A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow

DOI: 10.4236/am.2015.612179   PDF   HTML   XML   1,636 Downloads   2,176 Views  


A theoretical “drift-flux based thermal-hydraulic mixture-fluid coolant channel model” is presented. It is the basis to a corresponding digital “Coolant Channel Module (CCM)”. This purpose derived “Separate-Region Mixture Fluid Approach” should yield an alternative platform to the currently dominant “Separate-Phase Models” where each phase is treated separately. Contrary to it, a direct procedure could be established with the objective to simulate in an as general as possible way the steady state and transient behaviour of characteristic parameters of single- and/or (now non-separated) two-phase fluids flowing within any type of heated or non-heated coolant channels. Their validity could be confirmed by a wide range of verification and validation runs, showing very satisfactory results. The resulting universally applicable code package CCM should provide a fundamental element for the simulation of thermal-hydraulic situations over a wide range of complex systems (such as different types of heat exchangers and steam generators as being applied in both conventional but also nuclear power stations, 1D and 3D nuclear reactor cores etc). Thereby the derived set of equations for different coolant channels (distinguished by their key numbers) as appearing in these systems can be combined with other ODE-s and non-linear algebraic relations from additional parts of such an overall model. And these can then to be solved by applying an appropriate integration routine. Within the solution procedure, however, mathematical discontinuities can arise. This due to the fact that along such a coolant channel transitions from single- to two-phase flow regimes and vice versa could take place. To circumvent these difficulties it will in the presented approach be proposed that the basic coolant channel (BC) is subdivided into a number of sub-channels (SC-s), each of them being occupied exclusively by only a single or a two-phase flow regime. After an appropriate nodalization of the BC (and thus its SC-s) and after applying a “modified finite volume method” together with other special activities the fundamental set of non-linear thermal-hydraulic partial differential equations together with corresponding constitutive relations can be solved for each SC separately. As a result of such a spatial discretization for each SC type (and thus the entire BC) the wanted set of non-linear ordinary differential equations of 1st order could be established. Obviously, special attention had to be given to the varying SC entrance or outlet positions, describing the movement of boiling boundaries or mixture levels along the channel. Including even the possibility of SC-s to disappear or be created anew during a transient.

Share and Cite:

Hoeld, A. (2015) A Thermal-Hydraulic Coolant Channel Module (CCM) for Single- and Two-Phase Flow. Applied Mathematics, 6, 2014-2044. doi: 10.4236/am.2015.612179.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Liles, D.R., et al. (1988) TRAC-PF1/MOD1—Correlations and Models. NUREG/CR-5069, LA-11208-MS.
[2] US-NRC (2001) TRAC-M / FORTRAN90. Version 3.0, Theory Manual, NUREG/CR-6724.
[3] Hanna, B.N. (1998) CATENA. A Thermalhydraulic Code for CANDU Analysis. Nuclear Engineering and Design, 180, 113-131.
[4] Shultz, R.R. (2003) RELAP5-3D Code Manual. Volume V: User’s Guidelines. INEEL-EXT-98-00084.
[5] US-NRC (2001) RELAP5/ MOD3.3. Code Manual. NUREG/CR-5535.
[6] Bestion, D. (1990) The Physical Closure Laws in CATHARE Code. Nuclear Engineering and Design, 124, 229-245.
[7] Austregesilo, H., et al. (2003) ATHLET Mod 2.0, Cycle A, Models and Methods. GRS-P-1/Vol.4.
[8] Lerchl, G., et al. (2009) ATHLET Mod 2.2, Cycle B, User’s Manual. GRS-P-1/Vol.1.
[9] Hoeld, A. (1978) A Theoretical Model for the Calculation of Large Transients in Nuclear Natural Circulation U-Tube Steam Generators (Digital Code UTSG). Nuclear Engineering and Design, 47.
[10] Hoeld, A. (1990) UTSG-2. A Theoretical Model Describing the Transient Behaviour of a PWR Natural-Circulation U-Tube Steam Generator. Nuclear Technology, 90, 98-118.
[11] Hoeld, A. (1990) The Code ATHLET as a Valuable Tool for the Analysis of Transients with and without SCRAM. SCS Eastern MultiConference, Nashville, 23-26 April 1990.
[12] Hoeld, A. (2011) Coolant Channel Module CCM. An Universally Applicable Thermal-Hydraulic Drift-Flux Based Separate-Region Mixture-Fluid Model. In: Uchanin, V., Ed., INTECH Open Access Book “Steam Generator Systems: Operational Reliability and Efficiency”, InTech, Austria.
[13] Hoeld, A. (2011) The Thermal-Hydraulic U-Tube Steam Generator Model and Code UTSG3 (Based on the Universally Applicable Coolant Channel Module CCM). See INTECH Open Access Book Referred Above.
[14] Hoeld, A. (2013) The Coolant Channel Module CCM—A Basic Element for the Construction of Thermal-Hydraulic Models and Codes. In: Guillen, D.P., Ed., INTECH Open Access Book “Nuclear Reactor Thermal Hydraulics and other Applications”, InTech, Croatia, 3-44.
[15] Hoeld, A. (1996) Thermodynamisches Stoffwertpaket MPP für Wasser und Dampf. GRS, Technische Notiz, TN-HOD-1/96, Mai.
[16] Schmidt, E. and Grigull, U. (Ed.) (1982) Properties of Water and Steam in SI-Units. Springer-Verlag.
[17] Haar, L., Gallagher, J.S., Kell, G.S. and Grigull, U. (1988) NBS/NRC Wasserdampftafeln. London/Paris/New York.
[18] Moody, N.L.F. (1994) Friction Factors for Pipe Flow. Trans ASME, 66, 671. (See Also VDI-Wärmeatlas, 7 Auflage 1994,VDI-Verlag)
[19] Martinelli, R.C. and Nelson, D.B. (1948) Prediction of Pressure Drop during Forced-Circulation of Boiling Water. Trans.ASME, 70, 695.
[20] Sonnenburg, H.G. (1989) Full-Range Drift-Flux Model Based on the Combination of Drift-Flux Theory with Envelope Theory. NURETH-4, Karlsruhe, 10-13 October 1989, 1003-1009.
[21] Hoeld, A., Jakubowska, E., Miro, J.E. and Sonnenburg, H.G. (1992) A Comparative Study on Slip and Drift-Flux Correlations. GRS-A-1879.
[22] Hoeld, A. (2001) The Drift-Flux Correlation Package MDS. 9th International Conference on Nuclear Engineering (ICONE-9), Nice, 8-12 April 2001.
[23] Hoeld, A. (2002) The Consideration of Entrainment in the Drift-Flux Correlation Package MDS. 10th International Conference on Nuclear Engineering (ICONE-10), Arlington, 14-18 April 2002.
[24] Zuber, N. and Findlay, J.A. (1965) Average Volume Concentration in Two-Phase Flow Systems. Journal of Heat Transfer, 87, 453.
[25] Ishii, M. and Mishima, K. (1980) Study of Two-Fluid Model and Interfacial Area. NUREG/CR-1873 (ANL-80-111).
[26] Ishii, M. (1990) Two-Fluid Model for Two-Phase Flow. Multiphase Sci. and Techn. 5.1, Hemisphere Publ. Corp.
[27] Hoeld, A. (2004) A Theoretical Concept for a Thermal-Hydraulic 3D Parallel Channel Core Model. PHYSOR 2004, 25-29 April 2004, Chicago.
[28] Jewer, S., Beeley, P.A., Thompson, A. and Hoeld, A. (2005) Initial Version of an Integrated Thermal-Hydraulic and Neutron Kinetics 3D Code X3D. ICONE13, 16-20 May 2005, Beijing. See also NED 236(2006), 1533-1546.
[29] Hoeld, A. (1999) An Advanced Natural-Circulation U-Tube Steam Generator Model and Code UTSG-3. EUROTHERM-SEMINAR No. 63, 6-8 September 1999, Genoa.
[30] Hoeld, A. (2002) A Steam Generator Code on the Basis of the General Coolant Channel Module CCM. PHYSOR 2002, 7-10 October 2002, Seoul.
[31] Hoeld, A. (2000) The Module CCM for the Simulation of the Thermal-Hydraulic Situation within a Coolant Channel. International NSS/ENS Conference, Bled, 11-14 September 2000.
[32] Hoeld, A. (2004) Are Separate-Phase Thermal-Hydraulic Models Better than Mixture-Fluid Approaches. It Depends. Rather Not. International Conference on Nuclear Engineering for New Europe, Portoroz, 6-9 September 2004.
[33] Hoeld, A. (2005) A Thermal-Hydraulic Drift-Flux Based Mixture-Fluid Model for the Description of Single- and Two-Phase Flow along a General Coolant Channel. The 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-11), Paper 144, Avignon, 2-6 October 2005.
[34] Hoeld, A. (2007) Coolant Channel Module CCM. An Universally Applicable Thermal-Hydraulic Drift-Flux Based Mixture-Fluid 1D Model and Code. Nuclear Engineering and Design, 237, 1952-1967.
[35] Hoeld, A. (2007) Application of the Mixture-Fluid Channel Element CCM within the U-Tube Steam Generator Code UTSG-3 for Transient Thermal-Hydraulic Calculations. 15th International Conference on Nuclear Engineering (ICONE-15), Paper 10206, Nagoya, April 22-26 2007.
[36] Fabic, S. (1996) How Good Are Thermal-Hydraulics Codes for Analyses of Plant Transients. International ENS/HND Conference, Opatija, 7-9 October 1996, 193-201.
[37] Hoeld, A. (1988) HETRAC: A Heat Transfer Coefficients Package. GRS-A-1446.
[38] Hoeld, A. (1988) Calculation of the Time Behavior of PWR NPP during a Loss of a Feedwater ATWS Case. NUCSAFE 88, Avignon, 2-7 October 1988, 1037-1047.
[39] Bencik, V. and Hoeld, A. (1991) Experiences in the Validation of Large Advanced Modular System Codes. SCS Simulation MultiConference, New Orleans, 1-5 April 1991.
[40] Bencik, V. and Hoeld, A. (1993) Steam Collector and Main Steam System in a Multi-Loop PWR NPP Representation. Simulation MultiConference, Arlington, 29 March-1 April 1993.
[41] Hoeld, A. (2015) Coolant Channel Module CCM (Detailed Derivation of the Characteristic Model Equations). Private Communication.
[42] Hoeld, A. (2015) Quadratic Polygon Approximation Procedure PAX (Detailed Derivation of the Characteristic Model Equations). Private Communication.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.