The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.

Reactive mass transport modelling of a three-dimensional vertical fault zone with a finger-like convective flow regime

For a three-dimensional vertically-oriented fault zone, we consider the coupled effects of fluid flow, heat transfer and reactive mass transport, to investigate the patterns of fluid flow, temperature distribution, mineral alteration and chemically induced porosity changes. We show, analytically and numerically, that finger-like convection patterns can arise in a vertically-oriented fault zone. The onset and patterns of convective fluid flow are controlled by the Rayleigh number which is a function of the thermal properties of the fluid and the rock, the vertical temperature gradient, and the height and the permeability of the fault zone. Vigorous fluid flow causes low temperature gradients over a large region of the fault zone. In such a case, flow across lithological interfaces becomes the most important mechanism for the formation of sharp chemical reaction fronts. The degree of rock buffering, the extent and intensity of alteration, the alteration mineralogy and in some cases the formation of ore deposits are controlled by the magnitude of the flow velocity across these compositional interfaces in the rock. This indicates that alteration patterns along compositional boundaries in the rock may provide some insights into the convection pattern. The advective mass and heat exchanges between the fault zone and the wallrock depend on the permeability contrast between the fault zone and the wallrock. A high permeability contrast promotes focussed convective flow within the fault zone and diffusive exchange of heat and chemical reactants between the fault zone and the wallrock. However, a more gradual permeability change may lead to a regional-scale convective flow system where the flow pattern in the fault affects large-scale fluid flow, mass transport and chemical alteration in the wallrocks

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

The influence of cutting tool geometry upon aspects of chip flow and tool wear:a theoretical, three dimensional examination of the cutting geometry and the shape of the twist drill

This work is undertaken in the attempt to understand the processes at work at the cutting edge of the twist drill. Extensive drill life testing performed by the University has reinforced a survey of previously published information. This work demonstrated that there are two specific aspects of drilling which have not previously been explained comprehensively. The first concerns the interrelating of process data between differing drilling situations, There is no method currently available which allows the cutting geometry of drilling to be defined numerically so that such comparisons, where made, are purely subjective. Section one examines this problem by taking as an example a 4.5mm drill suitable for use with aluminium. This drill is examined using a prototype solid modelling program to explore how the required numerical information may be generated. The second aspect is the analysis of drill stiffness. What aspects of drill stiffness provide the very great difference in performance between short flute length, medium flute length and long flute length drills? These differences exist between drills of identical point geometry and the practical superiority of short drills has been known to shop floor drilling operatives since drilling was first introduced. This problem has been dismissed repeatedly as over complicated but section two provides a first approximation and shows that at least for smaller drills of 4. 5mm the effects are highly significant. Once the cutting action of the twist drill is defined geometrically there is a huge body of machinability data that becomes applicable to the drilling process. Work remains to interpret the very high inclination angles of the drill cutting process in terms of cutting forces and tool wear but aspects of drill design may already be looked at in new ways with the prospect of a more analytical approach rather than the present mix of experience and trial and error. Other problems are specific to the twist drill, such as the behaviour of the chips in the flute. It is now possible to predict the initial direction of chip flow leaving the drill cutting edge. For the future the parameters of further chip behaviour may also be explored within this geometric model.

Effect of blood flow patterns on localized platelet adhesion under physiologic flow conditions using two-dimensional and three-dimensional stent models: An experimental and computational approach

This dissertation presents dynamic flow experiments with fluorescently labeled platelets to allow for spatial observation of wall attachment in inter-strut spacings, to investigate their relationship to flow patterns. Human blood with fluorescently labeled platelets was circulated through an in vitro system that produced physiologic pulsatile flow in (1) a parallel plate blow chamber that contained two-dimensional (2D) stents that feature completely recirculating flow, partially recirculating flow, and completely reattached flow, and (2) a three-dimensional (3D) cylindrical tube that contained stents of various geometric designs. ^ Flow detachment and reattachment points exhibited very low platelet deposition. Platelet deposition was very low in the recirculation regions in the 3D stents unlike the 2D stents. Deposition distal to a strut was always high in 2D and 3D stents. Spirally recirculating regions were found in 3D unlike in 2D stents, where the deposition was higher than at well-separated regions of recirculation. ^

Three dimensional models of water flow in the Persian Gulf

Persian Gulf region is globally of great importance due to its economical and political reasons. The importance lies in oil sources and sea exports. Geophysical phenomena dominated in the water circulation affected this region is called Monsoon it stretches from African coasts to the half way of Red Seal affected all coasts of Persian Gulf and goes toward east to the Indian ocean. Other essential factors in the water circulation in this region are net evaporation (several meters in per year), high density and high salinity. In this article the effects of wind stress and evaporation in the water circulation in the region will be considered and model equations for wind forces, density, pressure, gradient, and bottom friction for Persian Gulf will be discussed.

Numerical investigation of the three-dimensional secondary instabilities in the time-developing compressible mixing layer

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. It is, therefore, a well researched subject, but there are aspects that require further studies. Here the instability of two-and three-dimensional perturbations in the compressible mixing layer was investigated by numerical simulations. In the numerical code, the derivatives were discretized using high-order compact finite-difference schemes. A stretching in the normal direction was implemented with both the objective of reducing the sound waves generated by the shear region and improving the resolution near the center. The compact schemes were modified to work with non-uniform grids. Numerical tests started with an analysis of the growth rate in the linear regime to verify the code implementation. Tests were also performed in the non-linear regime and it was possible to reproduce the vortex roll-up and pairing, both in two-and three-dimensional situations. Amplification rate analysis was also performed for the secondary instability of this flow. It was found that, for essentially incompressible flow, maximum growth rates occurred for a spanwise wavelength of approximately 2/3 of the streamwise spacing of the vortices. The result demonstrated the applicability of the theory developed by Pierrehumbet and Widnall. Compressibility effects were then considered and the maximum growth rates obtained for relatively high Mach numbers (typically under 0.8) were also presented.

Determination of Three-Dimensional Left Ventricle Motion to Analyze Ventricular Dyssyncrony in SPECT Images

A method to compute three-dimension (3D) left ventricle (LV) motion and its color coded visualization scheme for the qualitative analysis in SPECT images is proposed. It is used to investigate some aspects of Cardiac Resynchronization Therapy (CRT). The method was applied to 3D gated-SPECT images sets from normal subjects and patients with severe Idiopathic Heart Failure, before and after CRT. Color coded visualization maps representing the LV regional motion showed significant difference between patients and normal subjects. Moreover, they indicated a difference between the two groups. Numerical results of regional mean values representing the intensity and direction of movement in radial direction are presented. A difference of one order of magnitude in the intensity of the movement on patients in relation to the normal subjects was observed. Quantitative and qualitative parameters gave good indications of potential application of the technique to diagnosis and follow up of patients submitted to CRT.

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

Aerodynamic study of three-dimensional larynx models using finite element methods

The airflow velocities and pressures are calculated from a three-dimensional model of the human larynx by using the finite element method. The laryngeal airflow is assumed to be incompressible, isothermal, steady, and created by fixed pressure drops. The influence of different laryngeal profiles (convergent, parallel, and divergent), glottal area, and dimensions of false vocal folds in the airflow are investigated. The results indicate that vertical and horizontal phase differences in the laryngeal tissue movements are influenced by the nonlinear pressure distribution across the glottal channel, and the glottal entrance shape influences the air pressure distribution inside the glottis. Additionally, the false vocal folds increase the glottal duct pressure drop by creating a new constricted channel in the larynx, and alter the airflow vortexes formed after the true vocal folds. (C) 2007 Elsevier Ltd. All rights reserved.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.