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This paper examines the accuracy and performance of the RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system for the simulation of a used nuclear fuel (UNF) cask. RAPID is capable of determining eigenvalue, subcritical multiplication, and pin-wise, axially-dependent fission density throughout a UNF cask. We study the...
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... dose calculation has been recently implemented in RAPID and demonstrated in [11]. The average relative difference, weighted on the fission density distribution, amounts to 1.56%, comparable to the statistical uncertainty reported in Table 8. Table 9 shows the computational time requirements for both the methods, demonstrating how a large nuclear sys- tem as the full cask can be simulated in real time with RAPID, with a significant speedup with respect to MCNP. Figure 19 shows RAPID calculated 3-D fission density distribution. ...
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... The combined fission matrix theory can perform high-fidelity and efficient whole-core pin-wise transport calculations. It is validated on the BEAVRS PWR benchmark Walters, 2019, 2020), PSBR TRIGA reactor core (Topham et al., 2020;Rau and Walters, 2020), and UNF spent fuel cask benchmark (Mascolino et al., 2017). However, the promising methodology is mainly used and validated in thermal neutron systems. ...
The combined fission matrix theory is a recently-developed hybrid neutron transport method. It features high efficiency, fidelity, and resolution whole-core transport calculation. The theory is based on the assumption that the fission matrix element a i,j is dominated by the property of the destination cell i. This assumption can be well explained in thermal reactors, and the combined fission matrix method has been validated in a series of thermal neutron system benchmarks. This work examines the feasibility of the combined fission matrix theory in fast reactors. The European Sodium Fast Reactor is used as the numerical benchmark. Compared to the Monte Carlo method, the combined fission matrix theory reports a 64 pcm k eff difference and 8.3% 2D RMS error. The error is much larger than that in thermal reactors, and the correction ratio cannot significantly reduce the material discontinuity error in fast reactors. Overall, the combined fission matrix theory is more suited for thermal reactor transport calculations. Its application in fast reactors needs further developments.
... The RAPID Code System is based on the MRT methodology, and decouples the analysis of a nuclear system into a series of independent stages for which response coefficients are pre-calculated for a wide range of problem-dependent parameters, and then included in a database. For example, for spent fuel systems such as pools [2,3] and casks [4,5], these parameters include fuel burnup, spent fuel decay time, and fuel enrichment, while for nuclear reactor cores these parameters are fuel and moderator temperature, as well as fuel enrichment and burnup [6,7]. The user can then select any combination of parameters within the database range. ...
... This approach eliminates the typical source convergence issues [11] related to the power-iteration technique utilized in the standard eigenvalue Monte Carlo algorithms implemented in codes such as MCNP [12] or Serpent 2 [13]. In addition, the FM coefficients in multiplying systems have been shown to be highly localized [4,14]. This means that, when a region of the system changes, e.g., due to the insertion of a CR, the FM coefficients are only affected in the neighboring regions. ...
As part of a collaboration between Virginia Tech and the Jožef Stefan Institute (JSI) of Slovenia the Multi-stage Response-function Transport (MRT) code system RAPID has been undergoing an extensive computational and experimental validation campaign using the JSI TRIGA Mark-II reactor. To do so a novel algorithm for treatment of control rods based on the Fission Matrix (FM) method was implemented in RAPID, referred to as FM-CRd. In this paper, we discuss the methodology and compare RAPID predictions to a set of experimental data collected in February 2019 utilizing large in-core fission chambers during rod-swap experiments at the JSI TRIGA reactor. The FM-CRd algorithm is shown to be able to very accurately account for the neutron source redistribution, calculating detector responses within around 1% of the measurements throughout the experiment.
... The fission matrix based neutronics code RAPID has been originally developed for spent fuel system (Mascolino et al., 2017;Roskoff et al., 2017), and recently used on reactor core modeling (Walters et al., 2015;Walters et al., 2018;Walters, 2017). It is a stochastic-deterministic hybrid code, featuring an accuracy similar to Monte Carlo calculations while preserving the fast calculation speed of deterministic codes. ...
... The fission matrix based neutronics code RAPID has been originally developed for spent fuel system (Mascolino et al., 2017;Roskoff et al., 2017), and recently used on reactor core modeling (Walters et al., 2015;Walters et al., 2018;Walters, 2017). It is a stochastic-deterministic hybrid code, featuring an accuracy similar to Monte Carlo calculations while preserving the fast calculation speed of deterministic codes. ...
The RAPID hybrid transport code, based on the fission matrix method, has been developed and previously proven successful on BEAVRS benchmark at hot-zero-power condition. In this work, it is extended to the BEAVRS model to include fuel and moderator temperature feedback. The bi-linear fission matrix interpolation technique was applied to several artificial fuel and moderator temperature distributions. For almost all cases, it provides an accurate calculation result with a keff difference smaller than 70 pcm and 2D pin-wise RMS error smaller than 1% compared to Serpent 2 Monte Carlo reference. In order to decrease the number of databases needed, a plane interpolation routine is developed, which de-couples the fuel and moderator temperature. The RAPID calculation with the plane interpolation reports a similar accuracy to that with the bi-linear interpolation. The bi-linear interpolation required 24 database points from Monte Carlo calculations, while the plane interpolation only needed 10. The plane interpolation allows RAPID to prepare fewer databases while preserving a high accuracy.
... Recently, the Real-time Analysis for Particle-transport and In-situ Detection (RAPID) code has been developed for the spent fuel systems and reactor cores (Walters et al., 2018;Mascolino et al., 2017). RAPID is a hybrid stochastic and deterministic code that solves the deterministic fission matrix equations with coefficients generated from Monte Carlo calculations. ...
... The collapsing of the fission matrix from pin-cell to assembly-cell, together with a pin power reconstruction, have been proven accurate and be able to perform a transport calculation on the BEAVRS benchmark at hot-zero-power condition within minutes (Walters et al., 2018). RAPID calculations with the collapsing technique has also been validated on other problems, including different assembly loading pattern of BEAVRS (He and Walters, 2019), spent fuel storage system (Mascolino et al., 2017), BEAVRS benchmark with different insertions of control rods (He and Walters, 2020), as well as BEAVRS model with a heterogeneous temperature distribution. ...
... It should be noted that this fission matrix homogenization technique has been previously implemented and successfully used in RAPID (Walters et al., 2018;Mascolino et al., 2017;He and Walters, 2019), but the effect of different homogenization parameters have not been analyzed. ...
The fission matrix based radiation transport code RAPID is able to perform high fidelity and fast 3D, pin-wise whole core calculations. The code can quickly estimate the system fission matrix by combining pre-calculated database fission matrices, and solving for the system fission matrix provides the multiplication factor and a detailed fission distribution. In this work, RAPID acceleration and numerical techniques will be examined. These are the fission matrix collapsing or homogenization options, choice of the power iteration tolerance and estimation of iterative error. In old RAPID calculations, in order to achieve a fast power iteration convergence of the whole core fission matrix, the pin-wise fission matrix is collapsed into an assembly-wise one following a 2-D pin-wise core slice calculation. In addition to the radial collapsing from pin to assembly, other radial and axial collapsing options are tested to find out the best balance between accuracy and speedup. Applying the fission matrix collapsing technique, RAPID requires at least two eigenvalue calculations. Different tolerances of the 2-D and 3-D power iteration calculations are combined to investigate the convergence. A more sophisticated method to estimate the iterative error is provided to determine the convergence. Overall, a combination of all acceleration techniques speeds up the RAPID calculation on BEAVRS benchmark problem by three times, with only a negligible loss of accuracy.
... RAPID utilizes the Fission Matrix (FM) [1] methodology for solving the Linear Boltzmann Equation (LBE) [3] (both in its critical and subcritical form), and the Detector Response Function (DRF) [4] and adjoint function [3] methodologies for calculation of detector responses. RAPID has been benchmarked using different nuclear systems such as Spent Nuclear Fuel (SNF) pools [1] and casks [5], reactor cores [6], and subcritical facilities [7]. This work is part of a comprehensive benchmarking of the RAPID code system using the experimental data from the Jozef Stefan Institute (JSI) TRIGA Mark-II, and focuses on steady-state reactor conditions. ...
A validation of the RAPID code system using the Jozef Stefan Institute TRIGA Mark-II reactor has been performed. The nature of Fission Matrix coefficients in presence of control rods is discussed and, based on it, the FM-CRd methodology for simulation of control rods is implemented in RAPID and tested. RAPID calculations using FM-CRd are performed to determine keff and fission neutron distribution for core configuration 133 of the ICSBEP handbook with no control rods inserted and with a combination of the control rods. These results are compared with both a reference Serpent Monte Carlo calculation and to experimental data for the "all rods out" case, and with a Serpent calculation for the controlled configuration. The RAPID results are in good agreement with computational and experimental results. The FM-CRd methodology is validated as results are consistent with straightforward FM calculations and have good agreement with Serpent. The FM-CRd allows for significant reduction of the computational requirements for building the Fission Matrix coefficients database required for RAPID calculations, and establishes RAPID as a valuable tool for analysis of TRIGA and other LWR reactors with solid control systems.
... Initially developed for spent fuel pool and cask systems (Mascolino et al., 2017;Roskoff, 2017), RAPID has recently been evaluated for use in reactor core calculations (Walters, 2017). In reactor problems, RAPID performed very well with a uniform core loading but suffered from some errors at the boundaries of dissimilar assembly types. ...
... Initially developed for spent fuel pool and cask systems (Mascolino et al., 2017;Roskoff, 2017), RAPID has recently been evaluated for use in reactor core calculations (Walters, 2017). In reactor problems, RAPID performed very well with a uniform core loading but suffered from some errors at the boundaries of dissimilar assembly types. ...
... It has been shown that the above assumption in RAPID works well with the spent fuel system (Mascolino et al., 2017;Roskoff, 2017). In spent fuel systems, there is a strong absorber between assemblies, which makes the neutron spectrum in an assembly relatively independent of the surrounding assemblies. ...
The recently developed RAPID code uses a unique pre-calculated fission matrix method in order to solve the whole-core eigenvalue problem very quickly and accurately. However, in strongly heterogeneous cores, errors are introduced at the boundary between different assembly types. In this paper, two methods are discussed that uses a set of small, 2D, 2x2 assembly fixed source fission matrix calculations in order to correct the RAPID 3-D whole-core fission matrix. The methods are applied to the BEAVRS benchmark hot zero power case with 1.6%, 2.4%, and 3.1% enriched assemblies with varying amounts of burn-able absorbers. The standard and corrected RAPID methods are compared to a Serpent reference case on this highly heterogeneous core. Compared to the standard, the locally-corrected RAPID drops the 2D RMS pin-wise fission source error from 6.3% to 0.54% (compared to a Serpent RMS uncertainty of 0.09%). The 3D, pin-wise, 100 axial level RMS error drops from 6.6% to 2.2% (Serpent RMS uncertainty 1.9%). The k-eigenvalue difference drops from 157 pcm to 26 pcm (Serpent uncertainty 0.5 pcm). In order to obtain these levels of uncertainty, the Serpent reference required a calculation time of 80 h on 20 cores, compared to a RAPID time of 2.4 min on the same system. Though the RAPID database requires roughly 16 h on 20 cores, it can be used for any other RAPID calculations without performing any new Monte Carlo calculations.
... The RAPID Code System [1], developed based on the MRT methodology [2] with the Fission Matrix (FM) and the adjoint function methodologies, is capable of accurately calculating 3-D detailed fission density distribution, subcritical multiplication factor, criticality eigenvalue, and detector response for a nuclear system in real-time. RAPID achieves accurate solutions, comparable to Monte Carlo, while because of its FM method it does not suffer from the eigenvalue Monte Carlo shortcomings including particles under-sampling, source biasing and cycle-to-cycle correlation [3,4,5,6,7]. Additionally, because of its pre-calculation capability, RAPID can solve complex and large problems in real-time. ...
... Over the past five years, RAPID has been computationally benchmarked against Monte Carlo MCNP [8] calculations of Spent Nuclear Fuel (SNF) pools [9,10] and casks [3]. In this paper, we present the first experimental benchmark using the U.S. Naval Academy Subcritical Reactor (USNA-SCR) facility [11]. ...
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... Recently, however, there has been renewed interest in using pre-calculated fission matrices, and combining and/or interpolating them to the state of interest. This has been done as a function of burnup and cooling time to calculate spent fuel pool/cask criticality[1] [2]; as a function of temperature for molten salt reactor feedback [3]; and has recently been investigated in a 1-D model for temperature feedback in a TRIGA reactor [4]. ...
... Consider that the fission matrix has been calculated for the same system, but under two different conditions (e.g., temperature), denoted as (1) and (2) . If the fission matrix is desired for the system under mixed conditions (e.g., half the system at temperature 1, half at temperature 2), then the elements of the matrix can be estimated by using the value of the matrix that corresponds to the destination cell (i.e., ). ...
... The RAPID code system [1,2] is developed based on the Multi-stage Response function particle Transport (MRT) methodology [3] for real-time neutronics simulations. Currently, RAPID utilizes the Fission Matrix (FM) method [4] for eigenvalue and subcritical multiplication calculations, and adjoint function methodology [5] for detector response calculations. ...
A novel real-time detector response calculation methodology, referred to as Detector Response Function (DRF) methodology, has been developed and incorporated into the RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system. The DRFs are pre-calculated by performing a series of fixed-source Monte Carlo calculations using the CADIS (Consistent Adjoint Driven Importance Sampling) variance reduction technique. These DRFs are in turn used to determine a detector response. The methodology is applied to a 3 He detector placed on the stainless-steel canister outer surface of the GBC-32 Cask benchmark. This paper demonstrates that RAPID's new DRF methodology yields accurate solutions in real time.
The Real-time Analysis for Particle-transport and In-situ Detection (RAPID) Code System, developed based on the Multi-stage Response-function Transport (MRT) methodology, enables real-time simulation of nuclear systems such as reactor cores, spent nuclear fuel pools and casks, and sub-critical facilities. This paper presents the application of a novel fission matrix-based burnup methodology to the well-characterized JSI TRIGA Mark II research reactor. This methodology allows for calculation of nuclear fuel depletion by combination and interpolation of RAPID's burnup dependent fission matrix (FM) coefficients to take into account core changes due to burnup. The methodology is compared to experimentally validated Serpent-2 Monte Carlo depletion calculations. The results show that the burnup methodology for RAPID (bRAPID) implemented into RAPID is capable of accurately calculating the keff burnup changes of the reactor core as the average discrepancies throughout the whole burnup interval are 37 pcm. Furthermore, capability of accurately describing 3D fission source distribution changes with burnup is demonstrated by having less than 1% relative discrepancies compared to Serpent-2. Good agreement is observed for axially and pin-wise dependent fuel burnup and nuclear fuel nuclide composition as a function of burnup. It is demonstrated that bRAPID accurately describes burnup in areas with high gradients of neutron flux (e.g. vicinity of control rods). Observed discrepancies for some isotopes are explained by analyzing the neutron spectrum. This paper presents a powerful depletion calculation tool that is capable of characterization of spent nuclear fuel on the fly while the reactor is in operation.
