The article is devoted to the mathematical simulation of interconnected physical processes on sintering machine during agglomeration of iron ore pellets. The mathematical model uses system of partial differential equations and takes into account velocity of a horizontal movement of the layer and a vertical velocity of the air movement through the layer as well as phase transition and chemical reactions of pellet components. The purpose of the simulation is getting the time dependency of sinter and gas temperature and concentration of their components, distributed by length and height of the layer, to find rational parameters of the process further. A numerical experiment shows that the temperature front, which is lower in the layer cross-section, has a larger gradient in comparison with the upper front, where the finished agglomerate is cooled, because the water takes much energy to evaporate. The obtained results are consistent with the literature data.

Анотація наукової статті з будівництва та архітектури, автор наукової роботи - K. S. Krasnikov


МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ Тепломассоперенос в агломераційному ШАРІ

Стаття присвячена математичному моделюванню взаємопов'язаних фізичних процесів на агломераційної машині при спіканні гранул залізної руди. Математична модель використовує систему диференціальних рівнянь в приватних похідних і враховує швидкість горизонтального руху шару і вертикальну швидкість руху повітря через шар, а також фазовий перехід і хімічні реакції компонентів гранул. Мета моделювання полягає в отриманні тимчасової залежності температури агломерату, газу та концентрацію їх компонентів, розподілених по довжині і висоті шару, для пошуку раціональних параметрів даного процесу. Чисельний експеримент показав, що температурний фронт, який розташований нижче в поперечному перерізі, має більший градієнт в порівнянні з верхнім фронтом, де готовий агломерат охолоджується, оскільки вода вимагає значної енергії для випаровування. Отримані результати відповідають літературним даним.


Область наук:
  • Будівництво та архітектура
  • Рік видавництва: 2018
    Журнал: Вісник Херсонського національного технічного університету

    Наукова стаття на тему 'MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN SINTER LAYER'

    Текст наукової роботи на тему «MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN SINTER LAYER»

    ?UDC 669.1: 004.942: [536 + 519.63]

    K.S. KRASNIKOV

    Dniprovsky State Technical University, Kamianske

    MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER

    IN SINTER LAYER

    The article is devoted to the mathematical simulation of interconnected physical processes on sintering machine during agglomeration of iron ore pellets. The mathematical model uses system of partial differential equations and takes into account velocity of a horizontal movement of the layer and a vertical velocity of the air movement through the layer as well as phase transition and chemical reactions of pellet components. The purpose of the simulation is getting the time dependency of sinter and gas temperature and concentration of their components, distributed by length and height of the layer, to find rational parameters of the process further. A numerical experiment shows that the temperature front, which is lower in the layer cross-section, has a larger gradient in comparison with the upper front, where the finished agglomerate is cooled, because the water takes much energy to evaporate. The obtained results are consistent with the literature data.

    Keywords: mathematical model, ore sintering, thermodynamics, mass transfer, system of partial differential equations, explicit scheme.

    К.С. КРАСИКОВ

    Дншровській державний техшчній ушверсітет, м. Кам'янське

    Математичне моделювання тепломасопереносу В АГЛОМЕРАЦ1ЙНОМУ ШАР1

    Стаття присвячено математичне моделювання взаємопов 'язаних фгзічніх проце ^ в на агломерацшнш машин при спiканнi гранул зал1зног руди. Агломерацши машини достаточно розповсюджено Використовують на металургшніх комбiнат, что дае тдставі для економiчний ефект вiд оптімiзацii процесса. Агломерацшній куля розглядаеться як суцшьне середовище, Пожалуйста складаеться з ргзніх субстанцш, концентрацiя якіх змiнюеться у ходi фiзіко-хiмiчніх реакцш. Геометрiя кулі дозволяе використовуват Декартову систему координат. Математична модель вікорістовуе систему діференцiальніх рiвнянь у Частинами похiдніх i враховуе швідюсть горизонтального руху кулі та вертикальні швідюсть руху повiтря через шар, а такоже фазовий перехiд i хiмiчнi реакці компонентiв гранул. Мета моделювання полягае в здобуті часово! залежностi температури агломерату, газу та концентрацт Їх компонентiв, розподтеніх за Довжина i висота кулі, для поиска рацюнальніх параметрiв даного процесса. Рiвняння розв 'язуються чисельного, розбіваючі годин вкь кроками, на кожному з якіх стан системи визначаеться через попереднш. Чисельного експеримент показав, что Температурний фронт, Який розташованій нижчих в поперечному перерiзi, травні бшьшій градiент у порiвняннi з верхтм фронтом, де готов агломерат охолоджуеться, осюлькі вода потребуе значний! енергії для випаровуваності, что суттево вплівае на переб ^ процесса. Основним Джерелом тепловоi енергії е кокс, Який мктіться в шіхтi. ШД годину его Гортні високотемпературна фронт рухаеться вниз i по Довжина кулі, тдпалюючі новi частинки коксу. Шсля спкання агломерат поступово охолоджуеться до необхiдноi температури. Отримала результати вiдповiдають лтературном данім, но для бшьш Краще Наближення у подалі треба Було б окремо враховуваті Втрата тепла вiд стток агломерацшноi машини, додаючі вiдмiннiсть температури i концентрацт Речовини по ширин кулі шихти, таким чином модель стані трівімiрною у просторi.

    Ключовi слова: математична модель, агломерацшна машина, спкання руди, термодінамжа, масопереносу, діференщальн рiвняння у Частинами похiдніх, очевидна схема чисельного розв'язання язку.

    К.С. КРАСНІКОВ

    Дніпровський державний технічний університет, м Кам'янське

    МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ Тепломассоперенос в агломераційному ШАРІ

    Стаття присвячена математичному моделюванню взаємопов'язаних фізичних процесів на агломераційної машині при спіканні гранул залізної руди. Математична модель використовує систему диференціальних рівнянь в приватних похідних і враховує швидкість горизонтального

    руху шару і вертикальну швидкість руху повітря через шар, а також фазовий перехід і хімічні реакції компонентів гранул. Мета моделювання полягає в отриманні тимчасової залежності температури агломерату, газу та концентрацію їх компонентів, розподілених по довжині і висоті шару, для пошуку раціональних параметрів даного процесу. Чисельний експеримент показав, що температурний фронт, який розташований нижче в поперечному перерізі, має більший градієнт в порівнянні з верхнім фронтом, де готовий агломерат охолоджується, оскільки вода вимагає значної енергії для випаровування. Отримані результати відповідають літературним даним.

    Ключові слова: математична модель, агломераційна машина, спікання руди, термодинаміка, масоперенос, диференціальні рівняння в приватних похідних, явна схема чисельного рішення.

    Problem definition

    Nowadays more than a half of steel production uses the sinter as resource for loading of blast furnace. Lengthy agglomeration machine, which is used for sinter production, firstly heats the layer of pellets using gas-burners and then cools ready agglomerate. From the practical point of view the scientists is interested in mathematical modeling of this process to determine the state of the sinter inside the layer in a various points of time and to search for the rational parameters of the process saving resources eventually.

    Related publications

    Authors of work [1] presented: a mathematical model of agglomeration process that described by system of a differential equations including coke's average diameter decreasing and sinter temperature changing; drawings with visualization of calculation results; operation parameters of the agglomachine, which can be used in testing of a mathematical model. Some of multipliers in equations do not depend on temperature and the values ​​of the terms in the equations for the heat is not described well, so model can be improved.

    In paper [2] the authors performed a detailed analysis of the computational results based on the mathematical model developed in [1] with plots of the temperature, the amount of melt, concentration of FeO and gases (O2 and CO2) along the length and height of the sinter layer. A number of recommendations are given to increase the specific productivity of sinter plants.

    In work [3], a detailed review of the mathematical models of the sintering is made. The authors point out the need to improve considered models taking into account such important parameters as the layer height, the moisture of the sinter, its granulometric composition, carbon concentration, etc., which will allow technologists to consider a wider range of situations encountered in practice.

    The authors of [4] offer a detailed description of the sintering process on the agglomeration machine, starting with the ignition stage, paying attention to temperature, moisture concentration in the layer, rarefaction in vacuum chambers and the sinter cooling.

    At the conference ITMM-2017 [5] there was reported on existing mathematical models of agglomeration and was noted the need to take into account the speed of air movement with oxygen and water vapor through the sinter layer in the mathematical model.

    Author of the works [6, 7] considers convection and diffusion of chemical substances, momentum, and energy in three dimensions taking into account phase transitions in partial differential equations. They are solved for steady state. Also it is needed unsteady solution to fully understand of the sinter state changes depending on time.

    Agglomeration process includes air motion through sinter layer with speed, which depends on the sinter permeability. In work [8] author analyzes this permeability in case of sinter components melting considering basicity. Author of the work [9] proposes one-dimensional unsteady mathematical model of mass and heat transport in fixed sinter layer considering evaporation and condensation of moisture.

    Article [10] devoted to mathematical description of heat transfer coefficient taking into account set of chemical reactions of the sintering process.

    Authors of the works [11, 12] predict temperature inside sinter layer depending on time taking into account coke combustion rate. Also details of coke combustion are presented in [13] considering homogeneous, heterogeneous reactions and the heat exchange between solid and gas phases.

    In thesis [14] among other things the author notes importance of sufficient temperature level for sintering process: low temperature is not enough; very high temperature causes excessive melting of layer and decreasing of its permeability.

    Author of works [15, 16] models heat process inside sinter layer using finite volume method taking into account carbonates and hydrates dissociation. It is presented the plot of air speed and total amount of heat depending on layer height.

    In works [17, 18] authors describes details of agglomeration process including water phase transition, concentration change of air and sinter components, coke combustion, sinter melting and crystallization. Authors presented figures which show result of experiments.

    Articles [19, 20] devoted to peculiarities of gas circulation involved in sintering process. It is presented and compared temperature distributions for two technologies - FGRS and CS.

    Goal of research

    It is necessary to calculate the temperature distribution along the height and length of the layer, taking into account the change in the concentrations of the gas and the layer during the physicochemical reactions of carbon burning, iron oxidation, decomposition of calcium carbonate, evaporation and condensation of water, melting and crystallization of the sinter.

    Presentation of the research material

    It is assumed that the layer retains volume, and the sinter is a continuous medium. The geometry of a sinter layer, which has length about 30 meters and height - 0.5 meters, allows us to use Cartesian system of coordinates. The mathematical model includes a system of differential equations and additionally takes into account the influence of chemical reactions on the temperature distribution in the layer. Below the equations are supplemented by the initial and boundary conditions.

    The change in the oxygen concentration in the air, which vertically passes through the layer:

    dMO2 dMO2

    + Vz-T2 = ~ mrO2, (1)

    dt z dz

    The change in the FeO concentration in the layer:

    dt

    The change in the carbon concentration in the layer:

    dM ™ = -mrFeo, (2)

    dM,

    dt

    The change in the water's vapor concentration in the air:

    C = -mrc, (3)

    dMH2Og dMH2Og

    -+ Vz-Z- = mriH2O - mrkH2O > (4)

    dt z dz

    The change in the water concentration in the layer:

    dt

    The change in the CaCO3 concentration in the layer:

    dMCaCO3

    dMH

    = MrkH2O - mriH2O> (5)

    dt

    The change in the air temperature:

    = -MrCaCO3 '(6)

    dT dT

    -T + Vz = -Qob, (7)

    dt dz

    The change in the sinter temperature:

    - aATs = Qtob + QgC + QgFeO - QdCaCO3 - QiH2O + QkH2O - Qpl + Qkr, (8)

    For the equations the boundary condition on the layer bottom, which is exit for the air, is the free passing of flux, so:

    T

    Tgas

    bottom

    - 0, Mo2

    bottom - 0 'MH2Og

    = 0

    bottom

    For the layer top the boundary condition depends on the state of the entering air, which is heated by gas-burners only at the beginning of machine and is cooled at the defined part of remaining top surface of the layer:

    T

    Tgas

    I1200, if d < 2m

    top - \ 50, if d > 2m 'Mo2

    - 0.3

    top

    MH2Og

    - 0.01

    top

    In the above equations: a - coefficient of thermal conductivity, W / m / K; mrC - amount of reacted carbon, kg / m3 / s; mrFeO - amount of reacted FeO, kg / m3 / s; mrO2 - amount of reacted oxygen, kg / m3 / s; mriH2o and mrkH2O - amount of evaporated and condensed water respectively, kg / m3 / s; mrCaCO3 - amount of dissoluted carbonate, kg / m3 / s; Qtob - change in the temperature of the sinter due to heat transfer from the air to the sinter, K / s; QgC and QgFeO - change in the temperature of the sinter from combustion of carbon and FeO respectively, K / s; QdCaCO3 - change in the sinter temperature from CaCO3 dissolution, K / s; QiH2O and QkH2O - contributions to the sinter temperature from evaporation and condensation of water K / s; Qpl and Qkr - contributions to the sinter temperature from the melting and crystallization of the its components, K / s; Tgas - air temperature, K; Ts

    - sinter temperature, K; vz - vertical speed of air passing through sinter, which depends on its length, m / s; FeO

    - iron oxide; C - carbon; H2Og - water vapor; O2 - oxygen; CaCO3 - calcium carbonate; z - axis with the direction from the surface of the layer downward.

    The calculation was done in the computer program Octave. The following initial data were used for the calculation: layer height - 0.5 m; the length of the layer - 30 m; length of preheating part - 5 m; the average velocity of vertical gas flow through the layer is from 0.1 to 0.3 m / s, depending on the path traveled; the speed of the tape, which carries the layer, is 2.9 cm / s; the initial temperature of the layer and gas is 30 ° C (below the burners the gas temperature is 1200 ° C); the ignition temperature of the coke is 700 ° C; the number of steps for the computational grid along the length and height is 30 and 20 respectively; step by time - a quarter of the step along the height of the layer.

    Results and conclusions

    Figures (1 - 7) show the results of the numerical experiment. Legend in the figures: Tg - gas temperature; Ts - the temperature of the sinter; T (C + O2) - burning start temperature of the coke; O2 - the oxygen in the air, which comes from the surface of the layer; C - carbon in the layer (burns with the release of heat); FeO - iron oxide in the layer (under the action of O2 it is oxidized to Fe2O3 with the release of heat); CaCO3 - calcium carbonate in the layer (decomposes with absorption of heat); H2O is the water in the layer (evaporates with absorption of heat and upon condensation it condenses with release of heat in the lower layers of the sinter); H2Og - water in the air; the x-axis is the height of the layer in centimeters, where 0 is the surface of the layer; t and d in the titles of the figures - the time and distance traveled along the length of the sinter tape.

    In Fig. 2, one can see the decrease in the oxygen concentration during the combustion of coke. It is worth noting that in this paper, a decrease in the rate of all physicochemical reactions in a linear dependence on the concentration of reagents is assumed.

    In Fig. 2 and Fig. 3 shows the gradual accumulation of water in the lower layers of the sinter.

    This is because in this process the air moving down the layer acts as a carrier of steam.

    Fig. 1. State of the gas and sinter at the beginning of heating by gas-burners Ore sintering model (t = 35.1s, d = 1.01m)

    1600

    0:

    4-1

    2 --t- »-c

    01 u c

    0 u

    tf o (J

    ff 13 4 "

    ro

    01 Q_

    E

    70C

    50C

    -Tg

    -Ts

    * T (C + 0)

    +0 2

    / © c

    / * FeO

    F ^ CaCO

    BH dH j 0

    * \ V * * * * * * * * * * * * * * * z Oq

    2

    \ \ T - - V

    - -B- -B- |e- B-B-E -& -B- -H- -R- -R- B-B-B-B -f

    0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48

    height, sm (10 sm / s->) Fig. 2. Start of coke combustion reaction in the sinter (T>700 ° C)

    Fig. 3. Temperature increases to 1 300 ° C in sinter when coke is burned out at a depth of 6 sm

    In Fig. 4 the state of a layer's part is shown in the transition to the cooling region of the finished agglomerate, where it is cooled by air with a temperature of about 50 ° C.

    Fig. 4. Transition to cooling area

    In Fig. 5-6 with increasing air speed from 0.2 m / s to 0.3 m / s through the layer, you can see a more distinct

    difference between the temperature of the layer and the air temperature. Accordingly, the cooling rate of the layer also increases.

    Fig. 5. Speed ​​of air passing through sinter is increased to 0.2 m / s

    Fig. 6. Increasing of air speed to 0.3 m / s improves cooling further

    In Fig. 7, the external isolines correspond to low temperatures, and the internal ones correspond to the temperature around 1400 ° C.

    Fig. 7. Distribution of sinter temperature by length and height of layer

    The area of ​​coke ignition beneath the burners is clearly visible as well as the expansion of the high temperature region as the layer moves along tape.

    An optimization of the metallurgical process is needed to increase its effectiveness. In this work, when carrying out numerical studies using a computer program based on the description of the agglomeration process [1] and the above mathematical model, the temperature distribution in the layer is determined as a function of the gas velocity as it moves vertically through the layer, taking into account the change in the composition of the sinter during the accompanying physical and chemical reactions. The obtained results are consistent with the results and description of the agglomeration process of other researchers [1-2].

    The computer model can be adjusted and improved, taking into account other reactions and features of the agglomeration process. For example, in the future it is possible to take into account the heat losses from the walls of the pallets in which the sinter is located, thereby proceeding to a three-dimensional statement of the sintering problem, additionally taking into account the anisotropy over the width of the layer. It is also possible to take into account the features of the lower layer of the sinter (the so-called "bed"), which is usually quite different from the upper layers.

    References

    1. Frolov Y.A., Polotskii L.I. Three-dimensional mathematical (dynamic) model of the sintering process. Part I // Metallurgist. 2015. Vol. 58, Issue 11-12, pp. 1071-1079.

    2. Frolov Y.A., Polotskii L.I. Three-dimensional mathematical (dynamic) model of the sintering process. Part II // Metallurgist. 2015. Vol. 59, Issue 1-2, pp. 9-15.

    3. Ganin D.R., Druzhkov V.G., Panychev A.A., Shapovalov A.N. Review and analysis of mathematical models for calculating the performance of sintering machines // The theory and process engineering of metallurgical production. 2014. Vol. 15, Issue 2, pp. 20-25. (In Russian)

    4. Panychev A.A., Nikonova A.P. Use of mathematical models to optimize process parameters in the sintering of Mikhailovskii and Lebedinskii concentrates // Metallurgist. 2008. Vol. 52, Issue 9-10, pp. 544-551.

    5. Krasnikov K.S., Shuvaev S.P. Computer modeling of influence of sinter composition and average speed of air on temperature distribution in layer // Proceedings of the International Conference on Information Technology in Metallurgy and Machine building. Dnipro, March 28-30 2017, p. 39. (in Russian)

    6. Castro J.A. Modeling sintering process of iron ore, in: V.I. Shatokha (Ed.), Sintering - Methods and Products, InTech 2012, pp. 23-46. ISBN: 978-953-51-0371-4, DOI 10.13140 / RG.2.1.4666.7288

    7. Castro J.A., Sazaki Y., Yagi J. Three dimensional mathematical model of the iron ore sintering process based on multiphase theory // Materials Research. 2012. Vol. 15, Issue 6, pp. 848-858.

    8. Shatokha V.I., Velychko O.G. Study of softening and melting behaviour of iron ore sinter and pellets // High Temperature Materials and Processes. 2012. Vol. 31, pp. 215-220. DOI: 10.1515 / htmp-2012-0027

    9. Suman S., Giri B.K., Roy G.G. Mathematical modelling of iron ore sintering process using genetic algorithm: effect of moisture evaporation and condensation on the temperature profile // Computer Methods in Materials Science. 2013. Vol. 1, pp. 141-146.

    10. Nalevankova J., Varga A., Kukurugyova M., Dzurnak R. Heat transfer during the sintering process of iron ore // Proceedings of Conference ISEC. 2015. July 20-24.

    11. Muller J., Vries T.L., Dippenaar B.A., Vreugdenburg J.C. A finite difference model of the iron ore sinter process // Journal of the Southern African Institute of Mining and Metallurgy. 2015. Vol. 115, Issue 5, pp. 409-417.

    12. Muller J. // Journal of the Southern African Institute of Mining and Metallurgy, [Online]. URL: http://www.saimm.co.za/Conferences/PyroModelling/061-Muller.pdf

    13. Straka R., Telejk T. 1D mathematical model of coke combustion // International Journal of Applied Mathematics. 2015. Vol. 45, Issue 3, pp. 245-248.

    14. Egorova E.G. Operational control of the process of iron ore sinter production: thesis of Candidate of Technical sciences, St. Petersburg State Technological Institute (technical university), 2016, 133 p.

    15. Mnyh A.S. The study of the amount of heat release in the sinter charge layer // Eastern-European Journal of Enterprise Technologies. 2014. Vol. 6, Issue 5, pp. 14-18.

    16. Mnyh A.S. The improving of energy efficiency of thermal processes of bulk materials clotting with segregation intensification in stationary layers: thesis of Doctor of Technical sciences, Odessa National Polytechnic University, 2016, 355 p.

    17. Korotich V.I., Frolov Yu.A., Bezdezhskii G.N. Agglomeration of Ore-Bearing Materials, UGTU-UPI (Ural State Technical University - Ural Polytechnic Institute), Ekaterinburg, 2003 400 p. (In Russian) ISBN 5-321-00336-X

    18. Eliseev A.A. Research of heat and mass transfer processes during sinter agglomeration, Cherepovets state university, 2006, 24 p. (In Russian)

    19. Wang G., Wen Z., Lou G., Dou R., Li X., Liu X., Su F. Mathematical modeling and combustion characteristic evaluation of a flue gas recirculation iron ore sintering process // International Journal of Heat and Mass Transfer. 2016. Vol. 97, pp 964-974.

    DOI: 10.1016 / j.ijheatmasstransfer.2016.02.087

    20. Fan X.-H., Yu Z.-Y., Gan M., Li W.-Q., Ji Z. Influence of O2 Content in Circulating Flue Gas on Iron Ore Sintering // Journal of Iron and Steel Research International. 2013. Vol. 20, Issue 6, pp 1-6.

    DOI: 10.1016 / S1006-706X (13) 60103-X


    Ключові слова: mathematical model / ore sintering / thermodynamics / mass transfer / system of partial differential equations / explicit scheme. / математична модель / агломераційна машина / спікання руди / термодинаміка / массоперенос / диференціальні рівняння в приватних похідних / явна схема чисельного рішення.

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