DOI: https://doi.org/10.15587/1729-4061.2016.74826

### Development of mathematical models and the calculations of elements of convective heat transfer systems

Yosyf Mysak, Igor Galyanchuk, Marta Kuznetsova

#### Abstract

Despite the considerable number of papers on elaborating the methods of mathematical modeling of thermal power systems, at present little attention is paid to the development of methods of analysis of the influence of different factors on the performance indicators of work of an energy unit. In this article we substantiated principles of selection and mathematical modeling of the simplest elements of heat transfer systems, which clearly reflect the essence of processes in these systems and are convenient in terms of their mathematical modeling. The use of selection and mathematical description of elementary heat exchangers, mixers and dividers of flows may describe a variety of heat transfer system of any energy plants.

These methods allow comparing various modes of operation of the equipment, its design peculiarities and their possible combination significantly faster and economically efficient. A proposed mathematical model of the elements of HTS in the form of a temperature characteristic provides unification of models of all elements, subsystems and HTS as a whole, as well as the clarity and convenience of the description of connections of elements. The calculations of heat transfer systems may be efficiently used for analysis of the work and different types of design and checking calculations of heat transfer convective surfaces. The use of generalized dimensionless parameters makes it possible to perform calculations based on different parameters of the initial information and to improve efficiency of analysis of the work of heat exchangers.

#### Keywords

mathematical model; heat transfer system; thermal energy unit; heat carrier; heat exchanger; thermal energy parameters

#### Full Text:

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#### References

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#### GOST Style Citations

Rychkov, A. D. Modelyrovanye v teploenerhetyke [Text] / A. D. Rychkov // Vychyslytelnye tekhnolohyy. – 2002. – Vol. 7, Issue 2. – P. 94–105.

Baskar, P. A review of mathematical models for performance analysis of hybrid solar photovoltaic – thermal (PV/T) air heating systems [Text] / P. Baskar, G. Edison // Advanced Materials Research. – 2013. – Vol. 768. – Р. 29–39. doi: 10.4028/www.scientific.net/amr.768.29

Bhandari, B. Mathematical modeling of hybrid renewable energy system: a review on small hydro-solar-wind power generation [Text] / B. Bhandari, S. R. Poudel, K.-T. Lee, S.-H. Ahn // International journal of precision engineering and manufacturing-green technology. – 2014. – Vol. 1, Issue 2. – Р. 157–173. doi: 10.1007/s40684-014-0021-4

Verma, P. Review of mathematical modeling on latent heat thermal energy storage systems using phase-change material [Text] / P. Verma, S. K. Singal // Renewable and Sustainable Energy Reviews. – 2008. – Vol. 12, Issue 4. – Р. 999–1031. doi: 10.1016/j.rser.2006.11.002

Zhang, Q. Development of model and model-predictive control of an MEA-based postcombustion CO2 capture process [Text] / Q. Zhang, R. Turton, D. Bhattacharyya // Industrial & Engineering Chemistry Research. – 2016. – Vol. 55, Issue 5. – Р. 1292–1308. doi: 10.1021/acs.iecr.5b02243

Huilin, L. A coal ombustion model for circulating fluidized bed boilers [Text] / L. Huilin, Z. Guangbo, B. Rushan, C. Yongjin, D. Gidaspow // Fuel. – 2000. – Vol. 79, Issue 2. – P. 165–172. doi: 10.1016/s0016-2361(99)00139-8

Wang, J. Eulerian simulation of heterogeneous gas–solidflowsin CFB risers: EMMS–based sub–grid scale model with a revised cluster description [Text] / J. Wang, W. Ge, J. Li //  Chemical Engineering Science. – 2008. – Vol. 63, Issue 6. – P. 553–571. doi: 10.1016/j.ces.2007.11.023

Halashov, N. N. Avtomatyzyrovannyi raschet normatyvnykh y faktycheskykh pokazatelei TETs [Text] / N. N. Halashov, S. V. Metnev // Elektrycheskye stantsyy. – 2008. – Vol. 11. – P. 26–28.

Dulau, M. Mathematical modelling and simulation of the behaviour of the steam turbine [Text] / M. Dulau, D. Bica // Procedia Technology. – 2014. – Vol. 12. – P. 723–729. doi: 10.1016/j.protcy.2013.12.555

Guha, P. Mathematical modeling of spiral heat exchanger [Text] / P. Guha, V. Unde // International journal of engineering research. – 2014. – Vol. 3, Issue 4. – Р. 226–229. doi: 10.17950/ijer/v3s4/409

Srinivas, T. Study of a deaerator location in triple-pressure reheat combined power cycle [Text] / T. Srinivas // Energy. – 2009. – Vol. 34, Issue 9. – P. 1364–1371. doi: 10.1016/j.energy.2009.05.034

Mathematical modelling and simulation of steam power plant [Text]. – International Conference on Electrical, Electronics, Signals, Communication and Optimization (EESCO), 2015. – P. 1–5.

Kowalczyk, C. Mathematical model of combined heat and power plant using GateCycleTM software [Text] / C. Kowalczyk, R. M. Rolf, B. Kowalczyk, K. Badyda // Journal of Power Technologies. – 2015. – Vol. 95, Issue 3. – Р. 183–191.

Popyryn, L. S. Matematycheskoe modelyrovanye y optymyzatsyia teploenerhetycheskykh ustanovok [Text] / L. S. Popyryn. – Moscow: Enerhyia, 1978. – 416 p.

Hyl, A. V. Prymenenye chyslennoho modelyrovanyia topochnykh protsessov dlia praktyky perevoda kotlov na neproektnoe toplyvo [Text] / A. V. Hyl, A. V. Starchenko, A. S. Zavoryn. – Tomsk: STT, 2011. – 184 p.

Zeng, Y. A review on optimization modeling of energy systems planning and ghg emission mitigation under uncertainty [Text] / Y. Zeng, Y. Cai, G. Huang, J. Dai // Energies. – 2011. – Vol. 4, Issue 12. – Р. 1624–1656. doi: 10.3390/en4101624

Grabner, M. Numerical simulation of coal gasification at circulating fluidised bed conditions [Text] / M. Grabner, S. Ogriseck, B. Meyer // Fuel Processing Technology. – 2007. – Vol. 88, Issue 10. – P. 948–958. doi: 10.1016/j.fuproc.2007.05.006

Chaban, O. Y. Modeli i rozrakhunky elementarnykh konvektyvnykh teploobminnykiv [Text] / O. Y. Chaban, I. R. Halianchuk // Visnyk DU “Lvivska politekhnika”. “Teploenerhetyka. Inzheneriia dovkillia. Avtomatyzatsiia”. – 1999. – Vol. 365. – P. 32–40.

Andriushchenko, A. Y. Osnovy tekhnycheskoi termodynamyky realnykh protsessov [Text] / A. Y. Andriushchenko. – Moscow: Vysshaia shkola, 1975. – 264 p.

Halianchuk, I. R. Mathematical models of heat transfer system for two- and three-way heat exchangers [Text] / I. R. Halianchuk, M. Ya. Kuznetsova // Eastern-European Journal of Enterprise Technologies. – 2013. – Vol. 2, Issue 8 (62). – P. 29–32. – Available at: http://journals.uran.ua/eejet/article/view/12428/10325

Halianchuk, I. R. Matematychne modeliuvannia ta doslidzhennia vlastyvostei povitropidihrivnyka kotla [Text] / I. R. Halianchuk, M. Ya. Kuznetsova // Visnyk NU “Lvivska politekhnika”. Teploenerhetyka. Inzheneriia dovkillia. Avtomatyzatsiia”. – 2014. – Vol. 795. – P. 40–50.

Copyright (c) 2016 Yosyf Mysak, Igor Galyanchuk, Marta Kuznetsova