Verified calculation of compression process in a scroll compressor

Abstract

BACKGROUND: Because the geometric compression ratio of scroll compressors remains constant and the actual compression ratio (from suction to discharge pressure) varies depending on the operating conditions, allowing additional compression to occur in the first (central) cavity of scrolls up to the discharge pressure is necessary for correctness of the dynamic calculation of compressors. When the pressure in the different cavities in a scroll block during shaft rotation is determined, we need to take into account the surge that occurs immediately after the union of the first and second cavities between the scrolls. Simultaneously, during the design of the geometry of spirals, undercutting the end of the spirals must be considered to ensure the required geometric compression ratio.

AIM: The aim of this study is to create a refined methodology for the dynamic calculation of a scroll compressor, which takes into account the constancy of geometric compression ratio and pressure jumps when the first and second cavities (central and adjoining cavities) between the scrolls are combined.

METHODS: A step-by-step methodology for the dynamic calculation of a scroll compressor is presented. The principles of modeling the compression process in the scroll compressor in a Mathcad modeling environment are outlined. The case of different geometric and actual degrees of compression of the compressor is considered. The construction principle of the compressor indicator diagram is presented. Methods of determining the forces and moments that arise in the compressor-operation process are presented, and their graphs are shown. A practical example of modeling the advantage of the proposed methodology is shown.

RESULTS: Dependence that allows estimation of the change in the volumes and pressure in the compressor compression cavities according to the angle of scroll trimming is obtained. The dependence of the change in the forces and moments that arise during compressor operation, which takes into account the pressure jump caused by cavity unification, is obtained. The modeling accuracy of the scroll-compressor compression cavities and the processes that take place in these cavities are assessed by determining the relative error of the effective compressor power resulting from the thermal calculation and the power resulting from the dynamic calculation. The power error in the aforementioned calculations amounts to 8.8%, which indicates the high accuracy of the proposed methodology.

CONCLUSION: A refined method of dynamic calculation of a scroll compressor in a Mathcad modeling environment has been developed. This method allows calculation of the pressure in paired cavities of a scroll block, including all the necessary forces and moments that arise during the rotation process of the compressor shaft. This method also takes into account scroll trimming to obtain the given geometric degree of compression and the pressure jump when the first and second cavities between the scrolls are combined.

Keywords

scroll compressor / dynamic calculation of scroll compressor / compression cavities / axial forces / gas forces / design of compressor scrolls / geometric compression ratio

References

[1] Patent USA N 10/184,472 2019 / 22.01.2019. Ryu B, Ko Y, Kim B, et al. Scroll compressor and air conditioner including a scroll compressor. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US10184472B2/en?oq=Ryu%2c+B.%2c+Ko%2c+Y.%2c+Kim%2c+B.%2c+Kim%2c+B.%2c+%26+Chung%2c+B.+(2019).+U.S.+Patent+Application+No.+10%2f184%2c472

[2] Patent USA N 10/184,472 2019 / 22.01.2019. Ryu B., Ko Y., Kim B., et al. Scroll compressor and air conditioner including a scroll compressor. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US10184472B2/en?oq=Ryu%2c+B.%2c+Ko%2c+Y.%2c+Kim%2c+B.%2c+Kim%2c+B.%2c+%26+Chung%2c+B.+(2019).+U.S.+Patent+Application+No.+10%2f184%2c472

[3] Patent USA N 10/590,931 2020 / 17.03.2020. Park H, Kang S, Lee K, et al. Scroll compressor and air conditioner having the same. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US10590931B2/en?oq=Hansaem%2c+P.+A.+R.+K.%2c+Soojin%2c+K.+A.+N.+G.%2c+Lee%2c+K.%2c+JEONG%2c+H.%2c+%26+Kim%2c+C.+(2018).+U.S.+Patent+Application+No.+16%2f016%2c303

[4] Patent USA N 10/590,931 2020 / 17.03.2020. Park H., Kang S., Lee K., et al. Scroll compressor and air conditioner having the same. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US10590931B2/en?oq=Hansaem%2c+P.+A.+R. +K.%2c+Soojin%2c+K.+A.+N.+G.%2c+Lee%2c+K.%2c+JEONG%2c+H. %2c+%26+Kim%2c+C.+(2018).+U.S.+Patent+Application+No.+16%2f016%2c303

[5] He S, Guo W, Wai EW. Northern china heat pump application with the digital heating scroll compressor. In: International Refrigeration and Air Conditioning Conference. 2006. Accessed: 09.04.2023. Available from: http://docs.lib.purdue.edu/iracc/797

[6] He S., Guo W., Wai E.W. Northern china heat pump application with the digital heating scroll compressor // International Refrigeration and Air Conditioning Conference. 2006. Дата обращения: 09.04.2023. Режим доступа: http://docs.lib.purdue.edu/iracc/797

[7] Patent USA N 5/248,244 1993 / 28.09.1993. Ho Y, Barito TR, Hussein E, et al. Scroll compressor with a thermally responsive bypass valve. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US5248244A/en?oq=Ho%2c+Y.%2c+Barito%2c+T.+R.%2c+Khalifa%2c+H.+E.%2c+%26+Giffune%2c+J.+P.+(1993).+U.S.+Patent+No.+5%2c248%2c244

[8] Patent USA N 5/248,244 1993 / 28.09.1993. Ho Y., Barito T.R., Hussein E. et al. Scroll compressor with a thermally responsive bypass valve. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US5248244A/en?oq=Ho%2c+Y.%2c+Barito%2c+T.+R.%2c+Khalifa%2c+H.+E.%2c+%26+Giffune%2c+J.+P.+(1993).+U.S.+Patent+No.+5%2c248%2c244

[9] Patent USA N 4/818,195 1988 / 04.04.1989. Murayama A, Uchikawa N, Kuroshima R, et al. Scroll compressor with valved port for each compression chamber. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US4818195A/en?oq=Murayama%2c+A.%2c+Uchikawa%2c+N.%2c+Kuroshima%2c+R.%2c+Kuno%2c+H.%2c+Arata%2c+T.%2c+%26+Shiibayashi%2c+M.+(1989).+U.S.+Patent+No.+4%2c818%2c195.

[10] Patent USA N 4/818,195 1988 / 04.04.1989. Murayama A., Uchikawa N., Kuroshima R., et al. Scroll compressor with valved port for each compression chamber. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US4818195A/en?oq=Murayama%2c+A.%2c+Uchikawa%2c+N.%2c+Kuroshima%2c+R. %2c+Kuno%2c+H.%2c+Arata%2c+T.%2c+%26+Shiibayashi%2c+M. +(1989).+U.S.+Patent+No.+4%2c818%2c195.

[11] Patent USA N 20/160,123,326 2016 / 05.05.2016 Fogt JF, Kulkarni SS. Scroll compressor. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US20160123326A1/en?oq=Fogt%2c+J.+F.%2c+%26+Kulkarni%2c+S.+S.+(2016).+U.S.+Patent+Application+No.+14%2f529%2c219.

[12] Patent USA N 20/160,123,326 2016 / 05.05.2016 Fogt J.F., Kulkarni S.S. Scroll compressor. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US20160123326A1/en?oq=Fogt%2c+J.+F.%2c+%26+Kulkarni%2c+S. +S.+(2016).+U.S.+Patent+Application+No.+14%2f529%2c219.

[13] Patent USA N 9,435,340 2016 / 06.09.2016 Doepker RJ, Perevozchikov MM, Stover RC. Scroll compressor with variable volume ratio port in orbiting scroll. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US9435340B2/en?oq=Doepker%2c+R.+J.%2c+Perevozchikov%2c+M.+M.%2c+%26+Stover%2c+R.+C.+(2016).+U.S.+Patent+No.+9%2c435%2c340.+Washington%2c+DC:+U.S.+Patent+and+Trademark+Office

[14] Patent USA N 9,435,340 2016 / 06.09.2016 Doepker R.J., Perevozchikov M.M., Stover R.C. Scroll compressor with variable volume ratio port in orbiting scroll. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US9435340B2/en?oq=Doepker%2c+R.+J.%2c+Perevozchikov%2c+M.+M.%2c+%26+Stover%2c+R.+C.+(2016).+U.S.+Patent+No.+9%2c435%2c340.+Washington%2c+DC:+U.S.+Patent+and+Trademark+Office

[15] Patent USA N 9/458,847 2016 / 04.10.2016. Ignatiev KM, Fogt JF, Akei M. Scroll compressor having biasing system. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US9458847B2/en?oq=Ignatiev%2c+K.+M.%2c+Fogt%2c+J.+F.%2c+%26+Akei%2c+M.+(2016).+U.S.+Patent+No.+9%2c458%2c847.+Washington%2c+DC:+U.S.+Patent+and+Trademark+Office

[16] Patent USA N 9/458,847 2016 / 04.10.2016. Ignatiev K.M., Fogt J.F., Akei M. Scroll compressor having biasing system. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US9458847B2/en?oq=Ignatiev%2c+K.+M.%2c+Fogt%2c+J.+F.%2c+%26+Akei%2c+M.+(2016).+U.S.+Patent+No.+9%2c458%2c847.+Washington%2c+DC:+U.S.+Patent+and+Trademark+Office

[17] Patent USA N 9/850,903 2017 / 26.12.2017. Perevozchikov MM. Capacity modulated scroll compressor. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US9850903B2/en?oq=Perevozchikov%2c+M.+M.+(2017).+U.S.+Patent+No.+9%2c850%2c903.+Washington%2c+DC:+U.S.+Patent+and+Trademark+Office

[18] Patent USA N 9/850,903 2017 / 26.12.2017. Perevozchikov M.M. Capacity modulated scroll compressor. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US9850903B2/en?oq=Perevozchikov%2c+M.+M.+(2017).+U.S.+Patent+No.+9%2c850%2c903.+Washington%2c+DC:+U.S.+Patent+and+Trademark+Office

[19] Patent USA N 10/563,891 2020 / 18.02.2020. Smerud SJ, Mlsna ES, Betthauser TA, et al. Variable displacement scroll compressor. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US10563891B2/en?oq=Smerud%2c+S.+J.%2c+Mlsna%2c+E.+S.%2c+Betthauser%2c+T.+A.%2c+%26+Kimball%2c+A.+P.+(2018).+U.S.+Patent+Application+No.+15%2f416%2c925

[20] Patent USA N 10/563,891 2020 / 18.02.2020. Smerud S.J., Mlsna E.S., Betthauser T.A., et al. Variable displacement scroll compressor. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US10563891B2/en?oq=Smerud%2c+S.+J.%2c+Mlsna%2c+E.+S.%2c+Betthauser%2c+T.+A.%2c+%26+Kimball%2c+A.+P.+(2018).+U.S.+Patent+Application+No.+15%2f416%2c925

[21] Patent USA N 10/605,243 2020 / 31.03.2020. Akei M, Doepker RJ, Zhou G, et al. Scroll compressor with oil management system. Accessed: 09.04.2023. Available from: https://patents.google.com/patent/US10605243B2/en?oq=Akei%2c+M.%2c+Doepker%2c+R.+J.%2c+Zhou%2c+G.%2c+Sun%2c+Q.%2c+%26+Shu%2c+H.+(2018).+U.S.+Patent+Application+No.+16%2f047%2c675.

[22] Patent USA N 10/605,243 2020 / 31.03.2020. Akei M., Doepker R.J., Zhou G., et al. Scroll compressor with oil management system. [дата обращения: 09.04.2023] Доступ по ссылке: https://patents.google.com/patent/US10605243B2/en?oq=Akei%2c+M.%2c+Doepker%2c+R.+J.%2c+Zhou%2c+G.%2c+Sun%2c+Q.%2c+%26+Shu%2c+H.+(2018).+U.S.+Patent+Application+No.+16%2f047%2c675

[23] Hirano T, Hagimoto K, Matsuda S. Study on scroll compressor behavior in case of liquid refrigerant injection. Transactions of the Japan Society of Refrigerating and Air Conditioning Engineers. 2011;10(2):227–238.

[24] Hirano T., Hagimoto K., Matsuda S. Study on scroll compressor behavior in case of liquid refrigerant injectio // Transactions of the Japan Society of Refrigerating and Air Conditioning Engineers. 2011. Vol. 10, N 2. P. 227–238.

[25] Shishov VV, Talyzin MS. Improving the energy efficiency of refrigeration plants by decreasing the temperature difference in air-cooled condensers. Thermal Engineering. 2015;62(9):652–655. doi: 10.1134/S0040601515090098

[26] Shishov V.V., Talyzin M.S. Improving the energy efficiency of refrigeration plants by decreasing the temperature difference in air-cooled condensers // Thermal Engineering. 2015. Vol. 62, N 9. P. 652–655. doi: 10.1134/S0040601515090098

[27] Arkharov AM, Sychev VV. Actual energy loss due to entropy generation in low-and high-temperature machines and plants. Chemical and Petroleum Engineering. 2006;42(1-2):31–41. doi: 10.1007/s10556-006-0049-6

[28] Arkharov A.M., Sychev V.V. Actual energy loss due to entropy generation in low-and high-temperature machines and plants // Chemical and Petroleum Engineering. 2006. Vol. 42, N 1–2. P. 31–41. doi: 10.1007/s10556-006-0049-6

[29] Arkharov AM, Leont’ev AI, Sychev VV, et al. Problem of cold accumulation as a matter of energy saving and optimization of energy consumption // Chemical and Petroleum Engineering. 2009;45(9):621–623. doi: 10.1007/s10556-010-9225-9

[30] Arkharov A.M., Leont’ev A.I., Sychev V.V., et al. Problem of cold accumulation as a matter of energy saving and optimization of energy consumption // Chemical and Petroleum Engineering. 2009. Vol. 45, N 9. P. 621–623. doi: 10.1007/s10556-010-9225-9

[31] Voronov VA, Leonov VP. Testing of a Scroll Expander in Various Modes // Chemical and Petroleum Engineering. 2015;51(1-2):33–36. doi: 10.1007/s10556-015-9993-3

[32] Voronov V.A., Leonov V.P. Testing of a Scroll Expander in Various Modes // Chemical and Petroleum Engineering. 2015. Vol. 51, N 1–2. P. 33–36. doi: 10.1007/s10556-015-9993-3

[33] Kolosov MA, Borisenko AV, Manylov VV, et al. Losses of Power in Thermal Engines in Nonequilibrium Regenerative Heat Exchange. Chemical and Petroleum Engineering. 2018;54(3–4):239–246. doi: 10.1007/s10556-018-0469-0

[34] Kolosov M.A., Borisenko A.V., Manylov V.V., et al. Losses of Power in Thermal Engines in Nonequilibrium Regenerative Heat Exchange // Chemical and Petroleum Engineering. 2018. Vol. 54, N 3–4. P. 239–246. doi: 10.1007/s10556-018-0469-0

[35] Wang B, Li X, Shi W. A general geometrical model of scroll compressors based on discretional initial angles of involute. International journal of refrigeration. 2005;28(6):958–966. doi: 10.1016/j.ijrefrig.2005.01.015

[36] Wang B., Li X., Shi W. A general geometrical model of scroll compressors based on discretional initial angles of involute // International journal of refrigeration. 2005. Vol. 28, N 6. P. 958–966. doi: 10.1016/j.ijrefrig.2005.01.015

[37] Chen Y, Halm NP, Groll EA, et al. Mathematical modeling of scroll compressors—part I: compression process modelling. International Journal of Refrigeration. 2002;25(6):731–750. doi: 10.1016/S0140-7007(01)00071-8

[38] Chen Y., Halm N.P., Groll E.A., et al. Mathematical modeling of scroll compressors—part I: compression process modeling // International Journal of Refrigeration. 2002. Vol. 25, N 6. P. 731–750. doi: 10.1016/S0140-7007(01)00071-8

[39] Chen Y, Halm NP, Braun JE, et al. Mathematical modeling of scroll compressors—part II: overall scroll compressor modelling. International Journal of Refrigeration. 2002;25(6):751–764 doi: 10.1016/S0140-7007(01)00072-X

[40] Chen Y., Halm N.P., Braun J.E., et al. Mathematical modeling of scroll compressors—part II: overall scroll compressor modeling // International Journal of Refrigeration. 2002. Vol. 25, N 6. P. 751–764. doi: 10.1016/S0140-7007(01)00072-X

[41] Raikov AA, Bronstein MD, Burmistrov AV, et al. Analytical method for calculating forces and moments in oil-free scroll vacuum pumps and compressors. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie. 2014;7(652):35–42. (In Russ.).

[42] Райков А.А., Бронштейн М.Д., Бурмистров А.В., и др. Аналитический метод расчета сил и моментов в безмасляных спиральных вакуумных насосах и компрессорах // Известия высших учебных заведений. Машиностроение. 2014. № 7(652). С. 35–42.

[43] Qin F, Shao S, Tian C, et al. Model simplification of scroll compressor with vapor refrigerant injection. International journal of green energy. 2016;13(8):803–811. doi: 10.1080/15435075.2016.1161626

[44] Qin F., Shao S., Tian C., et al. Model simplification of scroll compressor with vapor refrigerant injection // International journal of green energy. 2016. Vol. 13, N 8. P. 803–811. doi: 10.1080/15435075.2016.1161626

[45] JN Harrison, S Koester, R Aihara et al. From CAD to 1D: a direct approach to modeling scroll compressors with multi-physics simulation // 24th International Compressor Engineering Conference at Purdue; July 9–12, 2018; West Lafayette. Available from: https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=3538&context=icec

[46] Harrison JN, Koester S, Aihara R, et al. From CAD to 1D: a direct approach to modeling scroll compressors with multi-physics simulation // 24th International Compressor Engineering Conference at Purdue; July 9-12, 2018; West Lafayette. [дата обращения: 09.04.2023] Доступ по ссылке: https://docs.lib.purdue.edu/icec/2539/

[47] Uchikawa N, Terada H, Arata T. Scroll compressors for air conditioners. Hitachi Rev. 1987;36(3):155.

[48] Uchikawa N., Terada H., Arata T. Scroll compressors for air conditioners // Hitachi Rev. 1987. Vol. 36, N 3. P. 155.

[49] Kosachevsky VA. About modeling the central region of a scroll compressor. Vestnik mezhdunarodnoy akademii kholoda. 2018. № 3. 45–52. (In Russ.). doi: 10.17586/1606-4313-2018-17-3-45-52

[50] Косачевский В. А. О моделировании центральной области спирального компрессора //Вестник Международной академии холода. – 2018. – №. 3. – С. 45–52. doi: 10.17586/1606-4313-2018-17-3-45-52

[51] Kosachevskiy VA. Razrabotka metoda rascheta i analiz rabochego protsessa spiralnykh kompressorov [dissertation] Saint Petersburg; 1998. (In Russ.).

[52] Косачевский В.А. Разработка метода расчета и анализ рабочего процесса спиральных компрессоров. дис… канд. техн. наук. Санкт-Петербург, 1998. Режим доступа: https://search.rsl.ru/ru/record/01000228178

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