SAMURA—A fast computer code for reactor fuel pin performance modelling and analysis

A very fast integral numerical computer code for the modelling of transient and steady-state thermal and mechanical behaviour of Zircaloy-clad UO₂ fuel pins in water reactors has been developed. The computational technique which determines the stress and deformation state of the fuel pin is based upon an extremely efficient finite difference scheme, i.e. the non-linear terms in the constitutive equations which produce a non-linear system of equations have been linearised using a Taylor expansion technique coupled with a very sophisticated error minimization algorithm and then solved with great accuracy. An improved numerical method has also been developed for the fast and efficient solution of the transient heat conduction equation. In this way a very stable and economical one-dimensional code (with appropriate provisions made for its conversion to a quasi two-dimensional code) has been obtained. The physical processes included are thermo-elastic deformation, thermal and irradiation creep, plasticity, fission gas swelling and release, formation of cracks in the fuel, hot pressing, densification, pore migration and dish or central void filling. Here the mathematical basis of SAMURA is presented along with some preliminary calculations and benchmarkings. It is concluded that SAMURA is quite fast indeed, converges to accurate results and within the margins of the error criterion chosen has very reasonable computer demands. It is also stable under all conditions tested.     

FARST — A computer code for the evaluation of FBR fuel rod behavior under steady-state/transient conditions

FARST, a computer code for the evaluation of fuel rod thermal and mechanical behavior under steady-state/transient conditions has been developed. The code characteristics are summarized as follows:

1. (i) FARST evaluates the fuel rod behavior under the transient conditions. The code analyzes thermal and mechanical phenomena within a fuel rod, taking into account the temperature change in coolant surrounding the fuel rod.

2. (ii) Permanent strains such as plastic, creep and swelling strains as well as thermoelastic deformations can be analyzed by using the strain increment method.

3. (iii) Axial force and contact pressure which act on the fuel stack and cladding are analyzed based on the stick/slip conditions.

4. (iv) FARST used a pellet swelling model which depends on the contact pressure between pellet and cladding, and an empirical pellet relocation model, designated as “jump relocation model”.

The code was successfully applied to analyses of the fuel rod irradiation data from pulse reactor for nuclear safety research in Cadarache (CABRI) and pulse reactor for nuclear safety research in Japan Atomic Energy Research Institute (NSRR).The code was further applied to stress analysis of a 1000 MW class large FBR plant fuel rod during transient conditions. The steady-state model which was used so far gave the conservative results for cladding stress during overpower transient, but underestimated the results for cladding stress during a rapid temperature decrease of coolant.     

ARARAT — A computer code for thermal design of cooling towers

A computer program is presented for thermal and hydraulic design of cooling towers. Options have been provided for the evaluation of cooling tower size and performance curves by applying a basic physical model of heat and mass transfer.The solution is conducted by multiple iteration, in which iteration loops are mutually inclusive. Both film and spray-filled cooling towers are considered with either induced or natural air circulation.Numerical solutions are presented to a number of natural draft cooling towers which serve present nuclear or conventional power plants.     

The computer code SEURBNUK-2 — Recent developments

The SEURBNUK-2 code is now being developed jointly by AEE Winfrith and JRC Ispra for use in Fast Reactor Containment Studies. To meet the needs of such studies and the needs of the COVA program, a number of improvements and extensions of the code have been made. A selection of these changes and illustrations of their use are given in this paper.The structural capability of SEURBNUK-2 was originally limited to the treatment of thin shells and shell junctions. Although this facility proved surprisingly useful, it was realised that a more versatile and powerful means of calculating the deformation of more complicated structural geometries would be required. The finite element code EURDYN which employs convected coordinates was adapted for the purpose, so that axially symmetric elements of the quadrilateral, triangular and thin shell families could be used to model various parts of the reactor structure. The method of coupling this finite element code to the fluid motion is described and the use of this new version of the code is illustrated and the results compared with those obtained by the original code and the ALE code EURDYN 1M. This last exercise revealed small differences between the solutions which were subsequently resolved by a further investigation involving a spherical cap problem.A feature of many reactor designs which is being modelled in the later COVA experiments is the perforated plate or porous structure. For fixed perforated plates and porous structures, the additional pressure drop and inertia effects can be included in the momentum equations by addition of suitable terms and the original technique of solution is unaltered. Details of the finite difference equations are given in this paper together with the results of check calculations which were performed to ensure the correct functioning of the code.The extensive use of SEURBNUK-2, particularly in conjunction with COVA, has highlighted a number of code problems which have been successfully resolved. Many of these related to particular circumstances, and are therefore of limited interest, but a general and quite frequent problem is that of gross bubble distortion which, if untreated, leads to logic problems within the code and consequent failure. Although the basic cause of this distortion is understood, eliminating it is not straightforward. A successful palliative is to manually rezone the bubble interface since this then avoids the logical problems in SEURBNUK with little or no effect on the calculation results. A further technique is the damping of the incipient discontinuities by automatic smoothing of the particle velocities. Examples of the use of rezoning and smoothing techniques are given.It is generally recognised that the numerical processes in an Eulerian code such as SEURBNUK introduce spurious diffusion into the solution so that pressure profiles, for example, are smoother than in an equivalent Lagrangian calculation. To give guidance to the calculator on the input parameters which affect these diffusion terms, an analysis of the truncation errors involved in the derivation of the finite difference equation was made. The various diffusion like terms are listed in this paper and their relevance to the calculation is discussed. An example is given which illustrates the changing nature of the solution as the amount of diffusion is modified.     

Senhor-II — A computer code for loss-of-coolant accidents of pressure tube type reactors

An ATR LOCA analysis code, SENHOR-II, was developed which evaluates the loss-of-coolant accident in a reactor primary loop composed of parallel pressure tubes and downcomers connecting a steam drum to a lower header. The reactor system is divided into reservoirs and channels. The reservoirs are assumed to be saturated and equilibrated. The channels are treated one-dimensionally and their flows are assumed quasi-steady. The reservoir effect of piping, the heating up of fuel rods, the thermal capacity of structures, and the effects of steam separators and water level in the steam drum are considered. Calculated results are compared with the experimental results of the blowdown test performed with the mock-up test loop in -arai Engineering Center of PNC, and the adequacy of the calculation model and formulae is confirmed.     

Assessment of the interchannel mixing model with a subchannel analysis code for BWR and PWR conditions

The influence of the interchannel mixing model employed in a traditional subchannel analysis code was investigated in this study, specifically on the analysis of the enthalpy distribution and critical heat flux (CHF) in rod bundles in BWR and PWR conditions. The equal-volume-exchange turbulent mixing and void drift model (EVVD) was embodied to the COBRA-IV-I code. An optimized model of the void drift coefficient has been devised in this study as the result of the assessment with the two-phase flow distribution data for the general electric (GE) 9-rod and Ispra 16-rod test bundles. The influence of the subchannel analysis model on the analysis of CHF was examined by evaluating the CHF test data in rod bundles representing PWR and BWR conditions. The CHFR margins of typical light water nuclear reactor (LWR) cores were evaluated by considering the influence on the local parameter CHF correlation and the hot channel analysis result. It appeared that the interchannel mixing model has an important effect upon the analysis of CHFR margin for BWR conditions.     

COMPBRN IIIe—a computer code for probabilistic fire risk analysis

The COMPBRN code has been used extensively to predict deterministically the time-to-damage of critical components in nuclear power plant fire risk analyses. Because there is a significant amount of uncertainties in the input parameters used in room fire simulations, the assessment of the damage time of the specified components must be performed probabilistically. This paper presents an updated version of the code, called COMPBRN IIIe, which emphasizes the importance of parameter uncertainty propagation by incorporating capabilities to provide probability distributions for component damage times. COMPBRN IIIe eliminates several errors from its previous versions and incorporates a user-friendly environment to assist users in preparing input files. With these improvements, the code can significantly reduce the time and effort required in the performance of a probabilistic fire risk assessment. A compartment fire simulation is also provided to demonstrate the application of the code.     

CFD study on coolant mixing in VVER-440 fuel rod bundles and fuel assembly heads

A CFD model of VVER-440 fuel assembly heads was developed based on the technical documentation of a full-scale test facility built in the Kurchatov Institute, Russia. Steady-state and transient calculations were performed to validate the model with a measurement set. Effects of the spatial resolution, turbulence models, difference schemes and different inlet boundary conditions were investigated. Inlet boundary conditions were determined with both the COBRA subchannel code and a fuel rod bundle CFD model that was built for this special purpose. The results were compared against experimental data. The sensitivity studies showed that a grid of about 8 million cells, high resolution scheme and BSL Reynolds stress model are suitable sets to provide accurate prediction for the signal of the in-core thermocouple. The best prediction was achieved with transient calculation using inlet boundary conditions generated with the CFD fuel rod bundle model. The results indicated that the coolant mixing is intensive but not perfect in the assembly head. Besides, the significant role of the outflow from the central tube was also proven. The transient runs revealed relatively large temperature fluctuations near the in-core thermocouple housing.     

FEMAXI-IV: A computer code for the analysis of fuel rod behavior under transient conditions

A fuel rod behavior code FEMAXI-IV, presently under development, is an improved version of the FEMAXI-III code for the analysis of fuel rod behavior under transient conditions. To apply the FEMAXI-III code to transient conditions, the following additional models have been incorporated into the FEMAXI-III code: transient heat transfer model: axial gas mixing model; diffusion-type fission gas release model. This paper summarizes the above additional models, and the comparison of the FEMAXI-IV calculations with the experimental data.     

CALIPSO—A computer code for the calculation of the thermodynamics, fluiddynamics and geometry changes following pin failure

The computer code CALIPSO calculates the thermodynamics and fluid-dynamics of fuel, fission gas and coolant as well as changes in geometry subsequent to pin failure in an anticipated liquid-metal fast breeder reactor (LMFBR) accident. In the documented version, CALIPSO is well suited for the analysis of the out-of pile SIMBATH experiments carried out at Kernforschungszentrum Karlsruhe (KfK) which simulate the above-mentioned accident with thermite technology. In two-dimensional geometry the fuel pin and its associated coolant channel, initially separated by the fuel cladding are treated as a single fluid domain. The conservation equations of mass, momentum and energy are solved separately for each component. The transient evolution of the temperature profile in the cladding is modeled in detail, thus permitting the analysis of various phase transition processes (melting, freezing and clad failure propagation). The coolant channel has a variable cross section and it is surrounded by an outer channel wall for single pin experiment analysis. Axially the coolant channel is connected to a simplified model of the whole sodium loop.     

SIMPLE-2: A computer code for calculation of steady-state thermal behavior of rod bundles with flow sweeping

A computer code has been developed for use in making single-phase thermal hydraulic calculations in rod bundle arrays with flow sweeping due to spiral wraps as the predominant crossflow mixing effect. This code, called SIMPLE-2, makes the assumption that the axial pressure gradient is identical for each subchannel over a given axial increment, and is unique in that no empirical coefficients must be specified for its use. Results from this code have been favorably compared with experimental data for both uniform and highly nonuniform power distributions. Typical calculations for various bundle sizes applicable to the LMFBR program are also included.     

Momentum losses and convective heat transfer in rod bundles — An overview

A critical survey is made of the prediction methods available for analysing the momentum and heat transfer characteristics of axial flow in a clustered rod bundle. The Navier-Stokes and energy equations are presented, their solution procedure is outlined and the boundary layer approximation discussed. Four levels of approximation to these equations, namely, slug flow, integral methods, eddy diffusivity and turbulence energy models are examined and their limitations presented for a simple situation. Consideration is then given to the problem of extending these models to more complex situations such as, variable property flows, rough surfaces and flow blockages.     

FIPMIGR — A computer program for studying migration of fission products in a temperature gradient

FIPMIGR is a computer program for studying migration of fission products in a fuel pin. Migration in a temperature gradient and in a concentration gradient is considered. The geometry is cylindrical with migration only in the radial direction.As an example the diffusion of Ba is calculated and compared with experimental results. The migration of Ba is well described using the diffusion constant for Ba in BaO and a heat of transport of −100 kJ mol⁻¹. The great sensitivity of the theoretical prediction to temperature is clearly demonstrated. Both theory and experiments show that there is a temperature or power above which migration becomes clearly visible. The critical temperature is about 1700 K and the power level in the S176 experiments [2] was then about 40 kW m⁻¹.     

The new code “RCC-MR” — Rules for design and construction of LMFBR components

In 1978, Commissariat à l'Energie Atomique, Electricité de France, and Novatome decided to undertake a common effort to gather a complete collection of rules to apply for design of LMFBR components. The first issue of this work is now being published by AFCEN as the “RCCM” code. The preparation of the design rules used largely the experience gained in Superphenix components analysis, and the results of the large R&D program performed as a support for the design of this plant or at longer term perspective, coordinated by a scientific advisary council of AFCEN (Association Française pour les règles de Conception et de Construction des matériels des Chaudières Electronucléaires).     

IAMBUS-1 — A digital computer code for the design, in-pile performance prediction and post-irradiation analysis of arbitrary fuel rods: Part I: Theory and modelling

IAMBUS-1^*, a digital computer code for the thermal and mechanical design, in-pile performance prediction and postirradiation analysis of arbitrary fuel rods, will be presented in two parts. Part I describes the theory and modelling and in Part II (to be published in a subsequent issue of Nuclear Engineering and Design) material behaviour will be discussed on a quantitative basis and some numerical results illustrating typical and diverse IAMBUS usage will be analysed.The multi-zone code IAMBUS is built around a sound but flexible mechanical analysis of fuel and cladding. A state of generalized plane strain approximates the cladding; the fuel is modelled by a state of plane stress, a state of generalized plane strain, or a combination of these two well-known stress—strain configurations depending on the macroscopic structure of the fuel prevailing. It is thus possible to follow closely the deformation of the fuel and cladding as these are subjected to varying (in part mutual) loads, beginning with a relatively loose, somewhat random assemblage of minute fuel fragments at BOL and progressing to a quasi compact continuum of fuel at EOL.Cladding analysis includes routines for plasticity, creep and swelling due to void nucleation and growth; in the fuel restructuring, plasticity, creep, swelling due to solid and gaseous fission products, fission-gas release and internal pressure build-up are modelled. Routines for friction and heat transfer between fuel and cladding are also incorporated. No strict temperature-dependent boundary is drawn between typically elastic and plastic behaviour, the multi-zone nature of the code models the gradual transition between these two types of material behaviour observed in practice with increasing temperature.Great care has been exercised in choosing numerical methods, since the most sophisticated/realistic modelling is of limited value if the effort expended in reaching a numerical solution becomes exorbitant. Multi-zone modelling lends itself readily to the method of finite differences. The finite difference equations are solved via the method of secants, modified to guarantee convergence for all IAMBUS functions in a feasible amount of computer time.     

Investigation of the mixing of the coolant in the distribution collector systems of fast and BBÉR reactors

Main Scientific Center of the Russian Federation. Physics and Power Engineering Institute. Translated from Atomnaya énergiya, Vol. 77, No. 5, pp. 340–344, November, 1994.     

URANUS — A computer programme for the thermal and mechanical analysis of the fuel rods in a nuclear reactor

The URANUS code, a digital computer programme for the thermal and mechanical analysis of integral fuel rods, is described. With this code the fuel rods found in the majority of power reactors can be analyzed. URANUS is built around a quasi two-dimensional analysis of fuel and cladding. The mechanical analysis can accommodate seven components of strain: elastic, time-independent plastic, creep and thermal strains, as well as strains due to swelling, cracking and densification. The heat generation and temperature distribution, cladding/fuel gap closure, pellet cracking and crack healing, fission-gas release, corrosion, O/M-distribution and plutonium redistribution are modelled. Geometric non-linearities (large displacements) are included; steady state or transient loading (pressure, temperature) is possible. In this paper special attention is paid to a theory for determining crack structures. The present status of the URANUS computer programme and a critical comparison with other fuel rod codes as well as sample analyses are given.