Results for “Numerical diffusion” — Page 44

DOE OSTI2018

Renovation of Thermal Vacuum Chambers at Idaho National Laboratory (INL) for Testing of Radioisotope Power Systems (RPS)

The Radioisotope Power Systems (RPS) program at Idaho National Laboratory (INL) fuels and performs environmental testing of RPS in support of National Aeronautics and Space Administration (NASA) missions. Recently the programs’ thermal vacuum chambers, housed within INL’s Space and Security Power Systems Facility (SSPSF), underwent successful renovations to improve functional capabilities and system control in support of customer missions. Thermal vacuum system renovations focused primarily on three core functions. The first focus area was integration of semi-automated Programmable Logic Controllers (PLC) to enhance operational feedback and process control. This included the use of numerically controlled vacuum valves and integration of real time feedback from process pressure transducers. Improvements to the system high vacuum pumping technology was the second priority focus. Legacy diffusion pumps were replaced with turbo-molecular and cryogenic pumps to help mitigate the possibility of back streaming diffusion pump oil onto the surface of the test article or radiative cooling surfaces located within the chambers. The third and final core function involved meeting emergent customer thermal requirements. This led to retro-fitting one of the vacuum chambers with a cryogenically cooled Thermal Conditioning Unit (TCU) and thermal shrouds. The TCU utilizes gaseous nitrogen to heat or cool a cylindrical shroud to maintain a set temperature with a programmable range of -I85 °C to I00 °C. With the successful completion of RPS acceptance testing, the newly renovated thermal vacuum chamber systems are operational and better equipped to support testing of Radioisotope Power Systems for space exploration missions.

42 ENGINEERING↗

DOE OSTI2018

Renovation of Thermal Vacuum Chambers at Idaho National Laboratory for Testing of Radioisotope Power Systems

The Radioisotope Power Systems (RPS) program at Idaho National Laboratory (INL) fuels and performs environmental testing of RPS in support of National Aeronautics and Space Administration (NASA) missions. Recently the programs’ thermal vacuum chambers, housed within INL’s Space and Security Power Systems Facility (SSPSF), underwent successful renovations to improve functional capabilities and system control in support of customer missions. Thermal vacuum system renovations focused primarily on three core functions. The first focus area was integration of semi-automated Programmable Logic Controllers (PLC) to enhance operational feedback and process control. This included the use of numerically controlled vacuum valves and integration of real time feedback from process pressure transducers. Improvements to the system high vacuum pumping technology was the second priority focus. Legacy diffusion pumps were replaced with turbo-molecular and cryogenic pumps to help mitigate the possibility of back streaming diffusion pump oil onto the surface of the test article or radiative cooling surfaces located within the chambers. The third and final core function involved meeting emergent customer thermal requirements. This led to retro-fitting one of the vacuum chambers with a cryogenically cooled Thermal Conditioning Unit (TCU) and thermal shrouds. The TCU utilizes gaseous nitrogen to heat or cool a cylindrical shroud to maintain a set temperature with a programmable range of -I85 °C to I00 °C. With the successful completion of RPS acceptance testing, the newly renovated thermal vacuum chamber systems are operational and better equipped to support testing of Radioisotope Power Systems for space exploration missions.

42 ENGINEERING↗

DOE OSTI2018

Renovation of Thermal Vacuum Chambers at Idaho National Laboratory (INL) for Testing of Radioisotope Power Systems (RPS)

The Radioisotope Power Systems (RPS) program at Idaho National Laboratory (INL) fuels and performs environmental testing of RPS in support of National Aeronautics and Space Administration (NASA) missions. Recently the programs’ thermal vacuum chambers, housed within INL’s Space and Security Power Systems Facility (SSPSF), underwent successful renovations to improve functional capabilities and system control in support of customer missions. Thermal vacuum system renovations focused primarily on three core functions. The first focus area was integration of semi-automated Programmable Logic Controllers (PLC) to enhance operational feedback and process control. This included the use of numerically controlled vacuum valves and integration of real time feedback from process pressure transducers. Improvements to the system high vacuum pumping technology was the second priority focus. Legacy diffusion pumps were replaced with turbo-molecular and cryogenic pumps to help mitigate the possibility of back streaming diffusion pump oil onto the surface of the test article or radiative cooling surfaces located within the chambers. The third and final core function involved meeting emergent customer thermal requirements. This led to retro-fitting one of the vacuum chambers with a cryogenically cooled Thermal Conditioning Unit (TCU) and thermal shrouds. The TCU utilizes gaseous nitrogen to heat or cool a cylindrical shroud to maintain a set temperature with a programmable range of -I85 °C to I00 °C. With the successful completion of RPS acceptance testing, the newly renovated thermal vacuum chamber systems are operational and better equipped to support testing of Radioisotope Power Systems for space exploration missions.

42 ENGINEERING↗

DOE OSTI2020

Experimental and theoretical study of the soot-forming tendencies of furans as potential biofuels

Sustainably-produced biofuels, including furans derived from lignocellulosic biomass, are being studied as potential next-generation fuels. Biofuels have unique structures that are absent in conventional fuels and they potentially emit fewer particulates than conventional fuels because of the presence of oxygen atoms. In this work, we focus on quantification and measurement of sooting tendency. A set of furans was selected and their sooting tendencies were characterized by Yield Sooting Index (YSI), which was obtained by measuring the line-of-sight spectral radiance (LSSR) of a coflow laminar diffusion flame doped with 1000 ppm of each test fuel. The measured YSIs are lower than traditional gasoline fuels and benzenoid aromatics (e.g., YSIbenzene = 100). We also performed numerical simulations with a detailed chemical kinetic mechanism to analyze the flame chemistry of 2-methylfuran (2MF). 4→5 H-atom migration in the furan ring causes 31.0% of the total decomposition and is the dominant fuel consumption pathway leading to soot. DFT calculations via the G4 composite method were carried out to obtain activation energies (Ea) and bond dissociation energies (BDE). The results showed that the 4→5 H-atom migration in the furan ring has the second lowest Ea and subsequently forms a 1,2-diene-substituted ketone derivative as a stable species. The ring-opening products of the 4→5 H-atom migration are propyne + a linear ketene for 2-n-alkylfurans, and 1-butyne + a methyl-substituted ketene for 2-t-butylfuran. These results can explain the trends of the measured YSIs of 2-alkylfurans.

09 BIOMASS FUELS↗

DOE OSTI2021

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗

DOE OSTI2015

Local radiation hydrodynamic simulations of massive star envelopes at the iron opacity peak

We perform three-dimensional radiation hydrodynamic simulations of the structure and dynamics of the radiation-dominated envelopes of massive stars at the location of the iron opacity peak. One-dimensional hydrostatic calculations predict an unstable density inversion at this location, whereas our simulations reveal a complex interplay of convective and radiative transport whose behavior depends on the ratio of the photon diffusion time to the dynamical time. The latter is set by the ratio of the optical depth per pressure scale height, τ{sub 0}, to τ{sub c}=c/c{sub g}, where c{sub g}≈50 km s{sup −1} is the isothermal sound speed in the gas alone. When τ{sub 0}≫τ{sub c}, convection reduces the radiation acceleration and removes the density inversion. The turbulent energy transport in the simulations agrees with mixing length theory and provides its first numerical calibration in the radiation-dominated regime. When τ{sub 0}≪τ{sub c}, convection becomes inefficient and the turbulent energy transport is negligible. The turbulent velocities exceed c{sub g}, driving shocks and large density fluctuations that allow photons to preferentially diffuse out through low-density regions. However, the effective radiation acceleration is still larger than the gravitational acceleration so that the time average density profile contains a modest density inversion. In addition, the simulated envelope undergoes large-scale oscillations with periods of a few hours. The turbulent velocity field may affect the broadening of spectral lines and therefore stellar rotation measurements in massive stars, while the time variable outer atmosphere could lead to variations in their mass loss and stellar radius.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Multi-fluid Approach to High-frequency Waves in Plasmas. II. Small-amplitude Regime in Partially Ionized Media

The presence of neutral species in a plasma has been shown to greatly affect the properties of magnetohydrodynamic waves. For instance, the interaction between ions and neutrals through momentum transfer collisions causes the damping of Alfvén waves and alters their oscillation frequency and phase speed. When the collision frequencies are larger than the frequency of the waves, single-fluid magnetohydrodynamic approximations can accurately describe the effects of partial ionization, since there is a strong coupling between the various species. However, at higher frequencies, the single-fluid models are not applicable and more complex approaches are required. Here, we use a five-fluid model with three ionized and two neutral components, which takes into consideration Hall’s current and Ohm’s diffusion in addition to the friction due to collisions between different species. We apply our model to plasmas composed of hydrogen and helium, and allow the ionization degree to be arbitrary. By analyzing the corresponding dispersion relation and numerical simulations, we study the properties of small-amplitude perturbations. We discuss the effect of momentum transfer collisions on the ion-cyclotron resonances and compare the importance of magnetic resistivity, and ion–neutral and ion–ion collisions on the wave damping at various frequency ranges. Applications to partially ionized plasmas of the solar atmosphere are performed.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Phase-shift speckle-shearing interferometry

We have numerically simulated the process of measuring stress – strain states by the method of speckle-shearing interferometry using the phase-shift technique. A computer model with the possibility of setting its strain and roughness is developed, which includes a model of a diffusely reflecting test object corresponding to the characteristics of a real membrane, as well as a speckle interferometer model that allows speckle interferograms to be obtained for different speckle sizes and angles between interfering beams. The process of reconstructing the object surface topogram from model speckle interferograms by the phase-shift technique is implemented. Using the developed models, a two-dimensional shearogram are obtained, which is a derivative of the strain field of a circular membrane. Comparison of the results of numerical simulation with experimental data shows that the differences (rms deviations) do not exceed 0.02 μm. It is also shown that the error of interferogram reconstruction by the phase-shift technique increases significantly when the test object strains exceed 12 μm. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Frequency-domain vs time-domain SP{sub N} equations to simulate neutron noise

Inside the reactor core mechanical vibrations of fuel assemblies can produce high fluctuations around a steady-state configuration, known as neutron noise. This effect can cause the triggering of power reduction measures. Classically, diffusion theory has been used to simulate this behavior. However, this equation has some limitations if the materials of the reactor have strong variations. In this work, we use the diffusive time-dependent simplified spherical harmonics equations that improve the previous results without the necessity of using high computational requirements. In particular, two types of analyses with these equations (SP{sub 3}) are made: a frequency-domain and a time-domain. A numerical neutron noise benchmark tests the methodology and compare both formulations. First, numerical results show a good agreement between the amplitudes and phases of the SP3 equations computed with the frequency-domain and time-domain. Therefore, as the frequency-domain computation only requires to solve a linear system, it is a recommendable option for neutron noise computations. Second, one can conclude that for this type of nuclear systems, where the assemblies are not homogenized, the SP{sub 3} approximation results improve considerably the accuracy of the diffusion theory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Multiscale convergence properties for spectral approximations of a model kinetic equation

Here in this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of the kinetic distribution and, as such, is accompanied by standard algebraic estimates of the form N -q , where N is the number of modes and q > 0 depends on the regularity of the solution. However, in the multiscale setting, the error estimate can be expressed in terms of the scaling parameter ϵ, which measures the ratio of the mean-free-path to the characteristic domain length. We show that, for isotropic initial conditions, the error in the spectral approximation is $\mathcal{O}$($ϵ^{N+1}$). More surprisingly, the coefficients of the expansion satisfy super convergence properties. In particular, the error of the ℓ th coefficient of the expansion scales like $\mathcal{O}$($ϵ^{2N}$ ) when ℓ = 0 and $\mathcal{O}$($ϵ^{2N+2-ℓ}$ ) for all 1 ≤ ℓ ≤ N. This result is significant, because the low-order coefficients correspond to physically relevant quantities of the underlying system. All the above estimates involve constants depending on N, the time t, and the initial condition. We investigate specifically the dependence on N, in order to assess whether increasing N actually yields an additional factor of ϵ in the error. Numerical tests will also be presented to support the theoretical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

First observation of increased DT yield over prediction due to addition of hydrogen

Here, in a number of reported instances, implosions utilizing fuel mixtures have resulted in anomalously low fusion yields below those predicted by radiation-hydrodynamics simulations. Inter-species ion diffusion has been suggested as a possible cause of the observed yield degradation in fuel mixture implosions. An experimental platform utilizing hydro-equivalent deuterium–tritium (DT), deuterium–tritium–hydrogen (DTH), and deuterium-tritium-helium3 (DT 3 He) capsule implosions was developed to determine whether the inter-species ion diffusion theory may describe the resulting fuel mixture implosion behavior. The implosion experiments were performed at the Omega laser facility. X-ray images and shell areal density diagnostics results show that the hydro-equivalent three capsules (DT, DTH, and DT 3 He) have similar compression behavior. However, nuclear yield deviation was observed from the scaling determined using a fusion yield formula. In the DT 3 He mixture, a reduced yield of a factor of 0.65 ± 0.13 was observed, which is similar to a yield reduction observed in D 3 He mixture by Rygg et al. (i.e., Rygg effect). In contrast, in the DTH mixture, a factor of 1.17 ±0.15 yield increase was observed, which we named the inverse Rygg effect. The yield increase observed in the DTH mixture is consistent with the inter-species ion diffusion theory where lighter H diffuses away from the core and concentrated DT in the core produces higher yield. An inter-species ion diffusion model, the Zimmerman–Paquette–Kagan–Zhdanov model, implemented in a Lagrangian radiation-hydrodynamics fluid code, was also used to analyze the present data, without the need to assume hydrodynamic equivalence of the capsules, but it does not completely explain the DTH or DT 3 He capsules although its effects are in the correct direction. Simulation-based Bayesian inference was used in the latter analysis to quantify the uncertainty in the numerical simulations. The simulation-based analysis resulted in an inferred Rygg-effect yield decrease factor of 0.91 ± 0.02 for the DT 3 He mixture, and an inferred inverse-Rygg yield increase factor of 1.21 ± 0.04 for the DTH mixture, based on simulations ignoring ion diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, used for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Anderson acceleration and application to the three-temperature energy equations

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton–Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Removing numerical pathologies in a turbulence parameterization through convergence testing

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, this noise can be amplified by an advective term in CLUBB's background diffusion. Smoothing the limiters and removing the advective component of the background diffusion reduces the noise and restores the expected first-order convergence in CLUBB's solutions. These model reformulations improve the results at coarser, near-operational grid spacing and time step in cumulus cloud and dry turbulence tests. In addition, convergence testing is proved to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

Mathematics and Computing, Geosciences↗

DOE OSTI2019

Analysis of Integrated Fuselage Composite Seat for Small Aircraft in Crashworthiness Applications

The research paper is addressed to develop and validate an aircraft seat cushion to be used for the passenger seat directly integrated in the fuselage. For very light aircraft, these systems result to be a good choice in terms of weight reduction and space optimization, but can represent a challenging problem for crashworthiness design and a key energy-absorbing function for human protection from injuries so to improve the level of the safety. The first issue was dedicated to investigate the mechanical properties of four commercial foams, diffused in different industrial applications, which present nonlinear and time-dependent viscoelastic behavior, and finally to determine whether typical seat cushion materials are rate sensitive or not. Then, numerical simulations were validated with measurements to simulate the mechanical properties of foams and to evaluate the contact pressures, stress distribution, and the dependence of stress on the strain rate in order to provide adequate levels of both comfort and energy absorption.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Thermodynamic modeling of countercurrent chemical looping reverse water gas shift process for redox material screening

The reverse water gas shift (RWGS) reaction is a key pathway for CO 2 utilization, particularly within Power-to-X process chains aimed at sustainable fuel and chemical production. Countercurrent chemical looping (CL-RWGS) using non-stoichiometric oxides can overcome equilibrium limitations of conventional RWGS reactors, enabling significantly higher CO 2 conversions. However, modeling the limiting performance of such systems is challenging due to their multiphase nature and coupled spatial and temporal variation in chemical composition. In this work, we present a discretized batch equilibrium model that simulates CL-RWGS reactors as a series of localized equilibrium exchanges between gas and solid elements. The model is numerically stable, computationally efficient, and free of kinetic source terms, making it well-suited for parametric studies and system-level integration. It is validated against established convection–diffusion models and shown to predict reasonable upper bounds on experimental results. Application of the model to a range of oxygen carrier materials identifies cerium–zirconium solid solutions, particularly Ce 0.80 Zr 0.20 O 2 , as a promising class offering superior oxygen storage characteristics compared to state-of-the-art La 0.6 Sr 0.4 FeO 3 . This framework provides a robust platform for materials screening, reactor sizing, and performance optimization in chemical looping systems. The model implementation is available as open-source software to support further research and development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Learning effective SDEs from Brownian dynamic simulations of colloidal particles

We construct a reduced, data-driven, parameter dependent effective stochastic differential equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian dynamics simulations. We use diffusion maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers–Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian dynamic simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Further, our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Asymmetric collapse by dissolution or melting in a uniform flow

An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-Analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-Analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In conclusion, the model raises fundamental mathematical questions about broken symmetries in finite-Time singularities of both continuous and stochastic dynamical systems.

42 ENGINEERING↗