Development of Conservative Form of RELAP5 Thermal Hydraulic Equations: Part I — Theory

2014 ◽  
Author(s):  
Zheng Fu ◽  
Fatih Aydogan ◽  
Richard J. Wagner
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Numerical Approximation ◽  
Numerical Approach ◽  
Phase System ◽  
Hydraulic Systems ◽  
Governing Equations ◽  
Two Phase ◽  
Current Form ◽  
Two Fluids

The design and analysis of the thermal/hydraulic systems of nuclear power plants necessitates system codes that can be used in the analysis of steady state and transient conditions. RELAP5 is one of the most commonly used system codes in nuclear organizations. RELAP5 is based on a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The “non-conservative” numerical approximation form (which is the current form of RELAP5 code versions) is obtained through the manipulation of selected derivative terms in the equations including the linearization of the product terms in the time derivatives of the equations. For non-conservative technique, the truncation errors introduced in the linearization process can produce mass and energy errors for some classes of transients during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. To eliminate these difficulties, a new, optional numerical approach has been introduced in RELAP/SCDAPSIM/MOD4.0. This new option uses a more consistent set of the “conservative” numerical approximation to solve non-linearized mass and energy governing equations. The RELAP/SCDAPSIM/MOD4.0 code, being developed as part of the international SCDAP (Severe Core Damage Analysis Package) Development and Training Program (SDTP), is the first version of RELAP5 completely rewritten to FORTRAN 90/95/2000 standards. This paper provides an overview of the original RELAP5 numerical approximations and describes the new theoretical approach. Then the second article introduces the solution strategy of conservative approach and presents some examples of transient problems that have been run using this new approach.

Development of Conservative Form of RELAP5 Thermal Hydraulic Equations: Part II — Numerical Approach and Code Results

2014 ◽  
Author(s):  
Zheng Fu ◽  
Fatih Aydogan ◽  
Richard J. Wagner
Keyword(s):  
Numerical Approach ◽  
Phase System ◽  
Current Version ◽  
Two Phase ◽  
Pressurized Water ◽  
Conservation Equations ◽  
Two Fluids ◽  
Conservative Form ◽  
Energy And Momentum ◽  
Single Pipe

One of the principle features of RELAP5-based system thermal hydraulic codes is the use of a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The current version of RELAP-5 uses non-conservative numerical approximation form of conservation equations. The current version of RELAP5 versions have mass and energy errors during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. Therefore, conservative conservation equations and closure equations were developed to address this problem in the first part of the paper series This part of the series demonstrates the numerical approach to implement the developed conservative conservation equations into RELAP5 and the results of RELAP5 including developed conservative form of conservation equations. RELAP5 versions including conservative and non-conservative conservation equations are compared for various tests from a single pipe to a whole Pressurized Water Reactor (PWR) model.

Comprehensive Analyses of Nuclear Safety System Codes

2013 ◽  
Author(s):  
Glenn A. Roth ◽  
Fatih Aydogan
Keyword(s):  
Power Plant ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Numerical Approach ◽  
Nuclear Industry ◽  
Nuclear System ◽  
Steam Generators ◽  
Two Phase ◽  
Closure Models

Many nuclear system codes have been developed for the main purpose of analyzing reactor performance of a nuclear power plant system during steady state and transient conditions. These codes generally include power plant component models for pumps, pipes, steam generators, pressurizers and other components. The parallel development of these nuclear system codes has been supported by government laboratories, universities, private entities and other organizations throughout the world. This has resulted not only in multiple codes, but multiple versions of the same code with different capabilities. The development paths of each code version have been driven by specific needs. The challenge for the user is to select a code that performs well for the desired analysis problem. Therefore, this work compares different aspects of various nuclear system codes. Firstly, it compares the governing equations for mass, momentum and energy in the evaluated system codes. Secondly, it compares all the codes’ closure models. Closure models are used in system codes to model thermal and mechanical non-equilibrium as well as the coupling of the phases. Thirdly, it compares the Separate Effect Tests (SET) and Integral Effect Tests (IET) employed for the verification and validation (V&V) during the development of each system code. These comparisons cover several thermal and hydraulic models, such as heat transfer coefficients for various flow regimes, two phase pressure correlations, two phase friction correlations, drag coefficients and interfacial models between the fields. Fourthly, major assumptions about the governing and closure equations in these codes are compared and discussed. Fifthly, numerical approach of every code is benchmarked with each other since numerical approach not only affects the speed of the system codes but also the accuracy of the results. Sixthly, the limitations of the codes are evaluated because these codes are challenged by analyzing not only existing nuclear power plants, but also next generation nuclear power plants. The nuclear industry is developing new, innovative reactor designs, such as Small Modular Reactors (SMRs), High-Temperature Gas-cooled Reactors (HTGRs) and others. Sub-types of these reactor designs utilize pebbles, prismatic graphite moderators, helical steam generators, innovative fuel types, and many other design features that may not be fully analyzed by current system codes. The results of this work serve as a guide for development of these system codes and indicate areas where models must be improved to adequately address issues with new reactor design and development activities.

Solution of Governing Equations for Six-Field System Code

2017 ◽  
Author(s):  
Glenn A. Roth ◽  
George L. Mesina ◽  
Fatih Aydogan
Keyword(s):  
Gas Phase ◽  
Nuclear Power ◽  
Power Plants ◽  
Governing Equations ◽  
Field Equations ◽  
Two Phase Flows ◽  
Two Phase ◽  
Drift Flux ◽  
Continuous Fields ◽  
Analysis System

Modeling of two phase flows in nuclear power plants is very important for design, licensing, and operator training and therefore must be performed accurately. As requirements have increased, the form and accuracy of the models and computer codes have improved along with them. Early formulations for the field equations include: single phase liquid with algebraic drift flux for the gas phase, modeled with mass, momentum and energy governing equations; and two separate fields, liquid phase and gas phase, typically modeled with six governing equations. These lump bubbles and droplets into the gas and liquid phases respectively and use flow regime maps based upon available experimental data. However, the experiments do not cover the entire spectrum of reactor conditions, so that transitions and extrapolations, which are inherently inaccurate, must be employed. Further, some reactor scenarios, such as boiling and condensation, can be more accurately resolved by modeling bubbles or droplets separately from the continuous fields. Introduction of an additional field, droplet or bubble, apart from the continuous liquid and gas fields, generally uses nine governing equations. Despite the successful development of the above-mentioned methods for modeling reactor coolant flow in modern software, such as RELAP, TRAC, TRACE, CATHARE and many others, there remain reactor scenarios that require greater resolution to model. This is particularly true of conditions during reflood, where emergency spray flows dominate the cooling profile within the core. Existing system codes use a lumped approach for two phase flows that groups the fields by their phase, thereby losing track of the physical interactions between the discrete fluid fields. The accuracy of these accident analysis system codes can be improved by characterizing the interactions between additional coolant fields. To capture the effect of the various field interactions, governing equations involving six-fields have been developed. The six fields are 1) continuous liquid, 2) continuous vapor, 3) large droplets, 4) small droplets, 5) large bubbles and 6) small bubbles. The additional fields and the related governing equations introduce additional variables and source terms that require new closure relationships and primary variables. This article presents the equations and variables and develops the discrete set of 18 equations that must be solved to model the system.

Measurement of Flow-Induced Forces: A Single Flexible Tube in a Rigid Triangular-Pitch Bundle Subjected to Two-Phase Cross-Flow

2015 ◽  
Author(s):  
Enrico Deri ◽  
Joël Nibas ◽  
Olivier Ries ◽  
André Adobes
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Tube Bundle ◽  
Fluid Dynamic ◽  
Cross Flow ◽  
Maintenance Policy ◽  
Excitation Spectra ◽  
Two Phase ◽  
Force Coefficients ◽  
Out Of Plane

Flow-induced vibrations of Steam Generator tube bundles are a major concern for the operators of nuclear power plants. In order to predict damages due to such vibrations, EDF has developed the numerical tool GeViBus, which allows one to asses risk and thereafter to optimize the SG maintenance policy. The software is based on a semi analytical model of fluid-dynamic forces and dimensionless fluid force coefficients which need to be assessed by experiment. The database of dimensionless coefficients is updated in order to cover all existing tube bundle configurations. Within this framework, a new test rig was presented in a previous conference with the aim of assessing parallel triangular tube arrangement submitted to a two-phase cross-flow. This paper presents the result of the first phase of the associated experiments in terms of force coefficients and two-phase flow excitation spectra for both in-plane and out-of-plane vibration.

scholarly journals Modelling of Passive Heat Removal Systems: A Review with Reference to the Framatome BWR Reactor KERENA: Part II

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 109 ◽  
Author(s):  
René Manthey ◽  
Frances Viereckl ◽  
Amirhosein Moonesi Shabestary ◽  
Yu Zhang ◽  
Wei Ding ◽  
...  
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Gravitational Force ◽  
Heat Removal ◽  
Dimensional System ◽  
Thermal Gradients ◽  
Two Phase ◽  
Passive Safety Systems ◽  
External Power ◽  
Safety Systems

Passive safety systems are an important feature of currently designed and constructed nuclear power plants. They operate independent of external power supply and manual interventions and are solely driven by thermal gradients and gravitational force. This brings up new needs for performance and reliably assessment. This paper provides a review on fundamental approaches to model and analyze the performance of passive heat removal systems exemplified for the passive heat removal chain of the KERENA boiling water reactor concept developed by Framatome. We discuss modeling concepts for one-dimensional system codes such as ATHLET, RELAP and TRACE and furthermore for computational fluid dynamics codes. Part I dealt with numerical and experimental methods for modeling of condensation inside the emergency condenser and on the containment cooling condenser. This second part deals with boiling and two-phase flow instabilities.

Design Methodology and Valve Sizing for Heater Drain Systems

2009 ◽  
Author(s):  
Casey Loughrin
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Pressure Losses ◽  
Solution Methods ◽  
Flow Phenomena ◽  
Flow Pressure ◽  
And Control

Heater drain systems in fossil and nuclear power plants have proven to be among the most complex systems to design due to the occurrence of two–phase flow phenomena. The overall performance of heater drain systems directly relates to proper sizing and design of the piping and control valves. Proper sizing is highly dependent upon accurate and conservative calculation of two-phase flow pressure losses. This paper outlines the various options of solution methods available to the engineer and details one possible method which is simple, yet adequate, and based on the homogeneous equilibrium model (HEM) for two phase flow for calculation of heater drain system performance. General comparisons are made to the more complex multi-fluid models, flow regime considerations, and non-equilibrium models.

Small Diameter Effects on Internal Flow Boiling

2001 ◽  
Author(s):  
Gail E. Kendall ◽  
Peter Griffith ◽  
Arthur E. Bergles ◽  
John H. Lienhard
Keyword(s):  
Heat Transfer ◽  
Thermal Management ◽  
Nuclear Power ◽  
Power Plants ◽  
Flow Instability ◽  
Flow Boiling ◽  
Small Diameter ◽  
Internal Flow ◽  
Two Phase ◽  
Wide Range

Abstract Since the 1950’s, the research and industrial communities have developed a body of experimental data and set of analytical tools and correlations for two-phase flow and heat transfer in passages having hydraulic diameter greater than 6 mm or so. These tools include flow regime maps, pressure drop and heat transfer correlations, and critical heat flux limits, as well as strategies for robust thermal management of HVAC systems, electronics, and nuclear power plants. Designers of small systems with thermal management by phase change will need analogous tools to predict and optimize thermal behavior in the mesoscale and smaller sizes. Such systems include a wide range of devices for computation, measurement, and actuation in environments that range from office space to outer space and living systems. This paper examines important proceses that must be considered when channel diameters decrease, including flow distribution issues in single, parallel, and split flows; flow instability in parallel passages; manufacturing tolerances effects; nucleation processes; and wall conductance effects. The discussion focuses on engineering issues for the design of practical systems.

Periodic Oscillations in Natural Circulation Boiling System

2017 ◽  
Author(s):  
Xianbing Chen ◽  
Puzhen Gao ◽  
Qiang Wang ◽  
Yinxing Zhang ◽  
Jiawei Liu
Keyword(s):  
Mass Flux ◽  
Nuclear Power ◽  
Power Plants ◽  
Two Phase Flow ◽  
Flow Instability ◽  
Natural Circulation ◽  
Flow Reversal ◽  
Phase Flow ◽  
Two Phase ◽  
Periodic Oscillations

Natural circulation has been widely used in some evolutionary and innovative nuclear power plants. Natural circulation systems are susceptible to flow instabilities which are undesirable in the nuclear power devices. An experimentally investigation of two phase flow instability in up-flow boing channel under natural circulation is presented in this paper. Flow instability with and without flow reversal have been found. A pulse signal of water temperature at the inlet of the test section can be detected when the channel suffers from flow reversal. Single phase and two phase flow alternate in the channel regardless of the occurrence of flow reversal. Periodic oscillations with multiple high-order harmonic waves are confirmed by applying Fast Fourier Transform to the time traces of flow rates. Period of flow instability which is the reciprocal of the frequency with the largest amplitude in the amplitude-frequency plane are obtained. Period of flow oscillation presents a nonlinear change with the increase of mass flux. Period of flow instability increases rapidly with the increase of mass flux and decreases slowly when it reaches the maximum value.

An Overview of Numerical Method for Fluid-Structure Interaction

2014 ◽  
Author(s):  
J.-H. Jeong ◽  
M. Kim ◽  
P. Hughes
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Nuclear Power ◽  
Power Plants ◽  
Fluid Structure Interaction ◽  
Phase Flow ◽  
Two Phase ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Deformable Structure

Fluid-structure interaction (FSI) is the interaction of some movable or deformable structure with an internal or surrounding fluid flow. Therefore, fluid-structure interaction problems are too complex to solve analytically and so they have to be analysed by means of experiments or numerical simulation. This paper provides an overview of numerical methods for fluid-structure interaction evaluation in an draft IAEA technical guideline: large eddy simulation (LES), direct numerical simulation (DNS), Lattice-Boltzmann method (LBM), finite element method (FEM) and computational fluid dynamics (CFD) method. In addition to providing general applications of numerical methods for fluid-structure interaction evaluation, the paper also describes some cases applied for problems associated with single-phase flow and two-phase flow in nuclear power plants.

scholarly journals Modelling of Passive Heat Removal Systems: A Review with Reference to the Framatome KERENA BWR Reactor: Part I

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 35 ◽  
Author(s):  
Amirhosein Moonesi Shabestary ◽  
Frances Viereckl ◽  
Yu Zhang ◽  
Rene Manthey ◽  
Dirk Lucas ◽  
...  
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Gravitational Force ◽  
Heat Removal ◽  
Dimensional System ◽  
Thermal Gradients ◽  
Two Phase ◽  
Passive Safety Systems ◽  
External Power ◽  
Safety Systems

Passive safety systems are an important feature of currently designed and constructed nuclear power plants. They operate independent of external power supply and manual interventions and are solely driven by thermal gradients and gravitational force. This brings up new needs for performance and reliably assessment. This paper provides a review on fundamental approaches to model and analyze the performance of passive heat removal systems exemplified for the passive heat removal chain of the KERENA boiling water reactor concept developed by Framatome. We discuss modelling concepts for one-dimensional system codes such as ATHLET, RELAP and TRACE and furthermore for computational fluid dynamics codes. Part I deals with numerical and experimental methods for modelling of condensation inside the emergency condensers and on the containment cooling condenser while part II deals with boiling and two-phase flow instabilities.

Sign in / Sign up

Export Citation Format

Share Document