Reactor Kinetics Research Articles

Control of Advanced Reactor-Coupled Heat Exchanger System: Incorporation of Reactor Dynamics in System Response to Load Disturbances

Abstract Alternative control schemes for an Advanced High Temperature Reactor system consisting of a reactor, an intermediate heat exchanger, and a secondary heat exchanger (SHX) are presented in this paper. One scheme is designed to control the cold outlet temperature of the SHX (Tco) and the hot outlet temperature of the intermediate heat exchanger (Tho2) by manipulating the hot-side flow rates of the heat exchangers (Fh/Fh2) responding to the flow rate and temperature disturbances. The flow rate disturbances typically require a larger manipulation of the flow rates than temperature disturbances. An alternate strategy examines the control of the cold outlet temperature of the SHX (Tco) only, since this temperature provides the driving force for energy production in the power conversion unit or the process application. The control can be achieved by three options: (1) flow rate manipulation; (2) reactor power manipulation; or (3) a combination of the two. The first option has a quicker response but requires a large flow rate change. The second option is the slowest but does not involve any change in the flow rates of streams. The third option appears preferable as it has an intermediate response time and requires only a minimal flow rate change.

Solution of the point reactor kinetics equations with temperature feedback by the ITS2 method

The ITS2 method is used to solve the point-reactor kinetics equations in the integral formulation with arbitrary number of delayed neutron groups and Newtonian temperature feedback. The method is based on low-order Taylor series expansions of neutron density and reactivity functions and uses variable time steps to control the numerical instabilities resulting from the stiff nature of the governing equations. Time steps are determined through an analytic criterion relating their magnitudes to the maximum admissible truncation error in the neutron-density expansion series. Temperature feedback is included in the reactivity as a function of the neutron density for different input types, including step change with adiabatic temperature feedback and compensated ramp functions. An iterative procedure is applied to determine the time steps while simultaneously updating the reactivity function. Numerical results show the ITS2 method is highly accurate for solving point reactor dynamics problems with temperature feedback.

Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem

In this paper, a qualitative approach has been used to explore nuclear reactor behaviors with nonlinear feedback. First, a system of four dimensional ordinary differential equations governing the dynamics of a typical nuclear reactor is introduced. These four state variables are the relative power of the reactor, the relative concentration of delayed neutron precursors, the fuel temperature and the coolant temperature. Then, the qualitative behaviors of the dynamical system near its equilibria have been studied analytically by using local bifurcation theory and Sotomayor’s theorem. The results indicated that despite the uncertainty of the reactivity, we can analyze the qualitative behavior changes of the reactor from the bifurcation point of view. Notably, local bifurcations that were considered in this paper include transcritical bifurcation, saddle-node bifurcation and pitchfork bifurcation. The theoretical analysis showed that these three types of local bifurcations may occur in the four dimensional dynamical system. In addition, to confirm the analytical results the numerical simulations are given.

Thermal Process Safety Based on Reaction Kinetics and Reactor Dynamics

The specific problem of non-converted reactant accumulation encountered in fed-batch reactor is a challenging task of process safety. In order to avoid such situation that may lead to a runaway reaction, the reaction kinetics and reactor dynamic must be known. In this work, an innovative approach to determine an optimal feed profile, based on a reaction kinetic and reactor dynamic, is presented. This approach was applied to the reaction system involved in the Morton International Inc. incident. Great improvements were observed in the control of the accumulation, decreasing the number of necessary experiments needed for the scale-up studies.

Accident analysis of heat pipe cooled and AMTEC conversion space reactor system

A space power with high power density, light weight, low cost and high reliability is of crucial importance to future exploration of deep space. Space reactor is an excellent candidate because of its unique characteristics of high specific power, low cost, strong environment adaptability and so on. Among all types of space reactors, heat pipe cooled space reactor, which adopts the passive heat pipe (HP) as core cooling component, is considered as one of the most promising choices and is widely studied all over the world.This paper develops a transient analysis code (TAPIRS) for heat pipe cooled space reactor power system (HPS) based on point reactor kinetics model, lumped parameter core heat transfer model, combined HP model (self-diffusion model, flat-front startup model and network model), energy conversion model of Alkali Metal Thermal-to-Electric Conversion units (AMTEC), and HP radiator model. Three typical accidents, i.e., control drum failure, AMTEC failure and partial loss of the heat transfer area of radiator are then analyzed using TAPIRS. By comparing the simulation results of the models and steady state with those in the references, the rationality of the models and the solution method is validated. The results show the following. (1) After the failure of one set of control drums, the reactor power finally reaches a stable value after two local peaks under the temperature feedback. The fuel temperature rises rapidly, however it is still under safe limit. (2) The fuel temperature is below a safe limit under the AMTEC failure and partial loss of the heat transfer area of radiator. This demonstrates the rationality of the system design and the potential applicability of the TAPIRS code for the future engineering application of heat pipe cooled space reactor.

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 reactor dynamics code DYN3D

Abstract The article provides an overview on the code DYN3D which is a three-dimensional core model for steady-state, dynamic and depletion calculations in reactor cores with quadratic or hexagonal fuel assembly geometry being developed by the Helmholtz-Zentrum Dresden-Rossendorf for more than 20 years. The current paper gives an overview on the basic DYN3D models and the available code couplings. The verification and validation status is shortly outlined. The paper concludes with the current developments of the DYN3D code. For more detailed information the reader is referred to the publications cited in the corresponding chapters.

Rotation profile flattening and toroidal flow shear reversal due to the coupling of magnetic islands in tokamaks

The electromagnetic coupling of helical modes, even those having different toroidal mode numbers, modifies the distribution of toroidal angular momentum in tokamak discharges. This can have deleterious effects on other transport channels as well as on magnetohydrodynamic (MHD) stability and disruptivity. At low levels of externally injected momentum, the coupling of core-localized modes initiates a chain of events, whereby flattening of the core rotation profile inside successive rational surfaces leads to the onset of a large m/n = 2/1 tearing mode and locked-mode disruption. With increased torque from neutral beam injection, neoclassical tearing modes in the core may phase-lock to each other without locking to external fields or structures that are stationary in the laboratory frame. The dynamic processes observed in these cases are in general agreement with theory, and detailed diagnosis allows for momentum transport analysis to be performed, revealing a significant torque density that peaks near the 2/1 rational surface. However, as the coupled rational surfaces are brought closer together by reducing q95, additional momentum transport in excess of that required to attain a phase-locked state is sometimes observed. Rather than maintaining zero differential rotation (as is predicted to be dynamically stable by single-fluid, resistive MHD theory), these discharges develop hollow toroidal plasma fluid rotation profiles with reversed plasma flow shear in the region between the m/n = 3/2 and 2/1 islands. The additional forces expressed in this state are not readily accounted for, and therefore, analysis of these data highlights the impact of mode coupling on torque balance and the challenges associated with predicting the rotation dynamics of a fusion reactor—a key issue for ITER.

Modification of thermal hydraulic code, THEATRe, with fuel rod behavior models and its application to reactivity-initiated accident (RIA)

ABSTRACTDuring reactor operation, many complex changes occur in fuel rod which affects its thermal, mechanical and material properties. These changes also affect the reactor response to the transient and accident situations. Realistic simulation of fuel rod behavior under transients such as reactivity-initiated accident (RIA) is of great significance. In this study, thermal hydraulic analysis code THEATRe (Thermal Hydraulic Engineering Analysis Tool in Real-time) has been modified by addition of fuel rod behavior models for dynamic simulation of nuclear reactor. Transient changes in gas-gap parameters were taken into account by modeling the gas-gap behavior. Thermo-mechanical behavior of fuel rod is modeled to take into account the thermal, elastic and plastic deformation. To simulate RIA, point reactor kinetics model is also incorporated in the THEATRe code. To demonstrate the transient fuel rod behavior, AP1000 reactor is modeled and three hypothetical RIA cases are simulated. The RIA is considered at three different reactor power levels, i.e. 100, 50 and 1% of nominal power. The investigated parameters are fuel temperature, cladding stress and strain, fuel and cladding thermal conductivity and heat transfer coefficient in gas-gap. Modified code calculates the fuel rod temperatures according to updated fuel, clad and gas-gap parameters at the onset of steady-state operation and during the transient. The modified code provides lower steady-state fuel temperature as compared to the original code. Stress and strain analyses indicate that the hoop and radial strain is higher at high power locations of the fuel rod; therefore, gap closure process will initially occur in the central portion of the fuel rod and it should be given more emphasis in the safety analysis of the fuel rod and nuclear reactor during accidents and transients.

Dynamics between the fishbone instability and nonlocal transient transport in HL-2A NBI plasmas

Understanding of nonlocal electron heat transport is of key importance for current magnetic confinement fusion research. Global nonlocal response presents a fundamental challenge to the standard anomalous transport model based on local microinstabilities and turbulence. Here, we present for the first time a new nonlocal phenomenon triggered by the fishbone instability in HL-2A neutral beam injection plasmas. Rapid core heating leads to a simultaneous decrease in temperature at the plasma edge. The effect reveals fast anomalous transport of core heat pulses to the plasma edge, not compatible with diffusive time scales. More importantly, variations at different locations are restricted by the intensity of magnetic fluctuations. The and form two types of hysteresis loops at two sides of the inversion radius. The ECEIs show that the 2D mode structure of the fishbone is intensive shearing/spiraling during the nonlocal transport. Experimental results suggest that magnetic perturbation, long-range correlation, mesoscale structure and flow play crucial roles in the nonlocal response. The Hurst exponent and auto-correlation coefficient indicate that the nonlocal transport is potentially linked to the self-organized critical (SOC) dynamics. This work will be beneficial for understanding of the plasma dynamics in future fusion reactors.

Stability analysis of the Korean prototype Generation-IV sodium-cooled fast reactor using linear frequency domain approach

Abstract The Korea Atomic Energy Research Institute (KAERI) has been developing the 150 MWe Prototype Generation-IV Sodium-cooled Fast Reactor (PGSFR). The design concept is highly based on passive safety mechanisms, minimizing the need for engineered safety systems. Presently, it is of primary importance to assure the reactor dynamics and stability against small reactivity disturbances under power operating conditions. KAERI has therefore developed the NuSTAB code for stability analysis of the PGSFR. In NuSTAB, the neutron-kinetic and thermal-hydraulic coupling equations are linearized to form the characteristic equation, which is solved as a generalized eigenvalue problem for determining the decay ratio, an indicator of the system stability. In this paper, the stability of the PGSFR was analyzed by applying the point kinetic and spatial kinetic options in the NuSTAB code. System responses to temperature feedbacks including the Doppler effect, thermal expansion, coolant density change, and overall feedback were studied. The results indicate that the initial U and final TRU cores of the PGSFR are both inherently stable thanks to the temperature feedbacks.

Simulation of nuclear reactor dynamics equations using reconfigurable computing

This paper describes the application of a multilayer discrete-time cellular neural network (DT-CNN1) and its hardware implementation on a field programmable gate array (FPGA2) to model and simulate the nuclear reactor dynamics equations. A new computing architecture model based on FPGA and its detailed hardware implementation are proposed for accelerating the solution of nuclear reactor dynamics equations. The proposed FPGA-based reconfigurable computing platform is implemented on a Xilinx FPGA device and is utilized to simulate step and ramp perturbation transients in typical 2D nuclear reactor cores. Properties of the implemented specialized architecture are examined in terms of speed and accuracy against the numerical solution of the nuclear reactor dynamics equations using MATLAB and C programs. Steady state as well as transient simulations, show a very good comparison between the two methods. Also, the validity of the synthesized architecture as a hardware accelerator is demonstrated.

The reactor dynamics code DYN3D – models, validation and applications

The article provides an overview of the reactor dynamics code DYN3D. The code comprises various 3D neutron kinetics solvers, a thermal-hydraulics reactor core model and a thermo-mechanical fuel rod model. The implemented models and methods and the capabilities and features of the code are described. Latest developments of models and methods are delineated. An overview on the status of verification and validation is given. Code applications for selected safety analyses are described. Furthermore, multi-physics code couplings to thermal-hydraulic system codes, CFD and sub-channel codes as well as to the fuel performance code TRANSURANUS are outlined. Developments for innovative reactor concepts, in particular Molten Salt Reactor, High Temperature Gas-cooled Reactor and Sodium Fast Reactor are delineated. The management of code maintenance is briefly described. An outlook on further code development is given.

A bifurcation analysis of boiling water reactor on large domain of parametric spaces

The boiling water reactors (BWRs) are inherently nonlinear physical system, as any other physical system. The reactivity feedback, which is caused by both moderator density and temperature, allows several effects reflecting the nonlinear behavior of the system. Stability analyses of BWR is done with a simplified, reduced order model, which couples point reactor kinetics with thermal hydraulics of the reactor core. The linear stability analysis of the BWR for steady states shows that at a critical value of bifurcation parameter (i.e. feedback gain), Hopf bifurcation occurs. These stable and unstable domains of parametric spaces cannot be predicted by linear stability analysis because the stability of system does not include only stability of the steady states. The stability of other dynamics of the system such as limit cycles must be included in study of stability. The nonlinear stability analysis (i.e. bifurcation analysis) becomes an indispensable component of stability analysis in this scenario. Hopf bifurcation, which occur with one free parameter, is studied here and it formulates birth of limit cycles. The excitation of these limit cycles makes the system bistable in the case of subcritical bifurcation whereas stable limit cycles continues in an unstable region for supercritical bifurcation. The distinction between subcritical and supercritical Hopf is done by two parameter analysis (i.e. codimension-2 bifurcation). In this scenario, Generalized Hopf bifurcation (GH) takes place, which separates sub and supercritical Hopf bifurcation. The various types of bifurcation such as limit point bifurcation of limit cycle (LPC), period doubling bifurcation of limit cycles (PD) and Neimark–Sacker bifurcation of limit cycles (NS) have been identified with the Floquet multipliers. The LPC manifests itself as the region of bistability whereas chaotic region exist because of cascading of PD. This region of bistability and chaotic solutions are drawn on the various parametric bifurcation diagrams

10 MW research reactor simulation using fuel plate type

A computer code was established named ET-RR-1-10 to investigate the thermal hydraulic behavior of the ETRR1 (first Egyptian research reactor) research reactor when its power upgraded to 10MW using the new fuel plate elements type. The work done include both normal and flow reduction conditions. The code modeled primary loop, secondary lop, and reactor kinetics. All code models used finite difference technique. The code results were tested against the available corresponding experimental data taken from a similar research reactor MITR (Massachusetts Institute of Technology research reactor) for the sake of code validation. The results showed good agreement, and the code can be used for thermal hydraulic calculations.

1-hexene autoignition control by prior reaction with ozone

The autoignition timing of 1-hexene was controlled in a Homogeneous Charge Compression Ignition (HCCI) engine by reacting the fuel with ozone-containing air prior to its combustion. The experiments were conducted in a single cylinder research engine instrumented with a cylinder pressure sensor. The fuel was chemically characterised using Nuclear Magnetic Resonance (NMR) spectroscopy before and after its reaction with ozone. The NMR analyses showed that this preliminary reaction produced several oxygenated products within the fuel, and was likely to have resulted in the formation of ozonide molecules having a peroxidic structure with several oxygen molecules in series. To understand how this would affect the ignition reactions, the ignition process was modelled numerically using a single-zone chemical kinetic reactor model. The modelling suggested that peroxide molecules decomposed during the compression of the reactants in the engine and advanced ignition timing by promoting early decomposition of the fuel through the formation of radicals.

Formulation of a point reactor kinetics model based on the neutron telegraph equation

A Telegraph model of the Point Reactor Kinetics (TPRK) is developed based on the monoenergetic, non-fractional order telegraph approximation of the neutron transport equation. The model was used to develop a complete theory of the point reactor kinetics based on the non-fractional neutron telegraph equation. The inhour equation in the new form was obtained alongside different known reactor kinetics approximations applied to the model and their analytical solutions. The matrix form of the model was also obtained, which is needed for numerical solutions of the model. We solved this model for a step insertion of reactivity for an infinite thermal nuclear reactor system. In our model the value of the velocity of the neutrons propagation is finite and equals v/3 because of the neutron telegraph equation. Although this value is still under research, it is different from infinite as in the diffusion approximation which contradicts causality. Values of the relaxation time (τ), which is the main difference between the (TPRK) and the Diffusion Point Reactor Kinetics (DPRK), is studied for different materials based on theoretical approach and its effect on the neutron density calculations have been calculated. The most important notice in the solution of the (TPRK) model is that there is a relaxation (retardation) in the time response of the solution. This is similar to what was found earlier in the literature concerning the solutions of the neutron telegraph equation.

Validation of the Serpent 2-DYNSUB code sequence using the Special Power Excursion Reactor Test III (SPERT III)

The Special Power Excursion Reactor Test III (SPERT III) is studied using the Serpent 2-DYNSUB code sequence in order to validate it for modeling reactivity insertion accidents (RIA) in PWRs. The SPERT III E-core was a thermal research reactor constructed to analyze reactor dynamics. Its configuration resembles a commercial PWR on terms of fuel type, choice of moderator, coolant flow and system pressure. The initial conditions of the rod ejection accident experiments (REA) performed cover cold startup, hot startup, hot standby and operating power scenarios. Eight of these experiments were analyzed in detail. Firstly, multi-dimensional nodal diffusion cross section tables were created for the three-dimensional reactor simulator DYNSUB employing the Monte Carlo neutron transport code Serpent 2. In a second step, DYNSUB stationary simulations were compared to Monte Carlo reference three-dimensional full scale solutions obtained with Serpent 2 (cold startup conditions) and Serpent 2/SUBCHANFLOW (operating power conditions) with a good agreement being observed. The latter tool is an internal coupling of Serpent 2 and the sub-channel thermal-hydraulics code SUBCHANFLOW. Finally, DYNSUB was utilized to study the eight selected transient experiments. Results were found to match measurements well. As the selected experiments cover much of the possible transient (delayed super-critical, prompt super-critical and super-prompt critical excursion) and initial conditions (cold and hot as well as zero, little and full power reactor states) one expects in commercial PWRs, the obtained results give confidence that the Serpent 2-DYNSUB tool chain is suitable to model REAs and other RIAs in PWRs.

Linear stability analysis of a nuclear reactor using the lumped model

The stability analysis of a nuclear reactor is an important aspect in the design and operation of the reactor. A stable neutronic response to perturbations is essential from the safety point of view. In this paper, a general methodology has been developed for the linear stability analysis of nuclear reactors using the lumped reactor model. The reactor kinetics has been modelled using the point kinetics equations and the reactivity feedbacks from fuel, coolant and xenon have been modelled through the appropriate time dependent equations. These governing equations are linearized considering small perturbations in the reactor state around a steady operating point. The characteristic equation of the system is used to establish the stability zone of the reactor considering the reactivity coefficients as parameters. This methodology has been used to identify the stability region of a typical pressurized heavy water reactor. It is shown that the positive reactivity feedback from xenon narrows down the stability region. Further, it is observed that the neutron kinetics parameters (such as the number of delayed neutron precursor groups considered, the neutron generation time, the delayed neutron fractions, etc.) do not have a significant influence on the location of the stability boundary. The stability boundary is largely influenced by the parameters governing the evolution of the fuel and coolant temperature and xenon concentration.

Multiphysics simulation of fast transients with the FINIX fuel behaviour module

FINIX is a recently developed fuel behaviour module that is designed to provide “simple but sufficient” descriptions of the most essential fuel behaviour phenomena in multiphysics simulations. In such simulations, it is possible to obtain significant improvement in the feedback to neutronics or thermal hydraulics modelling even with a relatively simple fuel performance model. In this work, FINIX is used as an internal fuel behaviour module both in reactor physics and in reactor dynamics codes to simulate coupled behaviour in fast transient scenarios. With the Monte Carlo reactor physics code Serpent we model a prompt transient in a VVER-1000 pin cell, and with the reactor dynamics code HEXTRAN, a control rod ejection accident in a VVER-440 reactor.