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DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Temporal changes in global soil respiration since 1987

As the second-largest terrestrial carbon (C) flux, soil respiration (R S ) has been stimulated by climate warming. However, the magnitude and dynamics of such stimulations of soil respiration are highly uncertain at the global scale, undermining our confidence in future climate projections. Here, we present an analysis of global R S observations from 1987–2016. R S increased (P < 0.001) at a rate of 27.66 g C m -2 yr -2 (equivalent to 0.161 Pg C yr -2 ) in 1987–1999 globally but became unchanged in 2000–2016, which were related to complex temporal variations of temperature anomalies and soil C stocks. However, global heterotrophic respiration (R h ) derived from microbial decomposition of soil C increased in 1987–2016 (P < 0.001), suggesting accumulated soil C losses. Given the warmest years on records after 2015, our modeling analysis shows a possible resuscitation of global R S rise. This study of naturally occurring shifts in R S over recent decades has provided invaluable insights for designing more effective policies addressing future climate challenges.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code

A passive yaw implementation is developed, validated, and explored for the WEC-Sim, an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01° was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than 1°, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗

NASA NTRS1988

Nondestructive construction error detection in large space structures

Continuum modeling of large space structures is extended to the problem of detecting construction errors in large space structures such as the proposed space station. First-order dynamic sensitivity equations for structures involving eigenfrequencies, modal masses, modal stiffnesses, and modal damping are presented. Matrix equations relating changes in element parameters to dynamic sensitivities are summarized. The sensitivity equations for the entire dynamical system are rearranged as a system of algebraic equations with unknowns of stiffness losses at selected locations. The feasibility of the formulation is numerically demonstrated on a simply-supported Euler-Bernouilli beam with simulated construction defects. The method is next extended to large space structures modelled as equivalent continua with simulated construction defects.

Stubbs, Norris↗

NASA NTRS2017

Semi-analytic preliminary design of low-thrust missions

Using generalized logarithmic spirals to approximate low-thrust trajectories, a new strategy for the design of low-thrust gravity-assist transfers has been developed. Each transfer leg is defined by a semi-analytic model, and its solution is equivalent to a hybrid Lambert’s problem. The method is suitable for approximating both flyby and rendezvous transfer legs. A branch and prune algorithm is used to generate a collection of initial guesses for further optimization. The analytic nature of the low-thrust model simplifies the pruning step, since dynamical and operational constraints (like maximum thrust or total v) can be imposed easily. The solutions obtained with the global search algorithm can be post-processed, filtered, and ranked according to various criteria. This is where the versatility of the method resides, because changing the selection criteria does not require a new search. Selected candidates are then optimized further, in order to generate actual low-thrust orbits. Two mission design examples are presented: an asteroid deflection mission using a kinetic impactor, and a rendezvous mission to Jupiter. These examples are used to analyze the convergence of the optimization stage, in particular how far from the optimal solution the initial guesses are.

Park, Ryan S.↗

NASA NTRS2024

Measurements of Titan’s Stratospheric Winds during the 2009 Equinox with the eSMA

Saturn’s moon Titan possesses stratospheric zonal winds that places it among a sparse class of planetary bodies known to have superrotation in their atmospheres. Few measurements have been made of these speeds in the upper stratosphere, leaving their seasonal variations still not well understood. We examined observations made with the extended Submillimeter Array in 2009 March ( L s = 355°) and 2010 February ( L s = 5°), shortly before and after Titanʼs northern spring equinox. Cassini observations and atmospheric models find equinoctial periods to be especially dynamic. Zonal wind calculations, derived from the Doppler frequency shift of CH 3 CN near 349.4 GHz, yielded speeds of 128 ± 27 m s −1 in 2009 and 209 ± 48 m s −1 in 2010. We estimated the measured emission to originate from vertical altitudes of 336 +112 - 88 km, equivalent to pressures of 3.8 +19.2 -3.4 Pa, commensurate with Titan’s upper stratosphere/lower mesosphere. This suggests a possible increase in zonal speeds during this period. The results are then compared to those from previous Cassini-inferred and direct-interferometric observations of winds, as well as general circulation model simulations, to form a more complete picture of the seasonal cycle of stratospheric zonal winds.

Siobhan Light↗

DOE OSTI2020

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code: Preprint

A passive yaw implementation is developed, validated, and explored for the Wave Energy Converter Simulator (WEC-Sim), an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01 was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than or equal to 1, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗

DOE OSTI2025

Porous Flow Modeling of Axial Gas Redistribution in Fragmented LWR Fuel Rods using MOOSE

Understanding how gas axially redistributes within fragmented fuel pellets is crucial for predicting the behavior of Light Water Reactor (LWR) fuel rods, particularly during transient and accidental scenarios. The time scale of this phenomenon plays a fundamental role in determining the progression and hazard of a Loss Of Coolant Accident (LOCA), especially when high burn-up fuel in a severe state of fragmentation is involved. Here, this study presents a Computational Fluid Dynamics (CFD) model developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE) to predict the time-scale of plenum depressurization in Light-Water Reactor (LWR) fuel rods driven by axial gas transport through fragmented pellets. The model examines the effects of incorporating non-linearities in the friction term by comparing the results with experimental data. The experiment employed surrogate fuel rods containing pellets subjected to mechanical and/or thermal loadings to simulate various severity of cracking, and aimed at studying the influence of fuel conditions on axial gas redistribution. The results of this analysis indicate that under certain flow regime conditions - determined by the value of an equivalent Reynolds number - accounting for the non-linear friction term in Navier-Stokes equations guarantees better predictions for the time-scale of plenum depressurization. Also, the model enabled the simulation of the pressure decay by assigning distinct permeability values to each pellet instead of a single uniform value. Multiple simulations were run across all possible pellet position combinations, having each pellet assigned with values of permeability extracted from the experimental data. This allows to quantify the impact of the considering various non-uniform distributions of permeability on the dynamics of axial gas redistribution. The present work findings enhance the understanding of axial gas transport, and provide valuable insights for the integration of a model for predicting the axial gas redistribution during a LOCA scenario into the BISON fuel performance code.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Design and Analysis of a Floating-Wind Shallow-Water Mooring System Featuring Polymer Springs

This paper presents a mooring system design featuring polymer springs for the VolturnUS-S 15-MW reference floating wind turbine in site conditions for the New York Bight at a 50-m water depth. Polymer springs have a nonlinear stress-strain curve that allows a stiffer response at low loads and a more flexible response at higher loads, potentially reducing peak mooring line tensions. The mooring dynamics model MoorDyn has been extended to model springs with nonlinear tension-strain curves from a user-inputted look-up table. This MoorDyn modeling advancement is verified against OrcaFlex simulation results. Using MoorDyn's updated capabilities, a spring-equipped catenary mooring system is designed for the 15-MW floating system, along with a baseline catenary mooring system that does not use polymer springs. The floating wind turbine simulator OpenFAST is used to simulate the mooring systems in design-driving load cases to show the effect of polymer springs on key dynamic behaviours. The results show that the spring-equipped design reduces peak tensions by up to 60%, whereas the turbine offsets stay within a maximum of 7.2 m, which is still a reasonable offset limit for cable considerations. The reduction in peak tensions results in a significant decrease in damage equivalent loads - on the order of 50% for upwind lines in fully loaded conditions. These results show that polymer springs can effectively reduce peak tensions and fatigue loads in mooring systems at shallow water depths.

floating offshore wind↗

DOE OSTI2021

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1988

A preliminary investigation of finite-element modeling for composite rotor blades

The results from an initial phase of an in-house study aimed at improving the dynamic and aerodynamic characteristics of composite rotor blades through the use of elastic couplings are presented. Large degree of freedom shell finite element models of an extension twist coupled composite tube were developed and analyzed using MSC/NASTRAN. An analysis employing a simplified beam finite element representation of the specimen with the equivalent engineering stiffness was additionally performed. Results from the shell finite element normal modes and frequency analysis were compared to those obtained experimentally, showing an agreement within 13 percent. There was appreciable degradation in the frequency prediction for the torsional mode, which is elastically coupled. This was due to the absence of off-diagonal coupling terms in the formulation of the equivalent engineering stiffness. Parametric studies of frequency variation due to small changes in ply orientation angle and ply thickness were also performed. Results showed linear frequency variations less than 2 percent per 1 degree variation in the ply orientation angle, and 1 percent per 0.0001 inch variation in the ply thickness.

Lake, Renee C.↗

NASA NTRS1988

A preliminary investigation of finite-element modeling for composite rotor blades

Lake, Renee C.↗

NASA NTRS1989

Seasonal variation of the temporal variance of long-lived trace gases measured during MAP

A series of balloon observations of long lived trace gases was performed in the midlatitude stratosphere during MAP. The temporal variance of the local mixing ratios of CH4, N2O, CFCl3, and CF2Cl2 indicates a substantial annual variability. The concept of the equivalent displacement height (EDH), introduced by Ehhalt et al., is used to investigate some features of transport activity in the lower stratosphere. It appears that most of the temporal variance originates from strong transport effects during the periods of the spring and autumn turn-around of the stratospheric circulation. The dynamical process was found to be considerably reduced during October.

Roeth, E. P.↗

NASA NTRS1994

An investigation of angular stiffness and damping coefficients of an axial spline coupling in high-speed rotating machinery

This paper provided an opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. A unique test methodology and data reduction procedures were developed. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating shaft was excited by an external shaker. A rotor dynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. In addition, sensitivity analyses were performed to show that the accuracy of the dynamic coefficients do not rely on the accuracy of the data reduction procedures.

Ku, C.-P. Roger↗

NASA NTRS2000

Internal Designs Application for Inlet and Nozzle Aeroperformance Improvement

The following research results are based on development of an approach previously proposed by the authors for optimum nozzle design to obtain maximum thrust. The design was denoted a Telescope nozzle. A Telescope nozzle contains one or several internal designs of certain location, which are inserted at certain locations into a divergent conical or planar main nozzle near its exit. Such a design provides additional thrust augmentation over 20% by comparison with the optimum single nozzle of equivalent lateral area. What is more, recent experimental acoustic tests have discovered an essential noise reduction due to Telescope nozzles application. In this paper, some additional theoretical results are presented for Telescope nozzles and a similar approach is applied for aeroperformance improvement of a supersonic inlet. In addition, a classic gas dynamics problem of a similar supersonic flow into a plate has been analyzed. In some particular cases, new exact analytical solutions are obtained for a flow into a wedge with an oblique shock wave. Numerical simulations were conducted for supersonic flow into a divergent portion of a 2D or axisymmetric nozzle with several plane or conuical designs as well as into a 2D or axisymmetric supersonic inlet with a forebody. The 1st order Kryko-Godunov marching numerical scheme for inviscid supersonic flows was used. Several cases were tested using the NASA CFL3d code based on full Navier-Stokes equations. Numerical simulation results have confirmed essential benefits of Telescope design applications in propulsion systems.

Gilinsky, M.↗

NASA NTRS2003

Three-Gorge Reservoir: A 'Controlled Experiment' for Calibration/Validation of Time-Variable Gravity Signals Detected from Space

With the advances of measurements, modern space geodesy has become a new type of remote sensing for the Earth dynamics, especially for mass transports in the geophysical fluids on large spatial scales. A case in point is the space gravity mission GRACE (Gravity Recovery And Climate Experiment) which has been in orbit collecting gravity data since early 2002. The data promise to be able to detect changes of water mass equivalent to sub-cm thickness on spatial scale of several hundred km every month or so. China s Three-Gorge Reservoir has already started the process of water impoundment in phases. By 2009,40 km3 of water will be stored behind one of the world s highest dams and spanning a section of middle Yangtze River about 600 km in length. For the GRACE observations, the Three-Gorge Reservoir would represent a geophysical controlled experiment , one that offers a unique opportunity to do detailed geophysical studies. -- Assuming a complete documentation of the water level and history of the water impoundment process and aided with a continual monitoring of the lithospheric loading response (such as in area gravity and deformation), one has at hand basically a classical forwardinverse modeling problem of surface loading, where the input and certain output are known. The invisible portion of the impounded water, i.e. underground storage, poses either added values as an observable or a complication as an unknown to be modeled. Wang (2000) has studied the possible loading effects on a local scale; we here aim for larger spatial scales upwards from several hundred km, with emphasis on the time-variable gravity signals that can be detected by GRACE and follow-on missions. Results using the Green s function approach on the PREM elastic Earth model indicate the geoid height variations reaching several millimeters on wavelengths of about a thousand kilometers. The corresponding vertical deformations have amplitude of a few centimeters. In terms of long-wavelength spherical harmonics, the induced geoid height variations are very close to the accuracy of GRACE- recoverable gravity field, while the low-degree (2 to 5) harmonics should be detectable. With a large regional time-variable gravity signal, the Three-Gorge experiment can serve as a useful calibration/verification for GRACE (including the elastic loading effects), and future gravity missions (especially for visco-elastic yielding as well as underground water variations).

Chao, Benjamin F.↗

NASA NTRS2000

Internal Designs Application for Inlet and Nozzle Aeroperformance Improvement

The following research results are based on development of an approach previously proposed by the authors for optimum nozzle design to obtain maximum thrust. The design was denoted a Telescope nozzle. A Telescope nozzle contains one or several internal designs of certain location, which are inserted at certain locations into a divergent conical or planar main nozzle near its exit. Such a design provides additional thrust augmentation over 20% by comparison with the optimum single nozzle of equivalent lateral area. What is more, recent experimental acoustic tests have discovered an essential noise reduction due to Telescope nozzles application. In this paper, some additional theoretical results are presented for Telescope nozzles and a similar approach is applied for aeroperformance improvement of a supersonic inlet. In addition, a classic gas dynamics problem of a similar supersonic flow into a plate has been analyzed. In some particular cases, new exact analytical solutions are obtained for a flow into a wedge with an oblique shock wave. Numerical simulations were conducted for supersonic flow into a divergent portion of a 2D or axisymmetric nozzle with several plane or conical designs as well as into a 2D or axisymmetric supersonic inlet with a forebody. The 1st order Kryko-Godunov marching numerical scheme for inviscid supersonic flows was used. Several cases were tested using the NASA CFL3d code based on full Navier-Stokes equations. Numerical simulation results have confirmed essential benefits of Telescope design applications in propulsion systems.

Gilinsky, M.↗

NASA NTRS2000

Internal Designs Application for Inlet and Nozzle Aeroperformance Improvement

The following research results are based on development of an approach previously proposed by the authors for optimum nozzle design to obtain maximum thrust. The design was denoted a Telescope nozzle. A Telescope nozzle contains one or several internal designs of certain location, which are inserted at certain locations into a divergent conical or planar main nozzle near its exit. Such a design provides additional thrust augmentation over 20% by comparison with the optimum single nozzle of equivalent lateral area. What is more, recent experimental acoustic tests have discovered an essential noise reduction due to Telescope nozzles application. In this paper, some additional theoretical results are presented for Telescope nozzles and a similar approach is applied for aeroperformance improvement of a supersonic inlet. In addition, a classic gas dynamics problem of a similar supersonic flow into a plate has been analyzed. In some particular cases, new exact analytical solutions are obtained for a flow into a wedge with an oblique shock wave. Numerical simulations were conducted for supersonic flow into a divergent portion of a 2D or axisymmetric nozzle with several plane or conical designs as well as into a 2D or axisymmetric supersonic inlet with a forebody. The 1st order Kryko-Godunov march- ing numerical scheme for inviscid supersonic flows was used. Several cases were tested using the NASA CFL3d code based on full Navier-Stokes equations. Numerical simulation results have confirmed essential benefits of Telescope design applications in propulsion systems.

Gilinsky, M.↗