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At least 487 records · Page 27

Multi-Dimensional, Non-Pyrolyzing Ablation Test Problems

Non-pyrolyzingcarbonaceous materials represent a class of candidate material for hypersonic vehicle components providing both structural and thermal protection system capabilities. Two problems relevant to this technology are presented. The first considers the one-dimensional ablation of a carbon material subject to convective heating. The second considers two-dimensional conduction in a rectangular block subject to radiative heating. Surface thermochemistry for both problems includes finite-rate surface kinetics at low temperatures, diffusion limited ablation at intermediate temperatures, and vaporization at high temperatures. The first problem requires the solution of both the steady-state thermal profile with respect to the ablating surface and the transient thermal history for a one-dimensional ablating planar slab with temperature-dependent material properties. The slab front face is convectively heated and also reradiates to a room temperature environment. The back face is adiabatic. The steady-state temperature profile and steady-state mass loss rate should be predicted. Time-dependent front and back face temperature, surface recession and recession rate along with the final temperature profile should be predicted for the time-dependent solution. The second problem requires the solution for the transient temperature history for an ablating, two-dimensional rectangular solid with anisotropic, temperature-dependent thermal properties. The front face is radiatively heated, convectively cooled, and also reradiates to a room temperature environment. The back face and sidewalls are adiabatic. The solution should include the following 9 items: final surface recession profile, time-dependent temperature history of both the front face and back face at both the centerline and sidewall, as well as the time-dependent surface recession and recession rate on the front face at both the centerline and sidewall. The results of the problems from all submitters will be collected, summarized, and presented at a later conference.

Ablation↗

Flow/Soot-Formation Interactions in Nonbuoyant Laminar Diffusion Flames

Nonpremixed (diffusion) flames are attractive for practical applications because they avoid the stability, autoignition, flashback, etc. problems of premixed flames. Unfortunately, soot formation in practical hydrocarbon-fueled diffusion flames reduces their attractiveness due to widely-recognized public health and combustor durability problems of soot emissions. For example, more deaths are attributed to the emission of soot (15,000-60,000 deaths annually in the U.S. alone) than any other combustion-generated pollutant. In addition, continuum radiation from soot-containing flames is the principle heat load to combustor components and is mainly responsible for engine durability problems of aircraft and gas turbine engines. As a result, there is considerable interest in controlling both soot concentrations within flames and soot emissions from flames. Thus, the objective of the present investigation is to study ways to control soot formation in diffusion flames by manipulating the mixing process between the fuel and oxidant streams. In order to prevent the intrusion of gravity from masking flow properties that reduce soot formation in practical flames (where effects of gravity are small), methods developed during past work will be exploited to minimize effects of buoyant motion.

Dai, Z.↗

Heat transfer, diffusion, and evaporation

Although it has long been known that the differential equations of the heat-transfer and diffusion processes are identical, application to technical problems has only recently been made. In 1916 it was shown that the speed of oxidation of the carbon in iron ore depends upon the speed with which the oxygen of the combustion air diffuses through the core of gas surrounding the carbon surface. The identity previously referred to was then used to calculate the amount of oxygen diffusing to the carbon surface on the basis of the heat transfer between the gas stream and the carbon surface. Then in 1921, H. Thoma reversed that procedure; he used diffusion experiments to determine heat-transfer coefficients. Recently Lohrisch has extended this work by experiment. A technically very important application of the identity of heat transfer and diffusion is that of the cooling tower, since in this case both processes occur simultaneously.

GASES - DIFFUSION↗

Effects of increased upward flux of dissolved salts caused by CO2 storage or other factors

Injection of CO2 in deep saline aquifers is being considered to reduce greenhouse gases in the atmosphere, and this process is expected to increase the pressure in these deep aquifers. One potential consequence of pressurization is an increase in the upward flux of saline water. Saline groundwater occurs naturally at shallow depths in many sedimentary basins, so an upward flux of solutes could degrade the quality of freshwater aquifers and threaten aquatic ecosystems. One problem could occur where saline water flowed upward along preferential paths, like faults or improperly abandoned wells. Diffuse upward flow through the natural stratigraphy could also occur in response to basin pressurization. This process would be slower, but diffuse upward flow could affect larger areas than flow through preferential paths, and this motivated us to evaluate this process. We analyzed idealized 2D and 3D geometries representing the essential details of a shallow, freshwater aquifer underlain by saline ground water in a sedimentary basin. The analysis was conducted in two stages, one that simulated the development of a freshwater aquifer by flushing out saline water, and another that simulated the effect of a pulse-like increase in the upward flux from the basin. The results showed that increasing the upward flux from a basin increased the salt concentration and mass loading of salt to streams, and decrease the depth to the fresh/salt transition. The magnitude of these effects varied widely, however, from a small, slow process that would be challenging to detect, to a large, rapid response that could be an environmental catastrophe. The magnitude of the increased flux, and the initial depth to the fresh/salt transition in groundwater controlled the severity of the response. We identified risk categories for salt concentration, mass loading, and freshwater aquifer thickness, and we used these categories to characterize the severity of the response. This showed that risks would likely be minor if the upward flux was smaller than a few tenths of the magnitude of recharge, according to the 2D analyses. The 3D analyses also show that upward flux could occur without a significant increase in the risk categories. The major contribution of this work is that it shows how a large increase in diffuse upward flux from a basin could cause significant problems, but a small increase in upward flux may occur without significantly affecting risks to the shallow freshwater flow system. This heightens the importance of understanding interactions between shallow and deep hydrologic systems when characterizing CO2 storage projects.

54 ENVIRONMENTAL SCIENCES↗

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Mazaheri, Alireza↗

Characterization of supersonic radiation diffusion waves

Supersonic and diffusive radiation flow is an important test problem for the radiative transfer models used in radiation-hydrodynamics computer codes owing to solutions being accessible via analytic and numeric methods. We present experimental results with which we compare these solutions by studying supersonic and diffusive flow in the laboratory. Here, we present results of higher-accuracy experiments than previously possible studying radiation flow through up to 7 high-temperature mean free paths of low-density, chlorine-doped polystyrene foam and silicon dioxide aerogel contained by an Au tube. Measurements of the heat front position and absolute measurements of the x-ray emission arrival at the end of the tube are used to test numerical and analytical models. We find excellent absolute agreement with simulations provided that the opacity and the equation of state are adjusted within expected uncertainties; analytical models provide a good phenomenological match to measurements but are not in quantitative agreement due to their limited scope.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

A computational investigation of high-flux, plate-and-frame membrane modules for industrial carbon capture

In this work, we study the application of membrane-based separation systems for carbon capture, considering plate-and-frame membrane modules. The successful deployment of membrane CO 2 capture system relies on high-performing membranes as well as effective membrane modules that can fully exploit the developed membranes. A plate-and-frame membrane module is especially attractive for CO 2 capture from industrial flue gas due to its lower pressure drop compared to its counterparts such as spiral wound modules and hollow fiber modules. To design better plate-and-frame modules, we investigate their basic unit - a single membrane stack through a combination of computational modeling and experimental investigations. The modeling approach is based on Computational Fluid Dynamics (CFD) to represent a multiphysics problem, including the fluid flow and diffusion processes within a membrane module. We use experimental data collected under different operating conditions to validate the CFD model. Numerical results suggest a good agreement between experiments and model outputs for the CO 2 recovery, CO 2 mole fraction in the retentate and permeate, and stage-cut. The CFD model is able to predict accurately the flow behavior, providing valuable insights on the effects of fluid dynamics on mass transfer of CO 2 . We also carry out a sensitivity analysis to identify the effect of key parameters on the CO 2 recovery and the CO 2 purity of the outlet streams.

CFD simulation↗

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Hejre, we introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. Moreover, the effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.

97 MATHEMATICS AND COMPUTING↗

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗

Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids

Here, we present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry-breaking structural changes of the crystal unit cell and reveals the importance of a mechanochemical spinodal, defined as the region in strain-composition space, where the free-energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechanochemical spinodal decomposition are variationally derived from a free-energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher-order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests that mechanochemical spinodal decomposition should occur in metal hydrides such as ZrH 2-2c . The rich physics that ensues is explored in several numerical examples in two and three dimensions, and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high-temperature ceramics.

36 MATERIALS SCIENCE↗

Equation-of-motion coupled-cluster method for doubly ionized states with spin-orbit coupling

In this work, we report implementation of the equation-of-motion coupled-cluster method for doubly ionized states (EOM-DIP-CC) with spin-orbit coupling (SOC) using a closed-shell reference. Double ionization potentials (DIPs) are calculated in the space spanned by 2h and 3h1p determinants with the EOM-DIP-CC approach at the CC singles and doubles level (CCSD). Time-reversal symmetry together with spatial symmetry is exploited to reduce computational effort. To circumvent the problem of unstable dianion references when diffuse basis functions are included, nuclear charges are scaled. Effect of this stabilization potential on DIPs is estimated based on results from calculations using a small basis set without diffuse basis functions. DIPs and excitation energies of some low-lying states for a series of open-shell atoms and molecules containing heavy elements with two unpaired electrons have been calculated with the EOM-DIP-CCSD approach. Results show that this approach is able to afford a reliable description on SOC splitting. Furthermore, the EOM-DIP-CCSD approach is shown to provide reasonable excitation energies for systems with a dianion reference when diffuse basis functions are not employed.

74 ATOMIC AND MOLECULAR PHYSICS↗

Iterative spectral method for solving electrostatic or magnetostatic problems in complex and evolving heterostructures

Electrostatic or magnetostatic problems involving complex heterogeneity are nontrivial for modeling and simulation. Most existing numerical methods focus on sharp interface models and the computational cost increases with increasing complexity of the geometry. Here we develop an iterative spectral method, the bound charge successive approximation algorithm, to solve electrostatic or magnetostatic heterogeneity problems in the context of diffuse-interface modeling. As tests and verifications, this algorithm is applied to calculation of the depolarization factor of an ellipsoid, and simulation of random dielectric mixtures and the dielectophoretic motion of multiple particles. The algorithm shows excellent efficiency and the computational cost mainly depends on the permittivity or permeability contrast in the whole system, regardless of the complexity of the geometry. Specifically, for evolving heterostructures the solution of bound charge in one time step can be used as input for the next, which could further significantly shorten the iteration (approximation) process, making it practical to simulate the long-range electrostatic or magnetostatic interaction in complex and evolving heterostructures.

97 MATHEMATICS AND COMPUTING↗

Enhanced resting-state dynamics of the hemoglobin signal as a novel biomarker for detection of breast cancer

Purpose: The work presented here demonstrates an application of diffuse optical tomography (DOT) to the problem of breast-cancer diagnosis. The potential for using spatial and temporal variability measures of the hemoglobin signal to identify useful biomarkers was studied. Methods: DOT imaging data were collected using two instrumentation platforms the authors developed, which were suitable for exploring tissue dynamics while performing a simultaneous bilateral exam. For each component of the hemoglobin signal (e.g., total, oxygenated), the image time series was reduced to eight scalar metrics that were affected by one or more dynamic properties of the breast microvasculature (e.g., average amplitude, amplitude heterogeneity, strength of spatial coordination). Receiver-operator characteristic (ROC) analyses, comparing groups of subjects with breast cancer to various control groups (i.e., all noncancer subjects, only those with diagnosed benign breast pathology, and only those with no known breast pathology), were performed to evaluate the effect of cancer on the magnitudes of the metrics and of their interbreast differences and ratios. Results: For women with known breast cancer, simultaneous bilateral DOT breast measures reveal a marked increase in the resting-state amplitude of the vasomotor response in the hemoglobin signal for the affected breast, compared to the contralateral, noncancer breast. Reconstructed 3D spatial maps of observed dynamics also show that this behavior extends well beyond the tumor border. In an effort to identify biomarkers that have the potential to support clinical aims, a group of scalar quantities extracted from the time series measures was systematically examined. This analysis showed that many of the quantities obtained by computing paired responses from the bilateral scans (e.g., interbreast differences, ratios) reveal statistically significant differences between the cancer-positive and -negative subject groups, while the corresponding measures derived from individual breast scans do not. ROC analyses yield area-under-curve values in the 77%–87% range, depending on the metric, with sensitivity and specificity values ranging from 66% to 91%. An interesting result is the initially unexpected finding that the hemodynamic-image metrics are only weakly dependent on the tumor burden, implying that the DOT technique employed is sensitive to tumor-induced changes in the vascular dynamics of the surrounding breast tissue as well. Computational modeling studies serve to identify which properties of the vasomotor response (e.g., average amplitude, amplitude heterogeneity, and phase heterogeneity) principally determine the values of the metrics and their codependences. Findings from the modeling studies also serve to clarify the influence of spatial-response heterogeneity and of system-design limitations, and they reveal the impact that a complex dependence of metric values on the modeled behaviors has on the success in distinguishing between cancer-positive and -negative subjects. Conclusions: The authors identified promising hemoglobin-based biomarkers for breast cancer from measures of the resting-state dynamics of the vascular bed. A notable feature of these biomarkers is that their spatial extent encompasses a large fraction of the breast volume, which is mainly independent of tumor size. Tumor-induced induction of nitric oxide synthesis, a well-established concomitant of many breast cancers, is offered as a plausible biological causal factor for the reported findings.

60 APPLIED LIFE SCIENCES↗

DREAM3D simulations of inner-belt dynamics

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of the problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown in the 1973 paper when we use the same physical models for radial diffusion and pitch-angle scattering from hiss. However, we show that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to understand the two-belt structure.

58 GEOSCIENCES↗

CFD modeling of high-flux plate-and-frame membrane modules for industrial carbon capture

In this work, we study the application of membrane-based separation systems for carbon capture, considering plate-and-frame membrane modules. The successful deployment of membrane CO2 capture system relies on high-performing membranes as well as effective membrane modules that can fully exploit the developed membranes. A plate-and-frame membrane module is especially attractive for CO2 capture from industrial flue gas due to its lower pressure drop compared to its counterparts such as spiral wound modules and hollow fiber modules. To design better plate-and-frame modules, we investigate their basic unit - a single membrane stack through a combination of computational modeling and experimental investigations. The modeling approach is based on Computational Fluid Dynamics (CFD) to represent a multiphysics problem, including the fluid flow and diffusion processes within a membrane module. We use experimental data collected under different operating conditions to validate the CFD model. Numerical results suggest a good agreement between experiments and model outputs for the CO2 recovery, CO2 mole fraction in the retentate and permeate, and stage-cut. The CFD model is able to predict accurately the flow behavior, providing valuable insights on the effects of fluid dynamics on mass transfer of CO2. We also carry out a sensitivity analysis to identify the effect of key parameters on the CO2 recovery and the CO2 purity of the outlet streams.

Dosso, Cheick↗

NASA/MSFC multilayer diffusion models and computer programs, version 5

The transport and diffusion models and algorithms developed for use by NASA in predicting concentrations and dosages downwind from normal and abnormal launches of rocket vehicles are described along with the associated computer programs for use in performing the calculations. Topics discussed include: the mathematical specifications and procedures used in the Preprocessor Program to calculate rocket exhaust cloud rise, cloud dimensions, and other input parameters to the transport and diffusion models; the revised mathematical specifications for the Multilayer Diffusion Models; users' instructions for implementing the Preprocessor and Multilayer Diffusion Models Programs; and worked example problems illustrating the use of the models and computer programs.

Dumbauld, R. K.↗

Some remarks on the design of transonic tunnels with low levels of flow unsteadiness

The principal sources of flow unsteadiness in the circuit of a transonic wind tunnel are presented. Care must be taken to avoid flow separations, acoustic resonances and large scale turbulence. Some problems discussed are the elimination of diffuser separations, the aerodynamic design of coolers and the unsteadiness generated in ventilated working sections.

Mabey, D. G.↗

Measuring the large-scale anisotropy in the microwave background radiation

Measurements of large-scale anisotropy in the 2.7 K microwave background radiation are reaching a sensitivity of Delta T/T = 0.0001 in the amplitudes of low-order spherical harmonics. At this level, interesting conditions and processes in the early universe can be studied. However, the measurements are difficult and very susceptible to systematic errors. The microwave instruments and techniques are discussed with the emphasis on the reduction and evaluation of spurious effects. The subtraction of foreground radiation, mainly from diffuse Galactic sources, is a major problem that already limits the accuracy of measurements near 1 cm wavelength. Current results for the dipole and quadrupole moments are compared and discussed.

Wilkinson, D. T.↗