Hydrodynamics of motion of spherical particles, drops, and bubbles in non-Newtonian fluid: Numerical methods of investigation

Sokovnin, O. M.; Zagoskina, N. V.; Zagoskin, S. N.

doi:10.1134/s0040579512040173

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…There are different formulas for effec tive viscosity [16][17][18], which are valid in certain α 2 and n ranges. The interfacial interaction force F 12 for non Newtonian liquids obeying the power law rheo logical equation (12) depends on the nonlinearity parameter n, Reynolds number, and α 2 and can be determined using the results of earlier studies [18][19][20].…”

Section: Theoretical Analysismentioning

confidence: 99%

“…The system of equations (1)-(10) under boundary conditions (20) at small Re values is solved in the same way as for the first zone of the thermal boundary layer, using Slezkin's approximate method for the energy conservation equation. The unknowns and appearing in the expressions for the phase veloc ities and temperature are determined from relation ship (16) and from the flow rate conservation condi tion for the continuous phase These relationships make up a system of a first order ordinary differential equation and an algebraic equa tion.…”

Section: Developed Thermal Layer Zonementioning

confidence: 99%

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Heat and mass transfer simulation for thin-film two-phase emulsion flow over heated surfaces

Akhmadiev

Gil’fanov

2015

Theor Found Chem Eng

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The thermohydrodynamic situation in a thin film two phase emulsion flow over heated, arbi trarily shaped surfaces has been investigated with account taken of heat and mass transfer to the environment. The process has been described using conservation equations of multiphase flow mechanics. These equations have been written and simplified in an arbitrary orthogonal coordinate system tied to the flow surface, with the specific features of the flow taken into consideration. The problem has been solved semi analytically, approximately, using the Slezkin method. Numerical calculations have been carried out using the mathemat ical model constructed, and significant results for particular applications of the process have been obtained.

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Section: Theoretical Analysismentioning

confidence: 99%

Section: Developed Thermal Layer Zonementioning

confidence: 99%

Heat and mass transfer simulation for thin-film two-phase emulsion flow over heated surfaces

Akhmadiev

Gil’fanov

2015

Theor Found Chem Eng

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“…Discrepancies between the modeled shapes of drops and those that actually occur are frequently [6][7][8][9] accepted as (sometimes rather significant) differences when comparing the results of theoretical studies of heat and mass transfer and hydrodynamics using such approaches and exper imental data. A determining influence of real shapes of drops, particles, and bubbles was also established for processes of their movement in liquids (see, e.g., [10][11][12][13]). …”

Section: Introductionmentioning

confidence: 99%

Experimental estimation of characteristic times of the existence of liquid drops in the form of a sphere and ellipse upon their movement in a gas environment under the conditions of moderate weber numbers

Волков

Кузнецов

2015

Theor Found Chem Eng

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The experimental procedure has been developed and studies using high speed (10 5 frames per sec ond) system of cross correlation video registration of a change in the shape of drops for the most typical liq uids that are widely used in various chemical technologies (water, kerosene, and ethyl alcohol) have been car ried out. The liquids move with significantly subsonic speeds (up to 5 m/s) in the air environment under the influence of gravitational forces. The initial sizes of drops varied in the range of 3-6 mm. The cyclic nature of the changes in the shapes of drops during movement has been established. Characteristic times of transi tions from one shape of drop to another have been measured. Characteristic times of the existence of drops in the form of spheres and ellipses have been defined. Recommendations about the use of geometrical models of liquid drops for theoretical study of heat and mass transfer and hydrodynamics in the course of their move ment through gas environments under the conditions of moderate Weber numbers have been formulated.

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“…; -величина F однозначно определяется параметром ϕ и геометрическим размером пузыря R пуз . Действительно: (7) а (8) где n -мгновенное количество пузырей в объеме расплава; ∑V пуз -суммарный объем пузырей, м 3 ; ∑F пуз -суммарная поверхность пузырей, м 2 .…”

unclassified

“…Решая совместно (7) и (8) относительно F, получим Автор [5,6] предлагает широкую статистику параметров пузырей при продувке, а в [7,8] представлены данные об изменении газонаполненности расплава по высоте и во время проведения различных технологических операций, которые коррелируют с расчетными данными [1]. Соответственно принимаем величину ϕ = 11,3 %, что согласуется с реальной обстановкой эксперимента.…”

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Mathematical Modeling of Ladle Furnace Thermal Conditions During Gas-Bubble Melt Blowing. Report Iv

Novokreschenov¹,

Shvydkii²,

Zhukov³

et al. 2016

Izv.VUZ. Tsvet. Met.

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Значительное влияние на теплообмен при проведении огневого рафинирования меди в печи-ковше оказывают не только формирование и движение газовых пузырей в расплаве, но и объемное содержание в нем газа в виде пузырей. В представ-ленной математической модели рассмотрено влияние газонаполненности расплава при продувке и температуры газов под крышкой на среднюю температуру рафинируемого расплава. Ключевые слова: пузырь, печь-ковш, рафинирование меди, пора, донная продувка. Mathematical modeling of ladle furnace thermal conditions during gas-bubble melt blowing. Report IVA significant effect on heat transfer during copper fire refining in a ladle furnace is caused not only by forming and motion of gas bubbles in a melt, but also by the volume content of gas bubbles. The presented mathematical model analyzes the effect of melt gas fullness during blowing and gas temperature under the cover on an average temperature of the melt being refined. Key words: bubble, ladle furnace, copper refining, gas bubble, bottom blowing. Novokreschenov S.A. -Cand. Sci. (Tech.), prof., Department of economies and managements at the metallurgical enterprises, Ural Federal Univercity (UFU) (620002, Russia, Yekaterinburg, Mira str., 19

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Hydrodynamics of motion of spherical particles, drops, and bubbles in non-Newtonian fluid: Numerical methods of investigation

Cited by 8 publications

References 22 publications

Heat and mass transfer simulation for thin-film two-phase emulsion flow over heated surfaces

Heat and mass transfer simulation for thin-film two-phase emulsion flow over heated surfaces

Experimental estimation of characteristic times of the existence of liquid drops in the form of a sphere and ellipse upon their movement in a gas environment under the conditions of moderate weber numbers

Mathematical Modeling of Ladle Furnace Thermal Conditions During Gas-Bubble Melt Blowing. Report Iv

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