Oscillations of the Helium II – Vapor Interface during Motion in a Channel of a Relatively Large Diameter
Keywords:
helium-II, U-shaped channel, interface oscillations, heat and mass transfer, interface dynamics, experiment
Abstract
The article considers the motion of superfluid helium in a U-shaped cylindrical channel with a diameter significantly larger than the helium capillary constant in the approximation of an inviscid incompressible fluid. When a heat flux is applied near the end-face section of one of the channel elbows, a vapor layer emerges near the heater, and the helium II – vapor interface begins to move. The purpose of the calculation is to determine the interface position as a function of time. The heat transfer in a liquid is described using the semi-empirical Gorter-Mellink theory. The processes in the vapor are analyzed based on the methods of molecular kinetic theory. The influence of the gravity field is studied. The system of equations is reduced to an ordinary second-order differential equation, which is solved numerically. Various process development scenarios depending on the heat flux are obtained. The occurrence of oscillations is described, and the influence of parameters on the oscillation amplitude and frequency is analyzed. In this way, the previously obtained experimental data have been interpreted.
References
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2. Eikoku Y., Ishida K., Iwamoto A., Tsuji Y. Periodic Oscillation of Liquid Helium Boiling in a Narrow Rectangular Duct // J. Low Temperature Phys. 2019. V. 196. Pp. 6—12.
3. Kobayashi H., Takahashi M., Ashimori T., Kurimura N. Effect of Superheating on Heat Transfer from a Good Thermal Conductor in a Two-dimensional Channel to He II Below the -point Pressure // Cryogenics. 2009. V. 49. Pp. 700—706.
4. Song Yu., Four A., Baudouy B. Nucleate Boiling Heat Transfer in a Helium Natural Circulation Loop Coupled with a Cryocooler // International J. Heat and Mass Transfer. 2013. V. 66. Pp. 64—71.
5. Nemirovskii S.K. Cavity Evolution and the Rayleigh-Plesset Equation in Superfluid Helium // Phys. Rev. B. 2020. V. 102. P. 064511.
6. Dergunov I., Kryukov A., Gorbunov A. The Vapor Film Evolution at Superfluid Helium Boiling in Conditions of Microgravity // J. Low Temperature Phys. 2001. V. 119. Pp. 403—411.
7. Kondaurova L.P., Andryushchenko V.A. Dynamics, Properties and Spectrum of Reconnecting Vortex Loops in Superfluid Helium (Review Article) // Low Temperature Phys. 2021. V. 47(9). Pp. 804—818.
8. Nemirovskii S., Yurkina O. On the Energy Spectrum of the 3D Velocity Field, Generated by an Ensemble of Vortex Loops // Low Temperature Phys. 2021. V. 47(8). Pp. 652—655.
9. Efimov V.B., Erlova A.A., Kondaurova L.P., Gorkun A.G. Heat Transfer under Pulsed Heating in Superfluid Helium // Low Temperature Phys. 2019. V. 45(9). Pp. 988—993.
10. Пузина Ю.Ю., Королев П.В., Крюков А.П. Течение гелия II в канале с пористой вставкой при безвихревом сверхтекучем движении // Вестник МЭИ. 2017. № 4. С. 8—14.
11. Vanderlaan M.H., Van Sciver S.W. He II Heat Transfer Through Random Packed Spheres: Pressure Drop // Cryogenics. 2014. V. 63. Pp. 37—42.
12. Vanderlaan M.H., Van Sciver S.W. Steady State He II Heat Transfer Through Random Packed Spheres // Cryogenics. 2013. V. 57. Pp. 166—172.
13. Allain H., Baudouy B., Quintard M., Prat M. Experimental Investigation of Heat Transfer Through Porous Media in Superfluid Helium // Cryogenics. 2015. V. 66. Pp. 53—62.
14. Allain H., Quintard M., Prat M., Baudouy B. Upscaling of Superfluid Helium flow in Porous Media // Intern. J. Heat and Mass Transfer. 2010. V. 53. Pp. 4852—4864.
15. Korolyov P.V., Kryukov A.P., Puzina Yu.Yu., Yachevsky I.A. Experiments of Superfluid Helium Flow in a Channel with a Monodisperse Backfill // J. Phys.: Conf. Series. 2020. V. 1683. P. 022017.
16. Крюков А.П., Королев П.В., Пузина Ю.Ю. Экспериментальное исследование кипения He II внутри пористого тела // Прикладная механика и техническая физика. 2017. № 4. С. 126—134.
17. Муратова Т.М., Лабунцов Д.А. Кинетический анализ процессов испарения и конденсации // Теплофизика высоких температур. 1969. Т. 7(5). С. 959—967.
18. Ястребов А.К., Крюков А.П. Тепломассоперенос через пленку пара с учетом движения межфазной поверхности жидкость–пар и роста температуры границы раздела фаз // Теплофизика высоких температур. 2006. Т. 44(4). С. 560—567.
19. Gorter C.J., Mellink J.H. On the Irreversible Processes in Liquid Helium II // Phys. 1949. V. XV. No. 3—4. Pp. 285—304.
20. Королев П.В., Крюков А.П. Движение сверхтекучего гелия в капилляре с паром при наличии продольного теплового потока // Вестник МЭИ. 2002. № 1. С. 43—46.
21. Амосов А.А., Дубинский Ю.А., Копченова Н.В. Вычислительные методы для инженеров. М.: Изд-во МЭИ, 2003.
22. Kryukov A.P., Van Sciver S.W. Calculation of the Recovery Heat Flux Film Boiling in Superfluid Helium // Cryogenics. 1981. V. 21(9). Pp. 525—528.
23. Van Sciver S.W. Helium Cryogenics. N.-Y.: Plenum Press. 2012.
---
Для цитирования: Пузина Ю.Ю., Крюков А.П. Колебания межфазной поверхности «гелий II—пар» при движении в канале относительно большого диаметра // Вестник МЭИ. 2023. № 3. С. 138—144. DOI: 10.24160/1993-6982-2023-3-138-144
---
Работа выполнена при поддержке: РФФИ (проект № 20-08-00342)
#
1. Takada S., Kobayashi H., Murakami M., Kimura N. Comparative Study of Heat Transfer Performance and Visualization Images of Superfluid Helium Boiling in Narrow Two-dimensional Channel. IOP Conf. Series: Materials Sci. and Eng. 2020;755:012142.
2. Eikoku Y., Ishida K., Iwamoto A., Tsuji Y. Periodic Oscillation of Liquid Helium Boiling in a Narrow Rectangular Duct. J. Low Temperature Phys. 2019;196:6—12.
3. Kobayashi H., Takahashi M., Ashimori T., Kurimura N. Effect of Superheating on Heat Transfer from a Good Thermal Conductor in a Two-dimensional Channel to He II Below the -point Pressure. Cryogenics. 2009;49:700—706.
4. Song Yu., Four A., Baudouy B. Nucleate Boiling Heat Transfer in a Helium Natural Circulation Loop Coupled with a Cryocooler. International J. Heat and Mass Transfer. 2013;66:64—71.
5. Nemirovskii S.K. Cavity Evolution and the Rayleigh-Plesset Equation in Superfluid Helium. Phys. Rev. B. 2020;102:064511.
6. Dergunov I., Kryukov A., Gorbunov A. The Vapor Film Evolution at Superfluid Helium Boiling in Conditions of Microgravity. J. Low Temperature Phys. 2001;119:403—411.
7. Kondaurova L.P., Andryushchenko V.A. Dynamics, Properties and Spectrum of Reconnecting Vortex Loops in Superfluid Helium (Review Article). Low Temperature Phys. 2021;47(9):804—818.
8. Nemirovskii S., Yurkina O. On the Energy Spectrum of the 3D Velocity Field, Generated by an Ensemble of Vortex Loops. Low Temperature Phys. 2021;47(8):652—655.
9. Efimov V.B., Erlova A.A., Kondaurova L.P., Gorkun A.G. Heat Transfer under Pulsed Heating in Superfluid Helium. Low Temperature Phys. 2019;45(9):988—993.
10. Puzina Yu.Yu., Korolev P.V., Kryukov A.P. Techenie Heliya II v Kanale S Poristoy Vstavkoy pri Bezvikhrevom Sverkhtekuchem Dvizhenii. Vestnik MEI. 2017;4:8—14. (in Russian).
11. Vanderlaan M.H., Van Sciver S.W. He II Heat Transfer Through Random Packed Spheres: Pressure Drop. Cryogenics. 2014;63:37—42.
12. Vanderlaan M.H., Van Sciver S.W. Steady State He II Heat Transfer Through Random Packed Spheres. Cryogenics. 2013;57:166—172.
13. Allain H., Baudouy B., Quintard M., Prat M. Experimental Investigation of Heat Transfer Through Porous Media in Superfluid Helium. Cryogenics. 2015;66:53—62.
14. Allain H., Quintard M., Prat M., Baudouy B. Upscaling of Superfluid Helium flow in Porous Media. Intern. J. Heat and Mass Transfer. 2010;53:4852—4864.
15. Korolyov P.V., Kryukov A.P., Puzina Yu.Yu., Yachevsky I.A. Experiments of Superfluid Helium Flow in a Channel with a Monodisperse Backfill. J. Phys.: Conf. Series. 2020;1683:022017.
16. Kryukov A.P., Korolev P.V., Puzina Yu.Yu. Eksperimental'noe Issledovanie Kipeniya He II Vnutri Poristogo Tela. Prikladnaya Mekhanika i Tekhnicheskaya Fizika. 2017;4:126—134. (in Russian).
17. Muratova T.M., Labuntsov D.A. Kineticheskiy Analiz Protsessov Ispareniya i Kondensatsii. Teplofizika Vysokikh Temperatur. 1969;7(5):959—967. (in Russian).
18. Yastrebov A.K., Kryukov A.P. Teplomassoperenos Cherez Plenku Para s Uchetom Dvizheniya Mezhfaznoy Poverkhnosti Zhidkost'–Par i Rosta Temperatury Granitsy Razdela Faz. Teplofizika Vysokikh Temperatur. 2006;44(4):560—567. (in Russian).
19. Gorter C.J., Mellink J.H. On the Irreversible Processes in Liquid Helium II. Phys. 1949;XV;3—4:285—304.
20. Korolev P.V., Kryukov A.P. Dvizhenie Sverkhtekuchego Geliya v Kapillyare s Parom pri Nalichii Prodol'nogo Teplovogo Potoka. Vestnik MEI. 2002;1:43—46. (in Russian).
21. Amosov A.A., Dubinskiy Yu.A., Kopchenova N.V. Vychislitel'nye Metody dlya Inzhenerov. M.: Izd-vo MEI, 2003. (in Russian).
22. Kryukov A.P., Van Sciver S.W. Calculation of the Recovery Heat Flux Film Boiling in Superfluid Helium. Cryogenics. 1981;21(9):525—528.
23. Van Sciver S.W. Helium Cryogenics. N.-Y.: Plenum Press. 2012.
---
For citation: Puzina Yu.Yu., Kryukov A.P. Oscillations of the Helium II – Vapor Interface during Motion in a Channel of a Relatively Large Diameter. Bulletin of MPEI. 2023;3:138—144. (in Russian). DOI: 10.24160/1993-6982-2023-3-138-144
---
The work is executed at support: RFBR (Project No. 20-08-00342)
2. Eikoku Y., Ishida K., Iwamoto A., Tsuji Y. Periodic Oscillation of Liquid Helium Boiling in a Narrow Rectangular Duct // J. Low Temperature Phys. 2019. V. 196. Pp. 6—12.
3. Kobayashi H., Takahashi M., Ashimori T., Kurimura N. Effect of Superheating on Heat Transfer from a Good Thermal Conductor in a Two-dimensional Channel to He II Below the -point Pressure // Cryogenics. 2009. V. 49. Pp. 700—706.
4. Song Yu., Four A., Baudouy B. Nucleate Boiling Heat Transfer in a Helium Natural Circulation Loop Coupled with a Cryocooler // International J. Heat and Mass Transfer. 2013. V. 66. Pp. 64—71.
5. Nemirovskii S.K. Cavity Evolution and the Rayleigh-Plesset Equation in Superfluid Helium // Phys. Rev. B. 2020. V. 102. P. 064511.
6. Dergunov I., Kryukov A., Gorbunov A. The Vapor Film Evolution at Superfluid Helium Boiling in Conditions of Microgravity // J. Low Temperature Phys. 2001. V. 119. Pp. 403—411.
7. Kondaurova L.P., Andryushchenko V.A. Dynamics, Properties and Spectrum of Reconnecting Vortex Loops in Superfluid Helium (Review Article) // Low Temperature Phys. 2021. V. 47(9). Pp. 804—818.
8. Nemirovskii S., Yurkina O. On the Energy Spectrum of the 3D Velocity Field, Generated by an Ensemble of Vortex Loops // Low Temperature Phys. 2021. V. 47(8). Pp. 652—655.
9. Efimov V.B., Erlova A.A., Kondaurova L.P., Gorkun A.G. Heat Transfer under Pulsed Heating in Superfluid Helium // Low Temperature Phys. 2019. V. 45(9). Pp. 988—993.
10. Пузина Ю.Ю., Королев П.В., Крюков А.П. Течение гелия II в канале с пористой вставкой при безвихревом сверхтекучем движении // Вестник МЭИ. 2017. № 4. С. 8—14.
11. Vanderlaan M.H., Van Sciver S.W. He II Heat Transfer Through Random Packed Spheres: Pressure Drop // Cryogenics. 2014. V. 63. Pp. 37—42.
12. Vanderlaan M.H., Van Sciver S.W. Steady State He II Heat Transfer Through Random Packed Spheres // Cryogenics. 2013. V. 57. Pp. 166—172.
13. Allain H., Baudouy B., Quintard M., Prat M. Experimental Investigation of Heat Transfer Through Porous Media in Superfluid Helium // Cryogenics. 2015. V. 66. Pp. 53—62.
14. Allain H., Quintard M., Prat M., Baudouy B. Upscaling of Superfluid Helium flow in Porous Media // Intern. J. Heat and Mass Transfer. 2010. V. 53. Pp. 4852—4864.
15. Korolyov P.V., Kryukov A.P., Puzina Yu.Yu., Yachevsky I.A. Experiments of Superfluid Helium Flow in a Channel with a Monodisperse Backfill // J. Phys.: Conf. Series. 2020. V. 1683. P. 022017.
16. Крюков А.П., Королев П.В., Пузина Ю.Ю. Экспериментальное исследование кипения He II внутри пористого тела // Прикладная механика и техническая физика. 2017. № 4. С. 126—134.
17. Муратова Т.М., Лабунцов Д.А. Кинетический анализ процессов испарения и конденсации // Теплофизика высоких температур. 1969. Т. 7(5). С. 959—967.
18. Ястребов А.К., Крюков А.П. Тепломассоперенос через пленку пара с учетом движения межфазной поверхности жидкость–пар и роста температуры границы раздела фаз // Теплофизика высоких температур. 2006. Т. 44(4). С. 560—567.
19. Gorter C.J., Mellink J.H. On the Irreversible Processes in Liquid Helium II // Phys. 1949. V. XV. No. 3—4. Pp. 285—304.
20. Королев П.В., Крюков А.П. Движение сверхтекучего гелия в капилляре с паром при наличии продольного теплового потока // Вестник МЭИ. 2002. № 1. С. 43—46.
21. Амосов А.А., Дубинский Ю.А., Копченова Н.В. Вычислительные методы для инженеров. М.: Изд-во МЭИ, 2003.
22. Kryukov A.P., Van Sciver S.W. Calculation of the Recovery Heat Flux Film Boiling in Superfluid Helium // Cryogenics. 1981. V. 21(9). Pp. 525—528.
23. Van Sciver S.W. Helium Cryogenics. N.-Y.: Plenum Press. 2012.
---
Для цитирования: Пузина Ю.Ю., Крюков А.П. Колебания межфазной поверхности «гелий II—пар» при движении в канале относительно большого диаметра // Вестник МЭИ. 2023. № 3. С. 138—144. DOI: 10.24160/1993-6982-2023-3-138-144
---
Работа выполнена при поддержке: РФФИ (проект № 20-08-00342)
#
1. Takada S., Kobayashi H., Murakami M., Kimura N. Comparative Study of Heat Transfer Performance and Visualization Images of Superfluid Helium Boiling in Narrow Two-dimensional Channel. IOP Conf. Series: Materials Sci. and Eng. 2020;755:012142.
2. Eikoku Y., Ishida K., Iwamoto A., Tsuji Y. Periodic Oscillation of Liquid Helium Boiling in a Narrow Rectangular Duct. J. Low Temperature Phys. 2019;196:6—12.
3. Kobayashi H., Takahashi M., Ashimori T., Kurimura N. Effect of Superheating on Heat Transfer from a Good Thermal Conductor in a Two-dimensional Channel to He II Below the -point Pressure. Cryogenics. 2009;49:700—706.
4. Song Yu., Four A., Baudouy B. Nucleate Boiling Heat Transfer in a Helium Natural Circulation Loop Coupled with a Cryocooler. International J. Heat and Mass Transfer. 2013;66:64—71.
5. Nemirovskii S.K. Cavity Evolution and the Rayleigh-Plesset Equation in Superfluid Helium. Phys. Rev. B. 2020;102:064511.
6. Dergunov I., Kryukov A., Gorbunov A. The Vapor Film Evolution at Superfluid Helium Boiling in Conditions of Microgravity. J. Low Temperature Phys. 2001;119:403—411.
7. Kondaurova L.P., Andryushchenko V.A. Dynamics, Properties and Spectrum of Reconnecting Vortex Loops in Superfluid Helium (Review Article). Low Temperature Phys. 2021;47(9):804—818.
8. Nemirovskii S., Yurkina O. On the Energy Spectrum of the 3D Velocity Field, Generated by an Ensemble of Vortex Loops. Low Temperature Phys. 2021;47(8):652—655.
9. Efimov V.B., Erlova A.A., Kondaurova L.P., Gorkun A.G. Heat Transfer under Pulsed Heating in Superfluid Helium. Low Temperature Phys. 2019;45(9):988—993.
10. Puzina Yu.Yu., Korolev P.V., Kryukov A.P. Techenie Heliya II v Kanale S Poristoy Vstavkoy pri Bezvikhrevom Sverkhtekuchem Dvizhenii. Vestnik MEI. 2017;4:8—14. (in Russian).
11. Vanderlaan M.H., Van Sciver S.W. He II Heat Transfer Through Random Packed Spheres: Pressure Drop. Cryogenics. 2014;63:37—42.
12. Vanderlaan M.H., Van Sciver S.W. Steady State He II Heat Transfer Through Random Packed Spheres. Cryogenics. 2013;57:166—172.
13. Allain H., Baudouy B., Quintard M., Prat M. Experimental Investigation of Heat Transfer Through Porous Media in Superfluid Helium. Cryogenics. 2015;66:53—62.
14. Allain H., Quintard M., Prat M., Baudouy B. Upscaling of Superfluid Helium flow in Porous Media. Intern. J. Heat and Mass Transfer. 2010;53:4852—4864.
15. Korolyov P.V., Kryukov A.P., Puzina Yu.Yu., Yachevsky I.A. Experiments of Superfluid Helium Flow in a Channel with a Monodisperse Backfill. J. Phys.: Conf. Series. 2020;1683:022017.
16. Kryukov A.P., Korolev P.V., Puzina Yu.Yu. Eksperimental'noe Issledovanie Kipeniya He II Vnutri Poristogo Tela. Prikladnaya Mekhanika i Tekhnicheskaya Fizika. 2017;4:126—134. (in Russian).
17. Muratova T.M., Labuntsov D.A. Kineticheskiy Analiz Protsessov Ispareniya i Kondensatsii. Teplofizika Vysokikh Temperatur. 1969;7(5):959—967. (in Russian).
18. Yastrebov A.K., Kryukov A.P. Teplomassoperenos Cherez Plenku Para s Uchetom Dvizheniya Mezhfaznoy Poverkhnosti Zhidkost'–Par i Rosta Temperatury Granitsy Razdela Faz. Teplofizika Vysokikh Temperatur. 2006;44(4):560—567. (in Russian).
19. Gorter C.J., Mellink J.H. On the Irreversible Processes in Liquid Helium II. Phys. 1949;XV;3—4:285—304.
20. Korolev P.V., Kryukov A.P. Dvizhenie Sverkhtekuchego Geliya v Kapillyare s Parom pri Nalichii Prodol'nogo Teplovogo Potoka. Vestnik MEI. 2002;1:43—46. (in Russian).
21. Amosov A.A., Dubinskiy Yu.A., Kopchenova N.V. Vychislitel'nye Metody dlya Inzhenerov. M.: Izd-vo MEI, 2003. (in Russian).
22. Kryukov A.P., Van Sciver S.W. Calculation of the Recovery Heat Flux Film Boiling in Superfluid Helium. Cryogenics. 1981;21(9):525—528.
23. Van Sciver S.W. Helium Cryogenics. N.-Y.: Plenum Press. 2012.
---
For citation: Puzina Yu.Yu., Kryukov A.P. Oscillations of the Helium II – Vapor Interface during Motion in a Channel of a Relatively Large Diameter. Bulletin of MPEI. 2023;3:138—144. (in Russian). DOI: 10.24160/1993-6982-2023-3-138-144
---
The work is executed at support: RFBR (Project No. 20-08-00342)
Published
2023-02-14
Section
Machines and apparatuses, processes of refrigeration and cryogenic engineering (technical sciences) (2.4.8.)
