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Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

South, J. C., Jr.↗

Numerical Simulations of Drop Collisions

Three-dimensional simulations of the off-axis collisions of two drops are presented. The full Navier-Stokes equations are solved by a Front-Tracking/Finite-Difference method that allows a fully deformable fluid interface and the inclusion of surface tension. The drops are accelerated towards each other by a body force that is turned off before the drops collide. Depending on whether the interface between the drops is ruptured or not, the drops either bounce or coalesce. For drops that coalesce, the impact parameter, which measures how far the drops are off the symmetry line, determines the eventual outcome of the collision. For low impact parameters, the drops coalesce permanently, but for higher impact parameters, a grazing collision, where the drops coalesce and then stretch apart again is observed. The results are in agreement with experimental observations.

Nobari, M. R. H.↗

The Flow Induced by the Coalescence of Two Initially Stationary Drops

The coalescence of two initially stationary drops of different size is investigated by solving the unsteady, axisymmetric Navier-Stokes equations numerically, using a Front-Tracking/Finite Difference method. Initially, the drops are put next to each other and the film between them ruptured. Due to surface tension forces, the drops coalesce rapidly and the fluid from the small drop is injected into the larger one. For low nondimensional viscosity, or Ohnesorge number, little mixing takes place and the small drop fluid forms a blob near the point where the drops touched initially. For low Ohnesorge number, on the other hand, the small drop forms a jet that penetrates far into the large drop. The penetration depth also depends on the size of the drops and shows that for a given fluid of sufficiently low viscosity, there is a maximum penetration depth for intermediate size ratios.

Nobari, M. R.↗

Instability Mechanisms of Thermally-Driven Interfacial Flows in Liquid-Encapsulated Crystal Growth

During the past year, a great deal of effort was focused on the enhancement and refinement of the computational tools developed as part of our previous NASA grant. In particular, the interface mollification algorithm developed earlier was extended to incorporate the effects of surface-rheological properties in order to allow the study of thermocapillary flows in the presence of surface contamination. These tools will be used in the computational component of the proposed research in the remaining years of this grant. A detailed description of the progress made in this area is provided elsewhere. Briefly, the method developed allows for the convection and diffusion of bulk-insoluble surfactants on a moving and deforming interface. The novelty of the method is its grid independence: there is no need for front tracking, surface reconstruction, body-fitted grid generation, or metric evaluations; these are all very expensive computational tasks in three dimensions. For small local radii of curvature there is a need for local grid adaption so that the smearing thickness remains a small fraction of the radius of curvature. A special Neumann boundary condition was devised and applied so that the calculated surfactant concentration has no variations normal to the interface, and it is hence truly a surface-defined quantity. The discretized governing equations are solved subsequently using a time-split integration scheme which updates the concentration and the shape successively. Results demonstrate excellent agreement between the computed and exact solutions.

Haj-Hariri, Hossein↗

Particle Engulfment and Pushing By Solidifying Interfaces

The study of particle behavior at solid/liquid interfaces (SLI s) is at the center of the Particle Engulfment and Pushing (PEP) research program. Interactions of particles with SLI s have been of interest since the 1960 s, starting with geological observations, i.e., frost heaving. Ever since, this field of research has become significant to such diverse areas as metal matrix composite materials, fabrication of superconductors, and inclusion control in steels. The PEP research effort is geared towards understanding the fundamental physics of the interaction between particles and a planar SLI. Experimental work including 1-g and mu-g experiments accompany the development of analytical and numerical models. The experimental work comprised of substantial groundwork with aluminum (Al) and zinc (Zn) matrices containing spherical zirconia particles, mu-g experiments with metallic Al matrices and the use of transparent organic metal-analogue materials. The modeling efforts have grown from the initial steady-state analytical model to dynamic models, accounting for the initial acceleration of a particle at rest by an advancing SLI. To gain a more comprehensive understanding, numerical models were developed to account for the influence of the thermal and solutal field. Current efforts are geared towards coupling the diffusive 2-D front tracking model with a fluid flow model to account for differences in the physics of interaction between 1-g and -g environments. A significant amount of this theoretical investigation has been and is being performed by co-investigators at NASA MSFC.

Source record↗

Modeling of the Ablation of Fibrous Materials in the Knudsen Regime

During atmospheric entry of planetary probes, the thermal protection system (TPS) of the probe is exposed to high temperatures under low pressures. In these conditions, carbonous TPS materials undergo gasification in the Knudsen regime leading to mass loss and wall recession called ablation. This work aims to improve the understanding of materiaVenvironment interactions through a study of the coupling between carbon dioxide transport in the Knudsen regime, heterogeneous oxidation of carbon, and sutface recession. A 3D Monte-Carlo simulation tool is used for this study. The fibrous architecture of the materiils, consisting of high porosity random array of carbon fibers, is numerically reproduced on a 3D Cartesian grid. Mass transport in the Knudsen regime from the boundary layer to the surface, and inside this porous material is simulated by random walk. A reaction probability is used to simulate the heterogeneous oxidation reaction. The surface recession is followed by front tracking using a simplified marching cube approach. The output data of the simulations are ablation velocity and dynamic evolution of the material porosity. A parametric study is carried out to analyze the material behavior as a function of Knudsen number for the porous media (length of the mean free path compared to the mean pore diameter) and the intrinsic reactivity of the carbon fibers. The results enable extrapolation of laboratory experimental data to actual entry conditions.

Lachaud, J.↗

Multiscale Modeling of Ablation and Pyrolysis in PICA-Like materials

During atmospheric entry of planetary probes, the thermal protection system (TIPS) of the probe is exposed to high temperatures under low pressures. In these conditions, carbonous fibrous TIPS materials may undergo oxidation leading to mass loss and wall recession called ablation. This work aims to improve the understanding of material/environment interactions through a study of the coupling between oxygen transport in the Knudsen regime, heterogeneous oxidation of carbon, and surface recession. A 3D Random Walk Monte Carlo simulation tool is used for this study. The fibrous architecture of a model material, consisting of high porosity random array of carbon fibers, is numerically represented on a 3D Cartesian grid. Mass transport in the Knudsen regime from the boundary layer to the surface, and inside this porous material is simulated by random walk. A reaction probability is used to simulate the heterogeneous oxidation reaction. The surface recession of the fibers is followed by front tracking using a simplified marching cube approach. The output data of the simulations are ablation velocity and dynamic evolution of the material porosity. A parametric study is carried out to analyze the material behavior as a function of Knudsen number for the porous media (length of the mean free path compared to the mean pore diameter) and the intrinsic reactivity of the carbon fibers. The model is applied to Stardust mission reentry conditions and explains the unexpected behavior of the TIPS material that underwent mass loss in volume.

Lachaud, Jean↗

Sorbent, Sublimation, and Icing Modeling Methods: Experimental Validation and Application to an Integrated MTSA Subassembly Thermal Model

This paper details the validation of modeling methods for the three core components of a Metabolic heat regenerated Temperature Swing Adsorption (MTSA) subassembly, developed for use in a Portable Life Support System (PLSS). The first core component in the subassembly is a sorbent bed, used to capture and reject metabolically produced carbon dioxide (CO2). The sorbent bed performance can be augmented with a temperature swing driven by a liquid CO2 (LCO2) sublimation heat exchanger (SHX) for cooling the sorbent bed, and a condensing, icing heat exchanger (CIHX) for warming the sorbent bed. As part of the overall MTSA effort, scaled design validation test articles for each of these three components have been independently tested in laboratory conditions. Previously described modeling methodologies developed for implementation in Thermal Desktop and SINDA/FLUINT are reviewed and updated, their application in test article models outlined, and the results of those model correlations relayed. Assessment of the applicability of each modeling methodology to the challenge of simulating the response of the test articles and their extensibility to a full scale integrated subassembly model is given. The independent verified and validated modeling methods are applied to the development of a MTSA subassembly prototype model and predictions of the subassembly performance are given. These models and modeling methodologies capture simulation of several challenging and novel physical phenomena in the Thermal Desktop and SINDA/FLUINT software suite. Novel methodologies include CO2 adsorption front tracking and associated thermal response in the sorbent bed, heat transfer associated with sublimation of entrained solid CO2 in the SHX, and water mass transfer in the form of ice as low as 210 K in the CIHX.

Bower, Chad↗

VUSAT - A VERA-CS Uncertainty and Sensitivity Analysis Toolkit

VERA-CS (the Virtual Environment for Reactor Applications, Core Simulator) is a high-fidelity multiphysics core simulator under development by the Consortium for Advanced Simulation of Light Water Reactors (CASL). VERA-CS includes three main components: MPACT for reactor physics and neutron transport, COBRA-TF for thermal-hydraulics, and ORIGEN for isotopic depletion. VERA-CS has been applied to an array of problems including core physics analysis, and the modeling for all of the fuel cycles of Watts Bar Nuclear Unit 1 (WBN1). MPACT is a 3D pin-resolved reactor transport code developed by Oak Ridge National Laboratory (ORNL) and the University of Michigan. COBRA-TF (CTF) is a three-field two-phase flow subchannel analysis code developed by ORNL and North Carolina State University. CTF solves the mass, momentum, and energy equations for the liquid, vapor, and droplet phases for each subchannel in the core and captures the axial flow within each channel as well as cross-flow between channels. Direct coupling between neutronics (MPACT) and thermal-hydraulics (CTF) in VERA-CS provides temperature and density feedback. CTF includes a number of models important for LWR safety and design analysis including flow regime dependent two-phase wall heat transfer, inter-phase heat transfer and drag, droplet breakup, and quench-front tracking. ORIGEN is developed by ORNL and released through the SCALE package. ORIGEN is directly integrated in MPACT through its API to calculate the changes in nuclides for every depletable cross-section region. Uncertainties exist in safety calculations with computer codes for nuclear reactor modeling and simulation, and they come from code limitations, scaling inaccuracies embedded in the experimental data, and uncertainties associated with the state of the reactor at the initiation of the transient. Consequently, for applications of high fidelity calculations using VERA-CS, proper uncertainty quantification (UQ) and sensitivity analysis (SA) of the computing models of reactor neutronics and thermal-hydraulics are important to comprehensively understand the results. New methods in UQ and SA have to be developed in multi-physics calculations using VERA-CS. Toward this end, a software package called VUSAT which stands for VERA-CS Uncertainty and Sensitivity Analysis Toolkit has been developed to facilitate the applications of VERA-CS within the context of best estimate plus uncertainty (BEPU) analysis framework. In this work, the VUSAT application to analyze departure from nucleate boiling (DNB) is presented.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Ultrafast Fiber Bragg Grating Interrogation for Sensing in Detonation and Shock Wave Experiments

Chirped fiber Bragg grating (CFBG) sensors coupled to high speed interrogation systems are described as robust diagnostic approaches to monitoring shock wave and detonation front propagation tracking events for use in high energy density shock physics applications. Taking advantage of the linear distributed spatial encoding of the spectral band in single-mode CFBGs, embedded fiber systems and associated photonic interrogation methodologies are shown as an effective approach to sensing shock and detonation-driven loading processes along the CFBG length. Two approaches, one that detects spectral changes in the integrated spectrum of the CFBG and another coherent pulse interrogation approach that fully resolves its spectral response, shows that 100-MHz–1-GHz interrogation rates are possible with spatial resolution along the CFBG in the 50 µm to sub-millimeter range depending on the combination of CFBG parameters (i.e., length, chirp rate, spectrum) and interrogator design specifics. In conclusion, results from several dynamic tests are used to demonstrate the performance of these high speed systems for shock and detonation propagation tracking under strong and weak shock pressure loading: (1) linear detonation front tracking in the plastic bonded explosive (PBX) PBX-9501; (2) tracking of radial decaying shock with crossover to non-destructive CFBG response; (3) shock wave tracking along an aluminum cylinder wall under weak loading accompanied by dynamic strain effects in the CFBG sensor.

36 MATERIALS SCIENCE↗

Single-molecule tracking reveals dual front door/back door inhibition of Cel7A cellulase by its product cellobiose

Degrading cellulose is a key step in the processing of lignocellulosic biomass into bioethanol. Cellobiose, the disaccharide product of cellulose degradation, has been shown to inhibit cellulase activity, but the mechanisms underlying product inhibition are not clear. We combined single-molecule imaging and biochemical investigations with the goal of revealing the mechanism by which cellobiose inhibits the activity of Trichoderma reesei Cel7A, a well-characterized exo-cellulase. We find that cellobiose slows the processive velocity of Cel7A and shortens the distance moved per encounter; effects that can be explained by cellobiose binding to the product release site of the enzyme. Cellobiose also strongly inhibits the binding of Cel7A to immobilized cellulose, with a K i of 2.1 mM. The isolated catalytic domain (CD) of Cel7A was also inhibited to a similar degree by cellobiose, and binding of an isolated carbohydrate-binding module to cellulose was not inhibited by cellobiose, suggesting that cellobiose acts on the CD alone. Finally, cellopentaose inhibited Cel7A binding at micromolar concentrations without affecting the enzyme’s velocity of movement along cellulose. Together, these results suggest that cellobiose inhibits Cel7A activity both by binding to the “back door” product release site to slow activity and to the “front door” substrate-binding tunnel to inhibit interaction with cellulose. These findings point to strategies for engineering cellulases to reduce product inhibition and enhance cellulose degradation, supporting the growth of a sustainable bioeconomy.

59 BASIC BIOLOGICAL SCIENCES↗

The fission track record of Apennine Front KREEP basalts

Whitlockite grains in two Apennine Front KREEP soil fragments contain extremely high densities of fission tracks. A new method is described in which particle tracks are examined in an actinide-poor phase bordering an actinide-rich whitlockite phase. This method clearly distinguishes the fission track contributions from other track sources; e.g., Fe-group cosmic rays, spallation recoils, and dislocations. Observed track excesses, when corrected for U- and Th-related fission sources, are 4-20 times greater than the contribution from spontaneous fission of U-238 (based on an age of 4 b.y.), and probably represent a large and variable contribution from the fission of Pu-244. These fragments may have pre-Imbrium ages, underscoring the importance of KREEP as a constituent of the pre-mare lunar crust. Track excesses are not correlated with the U or Th contents of the whitlockite grains. This behavior suggests that Pu fractionates differently from U and Th in lunar igneous KREEP.

Haines, E. L.↗

Color Image Processing and Object Tracking System

This report describes a personal computer based system for automatic and semiautomatic tracking of objects on film or video tape, developed to meet the needs of the Microgravity Combustion and Fluids Science Research Programs at the NASA Lewis Research Center. The system consists of individual hardware components working under computer control to achieve a high degree of automation. The most important hardware components include 16-mm and 35-mm film transports, a high resolution digital camera mounted on a x-y-z micro-positioning stage, an S-VHS tapedeck, an Hi8 tapedeck, video laserdisk, and a framegrabber. All of the image input devices are remotely controlled by a computer. Software was developed to integrate the overall operation of the system including device frame incrementation, grabbing of image frames, image processing of the object's neighborhood, locating the position of the object being tracked, and storing the coordinates in a file. This process is performed repeatedly until the last frame is reached. Several different tracking methods are supported. To illustrate the process, two representative applications of the system are described. These applications represent typical uses of the system and include tracking the propagation of a flame front and tracking the movement of a liquid-gas interface with extremely poor visibility.

Klimek, Robert B.↗

Implementation of compound refractive lenses for large field-of-view x-ray phase-contrast imaging during hypervelocity impact experiments

Synchrotron x-ray phase-contrast imaging (XPCI) offers time-resolved visualization of dynamic compression phenomena, but its intrinsically small field-of-view (FOV) limits the time that key features remain in frame. A novel approach to enlarge the FOV is achieved by positioning a two-dimensional parabolic compound refractive lens (CRL) upstream of the sample to deliberately defocus the white beam. Ray-tracing simulations and XPCI measurements show that this CRL configuration can expand the beam by ∼50% vertically and ∼15% horizontally based on the full width at half-maximum of the beam. Implementing the CRL, however, attenuates the photon flux and lowers signal-to-noise ratio (SNR). Task-based analysis using a calibration grid (30 μm dots) showed that both setups fail to consistently meet the Rose criterion (SNR ≥ 5) for features of this size in single-bunch imaging. Extrapolating the measured SNR Rose values suggests that the minimum consistently detectable feature lies closer to 30–40 μm for the standard XPCI setup and above 40 μm for CRL-XPCI. Despite this limitation, the CRL configuration nearly doubles the illuminated area, enabling simultaneous tracking of front and rear observations of boron carbide targets subjected to rod and sphere impacts at 1.0–2.6 km/s. Image tracking algorithms and photonic Doppler velocimetry were used to measure penetration and rear-surface velocity histories. Together, these measurements capture crack fronts, penetration, and material breakout, offering new benchmark data for validating high-strain-rate constitutive models of ceramic materials.

Ceramic materials↗

Remote sensing of coastal fronts and their effects on oil dispersion

The use of remote sensing techniques to determine the properties of coastal and estuarine fronts, which represent regions of discontinuities and high gradients in ocean physical parameters such as velocity and density, and to assess the influence of such fronts on oil pollutants is discussed. Results of an aircraft and boat verification study of an oil drift and spread model in Delaware Bay are indicated which illustrate the tendency of oil slicks to be attracted to frontal regions, where a denser fluid underlies a lighter fluid giving rise to an inclined interface with convergence zones. Landsat imagery of the bay acquired in order to incorporate frontal information into the interactive computer model is then presented which allows the locations of coastal fronts to be charted throughout a tidal cycle. It is noted that satellite observations of flood-associated fronts on the New Jersey side of the bay and ebb-associated fronts on the Delaware side agree with boat measurements and model predictions, and that the remote tracking of fronts by aircraft and satellites will aid in oil slick clean-up operations.

Klemas, V.↗