VTechWorks Repository :: Browsing by Author "Renardy, Yuriko Y."

Browsing by Author "Renardy, Yuriko Y."

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Analysis of the Radiation Mechanisms in and Design of Tightly-Coupled Antenna Arrays
Vogler, Terry Richard (Virginia Tech, 2010-09-10)
The objective of this research is to design well-tuned, wideband elements for thin planar or cylindrically conformal arrays of balanced elements fed over ground. These arrays have closely spaced elements to achieve wide bandwidths through mutual coupling. This dissertation develops two wideband designs in infinite, semi-infinite, and finite array configurations. The infinite array is best for element tuning. This research advances a concept of a distributed, parallel capacitance between elements and across feeds that must be mutually altered for tuning. Semi-infinite techniques limit the problem space and determine the proper resistive loads to control the low-frequency array-guided surface wave (AGSW). The tight physical placement also forms a periodic structure that, along with the array boundary, launches a wave across the array surface. Options to suppress this surface wave are resistive loading and cylindrical conformations. AGSW control is necessary to achieve a maximum bandwidth, but lower radiation or aperture efficiency results. Conformation is shown to be an ineffective method for AGSW control alone. The Wrapped Bowtie design emerges as a novel design offering nearly a 10:1 bandwidth as a finite array over ground. Some bandwidth comes from the losses in radiation efficiency, which is necessary to control the AGSW; however, its simulated VSWR < 3 bandwidth in an infinite array is 7.24:1 with full efficiency. Less than perfect efficiency is required to mitigate surface wave effects, unless bandwidth is to be compromised. That loss may be as radiation or aperture efficiency, but it is unavoidable if the infinite array bandwidth is to be maintained in finite array designs. Lastly, this research articulates a development path for tightly-coupled arrays that extends in stages from infinite to semi-infinite, and thence finite layouts. Distinctions are explained and defended for the design focus at each stage. Element design, tuning, and initial feed design occur at the infinite array stage; AGSW suppression occurs at the semi-infinite stage; and design confirmation occurs only with the finite array.
Bedload Transport in Gravel-Bed Streams under a wide range of Shields Stresses
Almedeij, Jaber H. (Virginia Tech, 2002-03-28)
Bedload transport is a complicated phenomenon in gravel-bed streams. Several factors account for this complication, including the different hydrologic regime under which different stream types operate and the wide range of particle sizes of channel bed material. Based on the hydrologic regime, there are two common types of gravel-bed streams: perennial and ephemeral. In terms of channel bed material, a gravel bed may have either unimodal or bimodal sediment. This study examines more closely some aspects of bedload transport in gravel-bed streams and proposes explanations based on fluvial mechanics. First, a comparison between perennial and ephemeral gravel-bed streams is conducted. This comparison demonstrates that under a wide range of Shields stresses, the trends exhibited by the bedload transport data of the two stream types collapse into one continuous curve, thus a unified approach is warranted. Second, an empirical bedload transport relation that accounts for the variation in the make-up of the surface material within a wide range of Shields stresses is developed. The accuracy of the relation is tested using available bedload transport data from streams with unimodal sediment. The relation is also compared against other formulae available in the literature that are commonly used for predicting bedload transport in gravel-bed streams. Third, an approach is proposed for transforming the bimodal sediment into two independent unimodal fractions, one for sand and another for gravel. This transformation makes it possible to carry out two separate computations of bedload transport rate using the bedload relation developed in this study for unimodal sediment. The total bedload transport rate is estimated by adding together the two contributions.
Comment on "A numerical study of periodic disturbances on two-layer Couette flow" [Phys. Fluids 10, 3056 (1998)]
Renardy, Yuriko Y.; Li, Jie (AIP Publishing, 1999-10)
The flow of fluids with different viscosities, subjected to an interfacial perturbation, can lead to fingering and migration...
A comparison of viscoelastic stress wakes for two-dimensional and three-dimensional Newtonian drop deformations in a viscoelastic matrix under shear
Afkhami, Shahriar; Yue, Pengtao; Renardy, Yuriko Y. (American Institute of Physics, 2009-07)
A recent experimental study of a Newtonian drop suspended in a viscoelastic matrix undergoing simple shear displays a transient overshoot in drop deformation which is qualitatively similar to two-dimensional (2D) numerical simulation results. Despite the similarity, an interpretation in light of the 2D result is misleading because the overshoot is absent in the fully three-dimensional (3D) simulation. This motivates a study of regimes where qualitatively different and interesting features such as overshoots in deformation occur for a 2D drop but not for a 3D drop. The influence of viscoelastic "wakes" that emanate from the drop tips is reported. The viscoelastic wakes are larger and of higher magnitude in 3D than in 2D, and lead to more deformation in 3D. During drop evolution, the less deformed drop is found to be aligned more with the flow direction. As the drop-to-matrix viscosity ratio increases from 1 to past 3, drop rotation is promoted, with accompanying retraction when the capillary number is sufficiently high. Thus, a 3D overshoot in deformation is promoted with increasing viscosity ratio.
Control of Dynamic Response of Thin-Walled Composite Beams Using Structural Tailoring and Piezoelectric Actuation
Na, Sungsoo (Virginia Tech, 1997-09-28)
A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is addressed. The cantilevered structure is modeled as a thin-walled beam of arbitrary cross-section and incorporates a number of non-classical effects such as transverse shear, warping restraint, anisotropy of constituent materials and heterogeneity of the construction. Whereas structural tailoring uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating/sensing capabilities of piezoelectric materials bonded or embedded into the host structure. Various control laws relating the piezoelectrically-induced bending moment with combined kinematical variables characterizing the response at given points of the structure are implemented and their effects on the closed-loop frequencies and dynamic response to external excitations are investigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. In addition, the influence of a number of non-classical effects characterizing the structural model on the open and closed-loop dynamic responses have been considered and their roles assessed.
Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields
Afkhami, Shahriar; Tyler, A. J.; Renardy, Yuriko Y.; Renardy, Michael J.; St Pierre, T. G.; Woodward, R. C.; Riffle, Judy S. (Cambridge University Press, 2010-11)
The effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium is investigated numerically and compared with experimental data. A numerical formulation for the time-dependent simulation of magnetohydrodynamics of two immiscible non-conducting fluids is used with a volume-of-fluid scheme for fully deformable interfaces. Analytical formulae for ellipsoidal drops and near-spheroidal drops are reviewed and developed for code validation. At low magnetic fields, both the experimental and numerical results follow the asymptotic small deformation theory. The value of interfacial tension is deduced from an optimal fit of a numerically simulated shape with the experimentally obtained drop shape, and appears to be a constant for low applied magnetic fields. At high magnetic fields, on the other hand, experimental measurements deviate from numerical results if a constant interfacial tension is implemented. The difference can be represented as a dependence of apparent interfacial tension on the magnetic field. This idea is investigated computationally by varying the interfacial tension as a function of the applied magnetic field and by comparing the drop shapes with experimental data until a perfect match is found. This estimation method provides a consistent correlation for the variation in interfacial tension at high magnetic fields. A conclusion section provides a discussion of physical effects which may influence the microstructure and contribute to the reported observations.
Deformations of Piezoceramic-Composite Actuators
Jilani, Adel Benhaj (Virginia Tech, 1999-11-11)
In the past few years a new class of layered piezoceramic and piezoceramic-composite actuators, known as RAINBOW and GRAPHBOW, respectively, that are capable of achieving 100 times greater out-of-plane displacements than previously available has been developed. Prior to the development of RAINBOW and GRAPHBOW, large stacks of piezoelectric actuators, requiring complicated electronic drive circuits, were necessary to achieve the displacement now possible through the use of a single RAINBOW actuator. The major issues with both RAINBOW and GRAPHBOW are the prediction of their room-temperature shapes after processing, and their deformation response under application of electric field. In this research, a methodology for predicting the manufactured shapes of rectangular and disk-style RAINBOW and GRAPHBOW is developed. All of the predictive analyses developed are based on finding approximate displacement responses that minimize the total potential energy of the devices through the use of variational methods and the Rayleigh-Ritz technique. These analyses are based on classical layered plate theory and assumed the various layers exhibited linear elastic, temperature-independent behavior. Geometric nonlinearities are important and are included in the strain-displacement relations. Stability of the predicted shapes is determined by examining the second variation of the total potential energy. These models are easily modified to account for the deformations induced by actuation of the piezoceramic. The results indicate that for a given set of material properties, rectangular RAINBOW can have critical values of sidelength-to-thickness ratio (Lx/H or Ly/H) below which RAINBOW exhibits unique, or single-valued, spherical or domed shapes when cooled from the processing temperature to room temperature. For values of sidelength-to-thickness ratio greater than the critical value, RAINBOW exhibits multiple room-temperature shapes. Two of the shapes are stable and are, in general, near-cylindrical. The third shape is spherical and is unstable. Similarly, disk-style RAINBOW can have critical values of radius-to-thickness ratios (R/H) below which RAINBOW exhibits axisymmetric room-temperature shapes. For values of R/H greater than the critical value, disk-style RAINBOW exhibits two stable near-cylindrical shapes and one unstable axisymmetric shape. Moreover, it is found that for the set of material properties used in this study, the optimal reduced layer thickness would be at 55%, since the maximum change in curvature is achieved under the application of an electric field, while the relationship between the change in curvatures and the electric field is kept very close to being linear. In general, good agreement is found for comparisons between the predicted and manufactured shapes of RAINBOW. A multi-step thermoelastic analysis is developed to model the addition of the fiber-reinforced composite layer to RAINBOW to make GRAPHBOW. Results obtained for rectangular RAINBOW indicate that if the bifurcation temperature in the temperature-curvature relation is lower than the composite cure temperature, then a unique stable GRAPHBOW shape can be obtained. If the RAINBOW bifurcation temperature is above the composite cure temperature, multiple room-temperature GRAPHBOW shapes are obtained and saddle-node bifurcations can be encountered during the cooling to room temperature of [0°/RAINBOW], [RAINBOW/0o], and [0o2/RAINBOW]. Rectangular [RAINBOW/0o/90o] seems to be less likely to encounter saddle-node bifurcations. Furthermore, the unstable spherical RAINBOW configuration is converted to a stable near-cylindrical configuration. For the case considered of disk-style GRAPHBOW, three stable room-temperature shapes are obtained and the unstable axisymmetric RAINBOW configuration is also converted to a stable near-cylindrical configuration. For both rectangular and disk-style GRAPHBOW, the relationship between the major curvature and the electric field is shown to be very close to being linear. This characteristic would aid any dynamic analysis of RAINBOW or GRAPHBOW.
Deformations of Unsymmetric Composite Panels
Ochinero, Tomoya Thomas (Virginia Tech, 2001-10-24)
This work discusses the deformations of various unsymmetric composite panels due to thermal and mechanical loads. Chapter 2 focuses on the warpage of large unsymmetric curved composite panels due manufacturing anomalies. These panels are subjected to a temperature change of -280°F to simulate the cooling from the autoclave cure temperature. Sixteen layer quasi-isotropic, axial-stiff, and circumferentially-stiff laminates are considered. These panels are intended to be symmetric laminates, but are slightly unsymmetric due to the manufacturing anomalies. Rayleigh-Ritz and finite-element models are developed to predict the deformations. Initially, to serve as a basis for comparison, warpage effects due to orthotropic thermal expansion properties in perfect panels are investigated and are found to produce deformations not captured in two-dimensional theories. This is followed by the investigation of the effects of ply misalignments. Ply misalignments of 5° are incorporated into the laminate, one layer at a time, to produce unsymmetric laminates. It is found that ply misalignments produce warpages much larger than those induced by orthotropic thermal expansion properties. Next, unsymmetric laminates resulting from ply thickness variations are investigated. Layers 10% thicker than nominal are incorporated into the laminate, one layer at a time, while the remaining layers are of uniform thickness. Due to the change in fiber volume fraction of the thicker layers, corresponding material properties are modified to reflect this change. The results show that ply thickness variations cause warpages of about 25-50% of those induced by ply misalignments. Finally, warpage of panels due to nonuniform cooling due to inplane thermal gradients during cure is investigated. A thermal gradient of 0.1°F/in. is used to construct six inplane distributions. It is found that the warpages induced by thermal gradients are very small. The warpages are negligible with respect to those induced by ply thickness variations or ply misalignments. Deformations induced by thermal gradients depend primarily on the magnitude of the thermal gradient, but not on the pattern of distribution. Overall, ply misalignments cause the most warpage, followed by ply thickness variations. Important variables for these imperfections are, the through-thickness location of the imperfections, the orientation of the layer containing the imperfections, and the lamination sequence. All cases show that geometric nonlinearities are important to accurately predict the deformations induced by these imperfections. Chapter 3 discusses the deformations of composite plates that are intentionally fabricated to be unsymmetric. Such plates, if flat, might be considered in applications where bending-stretching coupling effects can be used to advantage. It is assumed the laminates are cured at an elevated temperature and then cooled 280°F. Significant deformations result because of the high level of asymmetry in the laminate construction. Accordingly, geometric nonlinearities are included in the models. Four cross-ply laminates and three angle-ply laminates are considered. Four-term and 14-term Rayleigh-Ritz models are developed, together with finite-element models to model the deformations. Actual specimens were constructed and the deformations measured to compare with predictions. The results show that agreement between predictions and the experimental results are good. The 14-term Rayleigh-Ritz model is found to be the most useful due to its ability to find multiple solutions, its physical basis, and computational efficiency. Chapter 4 discusses the deformations of initially flat aluminum, symmetric, and unsymmetric composite plates due to axial endshortening under various boundary conditions, the aluminum and symmetric plates serving as a baseline. Seven plates are considered, each with three boundary condition combinations, namely, clamped ends and sides (CL-CL), clamped ends with simply-supported sides (CL-SS), and simply-supported ends and sides (SS-SS). Generally, the boundary conditions play a key role in the deformation characteristics of the plates. The aluminum and symmetric cross-ply plates have no out-of-plane deformations until classic buckling, or primary instability, then each exhibits two stable solutions. Each also exhibits secondary instability that results in two stable solutions. The symmetric laminates show less of a dependence on the boundary conditions compared to the unsymmetric laminates. Unsymmetric laminates show a mixture of characteristics. Some cases exhibit primary instability, other cases do not. Some cases exhibit secondary instability, while some case do not. The unsymmetric cross-ply laminates have only one stable solution after secondary buckling, while most other laminates and boundary condition combinations have two stable solutions. It is interesting to note that for the unbalanced unsymmetric [302/90/0]2T laminate, the boundary conditions controlled the sign of the out-of-plane deflection from the onset of axial endshortening. Generally speaking, the CL-CL cases carry the most load, followed by the CL-SS, and then the SS-SS cases. Like all the problems discussed in Chapter 2 and 3, geometric nonlinearities are found to be important for this case as well.
The Development and Control of Axial Vortices over Swept Wings
Klute, Sandra M. (Virginia Tech, 1999-08-02)
The natural unsteadiness in the post-breakdown flowfield of a 75° sweep delta wing at 40° angle of attack was studied with dual and single point hot-wire anemometry in the Engineering Science and Mechanics (ESM) Wind Tunnel at a Reynolds number Re = 210,000. Data were taken in five crossflow planes surrounding the wing's trailing edge. Results showed a dominant narrowband Strouhal frequency of St = 1.5 covering approximately 80% of the area with lower-intensity broadband secondary frequencies over 15% of that region. Cross-correlations between a fixed and traversing wire were calculated and phase and coherences mapped to determine the convection speed and trajectory of the helical mode instability. High-speed Particle Image Velocimetry (PIV) was conducted over a 75° sweep delta wing at 40° angle of attack in the ESM Water Tunnel II at Re = 45,000. Data were taken along the axis of the vortex in the breakdown flowfield at a speed of 0.1% of the convective time scale of the flow. Animations of instantaneous streamlines and velocity vectors revealed the impression of a helically spiralling vortex core on the measurement plane. Spectral analysis of the PIV data showed reduced frequencies which confirmed those found with the single-point measurements made in the ESM Wind Tunnel. The effect of four novel control surfaces on the breakdown flowfield of the delta wing was studied with surface pressure measurements along the axis of the vortex in the ESM Wind Tunnel. The apex flap was found effective and delayed vortex breakdown by 8° for a fixed wing. The flowfield was characterized over the delta wing executing a pitch-up maneuver at a reduced frequency of 0.06. Surface pressure measurements were taken in the ESM Wind Tunnel and Laser Doppler Velocimetry (LDV) was employed in the ESM Water Tunnel I as both the unmodified wing and then the wing with an apex flap deployed at an optimal angle b = 15° executed the pitch-up. Both sets of data confirmed the hysteresis of the flowfield. The LDV data, taken in two crossflow planes throughout the maneuver, showed an asymmetric breakdown development. As a practical extension of the study of the breakdown wake flowfield, hot-wire measurements were made over an F/A-18 model to determine the spectral characteristics of the flowfield. Three-dimensional vortex interactions were investigated with helium bubble flow visualization in the VPI Stability Tunnel.
Effect of inertia on drop breakup under shear
Renardy, Yuriko Y.; Cristini, V. (American Institute of Physics, 2001-01)
A spherical drop, placed in a second liquid of the same density and viscosity, is subjected to shear between parallel walls. The subsequent flow is investigated numerically with a volume-of-fluid continuous-surface-force algorithm. Inertially driven breakup is examined. The critical Reynolds numbers are examined for capillary numbers in the range where the drop does not break up in Stokes flow. It is found that the effect of inertia is to rotate the drop toward the vertical direction, with a mechanism analogous to aerodynamic lift, and the drop then experiences higher shear, which pulls the drop apart horizontally. The balance of inertial stress with capillary stress shows that the critical Reynolds number scales inversely proportional to the capillary number, and this is confirmed with full numerical simulations. Drops exhibit self-similar damped oscillations towards equilibrium analogous to a one-dimensional mass-spring system. The stationary drop configurations near critical conditions approach an inviscid limit, independent of the microphysical flow- and fluid-parameters.
The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia
Drumright-Clarke, M. A.; Renardy, Yuriko Y. (American Institute of Physics, 2004-01)
Direct numerical simulations are conducted with a volume-of-fluid continuous surface stress algorithm. The linear equation of state is used to characterize the effects of an insoluble surfactant at low concentration on a drop in strong shear. The drop and the surrounding liquid have the same viscosity and density. Surfactant migration induces a Marangoni force that acts toward the drop center. For low inertia, viscous force opposes the Marangoni force, so that a stationary drop with surfactant is more elongated and less tilted than without. The addition of surfactant promotes breakup, lowering the critical capillary number. The first daughter drops are smaller than for the case of clean drops. For high inertia, the Marangoni force retracts the drop and retards breakup. The local values of surface tension are computed during drop evolution.
Elongational Flows in Polymer Processing
Hagen, Thomas Ch. (Virginia Tech, 1998-12-01)
The production of long, thin polymeric fibers is a main objective of the textile industry. Melt-spinning is a particularly simple and effective technique. In this work, we shall discuss the equations of melt-spinning in viscous and viscoelastic flow. These quasilinear hyperbolic equations model the uniaxial extension of a fluid thread before its solidification. We will address the following topics: first we shall prove existence, uniqueness, and regularity of solutions. Our solution strategy will be developed in detail for the viscous case. For non-Newtonian and isothermal flows, we shall outline the general ideas. Our solution technique consists of energy estimates and fixed-point arguments in appropriate Banach spaces. The existence result for a simple transport equation is the key to understanding the quasilinear case. The second issue of this exposition will be the stability of the unforced frost line formation. We will give a rigorous justification that, in the viscous regime, the linearized equations obey the ``Principle of Linear Stability''. As a consequence, we are allowed to relate the stability of the associated strongly continuous semigroup to the numerical resolution of the spectrum of its generator. By using a spectral collocation method, we shall derive numerical results on the eigenvalue distribution, thereby confirming prior results on the stability of the steady-state solution.
Erratum: "derivation of amplitude equations and analysis of side-band instabilities in two-layer flows" (vol 5, pg 2738, 1993)
Renardy, Michael J.; Renardy, Yuriko Y. (AIP Publishing, 1994-10)
In the amplitude equations, one further term should have been taken into account. This term is formally of higher order when the original scaling of variables is used. However, the analysis of sideband instabilities involves various rescalings, and for one of the cases the term becomes of the same order as others. It therefore affects the criteria for sideband instability.
Experimental Evaluation and Simulations of Fiber Orientation in Injection Molding of Polymers Containing Short Glass Fibers
Velez-Garcia, Gregorio Manuel (Virginia Tech, 2012-01-31)
Injection molded short fiber reinforced composites have generated commercial interest in the manufacturing of lightweight parts used in semi-structural applications. Predicting these materials’ fiber orientation with quantitative accuracy is crucial for technological advancement, but the task is difficult because of the effect of inter-particle interactions at high concentrations of fiber found in parts of commercial interest. A complete sample preparation procedure was developed to obtain optical micrographs with optimal definition of elliptical and non-elliptical footprint borders. Two novel aspects in this procedure were the use of tridimensional markers to identify specific locations for analysis and the use of controlled-etching to produce small shadows where fibers recede into the matrix. These images were used to measure fiber orientation with a customized image analysis tool. This tool contains several modifications that we introduced in the method of ellipses which allow us to determine tridimensional fiber orientation and to obtain measurements in regions with fast changes in orientation. The tool uses the location of the shadow to eliminate the ambiguity problem in orientation and characterizes non-elliptical footprints to obtain the orientation in small sampling areas. Cavitywise measurements in two thin center-gated disks showed the existence of an asymmetric profile of orientation at the gate and an orientation profile that washed out gradually at the entry region until disappearing at about 32 gap widths. This data was used to assess the prediction of cavitywise orientation using a delay model for fiber orientation with model parameters obtained from rheometrical experiments. Model predictions combining slip correction and experimentally determined orientation at the gate are in agreement with experimental data for the core layers near the end-of-fill region. Radialwise measurements of orientation at the shell, transition and core layer, and microtextural description of the advancing front are included in this dissertation. The analysis and assessment of the radial evolution of fiber orientation and advancing front based on comparing the experimental data with simulation results are under ongoing investigation.
Experimental observation and matching numerical simulation for the deformation and breakup of immiscible drops in oscillatory shear
Wannaborworn, S.; Mackley, M. R.; Renardy, Yuriko Y. (AIP Publishing, 2002-09)
This paper describes experimental results on the way immiscible drops of a Newtonian fluid can deform and breakup when subject to oscillatory shear deformation. The paper also reports a matching three-dimensional numerical simulation of corresponding events. Using an optical shearing apparatus and a modified rheometer, experimental observations on the deformation of drops with a viscosity ratio of unity were carried out for a range of strain amplitudes and frequencies. For moderate strain deformations, it was discovered experimentally that the drop deformation oscillates between a maximum and a nonzero minimum deformation parameter and that the numerical simulation was able to capture both this and start up effects. For large strain deformations it was experimentally observed that breakup occurred only by one mechanism; namely, end pinching, and this was successfully matched by the numerical simulation. The results for oscillatory deformation and breakup are compared with those obtained in steady shear. (C) 2002 The Society of Rheology.
Ferrofluids and magnetically guided superparamagnetic particles in flows: a review of simulations and modeling
Renardy, Yuriko Y.; Afkhami, Shahriar (Springer Netherlands, 2017-08-18)
Ferrofluids are typically suspensions of magnetite nanoparticles, and behave as a homogeneous continuum. The ability of the ferrofluid to respond to an external magnetic field in a controllable manner has made it emerge as a smart material in a variety of applications, such as seals, lubricants, electronics cooling, shock absorbers and adaptive optics. Magnetic nanoparticle suspensions have also gained attraction recently in a range of biomedical applications, such as cell separation, hyperthermia, MRI, drug targeting and cancer diagnosis. In this review, we provide an introduction to mathematical modeling of three problems: motion of superparamagnetic nanoparticles in magnetic drug targeting, the motion of a ferrofluid drop consisting of chemically bound nanoparticles without a carrier fluid, and the breakage of a thin film of a ferrofluid.
Field-induced motion of ferrofluid droplets through immiscible viscous media
Afkhami, Shahriar; Renardy, Yuriko Y.; Renardy, Michael J.; Riffle, Judy S.; St Pierre, T. (Cambridge University Press, 2008-09)
The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. The governing equations are the Maxwell equations for a non-conducting flow, momentum equation and incompressibility. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. A continuum-surface-force formulation is used to model the interfacial tension force as a body force, and the placement of the liquids is tracked by a volume fraction function. Three cases are Studied. First, where inertia is dominant, the magnetic Laplace number Is varied while the Laplace number is fixed. Secondly, where inertial effects are negligible, the Laplace number is varied while the magnetic Laplace number is fixed. In the third case, the magnetic Bond number and inertial effects are both small, and the magnetic force is of the order of the viscous drag force. The time taken by the droplet to travel through the medium and the deformations in the drop are investigated and compared with a previous experimental study and accompanying simpler model. The transit times are found to compare more favourably than with the simpler model.
High-Quality Detection in Heavy-Traffic Avionic Communication System Using Interference Cancellation Techniques
Nguyen, Anh-Minh Ngoc (Virginia Tech, 2005-09-14)
This dissertation focuses on quantifying the effects of multi-user co-channel interference for an avionic communication system operating in a heavy-traffic aeronautical mobile environment and proposes advanced interference cancellation techniques to mitigate the interference. The dissertation consists of two parts. The first part of the work investigates the use of a visualization method to quantify and characterize the multi-user co-channel interference (multiple access interference) effects impinging on an avionic communication system. The interference is caused by complex interactions of thousands of RF signals transmitted from thousands of aircraft; each attempts to access a common communication channel, which is governed by a specific channel contention access protocol. The visualization method transforms the co-channel interference, which is specified in terms of signal-overlaps (signal collisions), from a visual representation to a matrix representation for further statistical analysis. It is found that the statistical Poisson and its cumulative distribution provide the best estimates of multi-user co-channel interference. It is shown, using Monte Carlo simulation, that the co-channel interference of a victim aircraft operating in the heavy-traffic environment could result in as high as eight signal-overlaps. This constitutes to approximately 83.4% of success rate in signal detection for the entire three thousand aircraft environment using conventional FSK receiver. One key finding shows that high-quality communications, up to 98.5% success rate, is achievable if only three overlapping signals can be decoded successfully. The interference results found in the first part set the stage for interference cancellation research in the second part. The second part of the work proposes the use of advanced interference cancellation techniques, namely sequential interference cancellation (SIC) and parallel interference cancellation (PIC), as potential solutions to mitigating the interference effects. These techniques can be implemented in radio receivers to perform multi-signal decoding functionality to remove the required interferers (three overlapping signals) so that high-quality communication, as described in the first part, can be achieved. Various performance graphs are shown for B-FSK and B-PSK for both SIC and PIC techniques. One key finding is that the system performance can be improved substantially to an additional 15% in signal reception success rate by using SIC or PIC. This means that critical information transmitted from 450 aircraft (out of approximately three thousand aircraft in the environment) is preserved and successfully decoded. Multi-signal decoding using these interference cancellation receivers comes at a small penalty of 2 - 4.5 dBs in Eb/No when sufficient signal-to-interference (SIR) ratio (7-12 dB) is provided.
Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems
Ben Romdhane, Mohamed (Virginia Tech, 2011-08-01)
A wide range of applications involve interface problems. In most of the cases, mathematical modeling of these interface problems leads to partial differential equations with non-smooth or discontinuous inputs and solutions, especially across material interfaces. Different numerical methods have been developed to solve these kinds of problems and handle the non-smooth behavior of the input data and/or the solution across the interface. The main focus of our work is the immersed finite element method to obtain optimal numerical solutions for interface problems. In this thesis, we present piecewise quadratic immersed finite element (IFE) spaces that are used with an immersed finite element (IFE) method with interior penalty (IP) for solving two-dimensional second-order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. An analysis of the constructed IFE spaces and their dimensions is presented. Shape functions of Lagrange and hierarchical types are constructed for these spaces, and a proof for the existence is established. The interpolation errors in the proposed piecewise quadratic spaces yield optimal O(h³) and O(h²) convergence rates, respectively, in the L² and broken H¹ norms under mesh refinement. Furthermore, numerical results are presented to validate our theory and show the optimality of our quadratic IFE method. Our approach in this thesis is, first, to establish a theory for the simplified case of a linear interface. After that, we extend the framework to quadratic interfaces. We, then, describe a general procedure for handling arbitrary interfaces occurring in real physical practical applications and present computational examples showing the optimality of the proposed method. Furthermore, we investigate a general procedure for extending our quadratic IFE spaces to p-th degree and construct hierarchical shape functions for p=3.
Immersed and Discontinuous Finite Element Methods
Chaabane, Nabil (Virginia Tech, 2015-04-20)
In this dissertation we prove the superconvergence of the minimal-dissipation local discontinuous Galerkin method for elliptic problems and construct optimal immersed finite element approximations and discontinuous immersed finite element methods for the Stokes interface problem. In the first part we present an error analysis for the minimal dissipation local discontinuous Galerkin method applied to a model elliptic problem on Cartesian meshes when polynomials of degree at most k and an appropriate approximation of the boundary condition are used. This special approximation allows us to achieve k + 1 order of convergence for both the potential and its gradient in the L² norm. Here we improve on existing estimates for the solution gradient by a factor √h. In the second part we present discontinuous immersed finite element (IFE) methods for the Stokes interface problem on Cartesian meshes that does not require the mesh to be aligned with the interface. As such, we allow unfitted meshes that are cut by the interface. Thus, elements may contain more than one fluid. On these unfitted meshes we construct an immersed Q₁/Q₀ finite element approximation that depends on the location of the interface. We discuss the basic features of the proposed Q₁/Q₀ IFE basis functions such as the unisolvent property. We present several numerical examples to demonstrate that the proposed IFE approximations applied to solve interface Stokes problems maintain the optimal approximation capability of their standard counterpart applied to solve the homogeneous Stokes problem. Similarly, we also show that discontinuous Galerkin IFE solutions of the Stokes interface problem maintain the optimal convergence rates in both L² and broken H¹ norms. Furthermore, we extend our method to solve the axisymmetric Stokes interface problem with a moving interface and test the proposed method by solving several benchmark problems from the literature.

Browsing by Author "Renardy, Yuriko Y."

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