SEARCH · Search NASA
Results for “DDES”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Numerical methods and hypoexponential approximations for gamma distributed delay differential equations
Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.
Using Density-Corrected DFT to Understand Density-Driven and Functional-Dependent Errors in Ab Initio Simulations of the Hydrated Electron
The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.
Effect of Surface Roughness on Dynamic Stall in Pitching Motion
Dynamic stall plays a critical role in determining the performance and stability of a wide range of fluid-dynamics systems in various engineering applications. This unsteady aerodynamic phenomenon is particularly significant for maneuvering aircraft wings, jet aircraft subjected to gust encounters, helicopter rotor blades, and wind turbine blades [1–3]. The prediction of the dynamic stall vortex (DSV) is challenging due to factors such as unsteady aerodynamics, three-dimensional (3-D) effects, turbulence and flow separation, incoming gust, and surface impact effects [4–6]. Hence, advanced computational techniques and modeling approaches in computational fluid dynamics (CFD) would be required to enhance the accuracy and reliability of DSV predictions in dynamic stall scenarios. In the past, Batther and Lee [7] employed delayed detached eddy simulations (DDES) to understand the flow physics associated with the onset of dynamic stall. Their approach demonstrated that DDES achieves results comparable to those obtained from large-eddy simulations at a reduced computational cost. In another study, Khalifa et al. [8] examined the 3-D aspects of dynamic stall on a NACA 0012 airfoil using DES solvers. In conclusion, the findings underlined the superiority of 3-D simulations over two-dimensional approaches, particularly in predicting the lift coefficient values and capturing dynamic stall stages more precisely.
MITR & NBSR DDE Irradiations in BR2 – Fluence in LEU Cladding and Structural Materials
The BR2 nuclear reactor is a material testing reactor (MTR) located in Mol, Belgium, and operated by the Belgian Nuclear Research Centre (SCK CEN) since 1963. The reactor is highly versatile as the number and location of fuel elements and control rods can change significantly from cycle to cycle to accommodate different needs. Argonne National Laboratory (ANL or Argonne) Reactor Conversion (RC) team has collaborated with SCK CEN for over a decade on the conversion of domestic and international research reactors from highly enriched uranium (HEU, ≥20 wt.% of 235 U) to low enriched uranium (LEU, <20 wt.% of 235 U) fuel. The U.S. High-Performance Research Reactor (USHPRR) project within the M3 Reactor Conversion Program aims at converting five U.S. high performance research reactors (MITR, MURR, NBSR, HFIR, and ATR) and one critical facility (ATR-C) to LEU fuel. These USHPRRs still use and regularly refuel with HEU fuel. Each facility has a unique reactor design, operating conditions, and fuel element design to accomplish its mission. The goal of the USHPRR project is to convert the USHPRRs and the critical facility to LEU fuel while maintaining experimental performance and ensuring safe facility operation. The current technical report focuses on two reactors requiring very high-density LEU fuel: the Massachusetts Institute of Technology Reactor (MITR) and the National Bureau of Standards Reactor (NBSR). To support the conversion of these reactors, so-called design demonstration elements (DDE) are planned to be irradiated in the BR2 reactor under conditions similar to the targeted reactors and using a prototypic geometry. In support of this experiment, SCK CEN studied and modeled the DDE irradiations using MCNP6.2 to investigate the feasibility of irradiating the MITR DDE and NBSR DDE in BR2. Argonne reviewed and confirmed the conclusions of this study. Structural analysis is another step toward converting USHPRR to LEU fuel. The objective of the current report is to provide information useful to the structural analysis of the NBSR & MITR DDEs to support its irradiation in BR2. Specifically, the goal is to provide the fast neutron (E>0.1MeV) fluence in the cladding of the fuel plates in BR2 for the whole period of irradiation (8 cycles for MITR DDE and 10 cycles for NBSR DDE). Additionally, fast neutron fluences in the side plates and in the NBSR DDE’s outside plates were calculated and reported. Neutronic calculations were performed using MCNP6.2 on the RTRHPC cluster.
Margin to Onset of Nucleate Boiling studies for MITR and NBSR Design Demonstration Experiments
The United State High Performance Research Reactor (USHPRR) program aims to eliminate more than 200kg of High Enriched Uranium (HEU) from commerce annually by converting five U.S. high-performance research reactors and one associated critical assembly to Low Enriched Uranium (LEU) fuel using a high-density alloy of uranium-10 wt% molybdenum (U-10Mo). The Massachusetts Institute of Technology Reactor (MITR) and the National Bureau of Standards Reactor (NBSR) are two of five research reactors selected for this program. Previous studies have addressed the thermal-hydraulics performance of the fuel Design Demonstration Elements (DDE) for these reactors under conservative assumptions in the Belgian Reactor (BR)-2. This report extends these previous studies by analyzing the margins to Onset of Nucleate Boiling (ONB) for these two DDEs under the conservative conditions used in the previous thermal-hydraulics analyses
High-Order Hybrid RANS-LES Study of NACA0012 Wing Sections
We develop hybrid RANS-LES strategies within Nek5000 for application to airfoil sections at small flight configurations. We present a validation and verification study of $k \space – \space \tau$ SST applied to a NACA 0012 wing section in a pure RANS and in a hybrid RANS-LES setup. The study shows good corroboration with existing experimental and numerical datasets. We also analyze some of the observed discrepancies with the experiments by evaluating the side wall “blocking” effect. We demonstrate that for the hybrid turbulence modeling approach a high-order spectral- element discretization converges faster (i.e., with less resolution) than a representative low-order finite-volume-based approach.