Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

A new high-order Fourier continuation-based elasticity solver for complex three-dimensional geometries

This thesis presents a new approach for the numerical solution of three-dimensional problems in elastodynamics. The new methodology, which is based on a recently introduced Fourier continuation (FC) algorithm for the solution of Partial Differential Equations on the basis of accurate Fourier expansions of possibly non-periodic functions, enables fast, high-order solutions of the time-dependent elastic wave equation in a nearly dispersionless manner, and it requires use of CFL constraints that scale only linearly with spatial discretizations. A new FC operator is introduced to treat Neumann and traction boundary conditions, and a block-decomposed (sub-patch) overset strategy is presented for implementation of general, complex geometries in distributed-memory parallel computing environments. Our treatment of the elastic wave equation, which is formulated as a complex system of variable-coefficient PDEs that includes possibly heterogeneous and spatially varying material constants, represents the first fully-realized three-dimensional extension of FC-based solvers to date. Challenges for three-dimensional elastodynamics simulations such as treatment of corners and edges in three-dimensional geometries, the existence of variable coefficients arising from physical configurations and/or use of curvilinear coordinate systems and treatment of boundary conditions, are all addressed. The broad applicability of our new FC elasticity solver is demonstrated through application to realistic problems concerning seismic wave motion on three-dimensional topographies as well as applications to non-destructive evaluation where, for the first time, we present three-dimensional simulations for comparison to experimental studies of guided-wave scattering by through-thickness holes in thin plates.

Three-dimensional nonlinear inelastic analysis of steel moment-frame buildings damaged by earthquake excitations

The Northridge earthquake of January 17, 1994, highlighted the two previously known problems of premature fracturing of connections and the damaging capabilities of near-source ground motion pulses. Large ground motions had not been experienced in a city with tall steel moment-frame buildings before. Some steel buildings exhibited fracture of welded connections or other types of structural degradation.

A sophisticated three-dimensional nonlinear inelastic program is developed that can accurately model many nonlinear properties commonly ignored or approximated in other programs. The program can assess and predict severely inelastic response of steel buildings due to strong ground motions, including collapse.

Three-dimensional fiber and segment discretization of elements is presented in this work. This element and its two-dimensional counterpart are capable of modeling various geometric and material nonlinearities such as moment amplification, spread of plasticity and connection fracture. In addition to introducing a three-dimensional element discretization, this work presents three-dimensional constraints that limit the number of equations required to solve various three-dimensional problems consisting of intersecting planar frames.

Two buildings damaged in the Northridge earthquake are investigated to verify the ability of the program to match the level of response and the extent and location of damage measured. The program is used to predict response of larger near-source ground motions using the properties determined from the matched response.

A third building is studied to assess three-dimensional effects on a realistic irregular building in the inelastic range of response considering earthquake directivity. Damage levels are observed to be significantly affected by directivity and torsional response.

Several strong recorded ground motions clearly exceed code-based levels. Properly designed buildings can have drifts exceeding code specified levels due to these ground motions. The strongest ground motions caused collapse if fracture was included in the model. Near-source ground displacement pulses can cause columns to yield prior to weaker-designed beams. Damage in tall buildings correlates better with peak-to-peak displacements than with peak-to-peak accelerations.

Dynamic response of tall buildings shows that higher mode response can cause more damage than first mode response. Leaking of energy between modes in conjunction with damage can cause torsional behavior that is not anticipated.

Various response parameters are used for all three buildings to determine what correlations can be made for inelastic building response. Damage levels can be dramatically different based on the inelastic model used. Damage does not correlate well with several common response parameters.

Realistic modeling of material properties and structural behavior is of great value for understanding the performance of tall buildings due to earthquake excitations.

Behaviour of unsteady transonic shock / boundary layer interactions with three-dimensional effects

An experimental investigation into the response of transonic SBLIs to periodic down-stream pressure perturbations in a parallel walled duct has been conducted. Tests have been carried out with a shock strength of M ∞ = 1.5 for pressure perturbation frequencies in the range 16-90 Hz. Analysis of the steady interaction at M∞ = 1.5 has also been made. The principle measurement techniques were high speed schlieren photography and laser Doppler anemometry. The structure of the steady SBLI was found to be highly three-dimensional, with large corner flows and sidewall SBLIs. These aspects are thought to influence the upstream transmission of pressure information through the interaction by affecting the post-shock flow field, including the extent of regions of secondary supersonic flow. At low frequency, the dynamics of shock motion can be predicted using an inviscid analytical model. At increased frequencies, viscous effects become significant and the shock exhibits unexpected dynamic behaviour, due to a phase lag between the upstream transmission of pressure information in the core flow and in the viscous boundary layers. Flow control in the form of micro-vane vortex generators was found to have a small impact on shock dynamics, due to the effect it had on the post-shock flow field outside the viscous boundary layer region. The relationship between inviscid and viscous effects is developed and potential destabilising mechanisms for SBLIs in practical applications are suggested. Copyright © 2009 by Paul Bruce and Holger Babinsky.

Three-dimensional effects on sliding and waving wings

Like large insects, micro air vehicles operate at low Reynolds numbers O(1; 000 - 10; 000) in a regime characterized by separated flow and strong vortices. The leading-edge vortex has been identified as a significant source of high lift on insect wings, but the conditions required for the formation of a stably attached leading-edge vortex are not yet known. The waving wing is designed to model the translational phase of an insect wing stroke by preserving the unsteady starting and stopping motion as well as three-dimensionality in both wing geometry (via a finite-span wing) and kinematics (via wing rotation). The current study examines the effect of the spanwise velocity gradient on the development of the leading-edge vortex along the wing as well as the effects of increasing threedimensionalityby decreasing wing aspect ratio from four to two. Dye flow visualization and particle image velocimetry reveal that the leading-edge vortices that form on a sliding or waving wing have a very high aspect ratio. The structure of the flow is largely two-dimensional on both sliding and waving wings and there is minimal interaction between the leading-edge vortices and the tip vortex. Significant spanwise flow was observed on the waving wing but not on the sliding wing. Despite the increased three-dimensionality on the aspect ratio 2 waving wing, there is no evidence of an attached leading-edge vortex and the structure of the flow is very similar to that on the higher-aspect-ratio wing and sliding wing. © Copyright 2010.

Experimentally validated three dimensional GCT wafer level simulations

In this paper we present a wafer level three-dimensional simulation model of the Gate Commutated Thyristor (GCT) under inductive switching conditions. The simulations are validated by extensive experimental measurements. To the authors' knowledge such a complex simulation domain has not been used so far. This method allows the in depth study of large area devices such as GCTs, Gate Turn Off Thyristors (GTOs) and Phase Control Thyristors (PCTs). The model captures complex phenomena, such as current filamentation including subsequent failure, which allow us to predict the Maximum Controllable turn-off Current (MCC) and the Safe Operating Area (SOA) previously impossible using 2D distributed models. © 2012 IEEE.

Fluid-structure interaction of three-dimensional magnetic artificial cilia

A numerical model is developed to analyse the interaction of artificial cilia with the surrounding fluid in a three-dimensional setting in the limit of vanishing fluid inertia forces. The cilia are modelled using finite shell elements and the fluid is modelled using a boundary element approach. The coupling between both models is performed by imposing no-slip boundary conditions on the surface of the cilia. The performance of the model is verified using various reference problems available in the literature. The model is used to simulate the fluid flow due to magnetically actuated artificial cilia. The results show that narrow and closely spaced cilia create the largest flow, that metachronal waves along the width of the cilia create a significant flow in the direction of the cilia width and that the recovery stroke in the case of the out-of-plane actuation of the cilia strongly depends on the cilia width. © 2012 Cambridge University Press.

HTGR fuel element depletion benchmark: Stage three results

Recently, a new numerical benchmark exercise for High Temperature Gas Cooled Reactor (HTGR) fuel depletion was defined. The purpose of this benchmark is to provide a comparison basis for different codes and methods applied to the burnup analysis of HTGRs. The benchmark specifications include three different models: (1) an infinite lattice of tristructural isotropic (TRISO) fuel particles, (2) an infinite lattice of fuel pebbles, and (3) a prismatic fuel including fuel and coolant channels. In this paper, we present the results of the third stage of the benchmark obtained with MCNP based depletion code BGCore and deterministic lattice code HELIOS 1.9. The depletion calculations were performed for three-dimensional model of prismatic fuel with explicitly described TRISO particles as well as for two-dimensional model, in which double heterogeneity of the TRISO particles was eliminated using reactivity equivalent physical transformation (RPT). Generally, good agreement in the results of the calculations obtained using different methods and codes was observed.

Joint experimental and numerical approach to three-dimensional shock control bump research

Previous studies of transonic shock control bumps have often been either numerical or experimental. Comparisons between the two have been hampered by the limitations of either approach. The present work aims to bridge the gap between computational fluid dynamics and experiment by planning a joint approach from the outset. This enables high-quality validation data to be produced and ensures that the conclusions of either aspect of the study are directly relevant to the application. Experiments conducted with bumps mounted on the floor of a blowdown tunnel were modified to include an additional postshock adverse pressure gradient through the use of a diffuser as well as introducing boundary-layer suction ahead of the test section to enable the in-flow boundary layer to be manipulated. This has the advantage of being an inexpensive and highly repeatable method. Computations were performed on a standard airfoil model, with the flight conditions as free parameters. The experimental and computational setups were then tuned to produce baseline conditions that agree well, enabling confidence that the experimental conclusions are relevant. The methods are then applied to two different shock control bumps: a smoothly contoured bump, representative of previous studies, and a novel extended geometry featuring a continuously widening tail, which spans the wind-tunnel width at the rear of the bump. Comparison between the computational and experimental results for the contour bump showed good agreement both with respect to the flow structures and quantitative analysis of the boundary-layer parameters. It was seen that combining the experimental and numerical data could provide valuable insight into the flow physics, which would not generally be possible for a one-sided approach. The experiments and computational fluid dynamics were also seen to agree well for the extended bump geometry, providing evidence that, even though thebumpinteracts directly with the wind-tunnel walls, it was still possible to observe the key flow physics. The joint approach is thus suitable even for wider bump geometries. Copyright © 2013 by S. P. Colliss, H. Babinsky, K. Nubler, and T. Lutz. Published by the American Institute of Aeronautics and Astronautics, Inc.

High-Q TM whispering-gallery modes in three-dimensional microcylinders

We present a generation condition for realizing high-Q TM whispering-gallery modes (WGMs) in semiconductor microcylinders. For microcylinders with symmetry or weak asymmetry vertical waveguiding, we show that TM WGMs can have a high Q factor, with the magnitude of 10(4) at the radius of the microcylinder of 1 mu m, by three-dimensional numerical simulation. The Q factor of TE WGMs is much less than that of TM WGMs in the semiconductor microcylinders due to a vertical radiation loss caused by mode coupling with the vertical propagating mode. The results open up a possible application of TM WGMs in semiconductor microcylinders for efficient current injection microlasers and single photon sources.

Large depth-of-view portable three-dimensional laser scanner and its segmental calibration for robot vision

A portable 3D laser scanning system has been designed and built for robot vision. By tilting the charge coupled device (CCD) plane of portable 3D scanning system according to the Scheimpflug condition, the depth-of-view is successfully extended from less than 40 to 100 mm. Based on the tilted camera model, the traditional two-step camera calibration method is modified by introducing the angle factor. Meanwhile, a novel segmental calibration approach, i.e., dividing the whole work range into two parts and calibrating, respectively, with corresponding system parameters, is proposed to effectively improve the measurement accuracy of the large depth-of-view 3D laser scanner. In the process of 3D reconstruction, different calibration parameters are used to transform the 2D coordinates into 3D coordinates according to the different positions of the image in the CCD plane, and the measurement accuracy of 60 mu m is obtained experimentally. Finally, the experiment of scanning a lamina by the large depth-of-view portable 3D laser scanner used by an industrial robot IRB 4400 is also employed to demonstrate the effectiveness and high measurement accuracy of our scanning system. (C) 2007 Elsevier Ltd. All rights reserved.

CFD-DEM simulation of three-dimensional aeolian sand movement

A three-dimensional CFD-DEM model is proposed to investigate the aeolian sand movement. The results show that the mean particle horizontal velocity can be expressed by a power function of heights. The probability distribution of the impact and lift-off velocities of particles can be described by a log-normal function, and that of the impact and lift-off angles can be expressed by an exponential function. The probability distribution of particle horizontal velocity at different heights can be described as a lognormal function, while the probability distribution of longitudinal and vertical velocity can be described as a normal function. The comparison with previous two-dimensional calculations shows that the variations of mean particle horizontal velocity along the heights in two-dimensional and three-dimensional models are similar. However, the mean particle density of the two-dimensional model is larger than that in reality, which will result in the overestimation of sand transportation rate in the two-dimensional calculation. The study also shows that the predicted probability distributions of particle velocities are in good agreement with the experimental results.

Effects of Ionizing Radiation on Three-Dimensional Human Vessel Models: Differential Effects According to Radiation Quality and Cellular Development

Little is known about the effects of space radiation on the human body. There are a number of potential chronic and acute effects, and one major target for noncarcinogenic effects is the human vasculature. Cellular stress, inflammatory response, and other radiation effects on endothelial cells may affect vascular function. This study was aimed at understanding the effects of space ionizing radiation on the formation and maintenance of capillary-like blood vessels. We used a 3D human vessel model created with human endothelial cells in a gel matrix to assess the effects of low-LET protons and high-LET iron ions. Iron ions were more damaging and caused significant reduction in the length of intact vessels in both developing and mature vessels at a dose of 80 cGy. Protons had no effect on mature vessels up to a dose of 3.2 Gy but did inhibit vessel formation at 80 cGy. Comparison with gamma radiation showed that photons had even less effect, although, as with protons, developing vessels were more sensitive. Apoptosis assays showed that inhibition of vessel development or deterioration of mature vessels was not due to cell death by apoptosis even in the case of iron ions. These are the first data to show the effects of radiation with varying linear energy transfer on a human vessel model. (C) 2011 In Radiation Research Society