John H. Mahaffy

Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model

The development of a fully-implicit scheme to model the two-phase three-field flow and heat transfer problem is presented here. The model was originally developed to simulate the complex phenomena occurring in proximity of the quench front of a nuclear reactor core during the reflood phase of a postulated LOCA. The fully-implicit method allows relative large time steps to be used even on very fine spatial grids which can not be considered when a semi-implicit scheme is applied to solve the conservation equation. The objective of this paper is to capture as much as possible, the lessons learned during the development and coding of the fully-implicit two-phase three-field model. The implementation of the model is one of the most time consuming and a challenging task. The literature on numerical models generally concentrates on the theoretical aspects of the numerical method but available information on the problems encountered during the implementation of such methods for real applications is scarce. The reason is that many of these methods are tailored to specific applications and sometimes are rather empirical. These techniques are the result of a long and tedious trial and error process from the developer. The article presented here attempts to provide some insights and guidelines for future development of this or similar models.

Numerics of codes: stability, diffusion, and convergence

Abstract The numerical methods used in the primary US reactor safety codes are summarized. The basic Courant-type stability limits for these codes are reviewed, and more subtle stability problems arising from the explicit evaluation of various friction and heat-transfer coefficients are discussed. Much of the stability and robustness of these codes has come at the expense of high numerical diffusion. The impact of numerical diffusion is illustrated. The question of convergence of solutions of the difference equations to those of the original differential equations is also addressed.

On the automated assessment of nuclear reactor systems code accuracy

Abstract An automated code assessment program (ACAP) has been developed to provide quantitative comparisons between nuclear reactor systems (NRS) code results and experimental measurements. The tool provides a suite of metrics for quality of fit to specific data sets, and the means to produce one or more figures of merit (FOM) for a code, based on weighted averages of results from the batch execution of a large number of code–experiment and code–code data comparisons. Accordingly, this tool has the potential to significantly streamline the verification and validation (V and V) processes in NRS code development environments which are characterized by rapidly evolving software, many contributing developers and a large and growing body of validation data. In this paper, a survey of data conditioning and analysis techniques is summarized which focuses on their relevance to NRS code accuracy assessment. A number of methods are considered for their applicability to the automated assessment of the accuracy of NRS code simulations. A variety of data types and computational modeling methods are considered from a spectrum of mathematical and engineering disciplines. The goal of the survey was to identify needs, issues and techniques to be considered in the development of an automated code assessment procedure, to be used in United States Nuclear Regulatory Commission (NRC) advanced thermal–hydraulic T/H code consolidation efforts. The ACAP software was designed based in large measure on the findings of this survey. An overview of this tool is summarized and several NRS data applications are provided. The paper is organized as follows: The motivation for this work is first provided by background discussion that summarizes the relevance of this subject matter to the nuclear reactor industry. Next, the spectrum of NRS data types are classified into categories, in order to provide a basis for assessing individual comparison methods. Then, a summary of the survey is provided, where each of the relevant issues and techniques considered are addressed. Several of the methods have been coded and/or applied to relevant NRS code–data comparisons and these demonstration calculations are included. Next, an overview of the basic design, structure and operational mechanics of ACAP is provided. Then, a summary of the data pre-processing, data analysis and FOM assembly processing elements of the software is included. Lastly, a number of NRS sample applications are presented which illustrate the functionality of the code and its ability to provide objective accuracy measures.

Numerical diffusion and the tracking of solute fields in system codes: Part II. Multi-dimensional flows

Advances in neutronics and thermohydraulic modeling have resulted in system codes capable of describing local interactions between the core neutronic behavior and the thermohydraulic conditions inside the vessel with full 3-dimensional real time coupling. Making use of these advances in the analysis of boron dilution transients requires a good description of the boron field inside the core, and of its transport along the primary system. However, the relatively low accuracy displayed by advanced system codes in the simulation of solute transport as a result of numerical diffusion is a major obstacle to performing accurate boron dilution studies. Implementation of high order numerical methods in system codes can considerably improve their accuracy when modeling solute transport by reducing the numerical diffusion to a level that is less than the physical diffusion expected from the turbulence of the flow; even when using relatively coarse noding schemes. In order to show this is feasible, the explicit QUICKEST-ULTIMATE scheme for 1-dimensional flow was adapted to the integration procedures used in system codes and implemented in TRAC-PF1/MOD2. Numerical tests were used to assess the performance of the methods implementation. A statistical methodology adapted from its original experimental formulation to the quantitative characterization of numerical diffusion in system codes was used for the analysis of the results. They showed that, for flow conditions commonly found in nuclear system simulations, high order tracking of a solute field can provide results whose diffusion is considerably less than that expected from the turbulence and characteristics of the flow field.

DEVELOPMENT OF BEST PRACTICE GUIDELINES FOR CFD IN NUCLEAR REACTOR SAFETY

In 2007 the Nuclear Energy Agency’s Committee on the Safety of Nuclear Installations published Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety. This paper provides an overview of the document’s contents and highlights a few of its recommendations. The document covers the full extent of a CFD analysis from initial problem definition and selection of an appropriate tool for the analysis, through final documentation of results. It provides advice on selection of appropriate simulation software, mesh construction, and selection of physical models. In addition it contains extensive discussion of the verification and validation process that should accompany any high-quality CFD analysis.

Numerical diffusion and the tracking of solute fields in system codes. Part III. Application to a boron dilution transient analysis in the AP600

A study of a pump restart scenario in the AP600 with an unborated coolant plug in two of the four cold legs is presented. It has been performed with TRAC-PF1/MOD2 coupled with a 3-dimensional core neutronics model based on the nodal expansion method (NEM), and high order boron tracking algorithms. These are based on ULTIMATE-QUICKEST for 1-dimensional components and a flux corrected method developed by Smolarckievicz in the 3-dimensional vessel in order to reduce the numerical diffusion inherent to the upwind method used by most system codes to solve the transport equations. No turbulent diffusion model was included in the calculation to produce more conservative results. The results show that reduction of the numerical diffusion yields predictions with a significantly reduced margin in the size of the unborated plugs allowed to form in the primary side piping. In addition, two pump restart strategies have been suggested by the results, which could substantially decrease the size of an unborated plug injected into the core, in case it was suspected to have formed in a primary loop.

A moving subgrid model for simulation of reflood heat transfer

Abstract In the quench front and froth region the thermal-hydraulic parameters experience a sharp axial variation. The heat transfer regime changes from single-phase liquid, to nucleate boiling, to transition boiling and finally to film boiling in a small axial distance. One of the major limitations of all the current best-estimate codes is that a relatively coarse mesh is used to solve the complex fluid flow and heat transfer problem in proximity of the quench front during reflood. The use of a fine axial mesh for the entire core becomes prohibitive because of the large computational costs involved. Moreover, as the mesh size decreases, the standard numerical methods based on a semi-implicit scheme, tend to become unstable. A subgrid model was developed to resolve the complex thermal-hydraulic problem at the quench front and froth region. This model is a Fine Hydraulic Moving Grid (FHMG) that overlies a coarse Eulerian mesh in the proximity of the quench front and froth region. The fine mesh moves in the core and follows the quench front as it advances in the core while the rods cool and quench. The FHMG software package was developed and implemented into the COBRA-TF computer code. This paper presents the model and discusses preliminary results obtained with the COBRA-TF/FHMG computer code.

A two-phase level tracking method

Interfacial closure models in most two-fluid system codes for reactor safety are usually tied to the flow regime map through the mean void fraction in a computational cell. When a void fraction discontinuity exists in a computational volume, neither heat nor momentum exchange at the phase interface for this particular cell can be properly represented in finite-difference equations governing the fluid flow. Moreover, finite-difference methods with a fixed, Eulerian grid will inaccurately predict the cell-to-cell convection of mass, momentum and energy when the mean cell macroscopic variables are convected from the cell containing the void fraction front. The adequate modeling of two-phase mixture levels requires the knowledge of front position and void fractions above and below the front. In order to obtain such information, an efficient and simple tracking method was implemented in the TRAC-BWR code (released April 1984). We have tested this method with a simple problem involving a moving two-phase air/water mixture level. The results revealed inconsistencies in the behavior of velocities, pressures and interfacial friction, and some bounded numerical oscillations. Following our numerical experiment, we developed a systematic approach to improve the two-phase level tracking method. We present this approach and the results of implementation in the TRAC-BWR code.

A MOVING SUBGRID MODEL FOR SIMULATION OF REFLOOD HEAT TRANSFER

In the quench front and froth region the thermal-hydraulic parameters experience a sharp axial variation. The heat transfer regime changes from single-phase liquid, to nucleate boiling, to transition boiling and finally to film boiling in a small axial distance. One of the major limitations of all the current best-estimate codes is that a relatively coarse is used to solve the complex fluid flow and heat transfer problem in proximity of the quench front of a reactor core during reflood. The use of a fine axial mesh for the entire core becomes prohibitive because of the large computational costs involved. Moreover as the mesh size decreases, the standard numerical methods based on a semiimplicit scheme, tend to become unstable. A sub-grid model was developed to resolve the complex thermal-hydraulic problem at the quench front and froth region. The model is a Fine Hydraulic Moving Grid that overlies a coarse Eulerian mesh in the proximity of the quench front and froth region. The fine mesh moves in the core and follows the quench front as it advances in the core while the rods cool and quench. The Fine Hydraulic Moving Grid (FHMG) software package was developed and implemented into the COBRA-TF computer code. This paper presents the model and discusses preliminary results obtained with the COBRA-TF/FHMG computer code.

Parallel applications of the USNRC consolidated code

The United States Nuclear Regulatory Commission has developed the thermal-hydraulic analysis code TRAC-M to consolidate the capabilities of its suite of reactor safety analysis codes. One of the requirements for the new consolidated code is that it supports parallel computations to extend code functionality and to improve execution speed. A flexible request driven Exterior Communication Interface (ECI) was developed at Penn State University for use with the consolidated code and has enabled distributed parallel computing. This paper reports the application of TRAC-M and the ECI at Purdue University to a series of practical nuclear reactor problems. The performance of the consolidated code is studied on a shared memory machine, DEC Alpha 8400, in which a Large Break Loss of Coolant Accident (LBLOCA) analysis is applied for the safety analysis of the new generation reactor, AP600. The problem demonstrates the importance of balancing the computational for practical applications. Other computational platforms are also examined, to include the implementation of Linux and Windows OS on multiprocessor PCs. In general, the parallel performance on UNIX and Linux platforms is found to be the most stable and efficient.