Planning of numerical and physical experiment in simulation of technological processes

Technological processes are multifactorial. The choice of the most significant of them for the correct analysis of the object of research is an important task. For such a ranking of factors, researchers usually rely on their own experience or the opinions of specialists in this field, assessing their consistency in terms of mathematical criteria. However, when developing a new process, this approach can not be used. In this case, experimental methods of selecting factors are preferable. But the cost, duration, and sometimes impossibility of using this method is obvious. In this paper we use a different approach. It was considered that thermodynamic modeling is an experiment, but only numerical. Therefore, you can apply it to the method of mathematical design of the experiment, allowing for one calculation to take into account the effect on the objective function of more than a dozen factors. The partial dependencies of the process indices obtained in this case make it possible, without setting up physical experiments, to weed out insignificant factors and leave strong ones, estimating them by the methods of mathematical statistics. Another important advantage of its application is the ability to evaluate the dynamics of changes in phase and elementary products of smelting, process feasibility according to convection and temperature conditions with the control of and mathematical criterion of the acquired data. The method also allows the process to be controlled by all the factors involved, which cannot be met in everyday modeling. For demonstration, this approach was applied during the development of the ferroborone production technology by carbothermic method using local raw materials. Thermodynamic modeling was performed using pre-selected factors. They were also used in physical simulation of the process in a high-temperature furnace. The experiment confirmed significance of the factors, which were chosen theoretically. The use of the planning method also reduced the number of numerical experiments in 25, and physical – in 125 times for predefined data.Using this approach, the authors have made it possible to compare the obtained data with the results of physical experiment to develop measures to approximate practical results to equilibrium ones with the use of strongly acting factor.

1. Andersson J.O., Helander T., Höglund L., Shi P.F., Sundman B. Thermo-Calc and DICTRA, Computational tools for materials science. Calphad. 2002, vol. 26, pp. 273–312.

2. Trusov B.G. Modelirovanie khimicheskikh i fazovykh ravnovesii pri vysokikh temperaturakh (ASTRA.4). Versiya 1.06 [Modeling of chemical and phase saturation at high temperatures (ASTRA4). Version 1.06]. Moscow: MGTU im. Baumana, 1991, 37 p. (In Russ.).

3. Belov G.V. Termodinamicheskoe modelirovanie: metody algoritmy, programmy [Thermodynamic modeling: methods, algorithms, programs]. Moscow: Nauchnyi Mir, 2002, 186 p. (In Russ.).

4. Vatolin N.A., Moiseev G.K., Trusov B.G. Termodinamicheskoe modelirovanie v vysokotemperaturnykh neorganicheskikh sistemakh [Thermodynamic modeling in high-temperature inorganic systems]. Moscow: Metallurgiya, 1994, 352 p. (In Russ.).

5. Moiseev G.K., Vyatkin G.P. Termodinamicheskoe modelirovanie v neorganicheskikh sistemakh [Thermodynamic modeling in inorganic systems]. Chelyabinsk: Izd-vo Yuzhno-Ural’skogo gosudarstvennogo universiteta, 1999, 256 p. (In Russ.).

6. Pupyshev A.A., Muzgin V.N., Vasil’eva N.L. Thermodynamic modeling of atomization of elements in acetylene-air flames, acetylenenitrogen oxide (I), propane (butane) -nitrous oxide (I) and methyl acetylene-air. Zhurnal analiticheskoi khimii. 1992, vol. 47, no. 8, pp. 1278–1292. (In Russ.).

7. Toleuova A.R. Phase analysis of the Al-Cu-Mn-Zr diagram using Thermo-Calc program. Vestnik KazNTU. 2011, no. 3(85), pp. 187–192. (In Russ.).

8. Lovshenko G.F. Thermodynamic modeling of phase transformations during reaction mechanical alloying of copper-based compositions. Vestnik Belorussko­Rossiiskogo universiteta. 2006, no. 1, pp. 130–137. (In Russ.).

9. Devyatkin P.N. Modern possibilities of determining the equilibrium composition of multicomponent chemical systems. Vestnik MGTU. 2010, vol. 13, no. 4/2, pp. 899–901. (In Russ.).

10. Pupyshev A.A., Vasil’eva N.L, Muzgin V.N. Thermodynamic simulations of thermochemical processes in an arc discharge with vaporization of a sample material from the electrode. Journal of Analytical Chemistry. 1997, vol. 52, no. 6, pp. 548–561.

11. Adler Yu.P., Markova E.V., Granovskii Yu.V. Planirovanie eksperimenta pri poiske optimal’nykh uslovii [Planning an experiment when searching for optimal conditions]. Moscow: Nauka, 1976, 269 p. (In Russ.).

12. Belov G.V., Trusov B.G. Termodinamicheskoe modelirovanie khimicheski reagiruyushchikh system [Thermodynamic modeling of chemically reacting systems]. Moscow: MGTU im. N.E. Baumana, 2013, 96 p. (In Russ.).

13. Trusov B.G. TERRA software system for modeling phase and chemical equilibria in plasma chemical systems. In: 3­i mezhdunarodnyi simpozium po teoreticheskoi i prikladnoi plazmokhimii. Sb. materialov [3rd Int. Symposium on Theoretical and Applied Plasma Chemistry. Collection of materials]. Vol. 1. Ivanovo, 2002, pp. 217–220. (In Russ.).

14. Protod’yakonov M.M., Teder R.I. Metodika ratsional’nogo plani rovaniya eksperimentov [Methods of experiments rational planning]. Moscow: Nauka, 1970, 76 p. (In Russ.).

15. Belyaev S.V., Malyshev V.P. Ways of development of the probabilistic-deterministic experiment planning. In: Kompleksnaya pererabotka mineral’nogo syr’ya Kazakhstana. Sostoyanie, problemy, resheniya. V 10­ti t. T. 9: Informatsionnye tekhnologii v mineral’nosyr’evom komplekse [Integrated processing of mineral raw materials in Kazakhstan. Status, problems, solutions. In 10 vols. Vol. 9: Information technologies in the mineral and raw materials complex]. Almaty, 2008, pp. 599-633. (In Russ.).

16. Malyshev V.P. Peculiarities of extrapolation and limitation of the Protodyakonov equation. Vestnik AN KazSSR. 1982, no. 2, pp. 43–47. (In Russ.).

17. Kim V.A., Nadyrbekov A.K., Li A.M., Nurmukhanbetov Zh.U., Kudarinov S.Kh. Technologies for obtaining and using special coke from Shubarkol coals. In: Trudy mezhdunar. Nauchno­prakt. konf., posv. 40­letiyu KarMetI. Nauchno­tekhnicheskii progress v metallurgii: sb. nauch. Tr. KGIU [Proc. of Sci.-Pract. Conf. referred to the 40th Anniversary of KarMetI. Scientific and technical progress in metallurgy: Coll. of Sci. Works of KGIU]. Temirtau, 2000, pp. 156–158. (In Russ.).

18. Nazarov B.K., Akberdin A.A. Thermodynamic analysis of the system B2O3-CaO-SiO2-Al2O3 . Russian Metallurgy (Metally). 1986, no. 6, pp. 61–63. (In Russ.).

19. Isagulov A., Akberdin A., Sultangaziyev R., Kim A., Kulikov V., Isagulova D. Diagram of equilibrium phase composition of Fe–C– Si–B system. Croatia Croatian Metalurgical Society Metalurgija. 2016, no. 3 (55), pp. 305–308.

20. Omes’ Yu.N., Vikhlevshchuk V.A., Kekukh A.V., Borovikov G.F., Gasik M.I., Rudenko V.K. Technology of microalloying of steel with carbothermic ferroboron. Metallurgicheskaya i gornorudnaya promyshlennost’. 1999, no. 4, pp. 40–43. (In Russ.).