Subcritical Reactor Research Articles

Proposal of a turbulent Prandtl number model for Reynolds-averaged Navier–Stokes approach on the modeling of turbulent heat transfer of low-Prandtl number liquid metal

Because of their high molecular heat conductivity, low-Prandtl number liquid metal is a promising candidate coolant for various designs of advanced nuclear systems such as liquid metal–cooled fast reactors and accelerator-driven sub-critical system (ADS). With the fast-growing computational capacity, more and more attention has been paid to applying computational fluid dynamics (CFD) methods in thermal design and safety assessment of such systems for a detailed analysis of three-dimensional thermal–hydraulic behaviors. However, numerical modeling of turbulent heat transfer for low-Prandtl number liquid metal remains a challenging task. Numerical approaches such as wall-resolved large eddy simulation (LES) or direct numerical simulation (DNS), which can provide detailed insight into the physics of the liquid metal flow and the associated heat transfer, were widely applied to investigate the turbulent heat transfer phenomenon. However, these approaches suffer from the enormous computational consumption and are hence limited only to simple geometrical configurations with low to moderate Reynolds numbers. The Reynolds-averaged Navier–Stokes (RANS) approach associated with a turbulent Prandtl number Prt accounting for the turbulent heat flux based on Reynolds analogy is still, at least in the current state in most of the circumstances, the only feasible approach for practical engineering applications. However, the conventional choice of Prt in the order of 0.9∼unity in many commercial computational fluid dynamics codes is not valid for the low-Prandtl number liquid metal. In this study, LES/DNS simulation results of a simple forced turbulent channel flow up to a friction Reynolds number Reτ of 2000 at Pr of 0.01 and 0.025 were used as references, to which the Reynolds-averaged Navier–Stokes approach with varying Prt was compared. It was found that the appropriate Prt for the RANS approach decreases with bulk Peclet number Peb and approaches a constant value of 1.5 when Peb becomes larger than 2000. Based on this calibrated relation with Peb, a new model for Prt used in the RANS approach was proposed. Validation of the proposed model was carried out with available LES/DNS results on the local temperature profile in the concentric annulus and bare rod bundle, as well as with experimental correlations on the Nusselt number in a circular tube and bare rod bundle.

Characterization, signal estimation and analyzing of cold button BPMs for a low-[formula omitted] helium/proton superconducting LINAC

CAFe is a low-β helium/proton superconducting LINAC. It is as a demo LINAC for China initiative Accelerator-Driven System and constructed at the Institute of Modern Physics, Chinese Academy of Sciences. In this paper, an off-site characterization focusing on the capacitance measurements of cold button BPMs is presented firstly. Furthermore, a signal estimation and analysis of cold button BPMs is performed with regard to two kinds of beam commissioning, helium and proton beams. A good agreement between the calculation and the measurement proves that the developed theoretical model could accurately estimate the output signal of cold button BPMs. It considers the influence of low-β effect and long cable issues. Based on the transformation of the estimated signal from the time domain to the frequency domain, it is found that the amplitude spectra of cold button BPMs expand with the energy increasing and the bunch length shortening. The amplitude at the first harmonic frequency decreases, which causes the summed values from BPM electronics to be declined in the LINAC. However, the decline in summed values is not proportional to the decreasing of beam current. This is the reason why BPMs only give relative intensity and not absolute value for low-β beams when BPMs’ electronics using a narrow-band digital signal processing. These developments will be used for the cold BPM system and the fast machine protection system. It is dedicated to the driven LINAC of China initiative Accelerator-Driven System, which will deliver a 500 MeV, 5 mA proton beam in continuous wave operation mode.

An engineering geological suitability comprehensive evaluation index (EGSCEI) for large-scale infrastructure site selection

The purpose of this paper is to present a quantitative method for evaluating the engineering geological suitability of potential sites in order to select the optimal site for large-scale infrastructure. Based on the fuzzy comprehensive evaluation decision method and analytic hierarchy process (AHP), an engineering geological suitability comprehensive evaluation index (EGSCEI) model was applied in the selection of a site for the construction of the China Initiative Accelerator-Driven System (CiADS) and the High-Intensity Heavy-Ion Accelerator Facility (HIAF). In this model, seven parameters, including land use, geomorphology, geological structure, lithology, hydrogeology, geological disaster and rock weathering, were selected as the evaluation factors. The factor evaluation matrices were established, and the weight vector of the seven factors was determined using the AHP. The engineering geological suitability fuzzy comprehensive evaluation vectors were then computed. Finally, according to the normalized engineering geological suitability comprehensive evaluation vectors and the quantified evaluation ranking vector, the EGSCEI values were calculated. As a result, site No. 3 was evaluated as the most optimal site of the three potential sites for the construction of the CiADS and HIAF. The result was adopted by the Chinese government, and site No. 3 became the selected location. This case study shows that the EGSCEI model is scientific, reasonable and applicable in providing a reference for similar large-scale infrastructure site selection.

Study of External Source Effects for Different Multibeam Concept for Accelerator-Driven Subcritical Reactor for Nuclear Waste Transmutation (ADS-NWT)

The multibeam concept for the accelerator-driven subcritical reactor (ADS) has advantages in the power distribution of the core, and it could reduce the requirement of proton beam current intensity for each beam. In comparison with the single-beam concept, the multibeam concept could also reduce the thermal load of the beam window significantly. This paper focuses on the study of external source effects for different multibeam concepts for an ADS for nuclear waste transmutation (ADS-NWT). The different multibeam concepts include the three-beam, four-beam, six-beam, and seven-beam concepts for the ADS-NWT. By using the calculation tools FLUKA and SuperMC with the nuclear data library ENDF/B-VII.1, the variations of the keff and total power, as the function of the position of the spallation targets, are provided for each multibeam concept. The results show that the keff and total power were affected by an interference effect between the spallation targets. For the transport of fission neutrons in the core, the maximum radius of the interference effect between the spallation targets was 40 cm. Considering the transport of spallation neutrons in the ADS-NWT, the maximum radius of the interference effect between the spallation targets was 60 cm. The spallation targets were moved from the inner circle to the outer circle of the fuel zone, and the different variations in keff and total power trend for the three-beam, four-beam, six-beam, and seven-beam concepts for the ADS-NWT were obtained.

Design and thermal-hydraulic analysis of a printed circuit heat exchanger for ADS applications

Printed circuit heat exchanger (PCHE) is considered a promising candidate for accelerator driven systems (ADS) due to its high compactness and efficiency. The preeminent high-temperature, high-pressure and corrosion resistance enables it to withstand the severe conditions of ADS and ensure the safe and efficient operation. In this paper, a PCHE applied to the ADS is proposed, adopting helium as the cold source and lead-bismuth eutectic (LBE) as the heat source. On this basis, a three-dimensional model is established and the flow and heat transfer characteristics of the PCHE are numerically investigated. The thermal performance is further improved by optimizing structural and operating parameters. The results indicate that the high thermal conductivity and superior field synergy degree of LBE ensures a strong heat transfer performance of PCHE. The velocity disturbance and double-vortex secondary flow generated in modified channels, which intensify the fluid mixing and improve the field synergy level, help to further enhance the overall heat transfer coefficient. Structural and operating parameters of the helium side are more critical to the thermal-hydraulic performance, an increase of helium mass flow rate within allowable pressure drop is conducive to the comprehensive performance.

Comparative Study on the Impact of endf/b-vii.1 Nuclear Library Uncertainty on the CERCER and CERMET Fueled Accelerator-Driven System Calculation Results Using Monte Carlo Method Codes

Abstract A new design of a small power accelerator-driven system (ADS) using inert matrix fuel—ceramic–ceramic matrix (CERCER) and ceramic-metallic matrix (CERMET) was proposed in our previous work for high transmutation rate, small reactivity loss due to burnup, and enhanced safety features. The fast neutron spectrum in the ADS showed a benefit for reducing minor actinides inventories in the fuel cycle. However, the reliability of the nuclear cross section data of evaluated libraries, especially at high energy, needs to be investigated and its impact on CERCER and CERMET fueled ADS calculation results needs to be assessed. In this study, the impact of endf/b-vii.1 nuclear library uncertainty on the CERCER and CERMET fueled ADS reactivity calculation are evaluated using the Monte Carlo method (scale6.2 and whisper-1.1). The sensitivity coefficients and uncertainty obtained by the two codes show a good agreement. The results reveal the uncertainty of the endf/b-vii.1 nuclear data caused significant uncertainty in the reactivity calculations (about 1000 pcm) and it is particularly higher in the CERMET fueled core due to a harder neutron spectrum. The paper identifies the major contributes—isotopes and related cross sections—to the core reactivity uncertainty by suggesting the enhancement of these nuclear data.

Simulation of a solid-phase oxygen control scheme in lead-bismuth eutectic system

It is known that solid-phase oxygen control scheme is one of the important methods to solve the corrosion problem when we choose lead–bismuth eutectic (LBE) as coolant in lead-cooled fast reactor (LFR) or Accelerator Driven System (ADS). The mass-exchanger (MX), a porous chamber filled with mechanically stable lead oxide (PbO spheroids), is the key component of solid-phase oxygen control. In order to study the characteristics of oxygen mass transfer, pressure drop, flow field and oxygen concentration field in MX, a randomly packed bed model is established using DEM method. The fluid domain is meshed with computational fluid dynamics (CFD) code STAR-CCM +. The particle–particle and wall–particle contact points are modified with short cylinder bridges to improve the cell qualities. The mass transfer boundary layer theory is applied to explain the oxygen supply process of PbO sphere dissolution to LBE. The results of the average porosity, radial porosity distribution and pressure drop match the previous literature pretty well. The CFD results related to Sherwood number (Sh) are validated by CRAFT experimental data with an acceptable error. The law of oxygen transfer and distribution is obtained by studying the CFD contours and the spatial distribution of oxygen concentration and velocity data. The temperature dependence and velocity dependence of Sherwood number are obtained through multiple linear regression processing of CFD data. Finally, the effects of different temperatures and mass flow rates on oxygen concentration and pressure drop are evaluated to determine the suitable operating domain for MX.

Sensitivity Coefficient Evaluation of an Accelerator-Driven System Using ROM-Lasso Method

We propose the use of reduced-order modeling to improve the sensitivity coefficient evaluation method based on Lasso-type penalized linear regression. In this method, cross sections of interest are uniformly randomly sampled, and corresponding perturbed core analyses are performed. The sensitivity coefficients of the higher-dimensional model are expanded by the active subspace (AS) attained by the lower-dimensional model, and the expansion coefficients are estimated by the Lasso regression. In addition, AS bases can be flexibly chosen according to neutronics parameters of interest. We conducted a verification calculation for an accelerator-driven system and clarified that the proposed method successfully reduces the calculation cost by a couple of orders of magnitude compared with the direct method. The proposed method can be used to practically evaluate the sensitivity coefficients of various parameters.

Investigation on the Use of the Monte Carlo Iterative k-Source Scheme for the Study of Neutron Subcritical Multiplication

Monte Carlo neutron transport codes have traditionally used a fixed-source scheme to simulate a subcritical system with an external source. The efficiency of this scheme is known to depend on the subcriticality level: The lower the subcriticality is, the worse is the efficiency. We have investigated an alternate iterative scheme, namely, the Monte Carlo iterative k-source (IKS) scheme, for the study of neutron subcritical multiplication. Our results show that the iterative scheme not only is as accurate, effective, and computationally efficient as the fixed-source scheme but also has the additional advantage of being weakly dependent on the subcriticality level. Also, the efficiency of this scheme is unaffected by the change in the location of the external source, unlike the fixed-source scheme where the efficiency decreases as the source is moved away from the fissile core center. The algorithm of this scheme is very similar to the algorithm of the eigenmode iterative scheme and hence can be easily implemented in the existing Monte Carlo codes. Our work establishes the validity and accuracy of the Monte Carlo IKS scheme, and with its incorporation in the production-level codes, it can be used for the physics design and analysis of accelerator-driven subcritical systems.

Modeling elaborate dead time in reactor monitoring using SDE’s

Dead time loses, caused due to a short time period following a detection in which the detection system is not operational, is perhaps the most prominent effect in non-ideal detector behavior. The dead time effect has a very strong and noticeable effect on reactor monitoring and physical in-pile experiments.The dead time effects has been largely studied in the past, by numerous authors. In the most basic setting, assuming that the the dead time is fixed and that the count distribution is strict Poissonic, the proper corrections for the count losses are well known for many years. However, a full quantification of the dead time loses in more elaborated settings, such as non-constants dead time or when the waiting time between consecutive detections is not exponential (such as in highly multiplicative systems) are still a subject of interest, and are not fully understood.In the present study we introduce a stochastic model, using Ito Stochastic Differential Equation, for the detector response with a random dead time (both paralyzing and non-paralyzing) in a sub-critical reactor under the point model approximation. Some specific new results are tested against experimental and simulation results, showing full agreement with the theoretical predictions.

Monte Carlo analysis of accelerator-driven systems: Studies on spallation neutron yield and energy gain

Abstract The neutron yield in the interaction of protons with lead and uranium targets has been studied using the LAHET code system. The dependence of the neutron multiplicity on target dimensions and proton energy has been calculated and the dependence of the energy amplification on the proton energy has been investigated in an accelerator-driven system of a given effective multiplication coefficient. Some of the results are compared with experimental findings and with similar calculations by the DCM/CEM code of Dubna and the FLUKA code system used in CERN.

Nuclear transmutation by flux compression

Abstract A new idea for the transmutation of minor actinides, long (and even short) lived fission products is presented. It is based an the property of neutron flux compression in nuclear (fast and/or thermal) reactors possessing spatially non-stationary critical masses. An advantage factor for the burn-up fluence of the elements to be transmuted in the order of magnitude of 100 and more is obtainable compared with the classical way of transmutation. Three typical examples of such transmuters (a subcritical ringreactor with a rotating reflector, a sub-critical ring reactor with a rotating spallation source, the socalled “pulsed energy amplifier”, and a fast burn-wave reactor) are presented and analysed with regard to this purpose.

Subcritical nuclear systems and their stability against changes in the geometrical set-up

Abstract A specific subcritical reactor system has been suggested and the stability of its parameters against small changes in the geometrical set-up has been estimated using the model calculation code DCM/CEM from Dubna. The dimensions of the system are 200 cm in diameter and 170 cm in length and it supplies a thermal power of 900 MW with keff =0.943, using a 20 mA proton beam of an energy of 1 GeV. Considering the thermal → electricity power and electricity → beam power conversion efficiencies, the electric power amplification is about 8. Energy deposition and neutron energy distribution in the fission core are also studied. Some properties, such as the heat production per unit volume, are rather similar to modern fast breeders. The neutron multiplication factor keff is very sensitive to small changes in the geometrical set-up within the fission core.

High-energy neutron transport file for the 209Bi isotope

Abstract The simulation of the nuclear processes, occurring in media irradiated with high-energy particles, promote the elaboration of high-energy transport files. These files being used in versatile computer codes, such as MCNP, allow to simulate with high accuracy particle transport. High-energy transport files are very important for the investigation of accelerator-driven systems. The detailed description of the methods and codes used for the elaboration of the file for 209 Bi is presented in this paper.

Self-sustainability and energy-balance in a fast Fusion–Fission Hybrid Reactor (FFHR) based on Dense Plasma Focus (DPF) and multiplicative cascade

A Fusion–Fission Hybrid Reactor (FFHR) is made of a subcritical reactor driven by the neutrons generated in a nuclear fusion device. The fast neutron spectrum produced by this system could be able to burn actinides from the spent nuclear fuel. Unfortunately, current fusion devices are unable to provide an adequate neutron yield with reasonable spending of energy. However, it is possible to design the subcritical set to multiply considerably the neutron flux by using the so-called multiplying cascades. In addition, given its simplicity, the Dense Plasma Focus (DPF) is an interesting candidate as a neutron source. In this work, we analyze a concept of a metallic-fuel hybrid reactor based on a subcritical set and driven by a DPF as a neutron source. Their spectra are evaluated to determine if they are compatible with the operation of a fast reactor. The energy balance is also studied to find its ability to be self-sufficient when using an existing DPF. Finally, its capability to generate tritium from its lithium blanket is also analyzed. The system is self-sustainable.

Transmutation of long-lived fission products in an advanced nuclear energy system

Disposal of long-lived fission products (LLFPs) produced in reactors has been paid a lot attention for sustainable and clean nuclear energy. Although a few transmutation means have been proposed to address this issue, there are still scientific and/or engineering challenges to achieve efficient transmutation of LLFPs. In this study, we propose a novel concept of advanced nuclear energy system (ANES) for transmuting LLFPs efficiently without isotopic separation. The ANES comprises intense photoneutron source (PNS) and subcritical reactor, which consist of lead–bismuth (Pb-Bi) layer, beryllium (Be) layer, and fuel, LLFPs and shield assemblies. The PNS is produced by bombarding radioactive cesium and iodine target with a laser-Compton scattering (LCS) γ-ray beam. We investigate the effect of the ANES system layout on transmutation efficiency by Monte Carlo simulations. It is found that a proper combination of the Pb-Bi layer and the Be layer can increase the utilization efficiency of the PNS by a factor of ~ 10, which helps to decrease by almost the same factor the LCS γ-beam intensity required for driving the ANES. Supposing that the ANES operates over 20 years at a normal thermal power of 500 MWt, five LLFPs including 99Tc, 129I, 107Pd, 137Cs and 79Se could be transmuted by more than 30%. Their effective half-lives thus decrease drastically from ~ 106 to less than 102 years. It is suggested that this successful implementation of the ANES paves the avenue towards practical transmutation of LLFPs without isotopic separation.

Inert-matrix fuel for transmutation: Selected mid- and long-term effects on reprocessing, fuel fabrication and inventory sent to final disposal

Partitioning and transmutation (P&T) fuel cycles provide a technical approach to ease the problem of radioactive waste disposal. Some of the partitioned components of the waste stream are irradiated while others can be used for energy production or are sent to final storage. Minor actinides are planned to be irradiated in a fast spectrum nuclear facility to transmute them into stable or short-lived isotopes. As minor actinides have negative effects on reactor dynamics, subcritical, accelerator-driven systems are proposed to increase their fraction in the fuel. An example is the MYRRHA research reactor to be built in Mol, Belgium.This reactor is modeled for depletion calculations. The behavior of special fuel elements that mirror fuel composition as envisioned for large scale transmutation facilities, namely inert-matrix fuels with an increased minor actinide content, are investigated within this reactor environment. It turns out that gamma dose rates, activity and residual heat from the spent fuel elements present significant challenges for implementing a P&T program. Spent inert-matrix fuel element show significantly higher levels than spent fuel elements from fast reactors. This requires long cooling periods and poses unprecedented challenges to reprocessing technology. The problem is amplified by the fact that it is generally agreed upon that due to low transmutation efficiencies several transmutation steps would be necessary. Looking at the radiotoxicity index, the efforts suggested to reduce the minor actinide content in a final repository are justified. The long-term safety case of deep geological repositories, however, implies that certain long-lived fission products are more relevant. The build-up of some of these radionuclides is investigated for two hypothetical German P&T scenarios. Naturally, the amount of fission products increases with continued irradiation. But namely the fraction of Cs-135 increases over-proportionally when inert-matrix fuel rich on minor actinides is used.

Imaging and reconstruction of high-energy proton beam spot before target based on secondary gamma rays.

The distribution and stability of the incident proton beam spot are critical for the stable operation of a high-power spallation target. This study proposes a method to capture images of the incident proton beam spot based on secondary gamma rays. The distribution of the backward secondary gamma rays irradiated by the primary proton beam on the incident surface of the target is close to the distribution of the protons and can be measured at a low-radiation position far from the target area. A relation of distributions between the incident protons and the secondary gammas is constructed by using the point response function of this pinhole imaging system. The proposed method of imaging is suitable for monitoring the distribution of the proton beam on the target in facilities that use a beam power of several megawatts or tens of megawatts, such as spallation neutron sources or accelerator-driven subcritical systems.

Beam-target configurations and robustness performance of the tungsten granular flow spallation target for an Accelerator-Driven Sub-critical system

The dense granular flow spallation target is a new target concept proposed for an Accelerator-Driven Sub-critical (ADS) system. In this paper, the beam-target configurations of a tungsten granular flow target for the ADS with a thermal power of 1 GW is explored. The beam profile options using different scanning methods are discussed. The critical geometry parameters are adjusted to investigate the performance of the granular target from the aspects of neutron efficiency, stability and temperature distribution in target medium. To figure out how the target under accident conditions would behave, different clogging conditions are induced in the simulation. The dynamic processes are analyzed and some important parameters such as abnormal temperature rise and beam cutoff time window are obtained. The response of the sub-critical reactor to a clogging accident is also investigated. It is indicated that the monitoring of the granular flow by the neutron detectors in the sub-critical core will be effective.

A design study on a metal fuel fast reactor core for high efficiency minor actinide transmutation by loading silicon carbide composite material

ABSTRACT A metal fuel fast reactor core for high efficiency minor actinide (MA) transmutation was designed by loading silicon carbide composite material (SiC/SiC) which can improve sodium-cooled fast reactor (SFR) core safety characteristics such as sodium void reactivity worth and Doppler coefficient due to neutron moderation. Based on a 750 MWe metal fueled SFR core concept designed in a prior work, the reactor core loading fuel subassemblies with SiC/SiC wrapper tubes and moderator subassemblies was designed. To improve the reactor core safety characteristics efficiently, three layers of SiC/SiC moderator subassemblies were loaded in the core by replacing 108 out of 393 fuel subassemblies with the moderators. The reactor core with approximately 20 wt% MA-containing metal fuel satisfied all safety design criteria and achieved the MA transmutation amount as high as 420 kg/GWe-y which is twice as high as that of the axially heterogeneous core with inner blanket and upper sodium plenum, and two-thirds of that of the accelerator-driven system.