1. MMC
  2. All Volumes and Issues
  3. Volume 8, Number 3, 2021
  4. Mathematical modeling bringing the operation of air split conditioners heat pumps to the same internal temperature conditions

Mathematical modeling bringing the operation of air split conditioners heat pumps to the same internal temperature conditions

MMC.
2021;
Volume 8, Number 3
: pp. 509–514
https://doi.org/10.23939/mmc2021.03.509
Received: November 20, 2020
Revised: April 08, 2021
Accepted: May 17, 2021

Mathematical Modeling and Computing, Vol. 8, No. 3, pp. 509–514 (2021)

Authors:
  1. V. Yo. Labay
  2. V. Yu. Yaroslav
  3. O. M. Dovbush
  4. A. Ye. Tsizda
1
Department of Heat, Gas Supply and Ventilation, Institute of Construction and Engineering Systems, Lviv Polytechnic National University
2
Department of Heat, Gas Supply and Ventilation, Institute of Construction and Engineering Systems, Lviv Polytechnic National University
3
Department of Heat, Gas Supply and Ventilation, Institute of Construction and Engineering Systems, Lviv Polytechnic National University
4
Department of Heat, Gas Supply and Ventilation, Institute of Construction and Engineering Systems, Lviv Polytechnic National University

Nowadays, the use of heat pumps (HP) of air split-conditioners in air conditioning and heating systems of small industrial, public and residential facilities is becoming more common.  It is known that the nominal heat capacity of HP of air split-conditioners is given in catalogs or reference literature under standard outdoor temperature conditions, namely: outdoor air temperature $+7\,{}^\circ$C, indoor air temperature $+21\,{}^\circ$C.  At the same time, manufacturers of air split-conditioners do not ensure that, regardless of the size of heating capacity, all air split-conditioners have the same internal temperature conditions, namely: the evaporation temperature of the refrigerant and its condensation temperature.  In this case, the thermodynamic efficiency, which can be best assessed by the exergetic output-input ratio (OIR) of different heating capacity of HP of air split-conditioners, is different; this, in our opinion, is incorrect.  However, today there is a lack of mathematical models of bringing the operation of air split-conditioners HP to the similar internal temperature conditions, which will allow us to obtain the same exergetic OIR for different heating capacity of HP.  To create the mathematical model of bringing the operation of HP of air split-conditioners to the equal internal temperature conditions, we have proposed them, namely: the evaporation temperature of the refrigerant $+0.7\,{}^\circ$C and its condensation temperature $+40\,{}^\circ$C. Taking these temperatures on the basis of the heat balances of the HP evaporator and HP condenser of air split-conditioners, we obtained the dependences for calculating air flow rates on the evaporator and condenser, which respectively maintain the proposed temperatures.

heat pump of air split-conditioner
exergy balance
exergy efficiency
equal internal temperature conditions
  1. Energy Strategy of Ukraine until 2030, http://www.ukrenergo.energy.gov.ua (in Ukrainian).
  2. Heat Pump, Types and Applications of Heat Pumps, http://www.ecosvit.net/ua/teplovij-nasos-vidi-ta zastosuvannya (in Ukrainian).
  3. Heat pumps, http://www.npblog.com.ua/index.php/hi-tech/teplovi-nasosi.html (in Ukrainian).
  4. Bezrodnyi M. N., Dranik T. V.  Thermodynamic Efficiency of Heat Pump Application for Providing Comfortable Conditions in Indoor Swimming Pools.  Eastern European Journal of Enterprise Technologies. 3 (8), 25–30 (2013), (in Ukrainian).
  5. Matsevityi Yu. M., Chirkin N. B., Bogdanovich A. S., Klepanda A. S.  Introduction of Heat Pumping Technologies. Ecotechnology and Resource Saving. 3, 4–10 (2008), (in Russian).
  6. Zalewski P. K.  Pompy ciepіa. Podstawy teoretyczne i przykіady zastosowania. Kraków (1995), (in Polish).
  7. Morozyuk T. V.  Theory of Refrigeration Machines and Heat Pumps. Odessa, Studio "Negotsiant" (2006), (in Russian).
  8. Szargut J., Petela R.  Exergy. Moscow, Energy (1968), (in Russian).
  9. Sokolov E. Y., Brodyansky V. M.  Energy Basis of Transformation of Heat and Cooling Processes. Moscow, Energoizdat (1981), (in Russian).
  10. Silvio de Oliveira Junior.  Exergy. Production, Cost and Renewability. Springer (2013).
  11. Sazhin B. S., Bulekov A. P., Sazhin B. S.  Exergy Analysis of Work of Industrial Plants: Monograph, Moscow (2000), (in Russian).
  12. Bejan A.  Advanced Engineering Thermodynamics. placeStateNew York: John Wiley & Sons (1988).
  13. Bejan A., Tsatsaronis G., Moran M.  Thermal Design and Optimization. New York, J. Wiley (1996).
  14. Morosuk T., Nikulshin R., Morosuk L.  Entropy-Cycle Method for Analysis of Refrigeration Machine and Heat Pump Cycles.  Thermal Science. 10 (1), 111–124 (2006).
  15. Tsatsaronis J.  The Interaction of Thermodynamics and Economy to Minimize Cost of Energy Conversion Systems.  Odessa, Studio "Negotsiant" (2002), (in Russian).
  16. Labay V., Dovbush O., Yaroslav V., Klymenko H.  Mathematical Modeling of a Split-conditioner Operation for Evaluation of Exergy Efficiency of the R600A Refrigerant Application.  Mathematical Modeling and Computing. 5 (2), 169–177 (2018).
  17. Labay V. Yo., Mysak Yo. S.  Bringing the Work of Air Split-conditioners Refrigeration Machines to the Same Internal Temperature.  Refrigeration Engineering and Technology. 4 (126), 19–22 (2010), (in Ukrainian).
  18. Labay V. Yo., Yaroslav V. Yu., Dovbush O. M., Tsizda A. Ye.  Mathematical Modeling of an Air Split-Conditioner Heat Pump Operation for Investigation its Exergetic Efficiency.  Mathematical Modeling and Computing. 7 (1), 169–178 (2020).
  19. Jakobsen A., Rassmussen B.-D., Skovrup M.-J., Andersen S.-E.  CoolPack –- a collection of simulation tools for refrigeration – Tutorial – Version 1.46. – Department of Energy Engineering Technical University of Denmark (2001).
  20. Mitsubishi Electric Catalog Split (2019).