Point Kinetics Model Research Articles

Stationary liquid fuel fast reactor SLFFR — Part II: Safety analysis

Safety characteristics have been evaluated for the stationary liquid fuel fast reactor (SLFFR) proposed for effective burning of hazardous TRU elements of used nuclear fuel. In order to model the geometrical configuration and reactivity feedback mechanisms unique to SLFFR, a multi-channel safety analysis code named MUSA was developed. MUSA solves the time-dependent coupled neutronics and thermal-fluidic problems. The thermal-fluidic behavior of the core is described by representing the core with one-dimensional parallel channels. The primary heat transport system is modeled by connecting compressible volumes by liquid segments. A point kinetics model with six delayed neutron groups is used to represent the fission power transients. The reactivity feedback is estimated by combining the temperature and density variations of liquid fuel, structural material and sodium coolant with the corresponding axial distributions of reactivity worth in each individual thermal-fluidic channel. Preliminary verification tests with a conventional solid fuel reactor agreed well with the reference solutions obtained with the SAS4A/SASSYS-1 code. Transient analyses of SLFFR were performed for unprotected transient over-power (UTOP), unprotected loss of heat sink (ULOHS) and unprotected loss of flow (ULOF) accidents. The results showed that the thermal expansion of liquid fuel provides sufficiently large negative feedback reactivity for passive shutdown of UTOP and ULOHS. The ULOF transient is also terminated passively with the negative reactivity introduced by the gas expansion modules installed at the core periphery. The maximum coolant temperatures have sufficient margins to the sodium boiling point for all three unprotected transient scenarios.

A point kinetics model for dynamic simulations of next generation nuclear reactor

An accurate, fast-running and stable six-group, point kinetics (PK) model is developed and applied successfully to the dynamic simulation of the operation of the prismatic core, high temperature next generation nuclear plant (NGNP) reactor. The model is unrestricted by the size of the time step, which could be as much as several seconds, accounts for Doppler Broadening and the fuel and graphite temperature reactivity feedbacks, and includes an active neutron source for zero-power reactor startup. An efficient and robust numerical technique that approximates the exponential matrix using 7th order-accurate Padé(3,3) function with a discretization error on the order of (Δt)3, solves the coupled nonlinear and stiff six-groups point kinetics equations. The PK model handles reactivity insertions in excess of a prompt critical, ρ/β¯> $1.0, with unrestrictive time step size. Model results are successfully benchmarked using the Inhour solution for a step insertion of external reactivity. To simulate the transient response of the NGNP reactor following an external reactivity insertion and during a startup, the PK model is coupled to 84-nodes thermal-hydraulics model of the reactor, also developed in this work. With a 2 s time step, the error of predicting the reactor thermal power is ∼0.001%, increasing exponentially to ∼0.08% and ∼1.5% with increased time step size to 5 and 8 s, respectively. The present PK model has been successfully incorporated into MELCOR-H2 nuclear reactor analysis code to simulate transient operation of Very High Temperature Reactor (VHTR) for electricity generation, using a Closed Brayton Cycle turbomachinery, and the co-generation of hydrogen using Sulfur Iodine (SI) thermochemical processes.

Development of the FHR advanced natural circulation analysis code and application to FHR safety analysis

The University of California, Berkeley (UCB) is performing thermal hydraulics safety analysis to develop the technical basis for design and licensing of fluoride-salt-cooled, high-temperature reactors (FHRs). FHR designs investigated by UCB use natural circulation for emergency, passive decay heat removal when normal decay heat removal systems fail. The FHR advanced natural circulation analysis (FANCY) code has been developed for assessment of passive decay heat removal capability and safety analysis of these innovative system designs. The FANCY code uses a one-dimensional, semi-implicit scheme to solve for pressure-linked mass, momentum and energy conservation equations. Graph theory is used to automatically generate a staggered mesh for complicated pipe network systems. Heat structure models have been implemented for three types of boundary conditions (Dirichlet, Neumann and Robin boundary conditions). Heat structures can be composed of several layers of different materials, and are used for simulation of heat structure temperature distribution and heat transfer rate. Control models are used to simulate sequences of events or trips of safety systems. A proportional-integral controller is also used to automatically make thermal hydraulic systems reach desired steady state conditions. A point kinetics model is used to model reactor kinetics behavior with temperature reactivity feedback. The underlying large sparse linear systems in these models are efficiently solved by using direct and iterative solvers provided by the SuperLU code on high performance machines. Input interfaces are designed to increase the flexibility of simulation for complicated thermal hydraulic systems. This paper mainly focuses on the methodology used to develop the FANCY code, and safety analysis of the Mark 1 pebble-bed FHR under development at UCB is performed.

The effect of a changing fuel solution composition on a transient in a fissile solution

This paper presents an extension to a point kinetics model of fissile solution undergoing a transient through the development and addition of correlations which describe neutronics and thermal parameters and physical models. These correlations allow relevant parameters to be modelled as a function of time as the composition of the solution changes over time due to the addition of material and the evaporation of water from the surface of the solution. This allows the simulation of two scenarios. In the first scenario a critical system eventually becomes subcritical through under-moderation as its water content evaporates. In the second scenario an under-moderated system becomes critical as water is added before becoming subcritical as it becomes over-moderated. The models and correlations used in this paper are relatively idealised and are limited to a particular geometry and fissile solution composition. However, the results produced appear physically plausible and demonstrate that simulation of these processes are important to the long term development of transients in fissile solutions and provide a qualitative indication of the types of behaviour that may result in such situations.

Development, validation and application of multi-point kinetics model in RELAP5 for analysis of asymmetric nuclear transients

Point kinetics approach in system code RELAP5 limits its use for many of the reactivity induced transients, which involve asymmetric core behaviour. Development of fully coupled 3D core kinetics code with system thermal-hydraulics is the ultimate requirement in this regard; however coupling and validation of 3D kinetics module with system code is cumbersome and it also requires access to source code. An intermediate approach with multi-point kinetics is appropriate and relatively easy to implement for analysis of several asymmetric transients for large cores. Multi-point kinetics formulation is based on dividing the entire core into several regions and solving ODEs describing kinetics in each region. These regions are interconnected by spatial coupling coefficients which are estimated from diffusion theory approximation. This model offers an advantage that associated ordinary differential equations (ODEs) governing multi-point kinetics formulation can be solved using numerical methods to the desired level of accuracy and thus allows formulation based on user defined control variables, i.e., without disturbing the source code and hence also avoiding associated coupling issues. Euler's method has been used in the present formulation to solve several coupled ODEs internally at each time step. The results have been verified against inbuilt point-kinetics models of RELAP5 and validated against 3D kinetics code TRIKIN. The model was used to identify the critical break in RIH of a typical large PHWR core. The neutronic asymmetry produced in the core due to the system induced transient was effectively handled by the multi-point kinetics model overcoming the limitation of in-built point kinetics model of RELAP5 and standalone 3D core kinetics codes.

Analytical exponential model for stochastic point kinetics equations via eigenvalues and eigenvectors

The stochastic point kinetics equations with a multi-group of delayed neutrons, which are the system of a couple of stiff stochastic differential equations, are presented. The analytical exponential model is used to solve the stochastic point kinetics equations in the dynamical system of the nuclear reactor. This method is based on the eigenvalues and corresponding eigenvectors of the coefficient matrix. The analytical exponential model calculates the mean and standard deviations of neutrons and precursor populations for the stochastic point kinetics equations with step, ramp, and sinusoidal reactivities. The results of the analytical exponential model are compared with published methods and the results of the deterministic point kinetics model. This comparison confirms that the analytical exponential model is an efficient method for solving stochastic stiff point kinetics equations.

CFD Analysis of the Primary Cooling System for the Small Modular Natural Circulation Lead Cooled Fast Reactor SNRLFR-100

Small modular reactor (SMR) has drawn wide attention in the past decades, and Lead cooled fast reactor (LFR) is one of the most promising advanced reactors which are able to meet the safety economic goals of Gen-IV nuclear energy systems. A small modular natural circulation lead cooled fast reactor-100 MWth (SNRLFR-100) is being developed by University of Science and Technology of China (USTC). In the present work, a 3D CFD model, primary heat exchanger model, fuel pin model, and point kinetic model were established based on some reasonable simplifications and assumptions, the steady-state natural circulation characteristics of SNCLFR-100 primary cooling system were discussed and illustrated, and some reasonable suggestions were proposed for the reactor’s thermal-hydraulic and structural design. Moreover, in order to have a first evaluation of the system behavior in accident conditions, an unprotected loss of heat sink (ULOHS) transient simulation at beginning of the reactor cycle (BOC) has been analyzed and discussed based on the steady-state simulation results. The key temperatures of the reactor core are all under the safety limits at transient state; the reactor has excellent thermal-hydraulic performance.

Thermal hydraulic analysis of reactivity accidents in MTR research reactors using RELAP5

Abstract The present paper comes in the line with the international approach which use the best estimate codes, instead of conservative codes, to get more realistic prediction of system behavior under off-normal reactor conditions. The aim of the current work is to apply this approach using the thermal-hydraulic system code RELAP5/Mod3.3 in a reassessment of safety of the IAEA benchmark 10 MW Research Reactor. The assessment is performed for both slow and fast reactivity insertion transients at initial power of 1.0 W. The reactor power is calculated using the RELA5 point kinetic model. The reactivity feedback terms are considered in two steps. In the first step the feedback from changes in water density and fuel temperature (Doppler effects) are considered. In the second step the feedback from the water temperature changes is added. The results from the first step are compared with that published in IAEA-TECDOC-643 benchmarks. The comparison shows that RELAP5 over predicts the peak power and consequently the fuel, clad and coolant temperatures in case of fast reactivity insertion. The results from the second step show unjustified values for reactor power. Therefore, the model of reactivity feedback from water temperature changes in the RELAP5 code may have to be reviewed.

Analysis of control rod drop accident in PWRs with multipoint kinetics method

A major group of accidents in PWRs is related to improper operation of control rods. Malfunction in control and protection system (CPS) of control rods or operator’s error can be a cause of such events. This paper presents a study of the drop of one control rod accident with multipoint kinetic approach. The main aim of this work is the introduction of multipoint kinetics method as an accurate model for accident analysis. In this way, a coupled dynamic model based on point and multipoint kinetics formulation is developed for transient analysis. Also for reactivity feedback calculation, a simple thermal hydraulic simulation of the core is employed. To illustrate the capability of the proposed scheme, Bushehr Nuclear Power Plant, BNPP, which is a WWER-1000 reactor, is chosen and multiples of the 1/6 symmetry slices of the core is considered as nodes. Thus, the reactor core is divided into two, three, and six nodes in each case study, and the drop of one control rod accident, CRDA, is simulated. These results demonstrate that the multi point kinetics model can reflect not only the average information but also the distribution information of the core such as the spatial power, fuel temperature and coolant temperature distribution in the core. In addition, the accuracy, simplicity, and fast computation speed of the multipoint kinetics model make it a reliable method for simulation and design of the control system for WWER-1000 reactors.

Dynamic rod worth simulation study for a sodium-cooled TRU burner

This paper presents a preliminary dynamic rod worth simulation study for a TRU burner core mockup of the PGSFR (Korean Prototype Gen-IV Sodium-cooled Fast Reactor) named BFS-76-1A so as to establish a calculation methodology for evaluating the rod worth of the PGSFR. The simulation method was mainly based on a three-dimensional multi-group nodal diffusion transient code for fast reactors in which the rod drop simulation for the BFS-76-1A was performed and all the fuel assemblies were taken into account for the detector response calculation. Then the dynamic rod worths were inferred from the simulated detector responses using an inverse point kinetics model and compared against the simulated static worths. The results show good agreement between the simulated pseudo detector response and the calculated core power as well as between the simulated dynamic and static rod worths, and thus indicate that the dynamic rod worth simulation method developed in this work can be applied to the rod worth estimation and validation for the PGSFR.

The neutron point kinetics equation: Suppression of fractional derivative effects by temperature feedback

A Riemann–Liouville fractional derivative point kinetics model is discussed with additional temperature feedback. The choice for the Riemann–Liouville definition is justified by preservation of homogeneity and integral transform properties. An analytical representation for the time dependent neutron density is derived for any fractional order and any relaxation time scale by the use of a recursive decomposition scheme. Without temperature effects scenarios with constant positive and negative, linear and oscillatory time dependent reactivity are presented. The case with additional temperature effects is solved and results are presented. The latter case showed that for a selection of fractional derivative parameter effects on the neutron density are completely suppressed.

Safety analysis of reactivity insertion accidents in a heavy water nuclear research reactor core using coupled 3D neutron kinetics thermal-hydraulic system code technique

Nuclear power plant Safety analysis using coupled 3D neutron kinetics/thermal-hydraulic codes technique is increasingly used nowadays. Actually, the use of this technique allows getting less conservatism and more realistic simulations of the physical phenomena. The challenge today is oriented toward the application of this technique to the operating conditions of nuclear research reactors. In the current study, a three-Dimensional Neutron Kinetics and best estimate Thermal-Hydraulic model based upon the coupled PARCS/RELAP5 codes has been developed and applied for a heavy water research reactor. The objective is to perform safety analysis related to design accidents of this reactor types. In the current study two positive reactivity insertion transients are considered, SCRAM protected and self-limiting power excursion cases. The results of the steady state calculations were compared with results obtained from conventional diffusion codes, while transient calculations were assessed using the point kinetic model of the RELAP5 code. Through this study, the applicability and the suitability of using the coupled code technique with respect to the classical models are emphasized and discussed.

Importance weighting of local flux measurements to improve reactivity predictions in nuclear systems

Abstract The reactivity monitoring is a key aspect for the safe operation of nuclear reactors, especially for subcritical source-driven systems. Various methods are available for both off-line and on-line reactivity determination from direct measurements carried out on the reactor. Usually the methods are based on the inverse point kinetic model applied to signals from neutron detectors and results may be severely affected by spatial and spectral effects. Such effects need to be compensated and correction procedures have to be applied. In this work, a new approach is proposed, by using the full information from different local measurements to generate a global signal through a proper weighting of the signals provided by single neutron detectors. A weighting techique based on the use of the adjoint flux proves to be efficient in improving the prediction capability of inverse techniques. The idea is applied to the recently developed algorithm, named MAρTA, that can be used in both off-line and on-line modes.

TRANSIENT EXPERIMENTS IN ZED-2 TO INVESTIGATE THE IMPACT OF LEAKAGE ON REACTOR PHYSICS PHENOMENA

This paper describes an experimental approach where reactor kinetics experiments are used to study reactor physics phenomena that are normally investigated using static-measurement techniques. This approach provides validation data relating to these phenomena for a range of core reactivities, rather than only providing data at critical conditions. Sub-critical and super-critical transient measurements were performed in the ZED-2 reactor. The transients were analyzed using a point kinetics model to derive the reactivity states that induced the transients. The reactor physics phenomenon of interest for the current study is Coolant Density Induced Reactivity. Initial measurements were performed using an air-cooled (i.e., voided) ZED-2 lattice; the measurements were then repeated using the same lattice cooled with light water. These measurements yielded reactivity values for both coolant conditions in the lattice for a range of super-critical and sub-critical states. This investigation avoids the inherent assumption of static-measurement analyses that the bias in predicting criticality for the two coolant conditions is identical to the bias in predicting the phenomenon of Coolant Density Induced Reactivity itself. The measured reactivity values are compared with calculations employing the 3-D stochastic neutron transport reactor code MCNP.

Space–time effects in the initiating phase of sodium fast reactors and their evaluation using a three-dimensional neutron kinetics model

The treatment of low probability events leading to core disruption is one of the key issues of R&D plans for the advanced reactor systems in general, and for sodium fast reactors in particular. Regarding sodium fast reactor systems, a major concern is that the core, at nominal, is not necessarily in its neutronically most reactive state. The simulation of the initiating phase of such accidents is of particular interest both for the prevention and the mitigation of routes leading to a large core disruption and recriticalities. Current analysis of the initiating phase relies on a Point Kinetics model, which neglects spatial variations of the neutron flux (i.e. the flux shape). Because the core geometry may be modified during such accidental conditions, the constant-shape approximation becomes questionable when applied to initiating phase simulations. The present paper investigates space–time effects during the degradation of a sodium fast reactor core. To this aim, a three-dimensional neutron kinetics model has been coupled to a multiple-channel thermal–hydraulics model and applied to evaluate spatial effects during a severe accident transient. As expected, it was found that spatial effects are not likely to be of importance in the pre-boiling portion of the transient reinforcing the use of a Point Kinetics model for the simulation of design-basis transient up to the boiling point. Departure from the Point Kinetics approach is noticeable after the fuel-pin breakup. The fuel being the source of neutrons, its motion within the core boundaries tends to create important spatial changes in the fission source. From this event, the Point Kinetics model fails in reproducing results obtained by the three-dimensional model and the study conducted in the present paper assesses this discrepancy.

Experimental assessment of the kinetic parameters of the JSI TRIGA reactor

An experimental campaign has been carried out at the TRIGA reactor of the Jozef Stefan Institute, in order to assess its mean neutron generation time Λ and effective delayed neutron fraction βeff. For that, the cross spectral densities (CPSD) of two fission chambers have been taken. The reactor has been operated in five core configurations corresponding to different control rod and chamber positions. A method of comparison between the cross spectral densities using the Welch statistical test, without assuming any kinetic model, has been performed; it shows that it is possible to distinguish between those configurations provided an high enough integration time (above 3000s) is used. Assuming a point-kinetic model, the parameters Λ and βeff have been robustly derived by a Cohn-α technique. The generation time is found to be rather constant from a configuration to another, but configurations with different fuel loading and control rod position yield an effective delayed neutron fraction that differ at 1σ level. The experimental values for both parameters agree with the values provided by the TRIGA manufacturers.

Coupling a CFD code with neutron kinetics and pin thermal models for nuclear reactor safety analyses

Most system codes are based on the one-dimensional lumped-parameter method, which is unsuitable to simulate multi-dimensional thermal-hydraulics problems. CFD method is a good tool to simulate multi-dimensional thermal-hydraulics phenomena in the nuclear reactor, which can increase the accuracy of analysis results. However, since there is no neutron kinetics model and pin thermal model in current CFD codes, the application of the CFD method in the area of nuclear reactor safety analyses is still limited. Coupling a CFD code with the neutron kinetics model (PKM) and the pin thermal model (PTM) is a good way to use CFD code to simulate multi-dimensional thermal-hydraulics problems of nuclear reactors. The motivation for this work is to develop a CFD/neutron kinetics coupled code named FLUENT/PK for nuclear reactor safety analyses by coupling the commercial CFD code named FLUENT with the point kinetics model (PKM) and the pin thermal model (PTM). The mathematical models and the coupling method are described and the unprotected transient overpower (UTOP) accident of a liquid metal cooled fast reactor (LMFR) is chosen as an application case. As a general validation, the calculated results are used to compare with that of another multi-physics coupled code named SIMMER-III and good agreements are achieved for various characteristic parameters.

Experimental study of natural circulation instability with void reactivity feedback during startup transients for a BWR-type SMR

The natural circulation boiling type SMR can experience flow instability during the startup transients due to the void reactivity feedback. A BWR-type natural circulation test loop has been built to perform the nuclear coupled startup transient tests for Purdue Novel Modular Reactor (NMR). This test loop is installed with different instruments to measure various thermal hydraulic parameters. The testing process can be monitored and controlled through PC with the assistance of LabVIEW procedure. The effects of power ramp rate on the flow instability during the nuclear coupled tests were investigated by controlling the power supply based on the point kinetics model with coolant void reactivity feedback. Two power ramp rates were investigated and the results were compared with those of the thermal hydraulic startup transients without void reactivity feedback. The time trace of power supply, system pressure, natural circulation rate, and void fraction profile are used to determine the flow stability during the transients. The results show that nuclear coupled startup transients also experience flashing instability and density wave oscillations. The power curves calculated from point kinetics model for startup transients show some fluctuations due to void reactivity feedback. However, the void reactivity feedback does not have significant effects on the flow instability during the startup procedure for the NMR.

Development of a kinetic model for safety studies of liquid-fuel reactors

Liquid-fuel reactors offer very fascinating problems in neutronics due to the effects of the fuel movements in the reactor core and loop. In the present study, a spatial kinetic model taking the fuel flow effects into account for liquid-fuel reactors is derived without approximation from the time–space-dependent equations of neutrons and delayed neutron precursors. The relation between such spatial kinetic model and the point kinetic model for the solid-fuel reactor is set up as well, which is useful for extending the safety codes developed for conventional solid-fuel reactors to liquid-fuel ones. The spatial kinetic model together with the other two approximated kinetic models are applied to the safety analysis of a typical liquid-fuel reactor MOSART (MOlten Salt Actinide Recycler and Transmuter). The steady state calculation and the ULOF (Unprotected Loss of Flow) calculation are performed, and the liquid-fuel flow effects are studied particularly. The steady state results show that the fuel flow influences the distributions of the delayed neutron precursors significantly. The ULOF results by all models show that the behavior of the relative power, fuel salt temperature, graphite temperature, and reactivity feedbacks are similar due to strong negative reactivity feedbacks. However, the developed spatial kinetic model obtains more safety margin to the fuel temperature limit.

Development of a Thermal-Hydraulic Analysis Code and Transient Analysis for a Fluoride-Salt-Cooled High-Temperature Test Reactor

The fluoride-salt-cooled high-temperature reactor (FHR) is an advanced reactor concept that uses high-temperature tristructural isotropic (TRISO) fuel with a low-pressure liquid salt coolant. Design of the fluoride-salt-cooled high-temperature test reactor (FHTR) is a key step in the development of the FHR technology and is currently in progress both in China and the United States. An FHTR based on pebble-bed core design with a coolant temperature of 600–700°C is being planned for construction by the Chinese Academy of Sciences’ (CAS) Thorium Molten Salt Reactor (TMSR) Research Center, Shanghai Institute of Applied Physics (SINAP). This paper provides preliminary thermal-hydraulic transient analyses of an FHTR using SINAP’s pebble-bed core design as a reference case. A point kinetic model is implemented using computer code by coupling with a simplified porous medium heat transfer model in the core. The founded models and developed code are applied to analyze the safety characteristics of the FHTR by simulating several transient conditions including the unprotected loss of flow, unprotected overcooling, and unprotected transient overpower accidents. The results show that SINAP’s pebble-bed core is a very safe reactor design.