Benchmarking of HEU mental annuli critical assemblies with internally reﬂected graphite cylinder

. Three experimental conﬁgurations of critical assemblies, performed in 1963 at the Oak Ridge Critical Experiment Facility, which are assembled using three different diameter HEU annuli (15-9 inches, 15-7 inches and 13-7 inches) metal annuli with internally reﬂected graphite cylinder are evaluated and benchmarked. The experimental uncertainties which are 0.00057, 0.00058 and 0.00057 respectively, and biases to the benchmark models which are − 0 . 00286, − 0 . 00242 and − 0 . 00168 respectively, were determined, and the experimental benchmark k ef f results were obtained for both detailed and simpliﬁed models. The calculation results for both detailed and simpliﬁed models using MCNP6-1.0 and ENDF/B-VII.1 agree well to the benchmark experimental results within difference less than 0.2%. The benchmarking results were accepted for the inclusion of ICSBEP Handbook.


Introduction
An extensive series of delayed critical experiments were performed at the Oak Ridge Critical Experiments Facility (ORCEF), using high enriched uranium (HEU) metal during the 1960s and 1970s in support of criticality safety operations at the Y-12 Plant. These experiments were designed to evaluate the storage, casting, and handling limits of the Y-12 Plant and to provide data for the verification of cross sections and calculation methods utilized in nuclear criticality safety applications.
In this paper another three experimental configurations of critical assemblies, which are internal graphite reflected metal uranium assemblies with three different diameter HEU annuli (15-9 inches, 15-7 inches and 13-7 inches) are taken to evaluate the experimental uncertainty and bias, and to benchmark the detailed and simplified model for further inclusion of ICSBEP Handbook [1]. These experiments can be found in Reference [4] and in their associated logbook [5].
Firstly, the experimental uncertainties were analyzed, then the experimental biases were determined, at last the benchmark models were developed for both detailed and simplified configurations. The calculation results agree to a e-mail: liu express11@yahoo.com the benchmark experimental results within difference less than 0.2% (equivalently less than 3 times of experimental 1 σ uncertainty). The benchmarking results for these three critical configurations were accepted for inclusion of ICSBEP Handbook.

Descriptions of assemblies
These experiments were performed on a vertical assembly machine previously described by Rohrer et al. [6]. The assemblies were coaxial high enriched uranium metal (HEU) annuli with outside diameters varying in two-inch steps from 11 to 15 inches and the inside diameters varying in two-inches steps from 7 to 9 inches, and had only internal graphite cylinder without reflector. The sketch map of vertical cross-section view for case 1 is shown in Fig. 1.
Each assembly comprised of two sections: lower and upper section, of which the lower one was supported on a low-mass support stand and the upper section was mounted on a 0.010-inch-thick stainless steel diaphragm. The radial alignment for each assembly were performed with level to the accuracy of ±0.001 inch. The lower section was raised until it made contact with the diaphragm and actually slightly lifted the upper section of material mounted on the diaphragm and then the reactivity was measured. The reactivity worth of each parts of the support structure was measured by perturbation experiments respectively, then the reactivity of each "clean" assembly was obtained.
The basic information and measured reactivity for the three cases was summarized in Table 1.

Experimental uncertainty analysis
Uncertainties are evaluated using two approaches. Measured data are used where sufficient experimental information is available to analyze the uncertainties.
For the last approach the bounding uncertainties and 1σ uncertainties for each of parameter were determined, and then the perturbations were introduced into MCNP model to calculate the uncertainties respectively. When the change in k e f f between the base case and the perturbed model (single-sided perturbation), or two perturbed models (double-sided perturbation directly comparing an upper and a lower perturbation from the base case), is less than the statistical uncertainty of the Monte Carlo results, the changes in the variable are amplified by scaling factor (SF), if possible. The resulting calculated change is then scaled to a value corresponding to the given uncertainty divided by SF, assuming linearity, which should be adequate for these small changes in k e f f . For double-sided perturbation with scaling factor, this method is equated as following: where k upper and k lower stand for the k e f f of perturbed models with an upper and a lower perturbation from the base model, respectively. Sometimes, to find the effect of one kind of parameter on the k e f f value (which is assumed to be negligible based on evaluator experience), this parameter from several similar parts was perturbed simultaneously and the combination of the uncertainty should be decoded for accounting for this circumstance. This is the case such as diameter, mass of HEU annuli parts for the all three configurations. The uncertainty from experiment, dimensions and displacement, mass, isotopic content and impurities are evaluated respectively and all the uncertainties for the three cases are summarized in Table 2.
The total experimental uncertainties for the three configurations are 0.00057, 0.00058 and 0.00057 respectively, in which the uncertainty from experiment itself accounts for most (more than 70%) contributions, otherwise the uncertainty from dimensions and mass accounts for almost negligible contribution due to high accurate manufacturing process and measuring.

Experimental bias analysis
Bias analysis included the effect of room return and air, temperature, the bias of removing the support structures, homogenization of the HEU annuli and graphite cylinder, and the removal of material impurities.
The same to uncertainty analysis, biases are also evaluated using two approaches. Measured data are used where sufficient experimental information is available to determine the correction. Where experimental data are not available, Monte Carlo calculations were performed using MCNP6-1.0 and ENDF/B-VII.1 neutron cross section libraries by comparing the benchmark models to a model with no simplifications.
Results of all the biases for both the detailed and simplified benchmark model are summarized in Table 3.

Benchmark results
The experiment benchmark k e f f for both detailed and simplified model can be obtained through the above uncertainty and bias analysis and the results are provided in Table 4.
The calculated results for both detailed and simplified benchmark models, using MCNP6-1.0 and ENDF/B-VII.1 neutron cross section libraries, are summarized in Table 5, which agree well to the benchmark experimental results within difference less than 0.2% (equiva lently less than 3 times of experimental 1 σ uncertainty) and accepted for inclusion of ICSBEP Handbook.

Conclusions
Three experimental configurations of critical assemblies, HEU annuli (15-9 inches, 15-7 inches and 13-7 inches) metal annuli with internally reflected graphite cylinder, are evaluated and benchmarked. The experimental uncertainties and biases were determined, and the experimental benchmark k e f f results were obtained for both detailed and simplified model. The calculation results for both detailed and simplified models using MCNP6-1.0 and ENDF/B VII.1 agree well to the benchmark experimental results within difference less than 0.2%. The three configurations are accepted for inclusion of ICSBEP Handbook.