Critical (choked) flow is a highly concerning phenomenon in safety analysis for nuclear energy. The discharge mass flow rate prediction is crucial for engineering design and emergency response in case of nuclear accidents. Unfortunately, the critical flow is difficult to predict especially when the two-phase flow exists. The accuracy is based on a deeper understanding of the complex phenomenon of critical flow. The influence of virtual mass force on the two-phase critical flow was seldom concentrated on owing to the lack of suitable critical flow models for studies in detail. This study is based on a developed 6-equation two-phase critical flow model. It is confirmed that the virtual mass force contributes to the stability and convergence of the critical flow simulation and it will impact not only the critical mass flux but also the thermal hydraulic parameters along the discharge duct. The magnitude depends on the geometry of the discharge duct and the upstream condition. It is larger when the duct is longer and the pressure is lower. Furthermore, the virtual mass force for each flow regime was studied in detail with a sensitivity study. The results show that the most sensible condition for the virtual mass force is annular flow along a long tube under relatively low pressure. The future work is to develop a correlation of virtual mass force for critical flow specifically since the correlations in the literature were developed under general two-phase flow process conditions.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
Al-Sahan, M.A. (1988). On the development of the flow regimes and the formulation of a mechanistic non-equilibrium model for critical two-phase flow. University of Toronto, Ph.D. thesis.Search in Google Scholar
Biesheuvel, A. and Spoelstra, S. (1989). The added mass coefficient of a dispersion of spherical gas bubbles in liquid. Int. J. Multiphas. Flow 15: 911–924, https://doi.org/10.1016/0301-9322(89)90020-7.Search in Google Scholar
Cao, F., Yang, W., Li, L., Qiu, J., and Shan, J. (2021). Eigenvalue analysis of well-posedness of two-fluid single pressure model with virtual mass force and interfacial pressure (ICONE28-64434). In: Proceedings of the 28th international conference on nuclear engineering (ICONE28), Virtual, Online.10.1115/ICONE28-64434Search in Google Scholar
Cheng, L.Y., Drew, D.A., and Lahey, R.T.Jr (1978). Virtual mass effects in two phase flow. Rensselaer Polytechnic Institute (USA), Department of Nuclear Engineering, Technical Report, NUREG/CR0020.Search in Google Scholar
Cheng, L.Y., Lahey, R.T.Jr, and Drew, D.A. (1983). The effect of virtual mass on the prediction of critical flow. Specialist meeting on transient two-phase flowMarch, Pasadena, CA (USA), 23-25 March, 1981.Search in Google Scholar
Dagan, R., Elias, E., Wacholder, E., und Olek, S. (1993). A two-fluid model for critical flashing flows in pipes. Int. J. Multiphas. Flow 19: 15–25, https://doi.org/10.1016/0301-9322(93)90019-Q.Search in Google Scholar
Dobran, F. (1987). Nonequilibrium modeling of two-phase critical flows in tubes. Transactions - ASME J. Heat Tran. 109: 731–738, https://doi.org/10.1115/1.3248151.Search in Google Scholar
Drew, D., Cheng, L., and Lahey, R.T.Jr (1979). The analysis of virtual mass effects in two-phase flow. Int. J. Multiphas. Flow 5: 233–242, https://doi.org/10.1016/0301-9322(79)90023-5.Search in Google Scholar
Dueñas, A.M. (2019). Investigation of drag coefficient and virtual mass coefficient on rising ellipsoidal bubbles, Master thesis. Oregon State University.Search in Google Scholar
Fullmer, W.D. and De Bertodano, M.A.L. (2015). An assessment of the virtual mass force in RELAP5/MOD3.3 for the bubbly flow regime. Nucl. Technol. 191: 185–192, https://doi.org/10.13182/NT14-110.Search in Google Scholar
Huang, Y. (2000). Sources and strategies of uncertainties of calculated results in large thermal-hydraulics safety analysis code. Nucl. Power Eng. 21: 248–252.Search in Google Scholar
Ishii, M. and Hibiki, T. (2011). Thermo-fluid dynamics of two-phase flow, 2nd ed. Springer, NewYork.10.1007/978-1-4419-7985-8Search in Google Scholar
Ishii, M. and Zuber, N. (1979). Drag coefficient and relative velocity in bubble droplet or particulate flows. AIChE J. 25: 843–855, https://doi.org/10.1002/aic.690250513.Search in Google Scholar
Javidmand, P. and Hoffmann, K.A. (2015). Comprehensive two fluid model simulation of critical two-phase flow through short tube orifices. In: Proceedings of the ASME 2015 international technical conference and exhibition on packaging and integration of electronic and photonic microsystems and ASME 2015 12th international Conference on nanochannels, microchannels, and minichannels, July 6–19, 2015. San Francisco, California, USA, pp. 1–13.10.1115/ICNMM2015-48047Search in Google Scholar
Lahey, R.T.Jr, Cheng, L.Y., Drew, D.A., and Flaherty, J.E. (1980). The effect of virtual mass on the numerical stability of accelerating two-phase flows. Int. J. Multiphas. Flow 6: 281–294, https://doi.org/10.1016/0301-9322(80)90021-X.Search in Google Scholar
Lamb, H. (1932). Hydrodynamics, 6th ed. Dover Publications, New York.Search in Google Scholar
No, H.C. and Kazimi, M.S. (1981). The effect of virtual mass on the characteristics and the numerical stability in two-phase flow. Massachusetts Institute of Technology, Energy Laboratory Report, No. MIT-EL 81-023.10.2172/5188099Search in Google Scholar
Richter, H.J. (1983). Separated two-phase flow model: application to critical two-phase flow. Int. J. Multiphas. Flow 9: 511–530, https://doi.org/10.1016/0301-9322(83)90015-0.Search in Google Scholar
Schwellnus, C.F. and Shoukri, M. (1991). A two-fluid model for non-equilibrium two-phase critical discharge. Can. J. Chem. Eng. 69: 188–197, https://doi.org/10.1002/cjce.5450690122.Search in Google Scholar
Van Wijngaarden, L. and Jeffrey, D.J. (1976). Hydrodynamic interaction between gas bubbles in liquid. J. Fluid Mech. 77: 27–44, https://doi.org/10.1017/S0022112076001110.Search in Google Scholar
Wein, M. (2002). Simulation von kritischen und nahkritischen Zweiphasenströmungen mit thermischen und fluiddynamischen Nichtgleichgewichtseffekten, Ph.D. thesis. Technische Universität Dresden.Search in Google Scholar
Xu, H. (2020). Improvement of PWR (LOCA) safety analysis based on PKL experimental data, PhD dissertation. Karlsruhe Institute of Technology.Search in Google Scholar
Xu, H. (2021). Review and outlook of the integral test facility PKL III corresponding studies. Kerntechnik 86: 391–399, https://doi.org/10.1515/kern-2021-1011.Search in Google Scholar
Xu, H., Badea, A.F., and Cheng, X. (2021a). Analysis of two phase critical flow with a non-equilibrium model. Nucl. Eng. Des. 372: 110998, https://doi.org/10.1016/j.nucengdes.2020.110998.Search in Google Scholar
Xu, H., Badea, A.F., and Cheng, X. (2021b). Development of a new full-range critical flow model based on non-homogeneous non-equilibrium model. Ann. Nucl. Energy 158: 108286, https://doi.org/10.1016/j.anucene.2021.108286.Search in Google Scholar
Xu, H., Badea, A.F., and Cheng, X. (2021c). Studies on the criterion for choking process in two-phase flow. Prog. Nucl. Energy 133: 103640, https://doi.org/10.1016/j.pnucene.2021.103640.Search in Google Scholar
Xu, H., Badea, A.F., and Cheng, X. (2022a). ATHLET simulation of PKL IBLOCA I2.2 benchmark test and quantitative assessment. Nucl. Technol. 208: 1324–1336, https://doi.org/10.1080/00295450.2021.2014755.Search in Google Scholar
Xu, H., Badea, A.F., and Cheng, X. (2022b). Optimization of the nodalization of nuclear system thermal-hydraulic code applied on PKL benchmark. J. Nucl. Eng. Radiat. Sci. 8: 1–12, https://doi.org/10.1115/1.4050770.Search in Google Scholar
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