Validation of the ADVANTG code on the ICSBEP Skyshine Benchmark
Domen Kotnik, Bor Kos, Luka Snoj Reactor Physics Division, Jozef Stefan Institute
Jamova cesta 39 1000, Ljubljana, Slovenia
domenk@ijs.si, bor.kos@ijs.si, luka.snoj@ijs.si
ABSTRACT
ADVANTG, Automated Variance Reduction Generator, is a code developed by the Oak Ridge National Laboratory (ORNL). Its aim is to automate the process of generating variance reduction parameters for fixed source MCNP calculations, which consequently accelerate the simulations in terms of the required CPU time.
ADVANTG’s reliability and consistent performance was tested on a computationally demanding benchmark, i.e. the skyshine benchmark experiment from the ICSBEP handbook where neutron and photon scattering in air above the open operating reactor is simulated. The speed-up factors or the increases in relative efficiency of up to 30000 and 1400 were achieved for neutrons and photons, respectively.
1 INTRODUCTION
Large and complex real-world problems, i.e. deep penetration/shielding or large radiation streaming problems, are challenging to solve using stochastic Monte Carlo particle transport codes [1]. To get statistically relevant results often large number of simulated histories are required, resulting in impractically high CPU time. The recently released hybrid code ADVANTG [2] utilizes the physical property of the deterministically calculated adjoint flux as an importance function to generate variance reduction parameters. By combining deterministic solvers and state of the art Monte Carlo (MC) particle transport codes, so called Hybrid codes enable simulations of a wide range of complex neutral particle transport simulations, which were not achievable with “analog” MC transport codes. ADVANTG was released in 2015 and has not been verified on many benchmark experiments by impartial revivers outside of ORNL.
In our previous research, ADVANTG has been tested on a shielding benchmark (ALARM-CF-AIR-LAB-001, i.e. the neutron flux in a concrete labyrinth [3]) and has proven to be a powerful tool for acceleration of MC simulations in term of required CPU time.
The purpose of this paper is to validate the use of ADVANTG and its variance reduction effectiveness on the ICSBEP (International Criticality Safety Benchmark Evaluation Project) skyshine benchmark with neutron and photon radiation scattering in air above the open operating reactor, which was published under ICSBEP identifier ALARM-REAC-AIR-SKY- 001 [4]. An estimation of the calculation speed-up factors due to the use of ADVANTG and validity of results (neutron/photon spectra and dose rates) were investigated by comparisons to the long analog simulations and measurements.
2 COMPUTATIONAL METHOD: ADVANTG HYBRID CODE
Hybrid methods for neutral particle transport combine the positive aspects of MC and deterministic methods. ADVANTG is a code that automatically generates variance reduction parameters for photon/neutron transport problems defined in the MCNP input file. Energy- and space-dependent mesh-based weight windows, and a biased source distribution are generated by ADVANTG using the 3D discrete ordinates solution of the adjoint transport equation.
Relation between forward and adjoint transport operator is shown in Eq. (1):
〈Ψ , Ψ〉 〈Ψ, Ψ 〉 (1)
where Ψ is angular flux, H the transport operator, and Ψ and their adjoint counterparts. The basic concept of accelerating the tally convergence in a MC simulation using ADVANTG is based on generating effective variance reduction parameters, more specifically weight-window parameters. ADVANTG determined weight windows are based on the Consistent Adjoint Driven Importance Sampling (CADIS) [2] method. The relation between statistical weight of particles and adjoint flux is given with Eq. (2) bellow
Ψ (2)
where is proportional to the inverse of the adjoint flux, R is referred to as a response or quantity of interest and , , the phase-space of position vector, energy and solid angle.
Detailed description and additional equations are described in the ADVANTG manual [2].
The primary MCNP input file is modified by added source definition biasing based on the direct and adjoint deterministic flux calculation. A card that enables the reading of weight windows from a file is added to the original input file with additional parameters.
3 EXPERIMENT
The studied experiment was performed in 1997 near Semipalatinsk (Russia) at the RA research reactor, which is a part of the “Baikal-1” unique complex of research reactors belonging to the Kurchatov Institute of Atomic Energy in the Kazakhstan National Nuclear Centre (IAE NNC RK). The aim of the experiment was to obtain experimental benchmark data for validation of the computer codes that are used to calculate the radiation safety of the population located near the nuclear power plants. In the experiment, the source of radiation was the RA research reactor with nominal power of 300 kW, which was able to emit a high-intensity flux of neutrons and photons into the atmosphere by removing the upper shielding block. The reactor’s cooling system was designed in such a way that compressed atmospheric air was able to provide sufficient cooling for the reactor at 300 kW. The following physical quantities flux, dose rates, energy and spatial distribution, of neutron and photon fluxes were measured at various distances from the reactor axis (50 m – 1000 m) at the height of 100 cm above ground level by a different set of spectrometric instruments, i.e. 1H spectrometer, 3He spectrometer, scintillation spectrometer with a stilbene crystal, multisphere spectrometer, sets of threshold and resonance detectors. The experiment was performed at a reduced power level of the reactor and the results were then normalised to the rated reactor power of 300 kW.
The schematic representation of the RA reactor with overall experimental configuration is shown in Figure 1. The reactor can be modelled as a cylinder of approximately 70 cm height and 70 cm diameter located on a concrete base. The reactor core was roughly 31 cm in diameter/height and contained 37 fuel assemblies (FA). Uranium, with enrichment of 90 %
235U, was used as reactor fuel and was encapsulated. Beryllium reflector with thickness of 10.2 cm, a 1.6 cm steel vessel and an additional graphite reflector with thickness of 18 cm were used for lateral reflection and radiation shielding. Heavy serpentine concrete with thickness of 110 cm – 140 cm was used as biological shielding and was arranged around the reactor core and reflectors. Additional water shielding (two ring-shaped steel tanks of water) were placed inside the reactor hall with the radial thickness of 34 cm and 90 cm. Last but not least, a steel bell-shaped structure, with thickness of 35 cm, was placed around the biological shielding.
Figure 1: Schematic representation of the RA research reactor (top) and configuration of the experiment showing on-site measurement positions (bottom). (not to scale)
The aim of the experiments was to firstly provide a detailed study of the spectra of neutrons/photons scattered in air and secondly, to obtain benchmark quality data for validation of the computer codes used for estimation of the radiation and ecological safety in close proximity to nuclear power plants.
Detailed information about measurement procedures, spectrometric detectors, full description of the experimental configuration, as well as the benchmark model specifications are thoroughly described in the ICSBEP handbook [4], only the main information is provided in the paper.
4 CALCULATIONS
The calculations were performed using the MCNP5 version 1.60 with the ENDF/B-VII library and the ADVANTG version 3.0.2. The radiation source in the model was evenly distributed along the reactor fuel assemblies and was characterized with the Watt fission spectrum where the default parameters were used. In order to get the statistically relevant results in reasonable time, radiation detectors in the model are modelled as spheres with radius 10 m, located in the air 10 m above ground level. With this modification, mean values remained within 1 statistical uncertainty, but the computational time for analog MCNP calculation with relevant results was drastically decreased.
In this particular case, the energy structure was well described by 27n19g library, a general shielding library distributed with ADVANTG based on ENDBF/B-VII.0 data evaluation with low memory requirements. The mesh was defined in such a way to cover all the major neutron pathways with around 3 million voxels. The number of Pn order (the degree of scattering anisotropy modeled) and azimuthal angles (Sn angular approximation) were unchanged and stayed at default values, 3 and 4 respectively. In order to speed up the calculations, for all detector positions at once, all measurement positions were defined as the response of interest for the FW-CADIS calculation (method for determining multiple tally or global variance reduction parameters). The time required for the ADVANTG calculation never exceeded 10 % of the total computational time (ADVANTG + MCNP).
4.1 Results
The total forward and adjoint neutron fluences are shown in Figure 2. Due to the size of the problem, the fluence values in air decrease for around 8 orders of magnitude through air from the reactor core. Values of the adjoint fluence can be interpreted as an importance factor for neutrons.
Additionally, a contributon field, shown in Figure 3, was examined in order to check that optimal weight windows were produced. High values of this field can be understood as an indication of the major geometrical neutron/photon pathways between the source and tallies. It is calculated by ADVANTG through multiplication of the forward and the adjoint fluences.
Figure 2: The Denovo calculated forward (left) and adjoint (right) neutron fluence in the XZ-cross section of the skyshine experiment for 11 on-site measurement positions (tallies) at height 10 m above ground level.
Figure 3: A scalar approximation of the contributon field in the XZ-cross section of the skyshine experiment for 11 on-site measurement positions (tallies) at height 10 m above ground level.
The calculated thermal neutron flux is consistently 3.8 to 4.6 times higher than measured values. Nevertheless, contribution of the thermal neutron flux to the total dose rate is small (less than 6 %). The overestimate is almost distance-independent. A probable reason could be a detector unit with/without cadmium casing, which was assumed to remove all neutrons with energy less than 0.414 eV. Detailed explanation about plausible discrepancies is described in benchmark [4].
To estimate radiation safety of the population residing in close proximity to nuclear power plants, neutron and photon dose rates / and dose rate / 1 ratios are examined and shown in Figure 4 for 11 on-site measurement positions (50 m - 1000 m) at height 10 m above the ground level. To calculate neutron and photon dose rates, flux-to-dose-rate conversion factors taken from the MCNP activation library LLLDOS1 [1] were used. The calculated neutron dose rates were consistent with the experimental values. The photon dose rates were 3 times underpredicted at smaller distances and then better matching at distant measurement positions, when the contribution of the secondary photon radiation to total dose rate from the ground becomes prevailing (60 % - 80 %). The estimates of the neutron and photon dose rates, at distance 50 m from the reactor, are 0.5 / and 5 / , respectively and then exponentially drop at greater distances.
Figure 4: Neutron (black, red) and photon (blue, dark cyan) dose rates / (left) and dose rate / 1 ratios (right) at height 10 m above ground level for 11 on-site measurement positions due to open RA research reactor at power 300 kW. (Lines connecting the points act as eye guide only)
4.2 Comparison with analog simulation
The primary objective of this article is not to compare the ADVANTG calculated results with the results obtained by the experiments as this kind of comparison would only confirm the accuracy of the MCNP model, which is not relevant for this work. The main purpose of the present work is to validate ADVANTG by checking that the speed up of the MCNP calculations due to ADVANTG-generated variance reduction parameters does not affect the estimates of the tally mean values. This was assessed through comparisons of accelerated simulations with long (10 times longer CPU time) analog MCNP simulations.
Detector response of the ADVANTG-accelerated MCNP simulation has been normalized to the mean values of the long MCNP simulation, shown in Figure 5. This was performed to check that no bias was introduced to the simulation by the use of ADVANTG. For the first 6 measurement positions the mean value of the ADVANTG assisted simulation did not differ from analog simulation for more than 0.4 % and both values have relative statistical uncertainties lower than 0.6 %. For measurement position from 600 m to 1000 m statistical uncertainties increased up to 5 %, exclusively for the analog MCNP calculations, due to the size/complexity of the geometry problem. Nevertheless, mean values remained inside 1 statistical uncertainty. Due to large differences in partial relative errors, error bars due to ADVANTG calculations are presented individually as red.
The convergence of the relative error was also observed through the varying measurement positions and proved to be smooth for all cases.
Figure 5: The normalized value of the neutron dose rates (calculated using MCNP and ADVANTG generated weight windows and then normalized to the long analog MCNP calculation) with 1 sigma statistical uncertainty for 11 different on-site measurement positions. Error bars of ADVANTG calculations are visible as red. (Lines connecting the points act as eye guide only)
4.3 Speed-up of simulations
The figure of merit (FOM), the parameter describing the efficiency of the simulation, is used to test the effectiveness of the variance reduction method. FOM is defined with Eq. (3) as
1
∙ Δ (3)
where T is the simulation CPU time and ΔR the tally relative statistical uncertainty. It can be interpreted as the efficiency factor where a higher value is desired. To estimate the overall speed-ups of the calculations, due to use of ADVANTG, it is useful to define as
(4) where and are FOM values for a variance reduction assisted (ADVANTG + MCNP) and an analog (MCNP) simulation, respectively.
The dependence of the values of neutron/photon dose rates for 11 on-site measurement positions at height 10 m above ground level are presented in Figure 6. An upward trend in relative efficiency from 10 3 ∙ 10 and from 1 1400 can be observed for neutrons and photons, respectively. Variance reduction becomes more and more effective with increase in the distance from the reactor as the number of the simulated particles reaching the tally in analog simulation decreases.
Figure 6: The dependence of the (speed-up) values of neutron/photon dose rates for 11 on-site measurement positions (50 m – 1000 m) for neutrons (black) and photons (blue). (Lines connecting the points act as eye guide only)
5 CONCLUSION
The recently developed hybrid code ADVANTG was tested on a large radiating problem where neutrons and photons scattered in the air near the ground-air interface from the open RA research reactor (300 kW). ADVANTG has proven to be a powerful, easy to use tool for acceleration of Monte Carlo simulations in terms of required CPU time and with relatively low user-time needed to produce effective variance reduction parameters (fraction of a time needed for generation of the Monte Carlo based variance reduction parameters). The speed-up factors or the increases in relative efficiency of up to 1400 or 30000 were achieved for photons and neutrons, respectively.
Experimental values are consistently lower than calculated ones, but more important is the fact that the discrepancies between mean values of ADVANTG assisted and long analog simulations in all cases remained within 1 statistical uncertainty. Therefore ADVANTG did not introduce any bias to the results.
ADVANTG gives excellent results, nevertheless it is still at an early stage of use and has to be validate against many other benchmarks with even more complex geometry.
REFERENCES
[1] X-5 Monte Carlo Team. (2004). MCNP- A General Monte Carlo N. Particle Transport Code, Version 5, LA-UR-03-1987. Los Alamos National Laboratory.
[2] S.W. Mosher, A.M. Bevill, S.R. Johnson, A.M. Ibrahim, C.R. Daily, T.M. Evans, J.C.
Wagner, J.O. Johnson, R.E. Grove. 2013. ADVANTG-An Automated Variance Reduction Parameter Generator. Oak Ridge National Laboratory, Oak Ridge.
[3] Domen Kotnik, Aljaž Čufar, Bor Kos, Luka Snoj "Validation of the ADVANTG Hybrid Code on an ICSBEP Labyrinth Benchmark Experiment", Submitted to Annals of Nuclear Energy, 2017.
[4] O. F. Dikareva, I. A. Kartashev, M. E. Netecha and V. P. Zharkov, Baikal-1 Skyshine Experiment, NEA/NSC/DOC/(95)03/VIII, ALARM-REACAIR-SKY-1, Sep. 30, 2009, revision 1, NEAICSBEP Database
