Temperature Reactivity Feedback Research Articles

Temperature feedback reactivity analysis for LEU-Fuelled SLOWPOKE-2 research reactor using DRAGON5 and DONJON5 codes

The purpose of this study is to provide a new deterministic model for the SLOWPOKE-2 nuclear research reactor at École Polytechnique de Montréal (EPM) with LEU (Low Enriched Uranium) core. Using the latest release of the code system DRAGON5 and DONJON5 and the cross-section data library ENDFB.VII rel.1 evaluation, the developed model is applied to simulate the neutronic behavior of the SLOWPOKE-2 research reactor. We studied the separate temperature effects of the main components of the core (i.e., fuel, coolant/moderator, beryllium reflector, and water reflector). The contribution of different physical phenomena to the RTC was assessed. The temperature reactivity feedback calculated using the deterministic approach based on the DRAGON5 and DONJON5 code system using the ENDF/B-VII.1 evaluated nuclear data library produced in the WIMD-D4 format is in good agreement. Therefore, this work proves the capability of DRAGON5 and DONJON5 codes, normally used for power reactors, to reliably simulate a low-power research reactor.

Possibility of YH1.85 and MgO–BeO as a moderator in high temperature reactors

This study compared the neutronic behaviors of the graphite material utilized in standard HTGR reactors to those of yttrium hydride and MgO–BeO moderator materials using the OpenMC and Serpent Monte Carlo codes. keff values for various fuel/moderator ratios in a TRISO particle-embedded moderator matrix were computed. The effect of packing fraction was then investigated, and the keff values for different packing fractions were compared for the MgO–BeO, YH1.85, and C (graphite) moderator matrices in the geometry layout containing randomly placed TRISO particles. In contrast to graphite and MgO–BeO moderators, the keff values for YH1.85 moderator indicated that a very small moderator volume is adequate for thermalization. We also investigated how temperature reactivity feedback impacts different packing fractions. In the temperature reactivity feedback analysis, the overall temperature coefficient was determined to be negative for all moderators. The temperature feedback coefficient for the fuel with the YH1.85 moderator was found to be significantly lower in magnitude than for the system with graphite and MgO–BeO. The burnup findings revealed that graphite and MgO–BeO behaved similarly; however, YH1.85 was shown to be useful only at very low moderator/fuel ratios. With typical HTGR power density, the fuel cycle time for YH1.85 was found to be around 516 days. Also, while the YH1.85 moderator system reduces the risk of proliferation by producing small amounts of 239Pu and 241Pu, it was determined that it is more suitable for small modular and microreactor designs for high-temperature reactors with low moderator/fuel ratio requirements.

Conceptual design of megawatt-level mobile nuclear power system based on heat pipe cooled reactor

Mobile nuclear power system has the advantages such as the well adaptability, the strong sustainability, and the convenient transportation, which can satisfy the energy demand of special environments such as island, and polar region. In this paper, the conceptual design of Mobile Nuclear Power System named MNPS-1000 is proposed, which is consist of the modular heat pipe cooled reactor and combined cycle energy conversion system to achieve the 1MWe output. The design characteristics include the operation lifetime of 3000 days in full power mode, negative temperature reactivity feedback, redundancy in reactivity control, 33% energy conversion efficiency. Due to the efficient heat transfer capability of lithium heat pipes, total of 216 heat pipes can ensure the heat transfer of 3MWt. The modular design of reactor and heat pipe heat exchanger decreases the volume of the system to achieve the compact arrangement in the standard containers with 12.0m×2.5m×2.5m size. The reactor physics and thermal hydraulics analysis, heat pipe design, and energy conversion system analysis are taken out to show the feasibility and performances of this conceptual design.

Transient thermal–hydraulic analysis of the thermionic space reactor TOPAZ-II

Space nuclear reactor system is of great significance in aerospace applications such as deep-space exploitation and exploration, high-power earth-orbiting satellites. A transient reactor system analysis code, RESYS, is developed for advanced non-light water reactor safety analysis recently. In this paper, the model of the thermionic space nuclear reactor TOPAZ-II including the thermionic fuel elements, thermionic energy conversion system, reactor core, coolant loop and radiator is established with RESYS code. The point reactor equation with six-group delayed neutron is utilized to calculate the fission power. The reactivity effect of various structural components and the reactivity insertion effects of control drums are considered. The thermionic emission model of cesium thermionic converter is based on the phenomenological model established by Rasor. Then, the steady state operation and three transient accidents including reactivity insertion accident (RIA), partial loss flow accident (LOFA), load resistance shortcircuit accident (LRSCA)are simulated. In the steady-state condition, the output electric power is about 5.8 kW with thermoelectric conversion efficiency of 5.0%. The results of steady calculation agree well with the design values. And in the three transient accidents, the moderator introduces a large temperature reactivity feedback which makes the reactor fission power increasing. The results indicate that the TOPAZ-II reactor system has a sufficient safety margin during these accidents. In addition, the calculation results preliminarily demonstrate the capability of RESYS code in modeling and simulation of thermionic space reactor.

Study of the thermal expansion effects of a space nuclear reactor with an integrated honeycomb core design using OpenMC and ANSYS

The negative reactivity feedback in the nuclear fuel plays an important role in maintaining the stable operation of nuclear reactors. For heat pipe cooled space reactors using highly enriched U, the fuel temperature reactivity feedback mainly due to Doppler effect and the thermal expansion of solid fuel. In this paper, based on an integrated heat pipe space reactor design, a one-way coupling of the Monte Carlo code OpenMC and finite element method ANSYS is used to evaluate the reactor expansion and the impacts to the reactor reactivity. The average expansion was 0.126 cm for the fuel block from cold state to full power operation state. The fuel thermal expansion introduces a negative reactivity feedback of −59 pcm, and the reflector expansion introduces another −675 pcm, resulting a temperature coefficient of −0.638 pcm/K.

Inversion Point of the Isothermal Reactivity Coefficient with Increasing System Temperature in a Heterogeneous Core Lattice of a Light Water Reactor

As part of efforts to develop coupled multiphysics experiments for the benchmark of modern multiphysics reactor simulators, a low-power and open-pool type of light water reactor at the Walthousen Reactor Critical Facility (RCF) was reconfigured with additional equipment, and its neutronic characteristics were fully surveyed. A water loop system was designed and installed to pass through the central region of the reactor core, making the central region overmoderated. The overmoderation would lead to a positive temperature reactivity feedback in the modified reactor configuration. This phenomenon is observed when the system temperature is between 10.69°C and 28.70°C. The inversion point of the isothermal reactivity coefficient is at 28.70°C ± 1.07°C. At this temperature, competition between the negative and positive thermal effects on reactivity compensate each other, and the isothermal reactivity coefficient becomes negative at temperatures higher than the inversion point. This paper presents the experimental determination of the isothermal reactivity and reactivity coefficient at different temperatures as well as the inversion point in the modified RCF reactor configuration. To obtain the best-quality results possible, special attention is given to the choice and adaptation of all the available methods for data postprocessing of experiment measurements. Neutron flux denoising is performed with multivariate wavelet transforms and principal component analysis. The Inverse Kinetics Method is applied to derive reactivity from the neutron flux measurements. To provide accurate and high-fidelity experiment benchmark data for modern code validation, in-depth experimental uncertainty quantification is developed. The results of the experiments show the mixed effects of system temperature on reactor reactivity due to the combined effects of Doppler broadening in the fuel, S(α,β) thermal scattering physics, and change in water density and can be used to validate previously developed cross-section interpolation models in the low-temperature range and positive isothermal reactivity coefficient conditions.

Stability and bifurcation analysis of Generation IV reactors via point reactor models with temperature reactivity feedback

While the stability of present-day reactors is well studied, stability analysis of Generation IV reactors is in its very beginning. In this paper, the stability of point nuclear reactor models with temperature reactivity feedbacks is analyzed. The examined models are referred to as G-L reactor models, which are point reactor models with G delayed neutron-emission groups, L temperature lumps (regions) and a linear reactivity feedback for each temperature. G-L reactor models are applicable for modeling four out of the six Generation IV reactor types (Gas Fast Reactor, Lead Fast Reactor, Sodium Fast Reactor and Very High Temperature Reactor).New analytical stability and bifurcation results of general G-L reactor models and of the G1-L2 reactor model are derived. These analytical results add a different perspective to the previous studies of Generation IV reactors, most of which are based only on numerical analysis. In particular, the codimension-1 bifurcations of general G-L reactor models are characterized, and a classification of the linear stability region in the G1-L2 model is derived.Then, stability and bifurcation analysis of a G1-L2 model of a Generation IV HTR-type microreactor is performed, using both analytical methods and the numerical continuation method. The nominal design point of this microreactor is shown to be globally asymptotically stable, while in other regions of the parameter space, a bistability of the operating steady state and a limit cycle, or of two limit cycles, is demonstrated.

Nuclear coupled thermal–hydraulic analysis of parallel channel density wave instabilities in a supercritical water reactor

In an attempt to obtain a realistic estimate of the density wave instability (DWI) thresholds of a typical supercritical water reactor (SCWR) in its relevant operating regime, the present numerical framework accounts for the nonlinear interdependence among the thermal–hydraulic (TH), neutronic and fuel dynamic field variables, by solving the coupled multi-physics conservation equations in a time-domain where the TH, neutron point-kinetic (NPK) and fuel heat conduction (FHC) solvers are integrated through coolant density and fuel temperature reactivity feedback coefficients, and supercritical water (SCW) heat transfer coefficient (HTC). The time dependent and radially non-uniform, but axially uniform reactor power distribution among the different fuel assemblies (FAs) are incorporated in the numerical framework by the employment of NPK solver and considering the existence of several parallel channels in the reactor core where every channel represents a group of FAs of similar reactor power assembled in a single region. The integrated model is next compared against the available numerical results to access its capability in analyzing thermal-hydraulically induced DWIs while being influenced with the neutronic reactivity feedback effects. Nuclear coupled core-wide and regional density wave oscillations (DWOs), two modes of parallel channel DWIs, are finally analyzed with the purpose to determine the effect of temporal reactor power variation and the channel to channel interactions on the stability thresholds of the SCWR under consideration. The conclusions are drawn and reported accordingly.

Feasibility Study on the Initial Kartini Reactor Core Using Plate Type Fuel Elements

The plate type fuel element conversion is proposed to solve a supply problem of TRIGA standard rod type fresh fuel in the long term and to extend the lifetime by reducing the dependence of buying imported elements. The plate type fuel is an alternative since the Indonesian industry has been able to produce such fuel elements. The change of core configuration is expected to improve the reactor performance for irradiation facilities and fuel element lifetime. The SRAC2006 is used to perform neutronic calculations while the nuclear fuel lifetime is calculated by SWAT. This study begins with performing a core properties comparison of UZrH1.6 as the current fuel material and U3Si2-Al as the fuel material candidate. The results show that the Kartini reactor core is possible to load U3Si2-Al as the fuel material and makes higher excess reactivity compared to the current fuel material. Furthermore, U3Si2-Al in the plate type element geometry is variedly arranged in the new reactor core configuration to optimize the neutronic core parameters. The new core configuration is composed of 10 standard fuel elements, 4 fuel control elements, and the graphite material baffle that is located between the active core and annular reflector for serves as an additional reflector. The configuration produced sufficient core excess reactivity and adequate shutdown margin. It also produced negative temperature feedback reactivity and power peaking factor that fulfilled the safety requirements. Improvement of new reactor core performance was obtained by more irradiation facilities, higher thermal neutron flux, and longer maximum estimated burn up compared to the current core configuration.

Numerical analysis of dynamic load following response in a natural circulation molten salt power reactor system

The Molten Salt Reactor (MSR) concept is a rapidly evolving Generation IV design that has recently attracted favorable attention due to the potential for reducing waste generation, realizing passive safety features, and seizing on the opportunity for cost effective economics. An investigation into the power transient behavior of an autonomous load-following, closed-loop, natural circulation MSR system is important to quantifying operational and safety performance under dynamic conditions. This paper presents the results of a STAR-CCM+ and a comparatively simple asymmetric, one-dimensional, numerical model to solve the compound dynamic MSR power behavior subject to flow and temperature reactivity feedback only. Results show that reactor power is affected by fuel salt flow velocity (global) and temperatures (local bulk volume averages) in a coupled, time-delayed manner that results in a unique compound dynamic, closed-loop power feedback mechanism. The 1-D simulation approach opens the possibility of performing inexpensive computations to evaluate time-dependent reactor performance relative to thermo-physical fuel salt limitations. Results also potentially motivate a convincing conclusion that natural circulation MSRs provide a leap in safety and reliability.

Stability and Bifurcation Analysis of Generation IV Reactors Via Point Reactor Models with Temperature Reactivity Feedback

Stability and Bifurcation Analysis of Generation IV Reactors Via Point Reactor Models with Temperature Reactivity Feedback

Disturbance observer-based robust backstepping load-following control for MHTGRs with actuator saturation and disturbances

This paper presents a disturbance observer-based robust backstepping load-following control (DO-RBLFC) scheme for modular high-temperature gas-cooled reactors (MHTGRs) in the presence of actuator saturation and disturbances. Based on reactor kinetics and temperature reactivity feedback, the mathematical model of the MHTGR is first established. After that, a DO is constructed to estimate the unknown compound disturbances including model uncertainties, external disturbances, and unmeasured states. Besides, the actuator saturation is compensated by employing an auxiliary function in this paper. With the help of the DO, a robust load-following controller is developed via the backstepping technique to improve the load-following performance of the MHTGR subject to disturbances. At last, simulation and comparison results verify that the proposed DO-RBLFC scheme offers higher load-following accuracy, better disturbances rejection capability, and lower control rod speed than a PID controller, a conventional backstepping controller, and a disturbance observer-based adaptive sliding mode controller.

DESIGN OF A TRISO PARTICLE FUEL BASED INTEGRATED GAS-COOLED SPACE NUCLEAR REACTOR

According to versatile and long-lasting requirements of deep space missions, space nuclear reactor (SNR) power system is becoming a more suitable choice compared to traditional solar and chemical power systems in large-scale and long-life applications. From NASA’s previous research, the gas-cooled reactor along with closed Brayton cycle (CBC) could achieve optimized weight-power ratio and be more applicable for large power system (100 kWe or MWe level). In this paper, a concept of integrated gas-cooled space nuclear reactor named IGCR-200 is introduced, which is designed based on the TRISO particle fuel and could achieve 200 kWe output combined with highly efficient He/Xe CBC generator. The design requirements include an operation lifetime of at least 10 years in full power mode, maximum fuel temperature < 1600K, negative temperature reactivity feedback, passive decay heat removal, redundancy in reactor control, and sub-criticality during water flooding accidents. It has an outer diameter of 70.0 cm, a height of 66.0 cm (reactor part), a total mass around 1000 kg, total Uranium inventory of 226.8 kg (235U enrichment as 93%), and 1 MW thermal power output. The reactor physics, thermal hydraulics and other required analysis are taken out to show the feasibility and performances of the design.

Yansıtıcılı reaktörlerin stokastik iki-nokta reaktör kinetik denklemlerinin sayısal simülasyonu

Deterministic numerical solutions of point reactor kinetic equations give us the mean values of the neutron population and delayed neutron precursor concentrations, whereas the actual dynamical process is stochastic and the neutron population and precursor concentrations fluctuate randomly with time. In the present study, a novel stochastic model for two-point reactor kinetics equations is developed and used to analyze the dynamical behavior of the source-free strongly reflected reactors with six groups of delayed neutron precursors. To derive the Itô stochastic differential equations system corresponding to this model, the two-point reactor kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and reflected neutrons. In the case of different perturbation scenarios, both with and without the Newtonian temperature reactivity feedback effects, this system of stochastic differential equations is solved using the Euler-Murayama numerical method. It is observed that the mean response of the system is comparable with the results of other deterministic numerical methods.

Neutronic and thermal-mechanical coupling analyses in a solid-state reactor using Monte Carlo and finite element methods

Improved computer capabilities and parallel algorithms have enabled high fidelity coupled analyses of classical nuclear power plant designs, which can also be applied to analyze the new heat pipe cooled reactor design. The neutronic/thermal coupling is a key part of multi-physics, high-fidelity reactor simulations. In a heat pipe cooled reactor, the solid-state core can reach temperatures over 1000 K which causes significant thermal expansion. The expansion then affects the neutronic and thermal conditions. Therefore, the mechanical conditions should also be carefully considered in the highly coupled solid-state system. The Monte Carlo program RMC and the commercial finite element program ANSYS Mechanical were used to develop coupled solutions of the neutronic (N), thermal (T), and mechanical (M) effects in a heat pipe cooled reactor with the ANSYS APDL interface used to link the two programs. The neutronic (N) and thermal–mechanical (T-M) coupled strategy was based on an iterative solution of the nonlinear governing equations. The method was used to study the reactivity changes occurring during startup of the MegaPower heat pipe cooled reactor. The most important effect of the temperature reactivity feedback during startup was the fuel temperature Doppler effect, while the monolith and reflector Doppler effects were much smaller. The radial expansion of the monolith and the reflector and the axial expansion of the fuel pellets have the most significant effects on the mechanical reactivity feedback. The results further show that the thermal–mechanical feedback in the solid-state reactor provides a negative reactivity feedback (-1500 pcm) and yet deteriorates the heat transfer due to the expansion. The peak fuel temperature increases 11 K when the thermal/mechanical feedback is considered. Therefore, the N/T-M coupling must be considered to produce conservative designs.

Determination of Temperature Feedback Coefficients for OPR-1000 Fuel Assembly Using Adjusted Cross Section Libraries

An important source of reactivity variation in an operating reactor is the change in the temperature of the system. This change affects the criticality of the reactor and is expressed by the temperature reactivity coefficients. The most important feedback coefficients are those caused specifically by fuel and by moderator temperature changes. In this paper, temperature reactivity feedback coefficients are calculated for two assemblies solid 16×16 and annular 12×12, designed for OPR-1000 reactor. Feedback coefficients calculated are the fuel temperature coefficient, moderator temperature coefficient, prompt reactivity coefficient and power coefficient. A thermal resistance model was adapted to solid and annular fuel and was used to calculate the power coefficient. MCNP6 code was used to determine the multiplication factor, and hence the feedback coefficients. Temperature adjusted libraries were produced using MAKXSF utility program, associated with MCNP6 code. The difference between the use of regular library and temperature adjusted one is clarified. It was assumed that both reactors, with either fuel assembly type, operate at 100% power. The results showed that both designs gave close values with better results of annular fuel for the prompt reactivity and power coefficients.

Time-space fractional neutron point kinetics: Theory and simulations

In this work the mathematical derivation and numerical analysis of a fractional nuclear reactor point kinetics in time and space (TSFNPK) is presented. The TSFNPK model was derived considering a non-Fickian law for the neutron density current where the differential operators in space and time are of fractional order. The TSFNPK equations presented in this work constitutes a novel model for nuclear reactor kinetics, thus represent an extended model with respect to other fractional models and the classical neutron point kinetics equations. The model considers two diffusion exponents: one for the differential operator dependent in time and another for the dependent operator in space. Both exponents effect is numerically analyzed considering changes of reactivity step type, and temperature feedback reactivity. A first approach of the TSFNPK is presented, without temperature effects, and then a second approach considering temperature feedback effects is analyzed. In a following work, as a demonstration of application, a detailed analysis along with verification will be presented.

Design of a hundred-kilowatt level integrated gas-cooled space nuclear reactor for deep space application

According to versatile and long-lasting requirements of deep space missions, space nuclear reactor (SNR) power system is becoming a more suitable choice compared to traditional solar and chemical power systems in large-scale and long-life applications. From NASA’s previous research, the gas-cooled reactor along with closed Brayton cycle (CBC) could achieve optimized weight-power ratio and be more applicable for large power system (100 kWe or MWe level). In this paper, a concept of integrated gas-cooled space nuclear reactor named IGCR-200 is introduced, which is designed based on the TRISO particle fuel and could achieve 200 kWe output combined with highly efficient He/Xe CBC generator. The design requirements include an operation lifetime of at least 10 years in full power mode, maximum fuel temperature <1600 K, negative temperature reactivity feedback, passive decay heat removal, redundancy in reactor control, and sub-criticality during water flooding accidents. It has an outer diameter of 70.0 cm, a height of 66.0 cm (reactor part), a total mass around 1000 kg, total Uranium inventory of 226.8 kg (235U enrichment as 93%), and 1 MW thermal power output. The reactor physics, thermal hydraulics and other required analysis are taken out to show the feasibility and performances of the design.

Assessment of the fractional neutron point kinetic equation to simulate core transients with Newtonian temperature feedback

The model of the Fractional Neutron Point Kinetic equations (FNPK) considers a relaxation time for neutrons, as they travel in surrounding media. Relaxation time is associated with a rapid variation in neutron flux, as reflection of fast change of reactivity, and it can be implemented in the differential operator of fractional order related with non-Fick effects, also known as anomalous diffusion exponent and represents non-local time memory. In this work the model of FNPK extended, by adding the temporal term to including the neutron density derivative, is using with the objective of studying the effect of this added term on the behavior of neutron density during a transient, when there exists Newtonian temperature feedback reactivity, using different values of the anomalous diffusion exponent. Although the one-group delayed neutron precursor is use for this analysis, the results of the neutron density behavior were compared with the classical neutron point kinetics equations. The results show that the additional term implemented in this study led to show how the sub-diffusion phenomena have noticeable relevance in the neutron density behavior in those scenarios where the dynamic of a nuclear system is associated to slow transients.

An analytical approach to bifurcations and stability in simplified mathematical models of nuclear reactors

Asymptotic analytical methods are applied to study some problems related with bifurcations (both local and global) and stability in three simple mathematical models of nuclear reactors.The first case is a reactor which is subcritical at rest and driven by a distributed external neutron source. Under suitable conditions in the temperature feedback reactivity, the mathematical model predicts a static global bifurcation with three critical states, two stable and one unstable, with the possibility of a runaway. The dynamics of this system is studied, in a framework of slow manifold theory, by methods of restricted nonlinear modal analysis, and the results of a digital simulation are summarized. The model could be modified and extended to study the space time dynamics of sub-critical multiplying systems driven by external neutron sources (neutron beams produced by accelerators).The second case is related with in phase and out of phase xenon oscillations in large thermal reactors. The known subcritical Hopf bifurcation that appears in the context of global mode oscillations is revisited. After applying a nonlinear modal analysis to the mathematical model, a normal form is derived by an averaging method. Approximate analytical formulae for the radii of the unstable limit cycles and for the trajectories of the state variables in a neighborhood of the bifurcation point are obtained.The third case is a non-trivial modification and development of a simple mathematical model intended to describe certain mechanical kinetic effects stemming from a possible coupling of nuclear, thermal and mechanical vibration processes. We show that, under suitable conditions, a dynamic supercritical Hopf bifurcation in the reactor power appears in the framework of our modified model. A normal form is derived by an averaging method. Analytical formulae for the radii of the stable limit cycles and the trajectories of the state variables in a neighborhood of the bifurcation are given.