of VSCMED-type devices was developed.
In general, the problem of selecting stable operation modes of VSCMED is very complex, and it's currently facing a number of difficulties. The uniform drop flow, which arises (spring) from the spraying fluid jets in the central region of the vortex chamber and their mutual influence on each other should be considered in order to search for an acceptable solution to resort a number of assumptions, when entering them in the condition of the problem.
Basically, it allows obtaining mathematical solutions and selecting the optimum conditions for a particular type of average and design for the device.
2. Analysis of literature data
The results' analysis of references and theoretical studies [1] allow developing a theoretical substantiated method for calculating the stability of VSCMED operation modes. Basically, this methodology is based on the following mathematical and experimental reasonable assumptions and estimates.
1. Vortex gas flow in a large part of the vortex mass exchange chamber is flat in nature.
2. The size of the drops, which are obtained from the spraying jets of liquid, is essential for the characteristic of the drop flow [2].
This size is determined by the ratio of surface tension forces, which depend on the type of fluid being sprayed, and the forces of aerodynamic influence on the drop from the side of the gas stream. The value of this ratio, and therefore the size of the drops is determined by the Weber criterion [3].
3. The ratio of the loads from the gas and liquid masses is less than one. In this case, density between gas and liquid differs by several orders of magnitude, the liquid volume in the chamber is less than the gas volume in the vortex mass exchange chamber and the distance between the drops in this flow is large. The mutual influence of drops on each other in such a flow can be ignored [4].
4. As a result of spray liquid (drops) flow by its composition close to monodisperse [5].
5. Considering above assumptions this allows to determine the hydrodynamic characteristics of the drop flow to conduct calculations of hydrodynamics of a single drop of the liquid.
6. Liquid drops are involved in a rotary motion from the energy of a vortex gas flow. Gas flow velocity in the circumferential direction is reduced. Decrease in these velocities can be determined by the law of conservation of angular momentum rotary motion. This allows considering the availability of drop flow in the vortex mass exchange chamber of VSCMED and its influence on the hydrodynamics vortex gas flow [6].
3. Problem statement
The purpose of the paper is to determine the influence of hydrodynamics of gas and drops on the efficiency of the VSCMED-type device in different operation modes and as a result to determine optimal and stable mode.
To achieve this goal it is necessary to consider the velocity of the gas flow and liquid drops both separately, and jointly, consider the forces, acting on the drop and track changes in the radius of the vortex chamber.
4. The results of theoretical research and experimental studies
Fig. 1 shows the direction of actions on liquid drops the centrifugal force Fc and aerodynamic effects Fs or the resistance force from the gas stream side. Centrifugal force involves a drop in movement from the center to the periphery of the vortex mass exchange chamber VSCMED.
And the resistance force involves a drop in movement from the periphery of the vortex mass exchange to the center of the chamber.
Task of determining the optimal operation VSCMED and its calculation and creation hydrodynamic conditions in the chamber VSCMED.
Which at any point along the radius of the vortex mass exchange chamber centrifugal forces will prevail over the resistances forces? In this case, will be almost completely absent or will be minimized drop loss, and the counter-movement the gas and liquid phases to ensure high efficiency of processes in mass exchange VSCMED [7].
Fig. 1. Effect on the drop centrifugal force and resistance farces: R — radius of the drop; r — radius (variable value), where is a drop in the vortex chamber of the axis of the chamber; Vji and Vj — circumferential velocities of the gas flow on both sides of the drop; A-A — the axis of the vortex mass exchange chamber
In this case, on liquid drops act two kinds' forces, the opposite direction acting centrifugal force [8]:
rcd| Wj
Fc = ~^Pg-.
6 s r
And, the resistance force: n
Fs Wr2dlpr.
(1)
(2)
One of the problems providing a counter-movement in the mass exchange in the vortex spray countercurrent mass exchange device is an early achievement rotational velocity enough to satisfy the condition [9]:
Fc > Fs.
(3)
ISSN 222B-3780
технологическим аудит
That is necessary to capture the drop in rotation velocity:
(4)
T„ 3PrVTI, Wa,>J--r- Wr.
4pg^K
In the case a uniform gas flow with the height of mass exchange chamber, substituting in (4) the value of (2), we obtain:
W > 3prW Qg W>V 4pgdK 2пгНк '
(5)
Under the third condition along the radius in the chamber will be a regular counter-movement phase. In counter-movement at some radius with equal acting forces resistance force and centrifugal force will cease move to the periphery. Maybe 'suspension' liquid drops [10].
In low rotational velocity liquid drops are captured by the gas stream and go out of the vortex mass exchange chamber, which cause increase in the drop loss and acutely decrease in the efficiency of the vortex mass exchange apparatus. At the input of the vortex mass exchange chamber velocity of gas flow, which for the droplets to the periphery, which provide movement to the periphery, at the wall of mass exchange chamber must be larger than the value:
Wj>
3pr¥ QgR 2 4pgdK 2nHK
1
F g wdFpg ( (r)- Wr (r)) .
Fig. 2. Dependence of the change between centrifugal farce (1) and the resistance force (2) along the radius of the vortex mass exchange chamber for the drops with diameter 100 mkm
To analyze the stability of VSCMED must know the value:
(6)
D = Fc- Fs.
(8)
The above analysis relation of forces acting on a liquid drop along the radius of the vortex mass exchange chamber shows, when calculating the total rotational and radial velocities for regular movement counter flow gas and liquid phases a conditional check should be made (3) over the entire section from the center to the periphery of the chamber, which can be perform by using the equation (6).
The presence of a liquid phase in the vortex gas flow and overlay a condition that is a countercurrent flow phases along the radius of the chamber, has influences the value of the hydraulic resistance of the mass exchange chamber. Liquid drops entrained in rotation movement by the energy of the gas flow. Gas flow velocities decreases, which leads to lower pressure drop between the center and the periphery of the vortex mass exchange chamber and reduction the hydraulic resistance of the working chamber.
Given that the determination of resistance forces should be considering that the determination of resistance forces should be considered values of the velocities drop with relatively of gas flow. Then the expression (2) becomes:
(7)
Fig. 2 shows an example of calculating the change in the resistance force and the centrifugal force for a drop of 100 m in the mass exchange chamber with dimensions R1 = 0,15 m, R2 = 0,05 m and the input velocity in the tangential slits equal to 50 m/s.
Which must take for regime of stable operation positive values all through motion of the drops along the radius of the vortex mass exchange chamber area until the spray drops mass exchange cylindrical walls of the vortex chamber.
5. Conclusions
In this paper, theoretical research, based on the developed mathematical model, which shows the expected results, needing to be more thoroughly tested experimentally was conducted.
In developing the existing model, previous developments on calculating the rate of gas and drop flow in the vortex devices were taken into account.
The next step in the research should be developing a comprehensive calculation of the geometric dimensions of the device depending on the initial conditions specified.
Fig. 3 is an example of a change of this value for the above example.
In this case, knowing the size of the vortex chamber VSCMED, the size of the tangential slits for input gas, capacity VSCMED of gas (steam), the load on the liquid phase can successively identify:
— Radial and rotation velocity gas flow along the
radius of the vortex mass exchange chamber.
— Radial and rotation velocity liquid flow along the
radius of the vortex mass exchange chamber.
The value of the centrifugal force and the resistance force, acting on the drops along the radius of the vortex mass exchange chamber VSCMED.
TECHNOLOGY AUDiT AND PRODUCTiON RESERVES — № 4/1(18], 2014
технологический аудит
ISSN 222Б-37В0
Fig. 3. Dependence of the value of the change for droplets of diameter 100 mm
The ratio between the values the centrifugal forces and resistance forces, and developing recommendations for creating conditions stable and effective work of VSCMED.
References
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2. Sklabinskyy, V. I. The Characteristics of Vortex Spray Coun-tercurrent Mass Exchange Device [Text] / V. I. Sklabinskyy, J. M. Abdullah, N. Mohammed Gasim // Engineering & Technology Journal. — 2011. — № 15, Vol. 29. — P. 3211-3223.
3. Mohammed Abdullah, J. The assessment of the processing chamber radial dimensions of vortex spray countercurrent mass exchange device [Text] / J. M. Mohammed Abdullah, V. I. Sklabinskyy, A. H. Mohammed // First Scientific Conference on Modern Technologies in Oil & Gas Refining, Baghdad. — 2011. — P. 24.
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9. Mokhammed, A. D. Opredelenye optymalnoho razmera ka-pel v VRPMA [Text]: tezysy dokladov / A. D. Mokhammed, N. K. Al Khaiiat Mokhamed // Mezhdunarodnaia nauchno-tekhnycheskaia konferentsyia «Tekhnolohyia-2012», 6-7 aprelia 2012 h. — Р. 171-172.
10. Shyliaev, M. Y. Dvukhtemperaturnaia model teplomassoobmena pry formyrovanyy puzyrei na otverstyiakh hazoraspredelytelnykh reshetok barbotazhnykh apparatov [Text] / M. Y. Shyliaev, A. V. Tolstykh, A. N. Derenok, E. M. Khromova // Teplofyzyka y aeromekhanyka. — 2004. — Tom 11, № 1. — Р. 127-136.
РАСЧЕТ УСТОЙЧИВОЙ РАБОТЫ ВИХРЕВОГО РАСПЫЛИВАЮЩЕГО ПРОТИВОТОЧНОГО МАССООБМЕННОГО АППАРАТА (ВРПМА) В ЗАВИСИМОСТИ ОТ ГИДРОДИНАМИЧЕСКИХ ХАРАКТЕРИСТИК ГАЗОКАПЕЛЬНОГО ПОТОКА
В данной работе приведена методика выбора устойчивых режимов работы вихревого распыливающего противоточного массообменного аппарата (ВРПМА). Она включает расчет полета капель с учетом однородности потока и их взаимного влияния друг на друга. В результате теоретических и практических исследований удалось определить скорость потока газа и капель, соотношение центробежных сил и сил аэродинамического сопротивления.
Ключевые слова: массоперенос, скорость, устройство, вихрь, капля, аппарат, расчет.
Абдуллах Джалал Мохаммед, аспрант, кафедра процеав та anapamie хжгчних i нафтопереробних виробництв, Сумський дер-жавний утверситет, Украта, e-mail: abdullahj783@gmail.com. Ал Хайят Мохаммед Надим Касим, астрант, кафедра процеав та anapamiв хжгчних i нафтопереробних виробництв, Сумський державний утверситет, Украта, e-mail: fench@ukr.net.
Абдуллах Джалал Мохаммед, аспирант, кафедра процессов и аппаратов химических и нефтеперерабатывающих производств, Сумский государственный университет, Украина. Ал Хайят Мохаммед Надим Касим, аспирант, кафедра процессов и аппаратов химических и нефтеперерабатывающих производств, Сумский государственный университет, Украина.
Abdullah Jalal Mohammed, Sumy State University, Ukraine, e-mail: abdullahj783@gmail.com.
Al Hayat Mohammed Nadim Qasim, Sumy State University, Ukraine, e-mail: fench@ukr.net
