Optimization of the operation mode of a simple two-step heat pump with a separator

The RELEVANCE of the research lies in the development of new methods for organizing the removal of low-potential heat from data centers, power electronics and other natural and technological sources, as well as in obtaining new dependencies for assessing the maximum increase in the effective coefficient of performance (COP) of simple two-stage heat pump (HP) cycles with a separator. The GOAL of the work is to optimize the operation of a simple two-stage heat pump with a separator. METHODS. The CoolProp library was used for calculating the thermodynamic cycle of the heat pump and the efficiency of the compressors was taken into account. A law was introduced to optimize the operation of the heat pump, which relates the power fraction of the first stage to the temperature in the separator. To assess the maximum efficiency of the heat pump, it was assumed that the refrigerant enters the compressor as an unsuperheated vapor and pure condensate enters the thermostatic valve. RESULTS. A general scheme is presented and the principle of operation of a two-stage heat pump is discussed. Based on thermodynamic calculations, the thermal performance of the cycles is obtained. The coefficient of relative increase in the effective COP for R410a, R141b, R600a and R134a refrigerants is determined. It is shown that the existence of a maximum in the effective heat transformation coefficient is due to the presence of two effects. Functions based on physical laws are derived that determine the maximum increase in the heat transformation coefficient and its position. CONCLUSION. A detailed analysis of the reasons for the increase in COP relative to a single-stage cycle has been conducted. The obtained dependencies are useful for assessing the effect of using a two-stage heat pump in practice. The developed heat pump scheme can be used to extract low-potential heat from data centers, power electronics, the ground and other sources with greater efficiency than a single-stage cycle.

1. Wang Z. et. al. Field test and numerical investigation on the heat transfer characteristics and optimal design of the heat exchangers of a deep borehole ground source heat pump system. Energy Conversion and Management. 2017; 153: 603-615. doi: 10.1016/j.enconman.2017.10.038.

2. Luo J. et. al. Heating and cooling performance analysis of a ground source heat pump system in Southern Germany. Geothermics. 2015; 53: 57-66. doi: 10.1016/j.geothermics.2014.04.004.

3. Purdin M.S., Magomedova R. Teplovye pritoki i poteri v gruntovykh teploobmennikakh i akkumulyatorakh teploty. Mezhdunarodnaya nauchno-tekhnicheskaya konferentsiya SPREHTT (XXII Benardosovskie chteniya), Ivanovo, 2023, pp. 234-236. (In Russ).

4. Sokolov I.S., Ryzhenkov A.V. et al. Experimental study of performance of building heating system based on HPS and equipped with thermal potential recovery system and heat load prediction. Energy and Buildings. 2024; 324: 114862. doi: 10.1016/j.enbuild.2024.114862.

5. Vedruchenko V.R., Alimbaev A.A., Kadtsyn I.I. et al. Aktual'nost' ispol'zovaniya gruntovykh teplotransformatorov v Sibiri. Zhurnal Sibirskogo federal'nogo universiteta. Seriya: Tekhnika i tekhnologii. 2024; 17(7): 863-877. (In Russ).

6. Purdin M.S., Garyaev A.B. Study of thermal characteristics of a solid insulated cylindrical heat accumulator. Bulletin of the South Ural State University. Ser. Power Engineering. 2023; 23(2): 73-82. DOI: 10.14529/power230207. (In Russ).

7. Purdin M.S. Metod chislennogo modelirovaniya teploobmena v akkumulyatorakh teploty s mnozhestvom faz i svobodnym peremeshcheniem fazovykh granits. EHTIP: trudy X Mezhd. shkoly-seminara molodykh uchenykh i spetsialistov, Moscow, 2020; pp. 77-81. (In Russ).

8. Garyaev A. B. et al. Methodological issues and prospective directions of usi ng low potential heat sources. Izvestiâ Akademii nauk SSSR. Ènergetika. 2025; 5: 19-46. doi: 10.7868/S3034649525050024. (In Russ).

9. Wang P. et al. District heating utilizing waste heat of a data center: High-temperature heat pumps. Energy and Buildings. 2024; 315: 114327. doi: 10.1016/j.enbuild.2024.114327.

10. Yurovskaya, V.D., Latushkina, S.V. Project of using low-potential energy sources at the Bratsk hydro power plant. Power engineering: research, equipment, technology. 2022; 24(5), 13-22. doi: 10.30724/1998-9903-2022-24-5-13-22. (In Russ).

11. Kalinina M.V., Plotnikova L.V. The system of complex recovery of low-potential secondary energy in the thermal technology scheme of pulp and paper production. Power engineering: research, equipment, technology. 2025; 27(5): 182-194. (In Russ).

12. Sukhikh A.A., Antanenkova I.S. Metodika sravneniya termodinamicheskoi ehffektivnosti tsiklov kholodil'nykh i teplonasosnykh ustanovok. Vestnik Mezhd. akademii kholoda. 2012; 4: 21-25. (In Russ).

13. Sukhikh A.A., Antanenkova I.S. Termodinamicheskaya ehffektivnost' teplonasosnykh ustanovok. Vestnik Mezhd. akademii kholoda, 2013; 1: 43-47. (In Russ).

14. Kondrashov A.V., Trinchenko A.A. Sistema utilizatsii teploty kondensatsii teplovykh mashin. Izvestiya vysshikh uchebnykh zavedenii. Problemy ehnergetiki. 2023; 25(6): 67-77. doi: 10.30724/1998-9903-2023-25-6-67-77. (In Russ).

15. Konakhina I. A. Primenenie teplovykh nasosov kaskadnogo tipa v utilizatsionnykh sistemakh teplosnabzheniya neftekhimicheskikh proizvodstv. Izvestiya vysshikh uchebnykh zavedenii. Problemy ehnergetiki. 2003; 11-12: 9-23. (In Russ).

16. Parshukov V.I., Efimov N.N., Bezuglov R.V. et al. Kaskadnaya teplonasosnaya ustanovka s promezhutochnoi akkumulyatsiei teploty. Patent RUS No. 183519. 25.09.2018. Byul. No. 27. Available at: https://www.fips.ru/iiss/document.xhtml?faces-redirect=true&id=74608bd1a9e9c568ae763240ba9b5323. Accessed: 19 Feb 2026. (In Russ).

17. Antipov Y.A., Shatalov I.K., Silin A.V. Mnogostupenchataya teplonasosnaya ustanovka. Patent RUS No. 2705696. 11.11.2019. Byul. No. 32. Available at: https://www.fips.ru/iiss/document.xhtml?faces-redirect=true&id=6bcfa38fc175ebba300e442437b9b042. Accessed: 19 Feb 2026. (In Russ).

18. Purdin M.S., Yuzyuk V.V. Investigation of the Efficiency of a Two-Stage Isobutane Heat Pump. Technical Physics. 2024; 69(9): 2472-2481. doi: 10.1134/S1063784224700786.

19. Mota-Babiloni A. et al. Ultralow-temperature refrigeration systems: Configurations and refrigerants to reduce the environmental impact. International Journal of Refrigeration. 2020; 111: 147-158. doi: 10.1016/j.ijrefrig.2019.11.016.

20. Antipov Y.A. et al. Features of modeling a highly efficient multistage vapor compression heat pump unit. Bulletin of Peoples' Friendship University of Russia. Series Engineering researches. 2021; 22(4): 339-347. doi: 10.22363/2312-8143-2021-22-4-339-347.

21. Kosoi A.S., Antipov Y.A., Shkarin K.V. et al. A multistage heat pump unit model for reducing energy consumption of space heating at low ambient temperatures. IOP Conference Series: Materials Science and Engineering. IOP Publishing, 2021; 1100(1): 012045. doi: 10.1088/1757-899X/1100/1/012045.

22. Jiang S. et al. A general model for two-stage vapor compression heat pump systems. International Journal of Refrigeration. 2015; 51: 88-102. doi: 10.1016/j.ijrefrig.2014.12.005.

23. Qiu K., Thomas M. Assessment of the performance of ultralow‐GWP refrigerants in a two‐stage heat pump system using simulation and MCMD. Environmental Progress & Sustainable Energy. 2025; e70132. doi: 10.1002/ep.70132.

24. Cao X. et al. Performance analysis of an ejector-assisted two-stage evaporation single-stage vapor-compression cycle. Applied Thermal Engineering. 2022; 205: 118005. doi: 10.1016/j.applthermaleng.2021.118005.

25. Yahya M., Rachman A., Hasibuan R. Performance analysis of solar-biomass hybrid heat pump batch-type horizontal fluidized bed dryer using multi-stage heat exchanger for paddy drying. Energy. 2022; 254: 124294. doi: 10.1016/j.energy.2022.124294.