Centerline Temperature Research Articles

Numerical Study of Heptane Pool Fires on a Hollow Square Pan

Abstract Heptane pool fires with different mass burning rates ranging from 0.00123kg/s (corresponding to steady burning stage in experiments) to 0.0247kg/s (corresponding to fuel boiling burning stage) on a hollow square pan are numercally studied in this paper. The fireFoam, the large eddy simulation (LES)–based fire simulation code within OpenFOAM®, was employed with the modified Eddy Dissipation Concept combustion model[13] and PaSR based soot model[14]. The predictions achieved good qualitative and quantitative agreement with the experimental data[9]. Further analysis was conducted on the fire behaviour and in particular the fire merging phenomena. The dependency betwwen the key parameters such as flame height, centerline temperature and soot distributions on the mass burning rate was also discussed.

Analysis of Control Rod Drop Accidents for the Canadian SCWR Using Coupled 3-Dimensional Neutron Kinetics and Thermal Hydraulics

The Canadian Supercritical Water-cooled Reactor (SCWR), a GEN IV reactor design, is a hybrid design of the well-established CANDU™ and Boiling Water Reactor with water above its thermodynamic critical point. Given the batch fueled design, control rods are used to manage the reactivity throughout the fuel cycle. This paper examines the consequences of a control rod drop accident (CRDA) for the Canadian SCWR. The asymmetry generated by the dropped rod requires an accurate 3-dimensional neutron kinetics calculation coupled to a detailed thermal-hydraulic model. Before simulating the CRDAs, the proper implementation of the 3D reactivity feedback was verified and various sensitivity studies were performed. This work demonstrates that the proposed safety systems for the SCWR core are capable of terminating the CRDA sequence prior to exceeding maximum sheath and centerline temperatures. In one instance involving a rod on the periphery of the core, the proposed trip setpoint (115% FP) was not exceeded and a new steady state was reached. Therefore it is recommended that the design also include provisions for a high-log rate and/or local Neutron Overpower Protection (NOP) trips, similar to existing CANDU designs such that reactor shutdown can be assured for such spatial anomalies.

Experimental Study on Flame Geometry along the Inclined Surface with and without Sidewalls by Using a Gas Burner

Abstract In this paper, a series of experiments was conducted by using a gas burner to characterize the flame geometry under the inclined surface condition and trench configuration. The inclination angle was systematically varied from 0° to 26°. The centerline temperature distribution of the inclined surface was measured and the flame geometry parameters were obtained by the post-processing of the side-view images. Results show that the flame tilt angle appears a linear decrease with the increase of the inclination angle for both the inclined surface and trench configuration experiments, and decreases faster for the trench configuration. The flame length shows a non-monotonic variation with the inclination angle and a transformation process of flame from the plume-type to attachment type is observed. There is no significant effect of the aspect ratio on the flame geometry parameters. The flame attachment length fluctuated with time was obtained. A variable-interval time-average (VITA) method was used to determine the level-crossing rate and the peak frequency location. The peak frequency location has a linear relationship with the horizontal flame length. The flame attachment length and the centerline temperature increase sharply from 15° to 20° under the inclined surface condition, indicating the occurrence of flame attachment.

Multi-Layer Cylindrical Flame Model for Predicting Radiant Heat Flux from Pool Fire

Pool fires are often reported to induce a series of domino accidents in the process of the storage and transportation of chemical fuels. The primary mechanism for this severe process is the thermal radiation from the pool fire that damages both people and facilities nearby. In this paper, a multi-layer cylindrical flame model is proposed to predict the radiant heat flux field of pool fire, in which the cylindrical flame is divided into multi small cylinders with the same height and different surface emissive powers. The surface emissive power correlation of each small cylinder is developed by considering the variation of the centerline flame temperature and flame emissivity along the axial direction. The atmospheric transmissivity to the thermal radiation is also considered for the new radiation model. Analysis shows that the centerline temperature and each layer height (defined as each small cylinder height) affects the new model prediction to significant and little extent, respectively. Compared with the experimental data, point source model and single cylindrical flame model (e.g. Shokri-Beyler model, Mudan model and classical solid flame model), the proposed new model is more competent to predict radiant heat flux from pool fires.

Predicting heat fluxes received by horizontal targets from two buoyant turbulent diffusion flames of propane burning in still air

An analytical method to estimate the heat fluxes received by horizontal targets from two buoyant turbulent diffusion flames was proposed. Two identical square gas burners with side length of 15 cm were used as the fire sources with propane burning in still air. The heat release rate (HRR) and burner edge spacing were changed in experiments. Heat fluxes received by four external horizontal targets were measured. In cases with one burner or two burners with zero spacing, there is one single flame and the vertical centerline temperature distribution were divided into four zones including core zone, constant zone, intermittent flame zone and plume zone. Based on the established piecewise function for predicting the flame temperature, the cuboid flame model with hierarchical temperatures was proposed to determine the flame emissivity, the mean flame temperature of the model and the corresponding blackbody emissive power. The results showed that when the HRR of single flame ranges from 10.8 kW to 64.8 kW, the flame emissivity of 15 cm square burner ranges from 0.125 to 0.387, and the absorption coefficient ranges from 0.99 m−1 to 3.62 m−1. At a given HRR, the flame emissivities of two burners with zero spacing and infinite spacing are nearly identical, suggesting that the influence of spacing on flame emissivity is marginal. For two burners with spacing higher than zero, by assuming that the flame radiative fraction of propane is 0.3 and the flame emissivity is equal to that of the single flame, the flame radiative heat fluxes received by external targets are calculated by modeling the flame shapes as two right or tilted cuboids. The comparison validates that the calculations using the proposed cuboid models for both one and two flames agree well with the experimental results.

Finite-rate chemistry modelling of non-conventional combustion regimes

The present work deals with the numerical simulation of Adelaide Jet in Hot Co-flow burner under Moderate or Intense Low oxygen Dilution (MILD) conditions, using the Partially Stirred Reactor (PaSR) model for turbulence-chemistry interactions. The PaSR model assumes that reactions are confined in specific regions of the computational cells, whose mass fractions depend both on the mixing and the chemical time scales. Therefore, the appropriate choice of mixing and chemical time scales becomes crucial to ensure the predictivity of the numerical simulations. Results show that the most appropriate choice for the evaluation of the mixing time scale in MILD regime consists in using the geometric mean of the Kolmogorov and the integral mixing time, rather than Kolmogorov or integral scales. This is supported by the validation of the numerical results against experimental profiles of temperature, major and minor species mass fractions. Moreover, the identification of the key species in the oxidation process allows to determine a chemical time scale that improves the prediction of centerline and upstream temperature predictions, compared to the results obtained by including all species in the evaluation of the chemical scale.

Numerical investigation of heat transfer in parallel channels with water at supercritical pressure

Thermal phenomena such as heat transfer enhancement, heat transfer deterioration, and flow instability observed at supercritical pressures as a result of fluid property variations have the potential to affect the safety of design and operation of Supercritical Water-cooled Reactor SCWR, and also challenge the capabilities of both heat transfer correlations and Computational Fluid Dynamics CFD physical models. These phenomena observed at supercritical pressures need to be thoroughly investigated.An experimental study was carried out by Xi to investigate flow instability in parallel channels at supercritical pressures under different mass flow rates, pressures, and axial power shapes. Experimental data on flow instability at inlet of the heated channels were obtained but no heat transfer data along the axial length was obtained. This numerical study used 3D numerical tool STAR-CCM+ to investigate heat transfer at supercritical pressures along the axial lengths of the parallel channels with water ahead of experimental data. Homogeneous axial power shape HAPS was adopted and the heating powers adopted in this work were below the experimental threshold heating powers obtained for HAPS by Xi. The results show that the Fluid Centre-line Temperature FCLT increased linearly below and above the PCT region, but flattened at the PCT region for all the system parameters considered. The inlet temperature, heating power, pressure, gravity and mass flow rate have effects on WT (wall temperature) values in the NHT (normal heat transfer), EHT (enhanced heat transfer), DHT (deteriorated heat transfer) and recovery from DHT regions. While variation of all other system parameters in the EHT and PCT regions showed no significant difference in the WT and FCLT values respectively, the WT and FCLT values respectively increased with pressure in these regions. For most of the system parameters considered, the FCLT and WT values obtained in the two channels were nearly the same. The numerical study was not quantitatively compared with experimental data along the axial lengths of the parallel channels, but it was observed that the numerical tool STAR-CCM+ adopted was able to capture the trends for NHT, EHT, DHT and recovery from DHT regions. The heating powers used for the various simulations were below the experimentally observed threshold heating powers, but heat transfer deterioration HTD was observed, confirming the previous finding that HTD could occur before the occurrence of unstable behavior at supercritical pressures. For purposes of comparing the results of numerical simulations with experimental data, the heat transfer data on temperature oscillations obtained at the outlet of the heated channels and instability boundary results obtained at the inlet of the heated channels were compared. The numerical results obtained quite well agree with the experimental data. This work calls for provision of experimental data on heat transfer in parallel channels at supercritical pressures for validation of similar numerical studies.

Centreline and cross-glacier air temperature variability on an Alpine glacier: assessing temperature distribution methods and their influence on melt model calculations

ABSTRACTThe spatio-temporal distribution of air temperature over mountain glaciers can demonstrate complex patterns, yet it is often represented simplistically using linear vertical temperature gradients (VTGs) extrapolated from off-glacier locations. We analyse a network of centreline and lateral air temperature observations at Tsanteleina Glacier, Italy, during summer 2015. On average, VTGs are steep (<−0.0065 °C m−1), but they are shallow under warm ambient conditions when the correlation between air temperature and elevation becomes weaker. Published along-flowline temperature distribution methods explain centreline observations well, including warming on the lower glacier tongue, but cannot estimate lateral temperature variability. Application of temperature distribution methods improves simulation of melt rates (RMSE) in an energy-balance model by up to 36% compared to the environmental lapse rate extrapolated from an off-glacier station. However, results suggest that model parameters are not easily transferable to glaciers with a small fetch without recalibration. Such methods have potential to improve estimates of temperature across a glacier, but their parameter transferability should be further linked to the glacier and atmospheric characteristics. Furthermore, ‘cold spots’, which can be >2°C cooler than expected for their elevation, whose occurrence is not predicted by the temperature distribution models, are identified at one-quarter of the measurement sites.

Sensitivity analysis of VERA-CS and FRAPCON coupling in a multiphysics environment

A demonstration and description of the LOCA Toolkit for US light water reactors (LOTUS) is presented. Through LOTUS, the core simulator VERA-CS developed by CASL is coupled with the fuel performance code FRAPCON. The coupling is performed with consistent uncertainty propagation with all model inconsistencies being well-documented. Monte Carlo sampling is performed on a single 17×17 fuel assembly with a three cycle depletion case. Both uncertainty quantification (UQ) and sensitivity analysis (SA) are used at multiple states within the simulation to elucidate the behavior of minimum departure from nucleate boiling ratio (MDNBR), maximum fuel centerline temperature (MFCT), and gap conductance at peak power (GCPP). The SA metrics used are the Pearson correlation coefficient, Sobol sensitivity indices, and the density-based, delta moment independent measures. Results for MDNBR show consistency among all SA measures, as well for all states throughout the fuel lifecycle. MFCT results contain consistent rankings between SA measures, but show differences throughout the lifecycle. GCPP exhibits predominantly linear relations at low and high burnup, but highly nonlinear relations at intermediate burnup due to abrupt shifts between models. Such behavior is largely undetectable to traditional regression or variance-based methods and demonstrates the utility of density-based methods.

Experimental Study of Combustion Characteristics of Circular Ring Thin-Layer Pool Fire

For clarifying the combustion behavior of circular ring thin-layer pool fire, a series of experiments with varying pool diameters were carried out. The equivalent pool area of 0.071 m^2 and an initial n-heptane thickness of 10 mm were fixed. Electronic balance, digital camera and K-type thermocouples were used respectively to measure burning rate, flame height as well as centerline temperature. The results show that more burning stages can appear with the increase of the inner and outer diameters of circular ring pool. Fire merging can occur at any one of initial growth, quasi-steady burning with surface boiling, transition to bulk boiling and bulk boiling burning stages, and moreover the maximum burning rate of fire merging is about 3.5 times the one of the ordinary pool fire with same area. The core hollow region plays an important effect in decreasing the burning rate, flame height and fire merging time etc. The evolutions of the characteristic parameters e.g. burning rate, flame height and centerline ...

Sensitivity and uncertainty analysis for ULOF of PGSFR using PAPIRUS

In this research, sensitivity and uncertainty analyses for 23 parameters were performed for unprotected loss of flow (ULOF) for the prototype Gen-IV sodium-cooled fast reactor (PGSFR) by using the parallel computing platform integrated for uncertainty and sensitivity analysis (PAPIRUS). Based on the development of the phenomena and model identification and ranking table (PIRT), the relative importance of the parameters was confirmed through the sensitivity analysis. The objective of the global uncertainty analysis is to evaluate all safety parameters of the system in the combined phase space formed by the parameters and dependent variables. The uncertainty propagation was performed by mapping the uncertainty bands of the model parameters through the MARS-LMR to determine the distributions for the fuel centerline, cladding, and coolant temperatures. The results show that the uncertainty bands of the temperatures are below the melting point.

Comparative analysis of different fidelity fuel performance models for fuel temperature predictions

Thermal-hydraulics subchannel models have proven to give an acceptable compromise between modeling fidelity and computational efficiency in coupled multi-physics steady state, depletion, and transient calculations. The accuracy in modeling both gas-gap conductance and fuel thermal conductivity is of significant importance for fuel temperature prediction, which, in turn, is crucial for calculation of Doppler feedback on power. A comparative analysis of fuel performance models of different fidelity was performed using the sub-channel code CTF, and the higher fidelity fuel performance codes FRAPCON and BISON. The purpose of this study was to ascertain the predictive accuracy of the informed fuel rod model in CTF, thus the potential to inform this model using data from higher fidelity fuel performance models. Excellent agreement was found between CTF and FRAPCON, and between CTF and BISON with respect to inside clad temperature as well as to fuel surface and fuel centerline temperatures when the CTF gap conductance was set to the BISON and FRAPCON calculated gap conductance values. With respect to the CTF and FRAPCON comparison, the maximum temperature difference between the two codes for a given power level and burnup value was below 2 degree Kelvin for clad inner surface and fuel surface temperature. For fuel centerline temperature, the maximum temperature difference was found to be below 7 degree Kelvin at the highest power level and burnup value. Similarly, the CTF and BISON comparison resulted in maximum temperature differences less than 5 degree Kelvin for the fuel centerline temperature. These results demonstrate that, if the gap conductance, dimensions, and radial power distribution is correctly set in CTF, the CTF-predicted rod temperature distribution will match closely with higher fidelity tools and licensed industry level fuel performance codes for normal operating conditions.

A numerical study on combustion and emission characteristics of premixed hydrogen air flames

Main challenges for micro power generators that utilize combustion process for energy production are inadequate residence time, destructive radical wall interactions and intensified heat loss which are mainly rooted from size limitation of such devices. To achieve high and uniform energy output, and bring in a solution to these challenges in an environment friendly manner without any kind of fundamental modification, effect of equivalence ratio on combustion and emission behavior of premixed hydrogen/air flames is numerically investigated in this study. For this purpose, an experimentally tested micro cylindrical combustor model is constructed and premixed hydrogen/air combustion in this model is simulated by varying equivalence ratio between 0.5 and 1.2 to find an optimal equivalence ratio with respect to drawbacks of micro power generators. Combustion and turbulence models implemented in this study are Eddy Dissipation Concept and Standard k-ε models, respectively. A detailed hydrogen/air reaction mechanism which consists of 9 species and 19 steps is employed to accurately gain insight into combustion process. Simulation results show that as the equivalence ratio decreases; centerline temperature distribution gets a lower value and the place where chemical reactions take place moves downstream. The most uniform temperature distribution is achieved between 0.8 and 1.0 equivalence ratios. The highest NOx formation is at 0.9 equivalence ratio and its mass fraction decreases sharply when the equivalence ratio reduces from 0.9 to 0.5.

TEM characterization of irradiated U-7Mo/Mg dispersion fuel

This paper presents the results of transmission electron microscopy (TEM) characterization on neutron-irradiated samples taken from the low-flux and high-flux sides of the same fuel plate with U-7Mo fuel particles dispersed in Mg matrix with aluminum alloy Al6061 as cladding material that was irradiated edge-on to the core in the Advanced Test Reactor. The corresponding local fission density and fission rate of the fuel particles and the average fuel-plate centerline temperature for the low-flux and high-flux samples are estimated to be 3.7 × 1021 f/cm3, 7.4 × 1014 f/cm3/s and 123 °C, and 5.5 × 1021 f/cm3, 11.0 × 1014 f/cm3/s and 158 °C, respectively. Complex interaction layers developed at the Al-Mg interface, consisting of Al3Mg2 and Al12Mg17 along with precipitates of MgO, Mg2Si and FeAl5.3. No interaction between Mg matrix and U-Mo fuel particle was identified. For the U-Mo fuel particles, at low fission density, small elongated bubbles wrapped around the clean areas with a fission gas bubble superlattice, which suggests that bubble coalescence is an important mechanism for converting the fission gas bubble superlattice to large bubbles. At high fission density, no bubbles or porosity were observed in the Mg matrix, and pockets of residual fission gas bubble superlattice were observed in the U-Mo fuel particle interior.

Effect of micro combustor geometry on combustion and emission behavior of premixed hydrogen/air flames

In this study, effect of micro combustor geometry on combustion and emission behavior of premixed hydrogen/air mixtures is numerically investigated. An experimentally tested micro combustor geometry is varied by establishing a cavity or a backward facing step or micro channels inside the combustor. Considering effect of combustor geometry on the amount of heat transferred through wall based on outer wall and combustor centerline temperature distributions, combustion behavior is analyzed. Emission behavior is examined by means of mixing conditions, combustion efficiency and maximum temperature value which are highly bound to geometric properties of a micro combustor. Turbulence model used in this study is Renormalization Group k-ε. For turbulence chemistry interaction, Eddy Dissipation Concept model is used. Multistep combustion reaction scheme includes 9 species and 19 steps. Numerical results obtained from this study are validated with published experimental data. Results of this study revealed that combustion in such combustors can be improved by means of quality of mixing process, residence time, combustor centerline and outer wall temperature distributions, conversion rate of input chemical energy to utilizable heat and emanated NOx levels from combustor outlet with proposed geometric variations.

Determination of the interfacial heat transfer coefficient between forced air and sand at Reynold’s numbers relevant to smouldering combustion

Heat transfer between flowing air and a fixed sand bed at low Reynold’s number (i.e., Re<30) is central to numerous natural and applied processes, including smouldering combustion. The most widely used correlation for the heat transfer coefficient (hsg) predicts Nusselt numbers so high, it effectively presumes local thermal equilibrium for these systems; an assumption that has never been tested. In this work, twelve column experiments combined with numerical modelling quantify hsg across a range of relevant sand grain sizes (0.125<dp<2.000mm) and air flow rates (0.5<Re<31). All of the sand properties were determined independently, with only hsg determined via inverse modelling. A new empirical correlation for hsg is obtained, Nu=0.001 (Re1.97Pr1/3), which is then validated against two additional experiments. A newly developed criterion for assuming local thermal equilibrium is shown to be violated in all of these convection-dominated experiments and the extent of non-equilibrium between sand and air is quantified. The centerline temperatures are demonstrated to be sensitive not only to hsg but also to a global heat loss coefficient quantified from the experiments in a novel manner. Overall, the new hsg correlation is demonstrated to be reliable for predicting the interphase heat transfer in these systems and its application is expected to be valuable for a wide range of processes including smouldering.

Evaluation of modeling options for in-pellet power distribution and gap gas conductance for accurate fuel temperature predictions

Having the ability to predict fuel temperatures for efficient multi-physics steady state, depletion, and transient calculations with reasonable accuracy without the added burden of prohibitively expensive computation costs has been a major driving force in the nuclear industry. There are several parameters that have an immense impact on fuel surface and centerline temperatures. Sensitivity studies were performed to investigate the impact of gap gas conductance and internal pin power distribution on the fuel temperature predictions. As a result, areas of improvement in the CTF fuel performance model were identified by separating different effects, and analyzing the sensitivity of results to each model improvement. The performed studies demonstrated the importance of modeling internal pellet power distribution for accurate prediction of fuel centerline temperature. Furthermore, a new gap gas conductance modeling option that leverages the fuel performance code FRAPCON was implemented in the fuel rod model of CTF. Gap gas conductance data was pre-computed as a function of linear heat rate and fuel exposure, and was integrated into CTF as part of the new model. Using FRAPCON as a reference solution, the new FRAPCON-informed gap conductance model of CTF was found to calculate results within 2 degrees Kelvin of FRAPCON predictions with respect to fuel surface temperature. This study indicated the feasibility of developing an efficient framework for informing the low fidelity fuel rod models of thermal-hydraulic codes, in this case CTF, with more accurate pre-computed values by leveraging high fidelity fuel performance codes such as FRAPCON. CTF was able to utilize this tabulated data provided by the FRAPCON fuel performance code as well as to include the above mentioned improvements in each axial node of a given rod to provide a full three-dimensional representation.

Neutronics and thermal hydraulic analysis of TRIGA Mark II reactor using MCNPX and COOLOD-N2 computer code

The neutronic analysis of TRIGA Mark II reactor has been performed. A detailed model of the reactor core was conducted including standard fuel elements, fuel follower control rods, and irradiation devices. As the approach to safety nuclear design are based on determining the criticality (keff), reactivity worth, reactivity excess, hot rod power factor and power peaking of the reactor, the MCNPX code had been used to calculate the nuclear parameters for different core configuration designs. The thermal-hydraulic model has been developed using COOLOD-N2 for steady state, using the nuclear parameters and power distribution results from MCNPX calculation. The objective of the thermal-hydraulic model is to determine the thermal safety margin and to ensure that the fuel integrity is maintained during steady state as well as during abnormal condition at full power. The hot channel fuel centerline temperature, fuel surface temperature, cladding surface temperature, the departure from nucleate boiling (DNB) and DNB ratio were determined. The good agreement between experimental data and simulation concerning reactor criticality proves the reliability of the methodology of analysis from neutronic and thermal hydraulic perspective.

Multiphysics modeling of novel UO2-BeO sandwich fuel performance in a light water reactor

The relatively poor thermal conductivity of the UO2 fuel is a major challenge for optimizing reactor operation and safety performance despite its widespread use in the majority of power reactors. The already low thermal conductivity further degrades with burnup due to accumulation of defects, fission product precipitates and fission gas bubbles. The high thermal stresses cause significant pellet cracking, leading to more pellet expansion and causing pellet cladding interaction and the release of fission product gases. Mitigation of these phenomena is currently accomplished by limiting operating power and ramp rates at high burnup. This study presents a novel design of the fuel pellet. The pellet was a combination UO2 fuel and ceramic BeO, and three types of geometry were proposed to mitigate the thermal stress. The corresponding fuel performances were compared based on the modified version of our previously developed CAMPUS code. The fuel pellets with BeO inner or middle layers in the radial direction were found to greatly decrease fuel centerline temperature, and mitigate the fuel and cladding mechanical interaction by delaying the gap closure time. So, the corresponding fuel performance and reactor safety would be improved. The fabrication cost of these two types of fuel pellets would also be decreased significantly compared to the UO2-BeO composite fuel due to the simplicity of the pellet design.

Irradiated microstructure of U-10Mo monolithic fuel plate at very high fission density

Monolithic U-10Mo alloy fuel plates with Al-6061 cladding are being developed for use in research and test reactors as low enrichment fuel (<20% U-235 enrichment) as a result of its high uranium loading capacity compared to that of U-7Mo dispersion fuel. These fuel plates contain a Zr diffusion barrier between the U-10Mo fuel and Al-6061 cladding that suppresses the interaction between the U-Mo fuel foil and Al alloy cladding that is known to be problematic under irradiation. Different methods have been employed to fabricate monolithic fuel plates, including hot-rolling with no cold-rolling. L1P09T is a hot-rolled fuel plate irradiated to high fission density in the RERTR-9B experiment. This paper discusses the TEM characterization results for this U-10Mo/Zr/Al6061 monolithic fuel plate (∼59% U-235 enrichment) irradiated in Advanced Test Reactor at Idaho National Laboratory with an unprecedented high local fission density of 9.8E+21 fissions/cm3. The calculated fuel foil centerline temperature at the beginning of life and the end of life is 141 and 194 °C, respectively. TEM lamellas were prepared using focus ion beam lift-out technique. The estimated U-Mo fuel swelling, based on the fuel foil thickness change from SEM, is approximately 76%. Large bubbles (>1 μm) are distributed evenly in U-Mo and interlink of these bubbles is evident. The average size of subdivided grains at this fission density appears similar to that at 5.2E+21 fissions/cm3. The measured average Mo and Zr content in the fuel matrix is ∼30 at% and ∼7 at%, respectively, in general agreement with the calculated Mo and Zr from fission density.