Heat-pipe microreactors (HPMRs) are very small-scale nuclear reactors that employ heat pipes (HPs) for heat removal. HPMRs can be easily integrated with other forms of renewable energies, can be used for emergency responses to disaster relief zones, can be deployed in remote locations not connected to the grid, and can be removed from sites and replaced by new ones. HPMRs can also be used for space missions as HPs do not rely on gravity for heat transfer. Conventional fuel materials, such as uranium oxide (UO2) and uranium oxycarbide (UCO), are currently considered in most existing HPMR designs, but ceramic uranium nitride (UN) fuel that has high uranium density, high thermal conductivity, and high melting point may become a better fuel candidate. Through neutronics calculations, this paper assesses the impact of using UN fuel in HPMRs with two different neutron spectra (fast and thermal) and two different fuel forms [traditional solid fuel pellets and TRi-structural-ISOtropic (TRISO) fuel compacts]. It was concluded that retrofitting HPMRs with UN fuel has the potential to reduce the initial U-235 enrichment requirement by similar to 3 wt% (to keep the same cycle length) or increase the cycle length (by keeping the same initial U-235 enrichment), which enables more compact and transportable HPMR core designs. However, using UN fuel decreases the control element worth [by up to 20% for the Special Purpose Reactor (SPR) and 5% for HP-MR] and is up to 80% more costly. Increasing N-15 enrichment can further decrease the initial U-235 enrichment requirement and increase the control element worth but is more costly. Compared to fast-spectrum HPMRs fueled with solid pellet fuels, retrofitting UN fuel is more suitable for thermal-spectrum HPMRs fueled with TRISO fuel compacts, where the neutron spectrum hardening caused by using UN is less significant.

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities.This paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

Equilibrium state generation for the pebble bed reactor (PBR) is challenging due to the need to simultaneously account for both pebble movement and changes in fuel compositions. Multigroup diffusion codes have been historically employed to generate the equilibrium state and perform conventional neutronics calculations for PBRs, while neutron cross-section generation has been challenging due to the double heterogeneity of PBRs. Thanks to the capability to treat the double heterogeneity naturally, continuous-energy Monte Carlo (MC) methods are more suitable for detailed PBR analysis, but at the cost of significantly higher computing power. This paper presents a new Methodology to Efficiently Estimate the Equilibrium State of a PBR (MEEES-PBR) to generate equilibrium-state MC models for PBRs at lower computational expense. The MEEES-PBR is expected to contribute to the future development of PBR designs by accelerating the efforts in core designs and parametric studies. The theory of the MEEES-PBR is introduced in detail in this paper, and the procedure is demonstrated via an example application to the 165-MW(thermal) Xe-100 design. The computational cost and the accuracy of the MEEES-PBR are discussed to prove its viability.

A one-dimensional (1-D) thermal stratification (TS) model was recently developed in our research group to predict the TS phenomenon in pool-type sodium-cooled fast reactors. This paper performs uncertainty quantification (UQ) of the 1-D TS model to evaluate its performance by considering the aleatoric uncertainties that existed in the model parameters and to identify the plausible sources of the epistemic uncertainties. The Latin hypercube sampling-Monte Carlo method (LHS-MC), which is elaborated with an example in this paper to facilitate its understanding and implementation, is used for the UQ process. The advantages of LHS-MC, including both better stability and better accuracy than the conventional random sampling-Monte Carlo method with fewer realizations, are demonstrated in this paper. In total, 648 temperature measurements acquired from nine experimental transients performed in a university-scale Thermal Stratification Experimental Facility are used to evaluate the performance of the computational 1-D TS model. The UQ result shows that 77.5% of the experimental data can be predicted by the 1-D TS model within uncertainty ranges, which indicates the good performance of the computational model when the aleatoric uncertainties are correctly captured. The rest 22.5% of the experimental data are found located outside of the uncertainty ranges, which reveals the existence of the epistemic uncertainties caused by the lack of understanding of the TS phenomenon and defects in the 1-D model. The simple jet model currently employed by the 1-D TS model is thought to be one of the attributors to these defects.

Thermal stratification (TS) is a thermal-fluid phenomenon that can introduce large uncertainties to nuclear reactor safety. The stratified layers caused by TS can lead to temperature oscillations in the reactor core. They can also result in damages to both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracks. More importantly, TS can impede the establishment of natural circulation, which is widely used for passive cooling and ensures the inherent safety of numerous reactor designs. A fast-running one-dimensional (1-D) model was recently developed in our research group to predict the TS phenomenon in pool-type sodium-cooled fast reactors. The efficient 1-D model provided reasonable temperature predictions for the test conditions investigated, but nonnegligible discrepancies between the 1-D predictions and the experimental temperature measurements were observed. These discrepancies are attributed to the model uncertainties (also known as model bias or errors) in the 1-D model and the parameter uncertainties in the input parameters. In this study, we first recognized through a forward uncertainty analysis that the observed discrepancies between the computational predictions and the experimental temperature measurements could not be explained solely by input uncertainty propagation. We then performed an inverse uncertainty quantification (UQ) study to reduce the model uncertainties of the 1-D model using a modular Bayesian approach based on experimental data. Inverse UQ serves as a data assimilation process to simultaneously minimize the mismatches between the predictions and experimental measurements, while quantifying the associated parameter uncertainties. The solutions of the modular Bayesian approach were in the form of posterior probability density functions, which were explored by rigorous Markov Chain Monte Carlo sampling. Results showed that the quantified parameters obtained from the inverse UQ effectively improved the predictive capability of the 1-D TS model.

Investigating thermal stratification in the upper plenum of a sodium fast reactor (SFR) is currently a technology gap in SFR safety analysis. Understanding thermal stratification will promote safe operation of the SFR before its commercial deployment. Stratified layers of liquid sodium with a large vertical temperature gradient could be established in the upper plenum of an SFR during a down-power or a loss-of-flow transient. These stratified layers are unstable and could result in uncertainties for the core safety of an SFR. In order to predict the occurrence of the thermal stratification efficiently, we developed a one-dimensional (1-D) transport model to estimate the temperature profile of the ambient fluid in the upper plenum. This model demands much less computational effort than computational fluid dynamics (CFD) codes and provides calculations with higher fidelity than historical system-level codes. Two flow conditions were considered separately in the current study depending on if in-vessel components are presented in the upper plenum. For the condition where in-vessel components, specifically the upper internal structure, are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the distance between the bottom of the in-vessel component and the jet inlet surface. For the condition where no in-vessel components are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the jet length, which was determined through data-driven trainings. The newly developed 1-D model showed similar performance with the CFD model in both cases. However, due to the assumption of flat profiles of the impinging jet axial dispersion rate, nonnegligible discrepancies between the 1-D prediction and the measured data were observed.

Computational modeling and simulations are widely used for evaluation of the performance and safety features of innovative nuclear reactor designs. Multigroup-based deterministic neutronics codes are often employed in these reactor design calculations because they can provide fast predictions of the neutron flux distribution and other neutronics characteristic parameters. Nevertheless, providing accurate multigroup cross sections for deterministic codes is an onerous job, which makes establishing an exhaustive cross-section library computationally prohibitive. Partly because of these reasons, multigroup neutron cross sections are normally stored only at certainty state points in the data library of these deterministic codes, and linear interpolation methodology is commonly utilized to estimate the cross sections at unknown states. However, the applicability of linear interpolation is limited, and the precision of its results is moderate. In this paper, we discuss a preliminary feasibility study that we performed on providing more precise multigroup cross sections for deterministic neutronics codes by using the linear regression methodology. Compared to the traditional linear interpolation method, the linear regression approach principally showed improved computational efficiency considering the use of more data in the cross-section library, and constructed hypothesis functions for the responses of interest with a higher order of accuracy. In this study, a case study on Lightbridge Corporation's metallic fuel element was carried out to demonstrate the feasibility and advantages of linear regression in multigroup cross-section interpretation. A reference cross-section library was established through calculations conducted with the Monte Carlo neutronic code Serpent. Because of the preliminary nature of this feasibility study, only the macroscopic total cross section is considered. Linear interpolation and linear regression were both used to estimate cross sections at unknown states based on the data available in the library. By comparing the performance of both methodologies, we demonstrated that the linear regression methodology achieved wider applicability and better precision in cross-section interpretation. Moreover, the linear regression process was finished within 15 s using a single processor core, which indicated that the additional computational burden brought by the implementation of linear regression methodology in the task was acceptable.

Understanding the thermal fluid phenomena in different components of the nuclear reactor systems is crucial for reactor safety analysis. The study of thermal stratification in liquid-metal-cooled reactors (LMRs), among the others, is especially indispensable due to its large impact. Thermal stratification could occur in an LMR in various conditions, including the down-power transients or the Protected Loss of Flow (PLOF) accidents, where cooler coolant flows out of the core to the upper plenum, or the Unprotected Loss of Flow (ULOF) accidents, where hotter coolant flows from the core to the upper plenum. Thermal stratified layers could be formed in the upper plenum of an LMR under the scenarios mentioned above and introduce uncertainties to the core safety. The stratified layers are unstable and could cause temperature oscillations with fairly large amplitude [1], which further result in neutronic and thermal-hydraulic instabilities. The stratified layers with a large temperature gradient could also damage both the reactor vessel and the in-vessel components through thermal fatigue crack growth. More importantly, the formation of the stratified layers could impede the establishment of natural circulation during accidental scenarios, which endangers the passive safety of LMRs. Various approaches with different fidelities have been investigated to provide predictions of this phenomenon to prevent its occurrence or to mitigate the damage caused. System-level codes require minimal time for the predictions, but can only provide approximated solutions for simple cases because of the highly simplified models employed. The CFD methodologies, on the other hand, provides high-fidelity calculations, but at high computational expenses. In our precious work [2, 3], we developed an integrated 1-D systemlevel model with improved fidelity for the prediction of the thermal stratification phenomenon in the pool-type sodiumcooled reactors (SFRs). The experimental data used for the development and validation of the 1-D thermal stratification model was acquired in the Thermal Stratification Experimental Facility (TSTF) [4] built at the University of Wisconsin-Madison, using sodium as the working fluid. In this paper we will investigate the applicability of the 1-D model, developed using the experimental data acquired in a sodium environment, to the gallium environment. In this study, the experimental data used for the model validation was acquired in the Gallium Thermal-hydraulic Experiment (GaTE) [5] built at Kansas State University, using gallium as the working fluid. EXPERIEMENTAL DESIGN

The thermal stratification phenomenon plays a crucial role in the safety of various nuclear systems, including the Gen-III + Light Water Reactors (LWR) and the Gen-IV reactors. The phenomenon is of particular importance for the pool-type Sodium-cooled Fast Reactors (SFRs) because it may cause neutronic and thermal-hydraulic instabilities in the reactor core, or lead to damages of both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracking. More significantly, thermal stratification could impede the establishment of the natural circulation during accidental scenarios and introduce uncertainties to the core safety of SFRs.

This paper presents a parameter sensitivity analysis on a thermal stratification (TS) model by using the discrete sensitivity method. The TS model was recently developed in our research group to efficiently predict the TS phenomenon in pool-type Sodium-cooled Fast Reactors. The fluid temperature gradient was considered as the figure of merit in the sensitivity analysis because it best characterizes the thermal stratification phenomenon. The sensitivities of the fluid temperature gradient with respect to four different parameters were investigated, including jet volumetric flow rate Q(jet), jet temperature T-jet, heat capacity of the ambient fluid C-p,C-amb, and static thermal conductivity of the ambient fluid k(c,amb). The sensitivity analysis was conducted through both the conventional forward sensitivity method and the advanced adjoint sensitivity method, which is more effective in cases where the number of outputs is small and the number of input parameters is large. The sensitivities obtained in this study suggested that perturbations in Q(jet), C-p,C-amb,C- and k(c, amb) could introduce either positive or negative changes to the temperature gradient, depending on the axial location and the elapsed time of the experiment. However, an increase in Tjet always decreased the temperature gradient. Moreover, the impact of T-jet on the maximum temperature gradient was several times higher than that of the other three parameters, which indicated that additional attention may need to be paid to the occurrence of thermal stratification in the sodium pool when the impinging jet has a large temperature change. This study also provides a step-by-step example for the application of the discrete adjoint sensitivity method to the time-dependent nonlinear systems.

This paper develops a best estimate plus uncertainty (BEPU) framework for research reactor transient safety analysis. The BEPU framework is developed based on the system level reactor safety analysis code RELAP5-3D and the data analysis platform RAVEN developed by Idaho National Laboratory. Within the framework, a sensitivity analysis procedure is first conducted to identify the contributions and ranks of individual input parameters to the user-defined figures-of-merit (FOMs) associated with specific transient phenomena. An uncertainty analysis procedure is then performed to quantify the uncertainties of the FOMs resulting from the uncertainties of the input parameters. Many useful outcomes can be realized through the BEPU analysis. Specifically, the sensitivity information obtained from the sensitivity analysis will provide insights about the influence of each different input parameter on FOMs. The uncertainty information obtained from the uncertainty analysis will imply the range of response deviations caused by the propagation of errors existing in various input components. As a case study for research reactors, the developed BEPU framework was employed to perform design-basis accident (DBA) analysis for one conceptual research reactor design proposed at the National Institute of Standards and Technology (NIST). Two hypothetical DBA scenarios, namely the reactivity insertion accident (RIA) and the loss of flow accident (LOFA), were modeled and analyzed through the BEPU framework. To demonstrate the value of the BEPU framework, the BEPU analysis results were compared to that obtained from the conventional transient safety analysis procedure, which was conducted by using commonly used transient safety analysis codes including RELAP5-3D and PARET. The comparison shows that the BEPU analysis is capable of providing additional sensitivity and uncertainty information that help confirm safety margins of the NIST conceptual research reactor during both RIA and LOFA situations, which justifies the advantages and benefits of the BEPU safety analysis framework developed in this work.

The thermal stratification phenomenon plays a crucial role in the safety of various nuclear systems, including the Gen-III + Light Water Reactors (LWR) and the Gen-IV reactors. The phenomenon is of particular importance for the pool-type Sodium-cooled Fast Reactors (SFRs) because it may cause neutronic and thermal-hydraulic instabilities in the reactor core, or lead to damages of both the reactor vessel and in-vessel components due to the growth of thermal fatigue cracking. More significantly, thermal stratification could impede the establishment of the natural circulation during accidental scenarios and introduce uncertainties to the core safety of SFRs. Efforts for modeling of the thermal stratification in SFRs have been made for decades to prevent or mitigate the damage caused by the phenomenon. This paper gives a review of the advances that have been made in recent 10 years on the computational modeling methods for thermal stratification phenomenon in SFRs. These methods can be generally drawn into two categories. The first one is the system-level methods which provide fast-running but approximate calculations, and the second one is the CFD methods which provide high-resolution calculations at high computational expense. After introducing the efforts that have been made to improve the one-dimensional (1-D) models, the paper envisioned the possible research directions that could be pursued to enhance the modeling of thermal stratification in the near future.

Fully ceramic microencapsulated (FCM) fuel may enhance the already strong inherent reactor safety characteristics of a conventional High-Temperature Gas-Cooled Reactor (HTGR). FCM fuel uses an SiC matrix that exhibits higher stability under irradiation with limited swelling relative to a conventional graphite matrix. Additionally, the SiC matrix is expected to exhibit improved mechanical performance relative to graphite. The feasibility of FCM-fueled HTGRs has been explored in a previous study (Lu et al., 2018), and three FCM fuel concepts were identified to be able to maintain the cycle length of the reference conventional General Atomics 350 MWt prismatic modular HTGR. In this work, the previous investigation of the reactor core safety characteristics of HTGRs fueled by these three FCM fuels was significantly extended to detailed thermal hydraulics and neutronics analysis of normal operation and design basis accident scenarios. We found that these FCM-fueled cores would have a maximum fuel temperature similar to 20-40 K higher than that of the reference HTGR core at the beginning of cycle (BOC) and similar to 30-60 K higher at the end of cycle (EOC) during normal operating conditions. Pressurized (P-) and depressurized (D-) loss of forced cooling (LOFC) accidents as well as the control rod withdrawal accident were explored. The FCM-fueled cores would at most have a maximum fuel temperature similar to 30-50 K higher than that of the reference core in a P- LOFC accident, similar to 10-30 K in a D- LOFC accident and similar to 30-50 K in a rod withdrawal accident. The conclusion of the study is that FCM fuel has a small impact on the reactor performance and safety characteristics during normal operation and design basis accident conditions within the existing and generic 350 MWt prismatic modular HTGR design we considered. Additionally, a fuel cycle cost comparison was also performed in the current study. We found that the FCM fuels may be up to 40%-74% more expensive than the conventional fuel. Further analysis of the economics of FCM fuel are needed, because the uncertainties in the assumptions for this study are high.

We conducted reactor performance calculations to assess the potential design basis accident performance of HTGR fuel designs. Three Fully Ceramic Microencapsulated (FCM) fueled HTGR designs were developed in a previous work (Lu et al., 2018). The maximum fuel temperature in the cores fueled by these three FCM fuels was predicted to be higher than that in the reference 350-MWt mHTGR core in both normal operating conditions and during representative design basis accidents (Lu and Brown, 2019). To better understand the potential safety margins in mHTGR design basis accidents, we performed thermal-hydraulics sensitivity studies to investigate how maximum fuel temperature varies considering various parameters, e.g. thermal properties, within the ranges corresponding to the differences between the FCM-fueled prismatic mHTGR cores and the reference core with conventional fuel compacts. We found that the difference in the steady-state axial power distribution contributed the most to the difference in the maximum fuel temperature, in both normal operation and design basis accidents. Experimental data suggested that the annealing process of irradiation defects in SiC would be rapid at mHTGR relevant fuel temperatures. The bounding potential impact of the SiC annealing on the maximum fuel temperature was analyzed considering both the thermal conductivity recovery and the Wigner energy release due to the annealing of SiC. We found that the defect annealing process in SiC would at most increase the peak maximum fuel temperature of an FCM-fueled core by 40 K in loss of forced cooling accidents and by 10 K in a control rod withdrawal accident. Additional experiments on the SiC defect annealing kinetics and Wigner energy release in more relevant conditions are needed.

This study performs an experimental investigation of frictional pressure drop in air-water two-phase flows in straight pipes. A reliable experimental database for the two-phase pressure drop and void fraction is established with a differential pressure transducer and a four-sensor conductivity probe, respectively. The two-phase flow investigated focuses on gas-dispersed flow regimes in different pipe diameters of 38.1 mm, 50.8 mm, and 101.6 mm. Systematic study on the effects of flow orientation, flow regime and pipe size is performed. The most commonly used predictive models for the two-phase frictional pressure drop are evaluated with the newly established database and the existing databases found in the literature. It is demonstrated that both the conventional Lockhart-Martinelli approach and the phi(f) - < alpha > correlation can generally predict the two-phase frictional pressure drop very well with different suggested values of coefficients C and n for different flow orientations, based on the established data. Meanwhile, the results show that the values of C and n are independent of the pipe size and the flow regime. The homogeneous flow model is evaluated with four beta (ratio of volumetric flow rates) based mixture viscosity correlations. The predictions with the Beattie and Whalley mixture viscosity correlation are found to be the best regardless of the flow orientation. The Lockhart-Martinelli approach with the coefficient C calculated by correlation employed in the nuclear system analysis code RELAP5-3D and the Muller-Steinhagen and Heck correlation are also evaluated. It is found that these two modeling approaches as well as the homogeneous flow model tend to underestimate most of the experimental data. Improvements for pressure drop prediction in nuclear reactor safety analysis codes are observed.