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The effects of hydride amount (20–850 wppm), orientation (circumferential and radial), and temperature (room temperature, 100 °C, 200 °C) on the axial mechanical properties of Zircaloy-4 cladding were comprehensively examined. The fraction of radial hydride fraction in the cladding was quantified using PROPHET, an in-house radial hydride fraction analysis code. Uniaxial tensile tests (UTTs) were conducted at various temperatures to obtain the axial mechanical properties. Hydride orientation has a limited effect on the axial mechanical behavior of hydrided Zircaloy-4 cladding. Ultimate tensile stress (UTS) and associated uniform elongation demonstrated limited sensitivity to hydride content under UTT. Statistical uncertainty of UTS was found small, supporting the deterministic approach for the load-failure analysis of hydrided Zircaloy-4 cladding. These properties notably decrease with increasing temperature in the tested range. The dependence of yield strength on hydrogen content differed from temperature to temperature. The ductility-related parameters, such as total elongation, strain energy density (SED), and offset strain decrease with increasing hydride contents. The abrupt loss of ductility in UTT was found at ∼700 wppm. Demonstrating a strong correlation between total elongation and offset strain, SED can be used as a comprehensive measure of ductility of hydrided zirconium alloy.

Stainless steel 316L specimens were snug fitted into a rotating disk submerged in molten LBE and subjected to spatially varying local flow velocity along the radial position. The specimens experienced LBE flow velocity from 0.50 m/s to 3.14 m/s depending on their radial location. The test was conducted at 600°C with an oxygen concentration of 2.87 × 10−8 wt% for 150 h. Resulting microstructural characteristics of the corroded zone were found to be sensitively affected by local flow velocity and were categorized into four regimes. For linear disk velocity > 2.0 m/s, the affected zone thickness became increasingly less sensitive to flow velocity as the overall reaction became reaction rate controlled. At the velocity of ~ 3.0 m/s, erosion-corrosion started to take place. The flow effect on the affected zone thickness ( $$l$$ ) agreed with the model based on the disk velocity ( $$v$$ ) effect on the mass transfer of a rotating disk as $$\frac{1}{l}\sim v^{ - 0.792}$$ .

Steady-state internal flow boiling experiments were conducted on various materials, including accident tolerant fuel cladding material Fe–12Cr–6Al (C26M2) alloy, Zircaloy, and metal-based m...

Considering the highly nonlinear behavior and phenomenological complexity of critical heat flux (CHF), this study proposes a novel method to predict CHF on microstructure surface using mach...

Several advanced nuclear reactors use Tristructural-isotropic (TRISO) fuel particles randomly distributed in a matrix to allow for aggressive operating conditions. Since those fuels are composites with randomly distributed fuel particles in a matrix, suitable smearing methods are needed to obtain fuel temperature fields for reactor design and safety analysis. By developing three-dimensional finite-element heat conduction models for randomly distributed heat generating particles in a matrix, this study evaluated the impact of the randomly distributed heat sources on the temperature fields of the fuel pebble. In addition, a two-regime heat conduction model was proposed in this study by assuming that all fuel particles are densely packed at the center of the fuel element. The present model provides a practical methodology to predict peak and average fuel temperatures of nuclear fuel elements with heat generating particles because, among the possible distribution patterns of the TRISO fuel particles, the peak fuel temperature is highest when all the fuel particles are densely packed at the center of the fuel element. Comparing to other models, the present model predicts more conservative temperature fields and shows improved agreement with both peak and average fuel temperatures of the simulated compacts and pebbles.

Steady and transient (with a heating rate of 685 °C/s) internal-flow CHF (Critical Heat Flux) experiments were conducted under atmospheric pressure at a fixed inlet temperature (40 °C or 60 °C) and mass flow (300 kg/m2 s) on Fe-13Cr-6Al alloy, Inconel 600 and Zircaloy-4 tube samples. Multiple experiments were repeated on the same specimen to investigate the effect of surface characteristic changes (i.e., roughness, wettability, and oxide scale morphology) on the occurrence of CHF. Despite notable changes of wettability, roughness, and oxide layer characteristics on samples that had already been subjected to CHF, measured flow CHF remained unchanged throughout repeated experiments for tested materials. This demonstrates that the surface effects on flow CHF are limited in the test conditions. In the steady-state flow boiling condition, Fe-13Cr-6Al alloy demonstrated a 22% and 14% increase in CHF compared to Zircaloy-4 and Inconel 600, respectively. Compared to the 2006 Groeneveld CHF lookup table, Fe-13Cr-6Al alloy gives a 13% increase in the tested flow boiling condition. Material properties are considered primarily responsible for the observed CHF differences among the tested materials. The surface thermal economy parameter ( ρ c p 3 / 2 k ) is proposed as an explanation for the observed CHF differences; this parameter is related to material’s ability to avoid an irreversible dry spot formation. The apparent disagreement of Zircaloy-4 CHF with both the look up table predictions and Inconel 600 shows the limitation of departure of nucleate boiling (DNB) evaluations that do not consider cladding materials. The transient Fe-13Cr-6Al CHF is 39% and 23% higher than the lookup table prediction and the steady-state condition experimental result, respectively.

This paper experimentally and theoretically investigates thermal stress of materials caused by non-uniform surface temperature fields due to bubble dynamics of nucleate boiling. The surface temperature of Calcium fluoride (CaF2) on a thin-film indium tin oxide (ITO) heater was measured by an Infrared high-speed camera. Then, the obtained temperature fields were used to calculate boiling induced thermal stresses. An analytical model was developed to predict thermal stress due to nucleate boiling. The localized cold spot under a growing bubble gives rise to the peak tensile stress. The magnitude of the peak stress is predominantly determined by liquid and solid properties, and applied heat flux to a limited extent. Nevertheless, higher heat flux is observed to result in a higher probability of material fracture due to an increased number of nucleation sites, which gives a larger effective surface area under stress. Newly discussing another cause of stresses for oxide layer mechanical integrity, the presented discovery of boiling induced stress implies potential effects on break-away of oxide scales under boiling conditions, including reactor fuel claddings and steam generator U-tubes. Moreover, the boiling stress can be potentially used to design self-cleaning surfaces by breaking unwanted deposits.

Post-Loss of Coolant Accident (LOCA) ductility assessments of Cr-coated Zircaloy cladding was conducted in compliance with the United States Nuclear Regulatory Commission (U.S.NRC)’s guidelines. The Equivalent Cladding Reacted (ECR) limit for Cr-coated cladding oxidized on both sides, representing the embrittlement process of an outer-side coated cladding near the burst hole followed by ballooning, is found to be 13.8% at steam oxidation temperature of 1204°C. Ring Compression Test (RCT) induces peak tensile stress at the inner surface of the cladding specimen at which the crack starts to propagate from the brittle phases (ZrO2 and α ( O ) -Zr). Such characteristic of RCT is responsible for the decrease in the ECR limit for the claddings coated on the external surface as its oxygen-affected brittle phases are developed at the inner cladding surface. Outer-side Cr-coated cladding gives approximately 10 minutes of extra accident coping time at the fixed steam oxidation temperature 1204°C before it reaches the cladding embrittlement limit.

A 2D axisymmetric SiC cladding mechanical model with anisotropic material properties based on finite difference method was developed. The developed model was used to analyze the behavior of SiC clad fuel (double-layer and full SiCf/SiC composites structure) in steady-state and large break loss of coolant accidents (LBLOCA) by coupling with the thermal-hydraulics simulation code MARS-KS (Multi-dimensional Analysis of Reactor Safety-Korean Standard). The multi-axial pseudo-ductile deformation model considering the characteristics of SiCf/SiC composites was employed, and the Weibull statistical failure model was applied to assess the failure probability of the cladding. Using anisotropic elastic properties, stronger tensile stress was induced in the outer monolith layer than in the isotropic case, which greatly increased the failure probability. In steady-state operation, this study shows that the failure probability of a double-layer SiC cladding is sensitive to the rod internal pressure. In-line with other studies, it was also found that the irradiation induced swelling accumulated in the refueling stage is a challenge to the structural integrity of the SiC cladding concept. The LBLOCA analysis demonstrates that the SiCf/SiC composite layer can maintain the coolable geometry of the fuel rod for both duplex and full composite cladding. Hermeticity is shown to depend on the arrestment of matrix cracks developed by pseudo-ductile deformation. Experimental support and validation on matrix crack propagation, pseudo-ductile behavior of SiCf/SiC composite under multiaxial loading, and rod-scale thermal shock with reflood quenching are necessary to further improve the model.

In this study, ν-Support Vector Machine (ν-SVM) is used to explore strategies for the data-driven CHF look-up table construction, based on sparingly distributed experimental data points. The CHF look-up table of Groeneveld et al. (2007) was used as the reference CHF data bank. In the data bank, the subcooled flow (Xe

Surface wettability analysis, including measurements of static (θ) advance (θ A ), and receding (θ r ) contact angles, and surface roughness, Ra, are effective parameters used in the literature to predict changes in the pool boiling Critical Heat Flux (CHF). The CHF is an important aspect of the thermal hydraulic performance that needs to be investigated for new Accident Tolerant Fuel (ATF) cladding materials, such as iron-chromium-aluminum alloys (FeCrAl). Surface wettability of FeCrAl samples oxidized under different simulated Light Water Reactor (LWR) water chemistry conditions was measured. These measurements were compared to as-machined and oxidized Zircaloy-4 (Zirc-4), the reference cladding material in LWRs, under the same conditions. Theoretical models were used to predict the pool boiling CHF using surface wettability measurements. Pool boiling experiments were conducted using the same samples to measure the CHF. The measured and predicted CHF data were compared for model validation. The obtained results showed no significant difference in the measured static contact angle and hence the predicted CHF between the as-machined samples of FeCrAl, 310 SS, and Zirc-4. The contact angles (static, advance, and receding angles) for corroded FeCrAl samples under different LWR water chemistry conditions are lower, and the measured surface roughness values are higher than Zirc-4 corroded under the same conditions. Existing models in the literature predicted higher pool boiling CHF of corroded FeCrAl compared to 310 stainless steel (SS), and Zirc-4. The measured pool boiling CHF for oxidized FeCrAl samples was higher than Zirc-4 samples. The measured and predicted CHF values are in good agreement. The CHF and the Departure from Nucleate Boiling Ratio (DNBR) were calculated using the Consortium for Advanced Simulation of Light Water Reactors (CASL) subchannel code COBRA-TF (CTF) for a one-eighth model of a 17 × 17 Pressurized Water Reactor (PWR) fuel assembly. The inlet conditions are consistent with typical PWR values except for the power, which was set 50% higher than is typical to represent possible accident conditions more accurately. The calculated distributions for the CHF and DNBR for oxidized FeCrAl showed significantly higher values throughout the fuel assembly octant compared to as machined Zirc-4 and as machined FeCrAl. These preliminary results show that oxidized FeCrAl may be able to withstand the proposed accident conditions without leading to a boiling crisis.

Several advance nuclear reactors use particle-type Tristructural-Isotropic (TRISO) fuels randomly distributed in a matrix to allow aggressive operating conditions. Since those fuels are composites with randomly distributed TRISO particles in a matrix, suitable smearing methods are needed to obtain effective pellet-level thermomechanical properties for reactor design, and safety analysis. Currently available smearing methods for effective thermal conductivity assume uniform or no heat generation, thereby neglecting the random heat source distribution. By developing three-dimensional finite-element heat conduction models for randomly distributed heat generating kernels in a matrix, this study demonstrates that the consideration of a randomly distributed heat source is important in predicting the peak fuel temperature. In this study, (1) random packing of heat generating fuel particles introduces the statistical distribution of peak and average temperatures, and (2) those statistical temperature distributions are quantified. In light of this, thermal conductivity models with randomly distributed heat generating kernels are developed to predict peak pellet temperature for Fully Ceramic Microencapsulated (FCM) fuel and Cermet fuel for space propulsion. The developed methodology and models provide a practical methodology to predict statistically-informed peak and average fuel temperatures of nuclear fuel pellets of heat generating particles. The presented methodology is useful to quantify uncertainties in predicting nuclear fuel temperatures with TRISO particles.

TRANOX-1.0 (TRANsient OXidation), a mechanistic model that calculates oxygen distribution for isothermal and non-isothermal transients (1000–1250 °C) has been developed. TRANOX solves radial transient diffusion equation using Finite Difference Method (FDM) with spatial phase changes for each time step. Diffusion coefficients of each resulting phase were obtained by searching a combination that best guarantees Equivalent Cladding Reacted (ECR) and α-Zr(O) thickness simultaneously. The model has been extensively validated by overarching experimental campaigns including isothermal and non-isothermal high temperature steam oxidation, and post-metallurgical characterization. Accounting for α+β equilibrium phase, TRANOX gives accurate predictions for ECR, spatially averaged radial oxygen distribution, and thicknesses of each phase. Mechanistically solving the diffusion equation, TRANOX exhibits unbiased predictability for isothermal and non-isothermal transients. TRANOX was used to understand the oxygen distribution of pre-hydrided high burnup fuel cladding. The diffusion resistance behavior of α-Zr(O) and α+β with respect to hydrogen content counteract, neutralizing the overall hydrogen effect on oxygen distribution. The limited hydrogen effect on diffusion resistance during the early stage of steam oxidation further reduces the hydrogen-sensitivity of oxygen profiles. This finding provides a cogent explanation for the effect of hydrogen on oxygen distribution and oxidation kinetics observed by a number of past studies.

The statistical nature of ductility of embrittled Zircaloy-4 cladding and its implications on the ECCS criteria (10 CFR 50.46) were investigated. Ductility of embrittled cladding specimens (ECR: 9-30%, and H: 171-1759 wppm) was measured by offset strains obtained from Ring Compression Tests (RCT) conducted in compliance with U.S NRC's guidelines. This study demonstrates the Weibull distribution of offset strains for the tested Zircaloy specimens. The current ECCS criteria (ECR 17% with 2% offset strain) ensure ∼97% ductile population, which may serve as a reference statistical confidence to determine the ductility criteria of high burnup fuel cladding. Characterized with low Weibull modulus (m), intermediate levels of embrittlement notably increase statistical uncertainties of the offset strain due to the possibility of having two distinctively different failure modes (i.e., ductile and brittle). Such a mixed failure mode can be used as a flag that instrumentally helps avoid excessive conservatism of the ECR limit being in a highly ductile regime. Griffith theory was employed to understand the mixed failure modes by comparing the critical flaw size of the ductile phase (prior- β ) and pre-existing flaw size estimated by the thickness of the brittle phases (ZrO2+ α -Zr(O)). Three guidelines were proposed to determine physically sound, yet statistically sufficing, offset strain criterion tied to ECR limit for cladding ductility. It was demonstrated that the current ECR 17% limit satisfies the proposed guidelines. The developed guidelines are readily applicable to the high burnup fuel cladding to revisit the statistical and physical sanity of the current draft rule.

Fourteen selected parameters of the reactor response were used to train a multi-connected Support Vector Machines (SVM) model. With proper optimization, the SVM model demonstrated accurate prediction for hot-leg break LOCA, cold-leg break LOCA, and SGTR, and their break sizes. The prediction accuracy is higher in the early phase (

A structural model for stress distributions of coated Zircaloy subjected to realistic incore pressure difference, thermal expansion, irradiation-induced axial growth, and creep has been developed in this study. In normal operation, the structural integrity of coating layers is anticipated to be significantly challenged with increasing burnup. Strain mismatch between the zircaloy and the coated layer, due to their different irradiation-induced axial growth, and creep deformation are found to be the most dominant causes of stress. This study suggests that the compatibility of the high temperature irradiation-induced strains (axial growth and creep) between zircaloy and the coating layer and the capability to undergo plastic strain should be taken as key metrics, along with the traditional focus on chemical protectiveness.

A parametric study that demonstrates a methodology for determining the optimum bilayer composition in a duplex SiC cladding is discussed. The structural performance of multi-layer SiC cladding design is significantly affected by radial thickness fraction of each layer. This study shows that there exists an optimal composite/monolith radial thickness fraction that minimizes failure probability for a duplex SiC cladding in steady-state operation. An exemplary reference case study shows that the duplex cladding with the inner composite fraction ∼0.4 and the outer CVD-SiC fraction ∼0.6 is found to be the optimal SiC cladding design for the current PWRs with the reference material choice for CVD-SiC and fiber reinforced composite. A marginal increase in the composite fraction from the presented optimal designs may lead to increase structural integrity by introducing some unquantified merits such as increasing damage tolerance. The major factors that affect the optimum cladding designs are temperature gradients and internal gas pressure. Clad wall thickness, thermal conductivity, and Weibull modulus are among the key design parameters/material properties.

Effects of cooling rates on mechanical behavior of steam-oxidized Zircaloy-4 are systematically investigated with the cladding material oxidized to the current ductility-based regulatory limits (17% ECR at 1204 °C). Three different cooling rates associated with distinctively different quenching environments are tested; ambient air cooled ( β phase with finer lamellar structures and reduced α incursion, fast cooling (i.e., 25 °C water quenching) effectively reduces statistical variation of RCT results. The presented results support regulatory validity of past experiments conducted irrespective of cooling rates for Zircaloy-4 with no pre-transient hydrogen content. The observed insensitivity of cooling rates on the ECCS criteria for non-hydrided Zircaloy-4 may represent a gap between ductility-based regulation and integral fuel rod behavior. Cooling rate effect is shown to become increasingly important for increasing pre-transient hydrogen embrittlement, as shown by the fracture strength changes.

This study investigates the engineering compatibility between emergency core cooling system criteria and safety water injection systems, in the pursuit of safety margin increase of light water reactors. This study proposes an acceptable temperature increase to 1370 °C as long as equivalent cladding reacted calculated by the Cathcart–Pawel equation is below 13%, after an extensive literature review. The influence of different ECCS criteria on the safety margin during large break loss of coolant accident is investigated for OPR-1000 by the system code MARS-KS, implemented with the KINS-REM method. The fracture-based emergency core cooling system (ECCS) criteria proposed in this study are shown to enable power margins up to 10%. In the meantime, the draft U.S. NRC’s embrittlement criteria (burnup-sensitive) and Japanese fracture-based criteria are shown to allow less than 5%, and around 5% of power margins, respectively. Increasing safety injection tank (SIT) water inventory is the key, yet convenient, way of assuring safety margin for power increase. More than 20% increase in the SIT water inventory is required to allow 15% power margins, for the U.S. NRC’s burnup-dependent embrittlement criteria. Controlling SIT water inventory would be a useful option that could allow the industrial desire to pursue power margins even under the recent atmosphere of imposing stricter ECCS criteria for the considerable burnup effects.

While most conventional PCHE designs for working fluid of supercritical CO2 require an extension of valid Reynolds number limits of experimentally obtained correlations, Computational Fluid Dynamics (CFD) code ANSYS CFX was used to explore validity of existing correlations beyond their tested Reynolds number ranges. For heat transfer coefficient correlations, an appropriate piece-wising with Ishizuka’s and Hesselgreaves’s correlation is found to enable an extension of Reynolds numbers. For friction factors, no single existing correlation is found to capture different temperature and angular dependencies for a wide Reynolds number range. Based on the comparison of CFD results with the experimentally obtained correlations, a new CFD-aided correlation covering an extended range of Reynolds number 2000–58,000 for Nusselt number and friction factor is proposed to facilitate PCHE designs for the supercritical CO2 Brayton cycle application.

Correlations for weight loss rate of pressureless sintered SiC with steam flow velocity, and temperature in pure steam at atmospheric pressure in laminar flow with a velocity range of 0.8–10 m/s and a temperature range of 1140–1500 °C have been developed. While preserving physical significance of non-dimensional numbers dictating boundary layer mass transfer phenomena, the correlations capture boundary layer diffusion effects on the SiO2 volatilization rate, which is affected by flow characteristics at the oxidizing surface. A correlation representing the additive resistances of the mass diffusion in the boundary layer and the volatilization reaction is found to best fit the experimental data. The developed correlations should help understand the SiO2 volatilization mechanism in steam, as well as predicting the lifetime of pressureless sintered SiC in oxidizing environments.

This study presents the importance of coherency in modeling thermal-hydraulics and mechanical behavior of a solid for an advanced prediction of cladding thermal shock fracture. In water quenching, a solid experiences dynamic heat transfer rate evolutions with phase changes of the fluid over a short quenching period. Yet, such a dynamic change of heat transfer rates has been overlooked in the analysis of thermal shock fracture. In this study, we are presenting quantitative evidence against the prevailing use of a constant heat transfer coefficient for thermal shock fracture analysis in water. We conclude that no single constant heat transfer could suffice to depict the actual stress evolution subject to dynamic fluid phase changes. Use of the surface temperature dependent heat transfer coefficient will remarkably increase predictability of thermal shock fracture of brittle materials. The presented results show a remarkable stress prediction improvement up to 80–90% of the actual stress with the use of the surface temperature dependent heat transfer coefficient. For thermal shock fracture analysis of brittle fuel cladding such as oxidized zirconium-based alloy or silicon carbide during LWR reflood, transient subchannel heat transfer coefficients obtained from a thermal-hydraulics code should be used as input for stress analysis. Such efforts will lead to a fundamental improvement in thermal shock fracture predictability over the current experimental empiricism for cladding fracture analysis during reflood.

Experimental investigations are conducted on sintered tubular SiC in oxidizing environments containing pure steam at 1 atm with temperature range of 1140–1500 °C and velocity between 0.8 and 10 m/s. Linear weight loss was observed with time. The linear weight loss rates exhibit sensitive dependence on flow rate at a given temperature, demonstrating effects of flow boundary-layer diffusion rate on silica volatilization kinetics. Silica scale exhibits morphology change with respect to exposure time in an oxidizing environment, progressively demonstrating bubble formation and surface smoothing, extensive formation of cracks and pores, and crack reduction. Yet, strength measurements of pressure-less sintered SiC show no significant change after oxidation in the tested conditions. Hence, the primary life-time limiting factor for structural application of pressure-less sintered SiC in the tested environments is anticipated to be the loss of the material.

High purity CVD-SiC, considered as a nuclear grade cladding material, exhibits thermal shock tolerance ∼1260 °C in room temperature water and beyond it (>1260 °C) in saturated water. Being thinner than the tested specimen thickness (1.5 mm × 2.0 mm), the actual cladding (0.57 mm) is anticipated to exhibit enhanced thermal shock tolerance. This implies that thermal shock alone may not shatter the SiC cladding in reflood. Level of fuel rod internal pressure will be a decisive factor in predicting cladding fracture during reflood. Decreasing water subcooling significantly reduces thermal shock fracture danger of ceramic materials. Thermal shock experiments showed strength retention for both pressureless sintered-SiC and CVD SiC, as well as Al 2 O 3 samples quenched from temperatures up to 1260 °C in saturated water. Solid–liquid contacts during nucleate and transition boiling, and boiling incipience upon water bath entering are a highly probable origin of thermal shock fracture in water quenching.

Steady-state internal flow boiling critical heat flux (CHF) experiments were carried out at 10℃ inlet subcooling and atmospheric pressure (84 kPa at an altitude of about 5300 feet) with mass flux ranging from 200 to 2,000 kg/m2-s on seven tube materials, including the accident-tolerant fuel cladding candidate FeCrAl (C26M) alloy. At a relatively low flow rate, the sensitivity of CHF to different materials was appreciable (the average difference among the tested materials was 19% at 200 kg/m2-s). As the absolute CHF differences stayed constant for higher flow rates, the increased flow rate led to reduced relative CHF differences among the tested materials (average relative difference of 15% at 1,000 kg/m2-s). FeCrAl alloy claddings that were oxidized under simulated Light Water Reactor (LWR) conditions yielded CHF comparable to as-received FeCrAl alloy cladding, with less than 1.8% difference. Experimental CHF results imply marginal material sensitivity impacts on the departure from nucleate boiling ratio in steady-state nuclear reactor cores. Yet, for accident progression analysis, material sensitivity may hold importance, as boiling behavior variation at low mass flux is appreciable. Macroscopic material parameters (surface wettability, surface roughness, and thermal properties) do not provide a suitable explanation for observed material-sensitive CHFs. Yet, surface roughness and thermal effusivity revealed power and linear relations, respectively, to the nucleate boiling heat transfer coefficients at low mass flux. At high mass flux, material sensitivity on nucleate boiling heat transfer significantly decreased due to the increased shear stress on boiling surface overwhelming material-related boiling implications.