Analysis of super delayed-critical transients in thermal reactors using 2-D and 3-D adiabatic and improved quasistatic models

A computer model 3d-fast is developed for solving the space-time kinetics equations in 1-D, 2-D or 3-D using the adiabatic and improved quasistatic (IQS) methods. Using this model, some super delayed-critical transients in 2-D and 3-D are analysed for varying reactivity insertion rates. It is shown that for transients where the reactivity insertion rate is small and change in flux shape is slow, the results obtained both by adiabatic and IQS models are in good agreement, while for fast reactivity insertion rates where changes in flux shapes are also rapid, the results obtained by the adiabatic method are grossly in error, while those obtained by the IQS method are more satisfactory.     

Assessment study of the coupled code RELAP5/PARCS against the Peach Bottom BWR turbine trip test

The modeling of complex transients in nuclear power plants (NPP) remains a challenging topic for best estimate three-dimensional coupled code computational tools. This technique is, nowadays, extensively used for simulating transients that involve core spatial asymmetric phenomena and strong feedback effects between core neutronics and reactor loop thermal–hydraulics. In this framework, the Peach Bottom BWR turbine trip experiment 2 is considered. The test involves a rapid positive reactivity addition into the core generated by a water hammer load. To perform a numerical simulation of such phenomenon a reference case was calculated using the coupled code RELAP5/PARCS. An overall data comparison shows good agreement between calculated and measured pressure wave trend in the core region. However, the predicted power response during the excursion phase did not match correctly the experimental tendency. For this purpose, a series of sensitivity analyses have been carried out to identify the most probable reasons of such discrepancy. It was found out that the uncertainties related to the cross-sections modeling and to the thermal–hydraulic closure relationships are the main source of the incorrect power feedback response during the transient.     

Neutronics modeling of the High Flux Isotope Reactor using COMSOL

The High Flux Isotope Reactor located at the Oak Ridge National Laboratory is a versatile 85 MWth research reactor with cold and thermal neutron scattering, materials irradiation, isotope production, and neutron activation analysis capabilities. HFIR staff members are currently in the process of updating the thermal hydraulic and reactor transient modeling methodologies. COMSOL Multiphysics has been adopted for the thermal hydraulic analyses and has proven to be a powerful finite-element-based simulation tool for solving multiple physics-based systems of partial and ordinary differential equations. Modeling reactor transients is a challenging task because of the coupling of neutronics, heat transfer, and hydrodynamics. This paper presents a preliminary COMSOL-based neutronics study performed by creating a two-dimensional, two-group, diffusion neutronics model of HFIR to study the spatially-dependent, beginning-of-cycle fast and thermal neutron fluxes. The 238-group ENDF/B-VII neutron cross section library and NEWT, a two-dimensional, discrete-ordinates neutron transport code within the SCALE 6 code package, were used to calculate the two-group neutron cross sections required to solve the diffusion equations. The two-group diffusion equations were implemented in the COMSOL coefficient form PDE application mode and were solved via eigenvalue analysis using a direct (PARDISO) linear system solver. A COMSOL-provided adaptive mesh refinement algorithm was used to increase the number of elements in areas of largest numerical error to increase the accuracy of the solution. The flux distributions calculated by means of COMSOL/SCALE compare well with those calculated with benchmarked three-dimensional MCNP and KENO models, a necessary first step along the path to implementing two- and three-dimensional models of HFIR in COMSOL for the purpose of studying the spatial dependence of transient-induced behavior in the reactor core.     

TRACE simulation of sodium boiling in pin bundle experiments under loss-of-flow conditions

In the framework of PSI's FAST code system, the thermal–hydraulic code TRACE is being extended for representation of sodium two-phase flow. As the currently available version (v.5) is limited to the simulation of only single-phase sodium flow, its applicability range is not enough to study the behavior of a Generation IV sodium-cooled fast reactor (SFR) during transients in which boiling is anticipated. The work reported here concerns the extension of the non-homogeneous, non-equilibrium two-fluid models, which are available in TRACE for steam-water, to sodium two-phase flow simulation. The conventional correlations for ordinary gas–liquid flows are used as basis, with optional correlations specific to liquid metal where necessary. A number of new models for representation of the constitutive equations specific to sodium, with a particular emphasis on the interfacial transfer mechanisms, have been implemented and compared with the original closure models.A first assessment of the extended TRACE version has been carried out, by using the code to model experiments that simulate a loss-of-flow (LOF) accident in a SFR. One- and two-dimensional representations of the test section have been considered. Comparison of the 1D model predictions, with both experiment and SIMMER-III code predictions, confirm the ability of the extended TRACE code to predict the principal sodium boiling phenomena. Two-dimensional representation of the test section, however, has been found necessary for providing more detailed comparisons with the experimental data and thereby studying, in greater detail, the influence of the physical models on the calculated results.The paper thus presents a first-of-its-kind application of TRACE to two-phase sodium flow. It shows the capability of the extended code to predict sodium boiling onset, flow regimes, pressure evolution, dryout, etc. Although the numerical results are in good agreement with the experimental data, the physical models should be further improved. Other integral experiments are planned to be simulated, in order to further develop and validate the two-phase sodium flow modeling.     

Simulation of reactivity transients in current MTRs

This work aims at simulation of reactivity induced transients in High Enriched Uranium (HEU) and Low Enriched Uranium (LEU) cores of a typical Material Test research Reactor (MTR) using PARET code. The transient problem was forced through specification of externally inserted reactivity as a function of time. Reactivity insertions are idealized by ramps and steps. Superdelayed-critical transients, superprompt-critical transients and quasistatic transients are selected for the analysis. Ramp and step reactivity functions were employed to simulate these perturbations. The effect of initial power on transient behavior has also been investigated. The low enriched uranium core is analyzed for transients without scram. The magnitudes of maximum reactivity insertions are chosen to be in the range of $0.05 to 2.0 for different reactivity insertion times. Transient simulation with scram reveals that response of both HEU and LEU-cores is similar for selected ‘ramps’ and ‘steps’. The difference is observed in the peak values of power and coolant, clad and fuel temperatures. Trip level is achieved earlier in case of LEU-core. The peak clad temperatures in both LEU and HEU-cores remain below the melting point of aluminum-clad for the selected reactivity insertions. Simulation show that the LEU-core is more sensitive to perturbations at low power as compared to the transients at full power. For reactivity transients at low power level, power rises sharply to a higher peak value. In transients at full power, the peak power barely exceeds the trip level. The power oscillations after the first peak are observed for transients without scram.     

A numerical procedure for computing the fragility of NPP components under random seismic excitation

A numerical procedure is proposed in the paper for computing seismic fragility functions for equipment components in Nuclear Power Plants. The procedure is based on the hypothesis, which is typical when seismic excitation of components is addressed, of linear behaviour of the building. Given the large size of the FE element models adopted for the building, which makes direct Monte Carlo simulation impossible, the response surface methodology is used to model the influence of the random variables on the dynamic response. To account for stochastic loading the latter is estimated by means of a simulation procedure. Once the response surfaces defining the statistical properties of the response are available, the Monte Carlo method is used to compute the failure probability. A procedure for refining the RS estimation is also proposed, based on the evaluation of risk for a prototype site.A validation example is given, regarding the simplified modelling of a reactor building resting on a base-isolation system; results obtained by plain Monte Carlo analysis are compared to those computed via the proposed procedure The latter is finally applied to a real life case, taken from the preliminary design of the auxiliary building within the IRIS international project.     

An analytical method for thermal-hydraulic transients in piping networks

To predict the thermal-hydraulic transients, an analytical method has been developed for single and two-phase flow in arbitrary piping networks. In this method the piping network is represented by vessels and flow channels. The thermal-hydraulic transients in the channel are described by partial differential equations derived from mass, momentum and energy conservation laws. The partial differential equations are solved implicitly, simultaneously for the whole network, with the ordinary differential equations that describe the change of vessel pressures and enthalpies.Numerical calculation error is evaluated in the implicit method for the integration of partial differential equations of channel flow. In the numerical calculation an artificial diffusion appers with a diffusion coefficient Δt λ²/2, where Δt is a time step and λ denotes the propagation velocity of the perturbation.     

Study of startup transients and power ramping of natural circulation boiling systems

Numerical models of a natural circulation test facility and its prototype have been developed with RELAP5/MOD3.4 code and verified for their grid independence by nodal sensitivity studies. The model of the test facility has been validated for its steady state as well as transient predictions with the help of experimental observations. The transient predictions and parametric trends obtained by the numerical model of the prototype have been compared with those of the numerical model of the test facility. Thus, the ability of RELAP5 code to predict the transients during startup of a natural circulation boiling water reactor is verified. A powering procedure for the test facility has been conceptualized with the help of its RELAP5 model and demonstrated experimentally. Based on this, a similar powering procedure for the prototype has been proposed and simulated numerically with its RELAP5 model.     

全厂断电事故下AP1000非能动余热排出系统瞬态特性数值分析

在一维质量、动量和能量守恒方程基础上建立了AP1000反应堆主冷却剂系统及非能动余热排出系统数学模型,并编制了用于该系统瞬态特性分析的动态仿真程序PRHRSDSC。模拟了非能动余热排出系统在全厂断电事故下的瞬态响应过程,并将计算结果与西屋公司的LOFTRAN程序结果进行对比。结果表明：系统可依靠自然循环有效导出堆芯余热,一回路冷却剂温度维持在过冷状态,峰值压力未超过运行压力限值,各参数的变化趋势符合良好,证明了建模的合理性。     

Mathematical foundations of the quasistatic approximation in reactor physics

The quasistatic method used in reactor-physics calculations is applied to a model integro-differential equation in a Banach space. The resulting quasistatic equations are shown to be locally consistent with the original initial-value problem. An iterative scheme to solve these equations is presented and shown to be convergent.     

A 2D numerical simulation of sub-cooled flow boiling at low-pressure and low-flow rates

The main purpose of this study is to apply a two-fluid mathematical model to numerical simulation of two-phase flow at low-pressure condition. Although models of sub-cooled boiling flow at one-dimension and high-pressure have been studied extensively, there are few equivalent studies for numerical simulation at two-dimension and low-pressure (1-2 bar) conditions. Recent literature studies on sub-cooled boiling flow at low-pressure have shown that empirical models developed for high-pressure situations are not valid at low-pressures. Since the mathematical model used in this study is accomplished at low-pressure, the transport equations for the variables of each phase are substituted in low-pressure. The governing equations of two-phase flow with an allowance to inter-phase transfer of mass, momentum and heat, are solved using a two-fluid; non-equilibrium model. The finite volume discretization scheme is used to create a linearized system of equations that are solved by SIMPLE staggered grid solution technique for a rectangular channel. Improvement of the void fraction prediction of our model for the case of low-pressure sub-cooled flow boiling conditions was achieved. It is found that the heat transfer due to evaporation and surface quenching is higher than that by convection. Good agreement is achieved with the predicted results against the experimental data’s available in the literatures for a number of test cases.     

Numerical boron mixing studies for Loviisa nuclear power plant

A program is in the process of studying numerically boron mixing in the downcomer of Loviisa NPP (VVER-440). Mixing during the transport of a diluted slug from the loop to the core might serve as an inherent protection mechanism against severe reactivity accidents in inhomogenous boron dilution scenarios for PWRs. The commercial general purpose Computational Fluid Dynamics (CFD) code PHOENICS is used for solving the governing fluid flow equations in the downcomer geometry of VVER-440. So far numerical analyses have been performed for steady state operation conditions and two different pump driven transients. The steady state analyses focused on model development and validation against existing experimental data. The two pump driven transient scenarios reported are based on slug transport during the start of the sixth and first loop, respectively. The results from the two transients show that mixing is case and plant specific; the high and open downcomer geometry of VVER-440 seems to be advantageous from mixing point of view. In addition the analyzing work for the ‘first pump start' scenario brought up some considerations about flow distribution in the existing experimental facilities.     

Modelling the loss and recovery of electric power

General analytical models are developed to quantify the frequencies and durations of transients involving loss of off-site power or total loss of alternating current. Such transients are often important initiating events in probabilistic safety studies of nuclear power plants. Recursive equations are developed for the frequencies of production loss events when there is one or more standby systems available and a grace period to start a reserve unit. The methodology is illustrated with numerical applications.     

Model development and simulation of transient behavior of helium turbine system

This paper describes a performance model for the transient analysis of helium turbine system. Governing equations have been derived from integral forms of unsteady basic conservation equations. The one-dimensional model is employed for flow-paths except turbine and compressor, which are considered as zero-dimensional components and volume-less treatment is employed. Component mathematical model results in a set of ordinary differential equations and algebraic equations. The simulation code is established on MATLAB, and the ordinary differential equations are solved a variable order solver of MATLAB, ode15s. The accidents of loss of load and loss of feedwater to precooler and intercooler, the transients of recuperator and the decreasing heat transfer capacity of intermediate heat exchanger are simulated respectively. The analysis of calculated results verifies the present model. The effects of bypass valve size and thermal inertia of the recuperator wall are also studied. The simulation results show that throttle size of bypass valve has important influence on the characteristics of turbine system and should be carefully selected to satisfy the requirement of system control and safety.     

A spatial kinetic model for simulating VVER-1000 start-up transient

An accurate prediction of reactor core behavior in transients depends on how much it could be possible to exactly determine the thermal feedbacks of the core elements such as fuel, clad and coolant. In short time transients, results of these feedbacks directly affect the reactor power and determine the reactor response. Such transients are commonly happened during the start-up process which makes it necessary to carefully evaluate the detail of process. Hence this research evaluates a short time transient occurring during the start up of VVER-1000 reactor. The reactor power was tracked using the point kinetic equations from HZP state (100 W) to 612 kW. Final power (612 kW) was achieved by withdrawing control rods and resultant excess reactivity was set into dynamic equations to calculate the reactor power. Since reactivity is the most important part in the point kinetic equations, using a Lumped Parameter (LP) approximation, energy balance equations were solved in different zones of the core. After determining temperature and total reactivity related to feedbacks in each time step, the exact value of reactivity is obtained and is inserted into point kinetic equations. In reactor core each zone has a specific temperature and its corresponding thermal feedback. To decrease the effects of point kinetic approximations, these partial feedbacks in different zones are superposed to show an accurate model of reactor core dynamics. In this manner the reactor point kinetic can be extended to the whole reactor core which means “Reactor spatial kinetic”. All required group constants in calculations are prepared using the WIMS code. In addition CITATION code was used to calculate the flux, power distribution and core reactivity inside the core. To update the last change in group constants and resultant reactivity in point kinetic equations, these neutronic codes were coupled with a developed dynamic program. This study is applied on a typical VVER-1000 reactor core to show the reactor response in short time transients caused during start-up procedure.     

Numerical simulation of a potential CO2 ingress accident in a SFR employing an advanced energy conversion system

A numerical simulation method for the potential tube rupture and the consequential CO₂ ingress accident possibly occurring inside the Na–CO₂ heat exchanger of a SFR employing a supercritical CO₂ Brayton cycle has been developed. Based on the thermo-chemical considerations and a reasonable hypothesis, the computer code, STASCOR was formulated by reflecting suitable chemical reaction processes and various system models. The physical models implemented in the numerical method were tentatively verified by using a scale-down mock-up test, and it was confirmed that the analysis model and its assumptions feasibly replicate the overall system transients with a physically reasonable understanding. By using the numerical simulation method, the potential pressure boundary failure accident for the shell-and-tube type Na/CO₂ heat exchanger was analyzed and the system dynamic responses were systematically evaluated. Based on the analysis results, it was demonstrated that the STASCOR code has the capabilities to simulate a system transient regarding the various design conditions associated with a pressure relief system. The applicability of the numerical simulation method to a micro-channel type heat exchanger, e.g. PCHE, was assessed qualitatively, and the possibility of a self-plugging or self-mitigation against the CO₂ ingress accident was discussed as well.     

Change of phase in compressible trans-phase calculations

The difficulties experienced in digital nuclear reactor LOCA codes at changes from two-phase to liquid state are examined and the methods used in various codes to overcome these difficulties are reviewed. Looking at the problem from a new point of view has enabled an entirely different solution to be proposed. A finite difference mass equation is deduced in which all coefficients are continuous across phase boundaries and which is accurate to order Δt. The new equation has been incorporated in the NAIAD code and applied to an international benchmark problem in which severe numerical transients at phase changes otherwise occur. No such numerical transients were found.     

Identification and modeling of nonlinear systems

A nonparametric identification technique is presented for use with discrete multidegree of freedom nonlinear dynamic systems of the type encountered in nuclear reactor technology. The method requires information regarding the system response and estimates of its pertinent “mode shapes” to determine, by means of regression techniques involving the use of two-dimensional orthogonal functions, an approximate expression for the system generalized restoring forces in terms of the corresponding generalized system state variables. For the special class of nonlinear systems that have chain-like characteristics, drastic simplifications in the procedure are realized, and the identification task can be easily and accurately accomplished without using any information regarding estimated “mode shapes”. The technique is applied to several example systems. The method can be used with deterministic or random excitation to identify dynamic systems with arbitrary nonlinearities, including those with hysteretic characteristics. It is also shown that the method is easy to implement and needs much less computer time and storage requirements compared to the Wiener-Kernel approach.