**RSICC CODE PACKAGE PSR-507**

**1. NAME AND TITLE**

** **COBRA-EN: Code System for Thermal-Hydraulic Transient Analysis of Light Water Reactor
Fuel Assemblies and Cores.

**2. CONTRIBUTORS**

ENEL SpA, Milano, Italy, through the Nuclear Energy Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE AND COMPUTER**

Fortran 77; IBM PC (P00507IBMPC00).

**4. NATURE OF PROBLEM SOLVED**

Starting from a steady-state condition in a LWR core or fuel element, COBRA-EN can be used to simulate the thermal-hydraulic transient response to user-supplied changes of the total power, of the outlet pressure and of the inlet enthalpy and mass flow rate. The COBRA-EN code was developed in the eighties to be used as the thermal-hydraulic section in the successive versions of the NORMA [Brega 1995], QUARK [Alloggio 1994] and NORMA-FP [Brega 1991] computer programs, which were all designed for application to light water power reactors. The first was designed as a long-term reactivity simulator, the second as a core dynamics analyzer and the last one to unfold the flux and power fine structure in the large homogenized nodes generally used by the first two.

**5. METHOD OF SOLUTION**

The first approach was to resort to the COBRA-3C/MIT module, i.e., the thermal-hydraulic section of the MEKIN core kinetics code [Bowring 1975]; but, soon after, the model was upgraded according to other computer codes, based on more refined and consistent features, in particular, COBRA-IV-I [Wheeler 1976] and, mainly, VIPRE-01 [Stewart 1983], both evolved from the original COBRA-3C [Rowe 1973] subchannel analysis code.

Compared with COBRA-3C/MIT, the new features implemented in COBRA-EN can be summarized as follows.

i) Besides the two-phase homogeneous model, essentially based on the conservation equations of the mixture mass, energy and momentum vector in axial and lateral directions, i.e., on three balance equations, an option has been added allowing to compute the void fraction directly from the vapor continuity equation, thus switching to a four-equation model.

ii) Following VIPRE-01, two solution schemes are available for the three-equation homogeneous model, viz., an implicit (iterative) algorithm that will be called "pressure gradient" solution (similar to the "crossflow" solution of COBRA-3C and COBRA-IV-I) and an implicit solution based on a Newton-Raphson iteration for nonlinear systems. In the former scheme, limited to positive axial flows, the axial and lateral momentum equations are combined into a single equation containing the axial pressure gradients instead of the crossflows. The Newton-Raphson scheme adjusts, through the local pressures, the axial flows and the crossflows to force continuity of the mixture mass.

iii) The Newton-Raphson method is also applied to the four-equation model but, in order to satisfy continuity of both mixture and vapor masses, local pressures and vapor (void) fractions are simultaneously involved.

iv) The capabilities of the three-equation homogeneous model have been expanded by adding the EPRI correlations for two-phase friction multiplier, subcooled boiling quality and bulk void fraction. Moreover, the already existing Levy model for subcooled boiling has been supplemented with the Zuber-Findlay quality/void relation. The four-equation model is completed by the EPRI vapor generation and Bankoff-Jones slip ratio correlations.

v) New and more refined functions to compute properties of both subcooled water and superheated steam have been provided with the additional option of choosing between direct calculation and interpolation in precomputed tables.

vi) To model the heat transfer between fuel rods and coolant, a full boiling curve can be defined, comprising five heat-transfer regimes, i.e., single-phase forced convection, subcooled nucleate boiling, saturated nucleate boiling, transition and film boiling (or post-CHF boiling).

vii) Temperature-dependent physical properties of both fuel and clad materials are allowed.

viii) The list of available correlations for Critical Heat Flux (CHF) and heat transfer coefficients has been suitably extended.

ix) A variable axial mesh size and the choice between the American Engineering (AE) and International (SI) unit systems for both input and output are allowed.

**6. RESTRICTIONS OR LIMITATIONS**

None noted.

**7. TYPICAL RUNNING TIME**

All seven samples were run on a Pentium III 600 Mhz, within ten minutes total.

**8. COMPUTER HARDWARE REQUIREMENTS**

The minimum configuration required is an 80486 chipset running at 20 megahertz with 4 megabyte of random access memory, a CD-ROM drive capacity and a fixed disk with at least 8 megabytes of free storage.

**9. COMPUTER SOFTWARE REQUIREMENTS**

COBRA-EN runs under WINDOWS 3.1 or higher; MS-DOS 5.x or higher. The included executable was created with Digital Visual Fortran V.5 under Windows 98.

**10. REFERENCES**

**a) included with package:**

D. Basile, M. Beghi, R. Chierici, E. Salina, and E. Brega, "COBRA-EN, An Upgraded Version of the COBRA-3C/MIT Code for Thermal-Hydraulic Transient Analysis of Light Water Reactor Fuel Assemblies and Cores," Report no. 1010/1 (September 1999).

**b) background information:**

G. Alloggio, E. Brega, E. Salina, "QUARK, a Computer Code for the Neutronic and Thermal-Hydraulic Space- and Time-Dependent Analysis of Light Water Reactor Cores by Advanced Nodal Techniques," Rep. 1034/1 (September 1994).

D. Basile, E. Salina, E. Brega, "TRAC-PF1-EN/MOD3: a TRAC-PF1 Revised Version Inclusive of a Three-Dimensional Neutron Kinetics Model Based on High-Accuracy Two-Group Nodal Diffusion Methods," Rep. 1037/3 prepared for ENEL-ATN/GNUM (February 1997).

E. Brega, R. Fontana, E. Salina, "The NORMA-FP Program to Perform a Subchannel Analysis from Converged Coarse-Mesh Nodal Solutions," Rep. ENEL-DSR-CRTN-N5/91/05/MI (September 1991).

E. Brega, E. Salina, "The NORMA Program for Simulating the Long-Term Neutronic and Thermal-Hydraulic Behaviour of Large LWR's by Three-Dimensional Coarse-Mesh Diffusion Methods," Rep. 1034/2 (June 1995).

R.W. Bowring, J.W. Stewart, R.A. Shober and R.N. Sims, "MEKIN, MIT-EPRI Nuclear Reactor Core Kinetics Code," CCM-1, Research Project 227 (September 1975).

Department of Chemical Engineering, Columbia University, "Parametric Study of CHF Data, Volume 2: a Generalized Subchannel CHF Correlation for PWR and BWR Fuel Assemblies," NP-2609 (March 1982).

D. J. Diamond, H.S. Cheng and D.L. Eisenhart, "BEAGL-01, a Computer Code for Calculating Rapid Core Transients: Mathematical Modelling," EPRI NP-3243-CCM, Vol. I, (1983).

H. Finnemann and A. Galati, "NEACRP 3-D LWR CORE TRANSIENT BENCHMARK Final Specifications," NEACRP-L-335 (Revision 1) (October 1991).

M. Genova, A. Stanchetti, "Programma CIPRE per il calcolo del margine di sicurezza verso la crisi termica (nei BWR) in base al criterio della potenza critica," CISE-77.068 (October 1977).

D.C. Groeneveld, "Post-Dryout Heat Transfer at Reactor Operating Conditions," AECL-4513 (June 1973).

D.L. Hagrman, G.A. Reymann, R.E. Mason, "MATPRO-Version 11 (Revision 2): a Handbook of Materials Properties for Use in the Analysis of Light Water Reactor Fuel Rod Behavior," NUREG/CR-0497 and TREE-1280, Revision 2 (August 1980).

Idaho National Engineering Laboratory, "RELAP5/MOD7 Blowdown Code, Version 2, Code Development and Analysis Program Report," CDAP-TR-78-036 (August 1978).

J.H. McFadden et al., "RETRAN-02: a Program for Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems. Volume 1: Theory and Numerics (Revision 2)," NP-1850-CCMA (November 1984).

G.S. Lellouche, L.A. Zolotar, "Mechanistic Model for Predicting Two-Phase Void Fraction for Water in Vertical Tubes, Channels and Rod Bundles," NP-2246-SR (February 1982).

D.G. Reddy, S.R. Sreepada, A.N. Nahavandi, "Two-Phase Friction Multiplier Correlation for High-Pressure Steam-Water Flow," NP-2522 (July 1982).

D.S. Rowe, "COBRA-3C: A digital Computer Program for Steady-State and Transient Thermal-Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements," BNWL-1965 (March 1973).

C.W. Stewart, et al., "VIPRE-01: a Thermal-Hydraulic Analysis Code for Reactor Cores," EPRI NP-2511-CCM (April 1983).

C.L. Wheeler, et al., "COBRA-IV-I: an Interim Version of COBRA for Thermal-Hydraulic Analysis of Rod Bundles Nuclear Fuel Elements and Cores," BNWL-1962 (March 1976).

N. Zuber, J.A. Findlay, "Average Volumetric Concentration in Two-Phase Flow Systems," Journal of Heat Transfer, pp. 453-468 (November 1965).

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced document in 10.a and a CD-ROM containing a PkWare® self-extracting WINDOWS® executable including the source code, executable and databases.

**12. DATE OF ABSTRACT**

May 2001.

** KEYWORDS:** HEAT TRANSFER; LWR: REACTOR ACCIDENT; REACTOR PHYSICS;
THERMAL HYDRAULICS