Distribution of Liquid between the Core and Liquid Film in Gas-Droplet Flows at High Reduced Pressures
Abstract
The aim of the study is to develop an approximate but well-grounded model of droplet entrainment and deposition processes in annular two-phase flows at high reduced pressures. Very scarce experimental data are available for these conditions except for the indicators obtained by Nakazatomi and Sekoguchi (1996), who studied the distribution of liquid between the core and liquid film in a two-phase flow of air--water mixture at high pressures up to 20 MPa. These data feature an abnormally high fraction of entrained liquid in the flow core at pressures above 10 MPa and manifest very strong deviation from any known empirical correlations, including the Cioncolini and Thome's procedure published in 2012. The proposed droplets entrainment model takes into consideration the experimental observations according to which a liquid film becomes thin and smooth at high reduced pressures. A plenty of tiny droplets detach from the liquid film surface at the points the mutual spacing of which is determined by the Weber number for steam flow. This spacing and the liquid film thickness are the parameters governing the detached droplet diameter. An equation for calculating the entrainment intensity at high reduced pressures was constructed proceeding from these assumptions. However, it is rather difficult to verify this equation directly against experimental data because only the integral effect (i.e., the liquid flow rate in the film at dynamic equilibrium between entrainment and deposition) is usually measured in the experiments. The balance between the droplet entrainment and deposition flows due to turbulent diffusion corresponds to the dynamic equilibrium. The equation obtained proceeding from this balance contains one unknown numerical multiplier and allows one to calculate the liquid flow rate in the film. A comparison between the calculation results and the experimental data for a water–air flow at high reduced pressures has shown their good agreement at the universal value of a numerical constant in case of using an additional dimensionless parameter reflecting the ratio of phase densities.
References
2. Нигматулин Р.И. Динамика многофазных сред. Ч. I, II. М.: Наука, 1987.
3. Ягов В.В., Минко М.В. Моделирование уноса капель в адиабатных дисперсно-кольцевых двухфазных потоках // Теплоэнергетика. 2013. No 7. C. 1—6.
4. Нигматулин Б.И., Рачков В.И., Шугаев Ю.З. Исследование интенсивности уноса влаги с поверхности жидкой пленки при восходящем течении пароводяной смеси // Теплоэнергетика. 1981. No 4. C. 33—36.
5. Cioncolini A., Thome J.R. Entrained Liquid Fraction Prediction in Adiabatic and Evaporating Annular Two-Phase Flow // Nuclear Engineering and Design. 2012. V. 243. Pp. 200—213.
6. Минко М.В. Исследование механизмов процесса и разработка методов расчета теплообмена двухфазных потоков в каналах: дисс. ... канд. техн. наук. М.: НИУ«МЭИ», 2012.
7. Bhagwat S.M., Ghajar A.J. Modified Liquid Entrainment Fraction Correlation for Varying Pipe Orientation and System Pressure // Int. J. Multiphase Flow. 2015. V. 74. Pp. 1—4.
8. Nakazatomi M., Sekoguchi K. Effect of Pressure on Entrainment Flow Rate in Vertical Upwards Gas-liquid Annular Two-Phase Flow. Pt. I: Experimental Results for System Pressures from 0,3 MPa to 20 MPa // Heat Transfer – Japanese Research. 1996. V. 25. No. 5. Pp. 267—280.
9. Ягов В.В., Минко М.В. Распределение доли унесенной жидкости в адиабатных дисперсно-кольцевых потоках при низком расходе в пленке // Теплоэнергетика. 2016. No 4. С. 60—65.
10. Kirillov P.L., Shtein Yu. Yu., Shumsky R.V., Levchenko Yu.D. Experimental data on Phase Distribution in the Upward High Pressure Steam-Water Flow in a Vertical Tube Under Annular-Dispersed Regime. Pt. 1. Profiles of phase Mass Fluxes and velocities // Multiphase Science and Technology. 2014. V. 26. No. 2. Pp. 83—137.
11. Kirillov P. L., Shtein Yu. Yu., Shumsky R. V., Levchenko Yu.D. Experimental Data on Phase Distri-bution in the Upward High Pressure Steam-Water Flow in a Vertical Tube Under Annular-Dispersed Regime. Pt. 2. Structural and Local Hydrodynamic Characteristics of Flow // Multiphase Science and Technology. 2014. V. 26. No. 2. Pp. 83—137.
12. Минко М.В., Ягов В.В. Приближенная модель начала уноса капель в дисперсно-кольцевом двухфазном потоке // Вестник МЭИ. 2012. No 2. С. 30—33.
13. Berna C., Escrivá A., Muñoz-Cobo J.L., Herranz L.E. Review of Droplet Entrainment in Annular Flow: Interfacial Waves anD Onset of Entrainment // Progress in Nuclear Energy. 2014. V. 74. Pp. 14—43.
---
Для цитирования: Минко М.В., Ягов В.В. Распределение жидкости между ядром и жидкой пленкой в газокапельных потоках при высоких приведенных давлениях // Вестник МЭИ. 2017. № 3. С. 53—59. DOI: 10.24160/1993-6982-2017-3-53-59.
#
1. Minko M.V., Yagov V.V. Modelirovanie Raspredeleniya Zhidkosti Mezhdu Yadrom i Plenkoy v Adiabatnykh Dispersno-kol'tsevykh Dvukhfaznykh Potokakh. Teploenergetika. 2014;1:68—74. (in Russian).
2. Nigmatulin R.I. Dinamika Mnogofaznykh Sred. Ch. I, II. M.: Nauka, 1987. (in Russian).
3. Yagov V.V., Minko M.V. Modelirovanie Unosa Kapel' v Adiabatnykh Dispersno-kol'tsevykh Dvukhfaznykh Potokakh. Teploenergetika. 2013;7:1—6. (in Russian).
4. Nigmatulin B.I., Rachkov V.I., Shugaev Yu.Z. Issledovanie Intensivnosti Unosa Vlagi s Poverkhnosti Zhidkoy Plenki pri Voskhodyashchem Techenii Parovodyanoy Smesi. Teploenergetika. 1981;4:33—36. (in Russian).
5. Cioncolini A., Thome J.R. Entrained Liquid Fraction Prediction in Adiabatic and Evaporating Annular Two-phase Flow. Nuclear Engineering and Design. 2012;243:200—213.
6. Minko M.V. Issledovanie Mekhanizmov Protsessa i Razrabotka Metodov Rascheta Teploobmena Dvukhfaznykh Potokov v kanalakh: diss. ... Kand. Tekhn. Nauk. M.: NRU«MPEI», 2012. (in Russian).
7. Bhagwat S.M., Ghajar A.J. Modified Liquid Entrainment Fraction Correlation for Varying Pipe Orientation and System Pressure. Int. J. Multiphase Flow. 2015;74:1—4.
8. Nakazatomi M., Sekoguchi K. Effect of Pressure on Entrainment Flow Rate in Vertical Upwards Gas-liquid Annular Two-phase Flow. Pt. I: Experimental Results for System Pressures from 0,3 MPa to 20 MPa. Heat Transfer – Japanese Research. 1996;25;5:267—280.
9. Yagov V.V., Minko M.V. Raspredelenie Doli Unesennoy Zhidkosti v Adiabatnykh Dispersno-kol'tsevykh Potokakh pri Nizkom Raskhode v Plenke. Teploenergetika. 2016;4:60—65. (in Russian).
10. Kirillov P.L., Shtein Yu. Yu., Shumsky R.V., Levchenko Yu.D. Experimental data on Phase Distribution in the Upward High Pressure Steam-water Flow in a Vertical Tube Under Annular-dispersed Regime. Pt. 1. Profiles of phase Mass Fluxes and velocities. Multiphase Science and Technology. 2014;26;2:83—137.
11. Kirillov P. L., Shtein Yu. Yu., Shumsky R. V., Levchenko Yu.D. Experimental Data on Phase Distribution in the Upward High Pressure Steam-water Flow in a Vertical Tube Under Annular-dispersed Regime. Pt. 2. Structural and Local Hydrodynamic Characteristics of Flow. Multiphase Science and Technology. 2014;26.;2:83—137.
12. Minko M.V., Yagov V.V. Priblizhennaya Model' Nachala Unosa Kapel' v Dispersno-kol'tsevom Dvukhfaznom Potoke. Vestnik MPEI. 2012;2:30—33. (in Russian).
13. Berna C., Escrivá A., Muñoz-Cobo J.L., Herranz L.E. Review of Droplet Entrainment in Annular Flow: Interfacial Waves and Onset of Entrainment. Progress in Nuclear Energy. 2014;74:14—43.
---
For citation: Minko M.V., Yagov V.V. Distribution of Liquid between the Core and Liquid Film in Gas-Droplet Flows at High Reduced Pressures. MPEI Vestnik. 2017; 3:53—59. (in Russian). DOI: 10.24160/1993-6982-2017-3-53-59.
