Use of information Technoiogies for Modeling the Dependence of Liquid Viscosity on Temperature in a Wide Temperature Range with a Certain Specified Relative Error

The purpose of research is to create a mathematical model that allows us to calculate the dependence of the viscosity coefficient of a liquid on the temperature over a wide temperature range with the necessary relative error.

 Methods. The method of nonlinear search and least squares was used as the basic methods. In the process of studying the dependence of liquid viscosity on temperature, a mathematical model was created, implemented in the form of a semi-empirical formula, which is an exponential-power form of the dependence of liquid viscosity on temperature. Analysis of the structure of the mathematical model showed that the resulting model is nonlinear. The use of only nonlinear search algorithms does not guarantee an unambiguous solution of the problem, which is due to the possible presence of several local extremes of the mathematical model, i e. its different sensitivity to changes in individual desired model parameters. The least squares method, which is usually used to solve linear mathematical models, does not have the disadvantages of non-linear search methods. In this case, there are several mathematical models that have a higher simulation accuracy for their temperature range.

Results. In the course of studying the mathematical model implemented in the form of a semi-empirical formula, a generalized algorithm for solving the problem was developed, combining nonlinear search and the method of least squares. The program in C++, created according to the developed algorithm, showed acceptable efficiency - a fairly high speed and stability of the solution. The sum of squared deviations of the experimental values from the model values was used as an objective function for identification. The results of numerical calculations showed that the relative error of the obtained models depends on the simulated fluid. So for water, where the dependence of viscosity on temperature is close to linear, the deviations of the model values from the experimental ones do not exceed two percent. Numerical simulations also showed that the higher the nonlinearity of the viscosity-temperature dependence (for example, for glycerol), the greater the deviations of some model values from the experimental ones. In such cases, the quality of the model can be improved by dividing the experimental data into two or more temperature segments. In this case, there are several mathematical models, each for its own temperature range, with higher modeling accuracy.

Conclusion. The conducted studies have shown that the presented mathematical model allows us to calculate the change in the viscosity coefficient of a liquid in a wide temperature range with a certain required relative error set in advance.

1. Informatsionnye tekhnologii i vychislitel'nye sistemy: Obrabotka informa-tsii i analiz dannykh. Programmnaya inzheneriya. Matematicheskoe modelirovanie. Prikladnye aspekty informatiki [Information technologies and computing systems: Information processing and data analysis. Software engineering. Mathematical modeling. Applied aspects of computer science]; ed. by S. V. Emelyanov. Moscow, Lenand Publ., 2015. 104 p.

2. Mertens P. Integrirovannaya obrabotka informatsii. Operatsionnye sistemy v promyshlennosti [Integrated information processing. Operating systems in industry]. Moscow, Finance and Statistics Publ., 2007. 424 p.

3. Lymareva O. A., Shchegoleva I. V. Informatsionnye tekhnologii kak sredstvo povysheniya effektivnosti upravleniya sovremennym predpriyatiem [Information technologies as a means of improving the efficiency of modern enterprise management]. Ekonomika i menedzhment innovatsionnykh tekhnologii = Economics and Management of Innovative Technologies, 2013, no. 12, p. 3.

4. Gorin E. A. Informatsionnye tekhnologii i innovatsionnoe razvitie promyshlennosti [Information technologies and innovative development of industry]. Innovatsii = Innovation, 2005, no. 7 (84), pp. 67–68.

5. Bashkirov V. E., Lazuko A. G., Gordeeva O. A. IT – kak sposob povysheniya effektivnosti upravleniya biznes-protsessami v ekonomicheskoi sfere organizatsii [IT – as a way to improve the efficiency of business process management in the economic sphere of organizations]. Ekonomika i menedzhment innovatsionnykh tekhnologii = Economics and Management of Innovative Technologies, 2013, no. 12, рр. 92–94.

6. Vilkov A. S., Vilkov S. L., Taraskin M. M. Informatsionnye tekhnologii v telekommunikatsionnykh sistemakh [Information technologies in telecommunications systems]. Informatsionnye tekhnologii v proektirovanii i proizvodstve = Information Technologies in Design and Production, 2020, no. 4 (180), pp. 57–62.

7. Zhirnov A. E., Lukovkin G. M., Arzhakov M. S., Arzhakov S. A. K voprosu o temperaturnoi i baricheskoi zavisimosti dinamicheskoi vyazkosti n-alkanov [On the question of the temperature and baric dependence of the dynamic viscosity of n-alkanes]. Vestnik Moskovskogo universiteta. Ser. 2, Khimiya = Bulletin of the Moscow University. Ser. 2, Chemistry, 2013, vol. 54, no. 2, рр. 121–126.

8. Boldyrev D. V., Anufriev S. D. Аpproksimatsiya temperaturnoi zavisimosti vyazkosti zhidkosti [Approximation of the temperature dependence of liquid viscosity]. Innovatsionnaya nauka = Innovative Science, 2015, no. 11, рр. 18–21.

9. Kolodezhnov V. N., Koltakov A.V. Analiz protsessa teploperenosa dlya beznapornogo, ustanovivshegosya techeniya zhidkosti v ploskom kanale s uchetom dissipatsii mekhanicheskoi energii i zavisimosti vyazkosti ot temperatury [Analysis of the heat transfer process for a non-pressurized, steady-state fluid flow in a flat channel, taking into account the dissipation of mechanical energy and the dependence of viscosity on temperature]. Teplofizika vysokikh temperatur = High Temperature Thermophysics, 2001, vol. 39, no. 2, рр. 297–303.

10. Bretschneider С. Svoistva gazov i zhidkostei. Inzhenernye metody rascheta [With Properties of gases and liquids. Engineering methods of calculation]. Leningrad, Chemistry Publ., 1966. 535 p.

11. Vogelson R. L., Likhachev E. R. Temperaturnaya zavisimost' vyazkosti [Temperature dependence of viscosity]. Zhurnal tekhnicheskoi fiziki = Journal of Technical Physics, 2001, vol. 71, is. 8, pp. 128–131.

12. Happel J., Brenner G. Gidrodinamika pri malykh chislakh Reinol'dsa [Hydrodynamics at small Reynolds numbers]. Moscow, Mir Publ., 1976. 630 p.

13. Borzenko E. I., Shrager G. R. Vliyanie vyazkoi dissipatsii na temperaturu, vyazkost' i kharakteristiki techeniya pri zapolnenii kanala [Influence of viscous dissipation on temperature, viscosity, and flow characteristics during channel fillin]. Teplofizika i aerodinamika =Thermal Physics and Aerodynamics, 2014, vol. 21. no. 2, рр. 221–231.

14. Landau L. D., Lifshits E. M. Gidrodinamika [Hydrodynamics]. Moscow, Fizmatlit Publ., 2003, vol. 6. 731 p.

15. Pueshel R. L., Verma S., Rohatschek M., Ferry G. V., Boiadjieva N., Hovard S. D. Strawa A. W. Vertical transport of anthropogenic soot aerosol into the middle atmosphere. J. Geophys. Res. D., 2000, vol. 105, no. 3, рр. 3727–3736.

16. Chyi-Yeou Soong, Wen-Ken Li, Chung-Ho, Pei-Yuan Tzeng. Effekt of thermal stress slip on microparticle photophoresis in gaseous media. Optics Letters, 2010, vol. 35, nо. 5, рр. 625–627.

17. Malay N. V., Shchukin E. R., Limanskaya A.V. Reshenie kraevoi zadachi dlya statsionarnoi sistemy uravnenii vyazkoi neizotermicheskoi zhidkosti [Solution of a boundary value problem for a stationary system of equations of a viscous nonisothermal liquid]. Izvestiya vysshikh uchebnykh zavedenii. Matematika = Proceedings of Higher Educational Institutions. Mathematics, 2018, no. 4, рр. 60–69.

18. Malai N. V., Glushak A. V., Shchukin E. R. Solution of a boundary value problem for velocity linearized Navier-Stokes equations in the case of a heated spherical solid particle settling in fluid. Computational Mathematics and Mathematical Physics, 2018, vol. 58, nо. 7, рр. 1132–1141.

19. Malay N. V., Shchukin E. R. Thermophoresis of heated moderately large spherical aerosol particles. Journal of Applied Mechanics and Technical Physics, 2019, vol. 60, nо. 3, рр. 517–525.

20. Horton A. Visual C++. Polnyi kurs [Visual C++. A complete course]. Moscow: Publishing House "I. D. Williams", 2011. 1216 p.

21. Bjarne S. Programmirovanie: printsipy i praktika s ispol'zovaniem S++ [Programming: Principles and practice using C++]. Moscow, Publishing House "I. D. Williams", 2016. 1328 p.

22. Medvedev D. I. Osobennosti ob"ektnoorientirovannogo programmirovaniya na S++/CLI, C# i Java [Features of objectoriented programming in C++ / CLI, C# and Java]. Kazan, Shkola Publ., 2010. 444 p.