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At least 235 records · Page 13

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗

Thermally-Induced Structural Disturbances of Rigid Panel Solar Arrays

The performance of a significant number of spacecraft has been impacted negatively by attitude disturbances resulting from thermally-induced motions of flexible structures. Recent examples of spacecraft affected by these disturbances include the Hubble Space Telescope (HST) and the Upper Atmosphere Research Satellite (UARS). Thermally-induced structural disturbances occur as the result of rapid changes in thermal loading typically initiated as a satellite exits or enters the Earth's shadow. Temperature differences in flexible appendages give rise to structural deformations, which in turn result in disturbance torques reacting back on the spacecraft. Structures which have proven susceptible to these disturbances include deployable booms and solar arrays. This paper investigates disturbances resulting from thermally-induced deformations of rigid panel solar arrays. An analytical model for the thermal-structural response of the solar array and the corresponding disturbance torque are presented. The effect of these disturbances on the attitude dynamics of a simple spacecraft is then investigated using a coupled system of governing equations which includes the effects of thermally-induced deformations. Numerical results demonstrate the effect of varying solar array geometry on the dynamic response of the system.

Johnston, John D.↗

Finite Element Modeling of Rigid-Flex PCB Robotic Structures for Dynamic Environments

Rigid-flex circuit boards are becoming moreprevalent as the limits are pushed on the size, mass, and geometryof electronic systems. A key aspect of designing a rigid-flexprinted circuit boards (PCB) system is an assessment of thedynamic properties of the PCB and predicting system perfor-mance under dynamic loading. Among current modeling method-ologies for rigid-flex PCB, a simplified modeling methodology thatadequately captures the system dynamics does not exist. This arti-cle presents a novel, computationally efficient approach formodeling rigid-flex PCB systems and the calibration of the mate-rial models via modal testing. The resulting simplified model isable to capture system frequencies, mode shapes, and representa-tive force-displacement behavior. The proposed methodology isused to model NASA Jet Propulsion Laboratory’s Pop-Up FlatFolding Explorer Robot (PUFFER) and assess the sensitivity of asystem model to input parameters.

John Bell↗

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

Herein this paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.

97 MATHEMATICS AND COMPUTING↗

Untangleing the effects of chain rigidity on the structure and dynamics of strongly adsorbed polymer melts

Here, we present a detailed analysis of coarse-grained molecular dynamics simulations of semiflexible polymer melts in contact with a strongly adsorbing substrate. We have characterized the segments in the interfacial layer by counting the number of trains, loops, tails and unadsorbed segments. For more rigid chains, a tail and an adsorbed segment (a train) dominate while loops are more prevalent in more flexible chains. The tails exhibit a non-uniformly stretched conformation akin to the polydispersed pseudobrush envisioned by Guiselin. To probe the dynamics of the segments we computed the layer z-resolved intermediate coherent collective dynamics structure factor, S(q, t, z), mean-square displacement of segments, and the 2nd Legendre polynomial of the time-autocorrelation of unit bond vectors, 2 [n i (t,z)•n i (0,z)]>. Our results show that segmental dynamics is slower for stiffer chains and there is a strong correlation between the structure and dynamics in the interfacial layer. There is no glassy layer, and the slowing down in dynamics of stiffer chains in the adsorbed region can be attributed to the densification and the more persistent layering of segments.

36 MATERIALS SCIENCE↗

Synthesis and Structural Investigation of Rigid Naphthyridine-Bis(carbene) for Trigonal Planar Coordination of Coinage Metals

Coinage metal complexes, particularly Cu(I) and Au(I), supported by N-heterocyclic carbenes are of broad interest in organometallic synthesis, catalysis, and luminescent materials. The d 10 coinage metals can adopt varied linear, trigonal planar, and tetrahedral geometries. However, two-coordinate, linear Cu(I) and Au(I) complexes supported by sterically demanding monodentate or chelating carbenes are generally observed. In most cases, chelating ligands generate multinuclear species with linear geometries at the corresponding Cu(I) centers rather than mononuclear complexes. In this report, we synthesized two bis(carbene) ligands anchored by a flexible bipyridine and a rigid naphthyridine backbone with tunable proximal and distal steric properties at the wingtips to examine the influence of backbone rigidity and directionality of carbene donors on the formation of trigonal planar coinage metal species. Here, the bipyridine-bis(carbene) (ImPy) 2 ligand exclusively stabilizes dinuclear chloride complexes of Cu(I) and Ag(I), whereas the naphthyridine-bis(carbene) (NBC) stabilizes mononuclear, trigonal planar chloride complexes of Cu(I) and Ag(I) and a dinuclear chloride Au(I) complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Correlating Local Compositions and Structures with the Macroscopic Optical Properties of Ce 3+ -Doped CaSc 2 O 4 , an Efficient Green-Emitting Phosphor

Calcium scandate (CaSc 2 O 4 ) substituted with small amounts (<1%) of Ce 3+ is a recently discovered bright-green-emitting phosphor with favorable light absorption and emission properties and robust temperature stability that make it well-suited for solid-state white-lighting applications. Combined analyses of scattering, solid-state nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), and photoluminescence measurements establish the compositional and structural origins of the macroscopic optical properties of this phosphor material. Simultaneous refinements of synchrotron X-ray and neutron diffraction data of Ce 3+ -doped CaSc 2 O 4 enable the average crystal structure to be determined, which is shown to correspond to an exceedingly rigid host structure, as corroborated by density functional theory (DFT) calculations. Such structural rigidity leads to high quantum efficiency, which is optimized by the substitution of as little as 0.5 mol % of Ce 3+ for Ca 2+ ions, with higher extents of Ce 3+ substitution leading to decreased photoluminescent quantum yields. Solid-state 43 Ca and 45 Sc magic-angle spinning (MAS) NMR spectra are sensitive to the effects of the paramagnetic Ce 3+ dopant ions on nearby atoms in the host structure and yield evidence for local structural distortions. EPR measurements provide direct insights on structures of the Ce 3+ ions, as a function of Ce 3+ substitution. The combined scattering and spectroscopic analyses yield detailed new understanding of the local and long-range structures of Ce 3+ -doped CaSc 2 O 4 , which account for the sensitive composition-dependent optical properties of this important phosphor material.

36 MATERIALS SCIENCE↗

A wave based method to predict the absorption, reflection and transmission coefficient of two-dimensional rigid frame porous structures with periodic inclusions

This paper presents an extension to the Wave Based Method to predict the absorption, reflection and transmission coefficients of a porous material with an embedded periodic set of inclusions. The porous unit cell is described using the Multi-Level methodology and by embedding Bloch–Floquet periodicity conditions in the weighted residual scheme. The dynamic pressure field in the semi-infinite acoustic domains is approximated using a novel wave function set that fulfils the Helmholtz equation, the Bloch–Floquet periodicity conditions and the Sommerfeld radiation condition. The method is meshless and computationally efficient, which makes it well suited for optimisation studies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Proton-detected 3D {sup 1}H/{sup 13}C/{sup 1}H correlation experiment for structural analysis in rigid solids under ultrafast-MAS above 60 kHz

A proton-detected 3D {sup 1}H/{sup 13}C/{sup 1}H chemical shift correlation experiment is proposed for the assignment of chemical shift resonances, identification of {sup 13}C-{sup 1}H connectivities, and proximities of {sup 13}C-{sup 1}H and {sup 1}H-{sup 1}H nuclei under ultrafast magic-angle-spinning (ultrafast-MAS) conditions. Ultrafast-MAS is used to suppress all anisotropic interactions including {sup 1}H-{sup 1}H dipolar couplings, while the finite-pulse radio frequency driven dipolar recoupling (fp-RFDR) pulse sequence is used to recouple dipolar couplings among protons and the insensitive nuclei enhanced by polarization transfer technique is used to transfer magnetization between heteronuclear spins. The 3D experiment eliminates signals from non-carbon-bonded protons and non-proton-bonded carbons to enhance spectral resolution. The 2D (F1/F3) {sup 1}H/{sup 1}H and 2D {sup 13}C/{sup 1}H (F2/F3) chemical shift correlation spectra extracted from the 3D spectrum enable the identification of {sup 1}H-{sup 1}H proximity and {sup 13}C-{sup 1}H connectivity. In addition, the 2D (F1/F2) {sup 1}H/{sup 13}C chemical shift correlation spectrum, incorporated with proton magnetization exchange via the fp-RFDR recoupling of {sup 1}H-{sup 1}H dipolar couplings, enables the measurement of proximities between {sup 13}C and even the remote non-carbon-bonded protons. The 3D experiment also gives three-spin proximities of {sup 1}H-{sup 1}H-{sup 13}C chains. Experimental results obtained from powder samples of L-alanine and L-histidine ⋅ H{sub 2}O ⋅ HCl demonstrate the efficiency of the 3D experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hybrid Inflatable Pressure Vessel

Figure 1 shows a prototype of a large pressure vessel under development for eventual use as a habitable module for long spaceflight (e.g., for transporting humans to Mars). The vessel is a hybrid that comprises an inflatable shell attached to a rigid central structural core. The inflatable shell is, itself, a hybrid that comprises (1) a pressure bladder restrained against expansion by (2) a web of straps made from high-strength polymeric fabrics. On Earth, pressure vessels like this could be used, for example, as portable habitats that could be set up quickly in remote locations, portable hyperbaric chambers for treatment of decompression sickness, or flotation devices for offshore platforms. In addition, some aspects of the design of the fabric straps could be adapted to such other items as lifting straps, parachute straps, and automotive safety belts. Figure 2 depicts selected aspects of the design of a vessel of this type with a toroidal configuration. The bladder serves as an impermeable layer to keep air within the pressure vessel and, for this purpose, is sealed to the central structural core. The web includes longitudinal and circumferential straps. To help maintain the proper shape upon inflation after storage, longitudinal and circumferential straps are indexed together at several of their intersections. Because the web is not required to provide a pressure seal and the bladder is not required to sustain structural loads, the bladder and the web can be optimized for their respective functions. Thus, the bladder can be sealed directly to the rigid core without having to include the web in the seal substructure, and the web can be designed for strength. The ends of the longitudinal straps are attached to the ends of the rigid structural core by means of clevises. Each clevis pin is surrounded by a roller, around which a longitudinal strap is wrapped to form a lap seam with itself. The roller is of a large diameter chosen to reduce bending of the fibers in the strap. The roller also serves to equalize the load in the portions of the strap on both sides of the clevis pin. The lap seam is formed near the clevis by use of a tapered diamond stitch: This stitch is designed specifically to allow fibers in the stitch and strap to relax under load in such a manner that the load becomes more nearly evenly distributed among all fibers in the stitch region. Thus, the tapered diamond stitch prevents load concentrations that could cause premature failure of the strap and thereby increases the strength of the strap/structural-core joint. The lap seam can be rated at >90 percent of the strength of the strap material.

Raboin, Jasen↗

Six new inorganic–organic hybrids based on rigid triangular ligands: Syntheses, structures and properties

Six new inorganic–organic hybrids based on rigid triangular N-containing ligands, NaCu{sup I}{sub 2}(tib){sub 4}(H{sub 2}O){sub 4}[H{sub 2}PW{sup V}W{sup VI}{sub 11}O{sub 40}][H{sub 2}PW{sup VI}{sub 12}O{sub 40}]·6H{sub 2}O (1), Cu{sup II}{sub 3}(tib){sub 4}Cl{sub 4}[H{sub 2}PW{sup VI}{sub 12}O{sub 40}]{sub 2}·4H{sub 2}O (2), Co(tib){sub 2}[PW{sup V}{sub 3}W{sup VI}{sub 9}O{sub 38}]·5H{sub 2}O (3), Cu{sup II}{sub 3}(tib){sub 2}[P{sub 2}Mo{sup VI}{sub 5}O{sub 22}(O{sub 2})]·4H{sub 2}O (4), Mn(pytpy){sub 2}Mo{sup VI}{sub 4}O{sub 13} (5) and Co(pytpy){sub 2}Mo{sup VI}{sub 4}O{sub 13} (6) (tib=1,3,5-tris(1-imidazolyl)benzene, pytpy=4’-(4”-pyridyl)2,4’:6’,4”-terpyridine), have been hydrothermally synthesized. Single crystal X-ray diffraction studies revealed that compounds 1–4 display two-dimensional (2D) layered structures, and in compounds 1–3, the adjacent Keggin anions link with each other by W–O–W covalent interactions to form 1D inorganic chains. Compounds 5–6 are 3D “pillar-layer” frameworks based on bimetal–oxide layers pillared by the pytpy ligands. The compounds have been characterized by elemental analysis, powder X−ray diffraction, X-ray photoelectron spectroscopy and thermo gravimetric analyses. Moreover, the electrochemical and catalytic properties of compound 1 have been investigated as well. - Graphical abstract: Six new inorganic–organic hybrids based on rigid triangular N-containing ligands have been obtained under hydrothermal conditions and characterized by single-crystal X-ray diffraction analyses, elemental analyses, IR spectra, and thermogravimetric (TG) analyses. Compounds 1–4 display two-dimensional (2D) layers structure, and in compounds 1–3, the adjacent Keggin anions link with each other by W–O–W covalent interactions to form 1D inorganic Keggin anions chains. Compounds 5–6 are 3D “pillar-layer” frameworks based on bimetal–oxide layers pillared by the pytpy ligands. - Highlights: • MOFs based on POMs have been prepared. • Six new compounds based on rigid triangular N-containing ligands. • The adjacent POMs only share the oxygen atom to form a 1D inorganic Keggin chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An incompressible Eulerian method for fluid–structure interaction with mixed soft and rigid solids

Here, we present a general simulation approach for incompressible fluid–structure interactions in a fully Eulerian framework using the reference map technique. The approach is suitable for modeling one or more rigid or finitely deformable objects or soft objects with rigid components interacting with the fluid and with each other. It is also extended to control the kinematics of structures in fluids. The model is based on our previous Eulerian fluid–soft solver [Rycroft et al., “Reference map technique for incompressible fluid–structure interaction,” J. Fluid Mech. 898, A9 (2020)] and generalized to rigid structures by constraining the deformation-rate tensor in a projection framework. Several numerical examples are presented to illustrate the capability of the method.

42 ENGINEERING↗