Comparison of two-fluid models on steam-water transients
Lochon, Hippolyte1, 2, 3 ; Daude, Frédéric1, 2 ; Galon, Pascal2, 4 ; Hérard, Jean-Marc5, 3
1 EDF R&D, Département AMA, 1 Avenue du Général de Gaulle, 92141 Clamart cedex, France.
2 IMSIA, UMR EDF/CNRS/CEA/ENSTA 9219, 1 Avenue du Général de Gaulle, 92141 Clamart cedex, France.
3 I2M, UMR CNRS 7373, Technopôle Château-Gombert, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, France.
4 CEA, DEN, DANS, DM2S, SEMT, DYN, 91191 Gif-sur-Yvette cedex, France.
5 EDF R&D, Département MFEE, 6 Quai Watier, 78401 Chatou cedex, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1631-1657.

This paper is devoted to the comparison of three two-fluid models in steam-water applications involving phase transition and shock waves. The three models are presented in a common formalism that helps to underline their shared properties. A numerical method based on previous work is extended to all models and to more complex Equations Of State. Particular attention is paid to the verification of every step of the method so that convergence studies can be carried out. Afterwards, models are compared with each other and with experimental data in two different cases of steam-water transients. The first one is Simpson water-hammer experiment and the second one is a rapid depressurization with flashing studied in Canon experiment.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016001
Classification : 76T10, 35L60, 35L67
Mots-clés : Two-phase compressible flows, entropy inequality, closure laws, relaxation effects, finite volume schemes
Lochon, Hippolyte 1, 2, 3 ; Daude, Frédéric 1, 2 ; Galon, Pascal 2, 4 ; Hérard, Jean-Marc 5, 3

1 EDF R&D, Département AMA, 1 Avenue du Général de Gaulle, 92141 Clamart cedex, France.
2 IMSIA, UMR EDF/CNRS/CEA/ENSTA 9219, 1 Avenue du Général de Gaulle, 92141 Clamart cedex, France.
3 I2M, UMR CNRS 7373, Technopôle Château-Gombert, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, France.
4 CEA, DEN, DANS, DM2S, SEMT, DYN, 91191 Gif-sur-Yvette cedex, France.
5 EDF R&D, Département MFEE, 6 Quai Watier, 78401 Chatou cedex, France. 
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Lochon, Hippolyte; Daude, Frédéric; Galon, Pascal; Hérard, Jean-Marc. Comparison of two-fluid models on steam-water transients. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1631-1657. doi : 10.1051/m2an/2016001. http://www.numdam.org/articles/10.1051/m2an/2016001/

A. Ambroso, C. Chalons and P.-A. Raviart, A Godunov-type method for the seven-equation model of compressible two-phase flow. Comput. Fluids 54 (2012) 67–91. | DOI | Zbl

N. Andrianov and G. Warnecke, The Riemann problem for the Baer–Nunziato two-phase flow model. J. Comput. Phys. 195 (2004) 434–464. | DOI | Zbl

M.R. Baer and J.W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiphase Flow 12 (1986) 861–889. | DOI | Zbl

J.B. Bdzil, R. Menikoff, S.F. Son, A.K. Kapila and D.S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues. Phys. Fluids 11 (1999) 378–402. | DOI | Zbl

R. Berry, L. Zou, H. Zhao, D. Andrs, J. Peterson, H. Zhang and R. Martineau, Relap-7: Demonstrating Seven-Equation, Two-Phase Flow Simulation in a Single-Pipe, Two-Phase Reactor Core and Steam Separator/Dryer, Technical Report INL/EXT-13-28750, Idaho National Laboratory (INL) (2013).

A. Chinnayya, E. Daniel and R. Saurel, Modelling detonation waves in heterogeneous energetic materials. J. Comput. Phys. 196 (2004) 490–538. | DOI | Zbl

F. Coquel, T. Gallouët, J.-M. Hérard and N. Seguin, Closure laws for a two-fluid two-pressure model. C. R. Math. 334 (2002) 927–932. | DOI | Zbl

F. Coquel, J.-M. Hérard, K. Saleh and N. Seguin, A robust entropy-satisfying finite volume scheme for the isentropic Baer–Nunziato model. ESAIM: M2AN 48 (2014) 165–206. | DOI | Numdam | Zbl

F. Crouzet, F. Daude, P. Galon, P. Helluy, J.-M. Hérard, O. Hurisse and Y. Liu, Approximate solutions of the Baer-Nunziato Model. ESAIM: Procs. 40 (2013) 63–82. | DOI | Zbl

F. Crouzet, F. Daude, P. Galon, J.-M. Hérard, O. Hurisse and Y. Liu, Validation of a two-fluid model on unsteady liquid-vapor water flows. Comput. Fluids 119 (2015) 131–142. | DOI | Zbl

F. Daude, P. Galon, Z. Gao and E. Blaud, Numerical experiments using a HLLC-type scheme with ALE formulation for compressible two-phase flows five-equation models with phase transition. Comput. Fluids 94 (2014) 112–138. | DOI | Zbl

V. Deledicque and M.V. Papalexandris, An exact Riemann solver for compressible two-phase flow models containing non-conservative products. J. Comput. Phys. 222 (2007) 217–245. | DOI | Zbl

P. Downar-Zapolski, Z. Bilicki, L. Bolle and J. Franco, The non-equilibrium relaxation model for one-dimensional flashing liquid flow. Int. J. Multiphase Flow 22 (1996) 473–483. | DOI | Zbl

D.A. Drew and S.L. Passman, Theory of Multicomponent Fluids. Springer Verlag (1999). | Zbl

Europlexus, User’s Manual. Technical Report, Joint Reasearch Center (JRC), Commissariat là’énergie atomique et aux énergies alternatives (CEA). Available at http://europlexus.jrc.ec.europa.eu/public/manual˙html/index.html (2015).

T. Gallouët, J.-M. Hérard and N. Seguin, Numerical modeling of two-phase flows using the two-fluid two-pressure approach. Math. Models Methods Appl. Sci. 14 (2004) 663–700. | DOI | MR | Zbl

T. Gallouët, P. Helluy, J.-M. Hérard and J. Nussbaum, Hyperbolic relaxation models for granular flows. ESAIM: M2AN 44 (2010) 371–400. | DOI | Zbl

S. Gavrilyuk, The structure of pressure relaxation terms: one-velocity case. Internal report H-I83-2014-00276-EN, EDF R&D (2014).

S. Gavrilyuk and R. Saurel, Mathematical and numerical modeling of two-phase compressible flows with micro-inertia. J. Comput. Phys. 175 (2002) 326–360. | DOI | Zbl

J. Glimm, D. Saltz and D.H. Sharp, Renormalization group solution of two-phase flow equations for Rayleigh-Taylor mixing. Phys. Lett. A 222 (1996) 171–176. | DOI | Zbl

V. Guillemaud, Modélisation et simulation numérique des écoulements diphasiques par une approche bifluide à deux pressions. Ph.D. thesis, Université de Provence - Aix-Marseille I. Available at https://tel.archives-ouvertes.fr/tel-00169178/document (2007).

J.-M. Hérard, A three-phase flow model. Math. Comput. Model. 45 (2007) 732–755. | DOI | Zbl

J.-M. Hérard, Une classe de modèles diphasiques bifluides avec changement de régime. Internal report H-I81-2010-00486-FR, EDF (2010).

J.-M. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas-liquid flows. Comput. Fluids 55 (2012) 57–69. | DOI | Zbl

J.-M. Hérard and Y. Liu, Une approche bifluide statistique de modélisation des écoulements diphasiques à phases compressibles. Internal report H-I81-2013-01162-FR, EDF (2013).

M. Ishii, Thermo-fluid dynamic theory of two-phase flows. Collection de la Direction des Etudes et Recherches d’Electricité de France. Eyrolles, Paris (1975). | Zbl

H. Jin, J. Glimm and D.H. Sharp, Entropy of averaging for compressible two-pressure two-phase flow models. Phys. Lett. A 360 (2006) 114–121. | DOI | Zbl

A.K. Kapila, S.F. Son, J.B. Bdzil, R. Menikoff and D.S. Stewart, Two-phase modeling of DDT: Structure of the velocity-relaxation zone. Phys. Fluids 9 (1997) 3885–3897. | DOI

J. Laviéville, M. Boucker, E. Quemerais, S. Mimouni and N. Méchitoua, NEPTUNECFD V1.0 - Theory Manual. Internal report H-I81-2006-04377-EN. EDF R&D (2006).

O. Le Métayer, J. Massoni and R. Saurel, Élaboration des lois d’état d’un liquide et de sa vapeur pour les modèles d’écoulements diphasiques. Int. J. Thermal Sci. 43 (2004) 265–276. | DOI

O. Le Métayer, J. Massoni and R. Saurel, Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena. ESAIM: Procs. 40 (2013) 103–123. | DOI | Zbl

H. Lochon, Modélisation d’écoulements diphasiques: fermetures entropiques de modèles bifluides. Internal report H-T63-2014-10406-FR. EDF (2014).

S. Müller, M. Hantke, and P. Richter. Closure conditions for non-equilibrium multi-component models. Contin. Mech. Thermodyn. 28 (2016) 1157–1189. | DOI | Zbl

M. Pelanti and K.-M. Shyue, A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259 (2014) 331–357. | DOI | MR | Zbl

V.H. Ransom and D.L. Hicks, Hyperbolic two-pressure models for two-phase flow. J. Comput. Phys. 53 (1984) 124–151. | DOI | Zbl

RELAP5-3d, Code Manual Volume IV: Models and Correlations. Technical Report INEEL-EXT-98-00834, Idaho National Laboratory (INL) (2012).

B. Riegel, Contribution àl’étude de la décompression d’une capacité en regime diphasique. Ph.D. thesis, Université Scientifique et Médicale et Institut National Polytechnique de Grenoble (1978).

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows. J. Comput. Phys. 150 (1999) 425–467. | DOI | Zbl

D.W. Schwendeman, C.W. Wahle and A.K. Kapila, The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow. J. Comput. Phys. 212 (2006) 490–526. | DOI | Zbl

A.R. Simpson, Large water hammer pressures due to column separation in sloping pipes. Ph.D. thesis, University of Michigan (1986).

S. Tokareva and E. Toro, HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow. J. Comput. Phys. 229 (2010) 3573–3604. | DOI | Zbl

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