A Review of the Relaxation Models for Phase Transition Flows Centered on the Topological Aspects of the Nonequilibrium Mass Transfer Modelling

1 Saha P. Review of two-phase steam-water critical flow models with emphasis on thermal nonequilibrium.1977; NUREG/CR-0417. United States. Search in Google Scholar

2 Richter HJ. Separated two-phase flow model: application to critical two-phase flow. International Journal of Multiphase Flow. 1983; 9(5): 511-530. ISSN 0301-9322. https://doi.org/10.1016/0301-9322(83)90015-0 Search in Google Scholar

3 Ishii M, Hibiki T. Thermo-Fluid Dynamics of Two-Phase Flow. 1975. Second Edition. Springer. Search in Google Scholar

4 Staedtke H. Gasdynamic Aspects of Two-Phase Flow: Hyperbolicity, Wave Propagation Phenomena and Related Numerical Methods. Wiley-VCH. 1st edition (October 6, 2006). Search in Google Scholar

5 Baer MR, Nunziato, JW. A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiph. Flow. 1986;12: 861–889. Search in Google Scholar

6 Zhang C, Menshov I, Wang L, Shen Z. Diffuse interface relaxation model for two-phase compressible flows with diffusion processes. Journal of Computational Physics. 2022; 466: 111356. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2022.111356 Search in Google Scholar

7 Bdzil JB, Menikoff R, Kapila AK, Stewart DS. Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues. Physics of fluids. 1999; 11: 2; 378-402. https://doi.org/10.1063/1.869887 Search in Google Scholar

8 Kapila AK, Menikoff R, Bdzil JB, Stewart DS. Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations. Physics of fluids. 2001;13(10):3002-3024. https://doi.org/10.1063/1.1398042 Search in Google Scholar

9 Pelanti M. Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer. International Journal of Multiphase Flow. 2022;153:104097. ISSN 0301-9322. https://doi.org/10.1016/j.ijmultiphaseflow.2022.104097 Search in Google Scholar

10 Saurel R, Petitpas F, Abgrall R. Modelling phase transition in meta-stable liquids: application to cavitating and flashing flows. Journal of Fluid Mechanics. 2008;60:313–350. https://doi.org/10.1017/S0022112008002061 Search in Google Scholar

11 LeMartelot S, Nkonga B, Saurel R, Liquid and liquid-gas flows at all speeds. Journal of Computational Physics 255. 2013;53–82. https://doi.org/10.1016/j.jcp.2013.08.001 Search in Google Scholar

12 Lund H, Aursand P. Two-Phase Flow of CO2 with Phase Transfer. Energy Procedia. 2012;23:246-255. ISSN 1876-6102. https://doi.org/10.1016/j.egypro.2012.06.034 Search in Google Scholar

13 Le Martelot S, Saurel R, Nkonga B. Towards the direct numerical simulation of nucleate boiling flows. International Journal of Multi-phase Flow. 2014;66:62-78. ISSN 0301-9322. https://doi.org/10.1016/j.ijmultiphaseflow.2014.06.010 Search in Google Scholar

14 Saurel R, Boivin P, Le Métayer O. A general formulation for cavitating, boiling and evaporating flows. Computers & Fluids. 2016; 128: 53-64, ISSN 0045-7930. https://doi.org/10.1016/j.compfluid.2016.01.004 Search in Google Scholar

15 Chiapolino A, Boivin P, Saurel. A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows. Computers & Fluids. 2017; 150: 31-45. ISSN 0045-7930. https://doi.org/10.1016/j.compfluid.2017.03.022 Search in Google Scholar

16 Demou AD, Scapin N, Pelanti M, Brandt L. A pressure-based diffuse interface method for low-Mach multiphase flows with mass transfer. Journal of Computational Physics. 2022;448:110730. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2021.110730 Search in Google Scholar

17 Stewart HB, Wendroff B. Two-phase flow: models and methods. Journal of Computational Physics. 1984;56(3):363-409. Search in Google Scholar

18 Bilicki Z, Kestin J. Physical aspects of the relaxation model in two-phase flow. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 1990;428(1875):379-397. Search in Google Scholar

19 Downar-Zapolski P, Bilicki Z, Bolle L, Franco J. The non-equilibrium relaxation model for one-dimensional flashing liquid flow. International Journal of Multiphase Flow. 1996;22(3): 473-483. ISSN 0301-9322. https://doi.org/10.1016/0301-9322(95)00078-X Search in Google Scholar

20 Atkins P, de Paula J. Physical Chemistry. 2006; 8th ed. W.H. Freeman: 805-7. ISBN 0-7167-8759-8 Search in Google Scholar

21 Einstein A. Schallausbreitung in teilweise dissoziierten Gasen [Sound propagation in partly dissociated gases]: 380-385. Search in Google Scholar

22 Mandelshtam, LI, Leontovich EM. A theory of sound absorption in liquids. Zh. Exp. Teor Fiz. 1937;7:434-449 (in Russian). Search in Google Scholar

23 Bauer EG, Houdayer, GR, Sureau HM. A non-equilibrium axial flow model in application to loss-of-coolant accident analysis. The CYSTERE system code. OECD/NEA Specialist Meeting on Transient Two-phase Flow. 1976. Toronto Canada. Search in Google Scholar

24 Angielczyk W, Bartosiewicz Y, Butrymowicz D, Seynhaeve J-M. 1-D modelling of supersonic carbon dioxide two-phase flow through ejector motive nozzle. International Refrigeration and Air Conditioning Conference. 2010. Purdue USA. Search in Google Scholar

25 Haida M, Smolka J, Hafner A, Palacz M, Banasiak K, Nowak AJ. Modified homogeneous relaxation model for the R744 transcritical flow in a two-phase ejector, International Journal of Refrigeration. 2018;85:314-333. ISSN 0140-7007. https://doi.org/10.1016/j.ijrefrig.2017.10.010 Search in Google Scholar

26 Feburie V, Giot M, Granger S, Seynhaeve J. A model for choked flow through cracks with inlet subcooling. International Journal of Multi-phase Flow. 1993;19(4):541–562. https://doi:10.1016/0301-9322(93)90087-b Search in Google Scholar

27 Attou A, Seynhaeve JM. Steady-state critical two-phase flashing flow with possible multiple choking phenomenon. Part 1: physical modelling and numerical procedure. Journal of Loss Prevention in the Industries. 1999;12:335-345. https://doi.org/10.1016/S0950-4230(98)00017-5 Search in Google Scholar

28 De Lorenzo M, Lafon P, Seynhaeve JM, Bartosiewicz Y. Benchmark of Delayed Equilibrium Model (DEM) and classic two-phase critical flow models against experimental data. International Journal of Multiphase Flow. 2017;92:112-130. ISSN 0301-9322. https://doi.org/10.1016/j.ijmultiphaseflow.2017.03.004 Search in Google Scholar

29 Angielczyk W, Bartosiewicz Y, Butrymowicz D. Development of Delayed Equilibrium Model for CO2 convergent-divergent nozzle transonic flashing flow. International Journal of Multiphase Flow. 2020;131:103351. ISSN 0301-9322. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103351 Search in Google Scholar

30 Tammone C, Romei A, Persico G, Haglind F. Extension of the delayed equilibrium model to flashing flows of organic fluids in converging-diverging nozzles. International Journal of Multiphase Flow. 2024; 171:104661. ISSN 0301-9322. https://doi.org/10.1016/j.ijmultiphaseflow.2023.104661 Search in Google Scholar

31 Ambroso A, Hérard J-M, Hurisse O. A method to couple HEM and HRM two-phase flow models. Computers & Fluids. 2009;38(4):738-756, ISSN 0045-7930. https://doi.org/10.1016/j.compfluid.2008.04.016 Search in Google Scholar

32 Palacz M, Haida M, Smolka J, Nowak AJ, Banasiak K, Hafner A. HEM and HRM accuracy comparison for the simulation of CO2 expansion in two-phase ejectors for supermarket refrigeration systems. Applied Thermal Engineering. 2017;115:160-169. ISSN 1359-4311. https://doi.org/10.1016/j.applthermaleng.2016.12.122 Search in Google Scholar

33 James F, Mathis H. A relaxation model for liquid-vapor phase change with metastability. 2015 arXiv preprint arXiv:1507.06333. https://doi.org/10.48550/arXiv.1507.06333 Search in Google Scholar

34 De Lorenzo M, Lafon Ph, Pelanti M. A hyperbolic phase-transition model with non-instantaneous EoS-independent relaxation procedures. Journal of Computational Physics. 2019;379: 279-308. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2018.12.002 Search in Google Scholar

35 De Lorenzo M, Lafon Ph, Pelanti M, Pantano A, Di Matteo M, Bartosiewicz Y, Seynhaeve JM. A hyperbolic phase-transition model coupled to tabulated EoS for two-phase flows in fast depressurizations. Nuclear Engineering and Design. 2021;371:110954. ISSN 0029-5493. https://doi.org/10.1016/j.nucengdes.2020.110954 Search in Google Scholar

36 Ward CA. The rate of gas absorption at a liquid interface. The Journal of Chemical Physics. 1977; 67(1): 229-235. https://doi.org/10.1063/1.434547 Search in Google Scholar

37 Ward CA, Findlay RD, Rizk M. Statistical rate theory of interfacial transport. I. Theoretical development. The Journal of Chemical Physics. 1982;76(11):5599-5605. https://doi.org/10.1063/1.442865 Search in Google Scholar

38 Ward CA, Fang G. Expression for predicting liquid evaporation flux: Statistical rate theory approach. Physical Review. 1999;59(1): 429. https://doi.org/10.1103/PhysRevE.59.429 Search in Google Scholar

39 Schrage RW. A theoretical study of interphase mass transfer. 1953. Columbia University Press. https://doi.org/10.7312/schr90162 Search in Google Scholar

40 Banasiak K, Hafner A. 1D Computational model of a two-phase R744 ejector for expansion work recovery. International Journal of Thermal Sciences. 2011;50(11):2235-2247. ISSN 1290-0729. https://doi.org/10.1016/j.ijthermalsci.2011.06.007 Search in Google Scholar

41 Bodys J, Smolka J, Palacz M, HaidaM, Banasiak K. Non-equilibrium approach for the simulation of CO2 expansion in two-phase ejector driven by subcritical motive pressure. International Journal of Refrigeration. 2020;114:32-46. ISSN 0140-7007. https://doi.org/10.1016/j.ijrefrig.2020.02.015 Search in Google Scholar

42 Bodys J, Smolka J, Palacz M, Haida M, Banasiak K, Nowak AJ. Effect of turbulence models and cavitation intensity on the motive and suction nozzle mass flow rate prediction during a non-equilibrium expansion process in the CO2 ejector. Applied Thermal Engineering. 2022;201:117743, ISSN 1359-4311. https://doi.org/10.1016/j.applthermaleng.2021.117743 Search in Google Scholar

43 Bilicki Z, Dafermos C, Kestin J, Majda G, Zeng DL. Trajectories and singular points in steady-state models of two-phase flows. International journal of multiphase flow. 1987; 13(4): 511-533. Search in Google Scholar

44 De Sterck H. Critical point analysis of transonic flow profiles with heat conduction. SIAM Journal on Applied Dynamical Systems. 2007; 6(3): 645-662. https://doi.org/10.1137/060677458 Search in Google Scholar

45 Angielczyk W, Bartosiewicz Y, Butrymowicz, Seynhaeve, JM. 1-D modeling of supersonic carbon dioxide two-phase flow through ejector motive nozzle. International Refrigeration and Air Conditioning Conference. 2010. Search in Google Scholar

46 Angielczyk W, Śmierciew K, Butrymowicz D. Application of a fast transonic trajectory determination approach in 1-D modelling of steady-state two-phase carbon dioxide flow. In E3S Web of Conferences. 2019; 128: 06005, EDP Sciences. https://doi.org/10.1051/e3sconf/201912806005 Search in Google Scholar

47 Angielczyk W, Seynhaeve JM, Gagan J, Bartosiewicz Y, Butrymowicz D. Prediction of critical mass rate of flashing carbon dioxide flow in convergent-divergent nozzle. Chemical Engineering and Processing - Process Intensification. 2019; 143: 107599. ISSN 0255-2701. https://doi.org/10.1016/j.cep.2019.107599 Search in Google Scholar

48 Angielczyk W, Butrymowicz D. Revisiting the relaxation equations describing nonequilibrium mass transfer in the transonic homogeneous flashing flow models. Postępy w badaniach wymiany ciepła i masy: Monografia Konferencyjna XVI Sympozjum Wymiany Ciepła I Masy. 2022; 113-123. Białystok. Oficyna Wydawnicza Politechniki Białostockiej. ISBN 978-83-67185-30-1. https://doi.org/10.24427/978-83-67185-30-1_13 Search in Google Scholar