Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

A marker-and-cell approach to free surface 2-D multiphase flows

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Simulation of free surface flows in a distributed memory environment

A parallel technique, for a distributed memory machine, based on domain decomposition for solving the Navier-Stokes equations in cartesian and cylindrical coordinates in two dimensions with free surfaces is described. It is based on the code by Tome and McKee (J. Comp. Phys. 110 (1994) 171-186) and Tome (Ph.D. Thesis, University of Strathclyde, Glasgow, 1993) which in turn is based on the SMAC method by Amsden and Harlow (Report LA-4370, Los Alamos Scientific Laboratory, 1971), which solves the Navier-Stokes equations in three steps: the momentum and Poisson equations and particle movement, These equations are discretized by explicit and 5-point finite differences. The parallelization is performed by splitting the computation domain into vertical panels and assigning each of these panels to a processor. All the computation can then be performed using nearest neighbour communication. Test runs comparing the performance of the parallel with the serial code, and a discussion of the load balancing question are presented. PVM is used for communication between processes. (C) 1999 Elsevier B.V. B.V. All rights reserved.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Three-dimensional transient complex free surface flows: Numerical simulation of XPP fluid

In this paper we present a finite difference MAC-type approach for solving three-dimensional viscoelastic incompressible free surface flows governed by the eXtended Pom-Pom (XPP) model, considering a wide range of parameters. The numerical formulation presented in this work is an extension to three-dimensions of our implicit technique [Journal of Non-Newtonian Fluid Mechanics 166 (2011) 165-179] for solving two-dimensional viscoelastic free surface flows. To enhance the stability of the numerical method, we employ a combination of the projection method with an implicit technique for treating the pressure on the free surfaces. The differential constitutive equation of the fluid is solved using a second-order Runge-Kutta scheme. The numerical technique is validated by performing a mesh refinement study on a pipe flow, and the numerical results presented include the simulation of two complex viscoelastic free surface flows: extrudate-swell problem and jet buckling phenomenon. © 2013 Elsevier B.V.

A marker-and-cell approach to free surface 2-D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.

Using the level set method to model endogenous lava dome growth

Modeling volcanic phenomena is complicated by free-surfaces often supporting large rheological gradients. Analytical solutions and analogue models provide explanations for fundamental characteristics of lava flows. But more sophisticated models are needed, incorporating improved physics and rheology to capture realistic events. To advance our understanding of the flow dynamics of highly viscous lava in Peléean lava dome formation, axi-symmetrical Finite Element Method (FEM) models of generic endogenous dome growth have been developed. We use a novel technique, the level-set method, which tracks a moving interface, leaving the mesh unaltered. The model equations are formulated in an Eulerian framework. In this paper we test the quality of this technique in our numerical scheme by considering existing analytical and experimental models of lava dome growth which assume a constant Newtonian viscosity. We then compare our model against analytical solutions for real lava domes extruded on Soufrière, St. Vincent, W.I. in 1979 and Mount St. Helens, USA in October 1980 using an effective viscosity. The level-set method is found to be computationally light and robust enough to model the free-surface of a growing lava dome. Also, by modeling the extruded lava with a constant pressure head this naturally results in a drop in extrusion rate with increasing dome height, which can explain lava dome growth observables more appropriately than when using a fixed extrusion rate. From the modeling point of view, the level-set method will ultimately provide an opportunity to capture more of the physics while benefiting from the numerical robustness of regular grids.

Influence of Final Rinse Technique on Ability of Ethylenediaminetetraacetic Acid of Removing Smear Layer

Introduction: There is ongoing debate regarding the ideal sequence, volume, and concentration of irrigants, length of time for irrigation, and irrigation technique to achieve debridement of the root canal system. The aim of this study was to verify the impact of the final rinse technique on smear layer removal ability of 17% ethylenediaminetetraacetic acid (EDTA). Methods: Sixteen single-rooted human teeth were instrumented and divided into 2 groups at the final rinse step according to the following final rinse techniques used: continuous rinse group, continuous rinse with EDTA during 3 minutes, and rinse and soaking group, rinse with 1 mL of EDTA, soaking of the canal for 2 minutes and 30 seconds, and rinse completion with the remaining 4 mL for 30 seconds. The specimens were split lengthwise and observed under scanning electron microscope. Results: Data were analyzed with Kruskal-Wallis and Dunn tests. The continuous rinse group presented more debris-free surfaces when compared with the rinse and soaking group (P <. 01). When the root canal areas were compared within the groups, no statistical differences were found (P > .05). Conclusions: It can be concluded that a continuous rinse with 5 mL of EDTA for 3 minutes can more efficiently remove the smear layer from root canal walls. (J Endod 2010;36:512-514)

Influence of different volumes of EDTA for final rinse on smear layer removal

Objective. The aim of this study was to analyze the influence of different volumes of 17% EDTA for final rinse on smear layer removal on the different areas of the root canal. Study design. Forty single-rooted teeth were instrumented using rotary instruments. The teeth were divided into 3 test groups according to the EDTA volume for final rinse (5 mL, 10 mL, 15 mL) and 1 control group (10 mL of 1% sodium hypochlorite). The roots were axially split into halves, and the smear layer removal from the canals was determined under scanning electron microscope. The data were analyzed using Kruskal Wallis and Dunn tests. Results. The 3 experimental groups showed no statistical difference (P > .05); however, when the test groups were compared to the control group statistically significant differences were found (P < .01). The root canal wall surfaces of teeth in the control group showed the presence of heavy smear layer through the entire length of the root canals. The other groups showed mainly smear layer-free surfaces or a small amount of debris. When coronal, middle and apical thirds were compared, there was no statistically significant difference (P > .05). Conclusions. Based on the results, it appears that a final rinse with 5 mL of EDTA per canal provides good smear layer removal, with root canal walls free of debris and mostly open dentinal tubules in all areas. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008;106:e40-e43)

Microtubule integrity is essential for apical polarization and epithelial morphogenesis in the thyroid

In this study, we examined the contribution of microtubules to epithelial morphogenesis in primary thyroid cell cultures. Thyroid follicles consist of a single layer of polarized epithelial cells surrounding a closed compartment, the follicular lumen. Freshly isolated porcine thyroid cells aggregate and reorganize to form follicles when grown in primary cultures. Follicular reorganization is principally a morphogenetic process that entails the assembly of biochemically distinct apical and basolateral membrane domains, delimited by tight junctions. The establishment of cell surface polarity during folliculogenesis coincided with the polarized redistribution of microtubules, predominantly in the developing apical poles of cells. Disruption of microtubule integrity using either colchicine or nocodazole caused loss of defined apical membrane domains, tight junctions and follicular lumina. Apical membrane and tight junction markers became randomly distributed at the outer surfaces of aggregates. In contrast, the basolateral surface markers, E-cadherin and Na+,K+-ATPase, remained correctly localized at sites of cell-cell contact and at the free surfaces of cell aggregates. These findings demonstrate that microtubules play a necessary role in thyroid epithelial morphogenesis. Specifically, microtubules are essential to preserve the correct localization of apical membrane components within enclosed cellular aggregates, a situation that is also likely to pertain where lumina must be formed from solid aggregates of epithelial precursors. (C) 2001 Wiley-Liss, Inc.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom-Pom model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Damage Detection in Flexible Plate Using Lamb Waves

This paper presents an experimental technique for structural health monitoring (SHM) based on Lamb waves approach in an aluminum plate using piezoelectric material as actuators and sensors. Lamb waves are a form of elastic perturbation that remains guided between two parallel free surfaces, such as the upper and lower surfaces of a plate, beam or shelf. Lamb waves are formed when the actuator excites the surface of the structure with a pulse after receiving a signal. Two PZTs were placed in the plate surface and one of them was used to send a predefined wave through the structure. Thus, the other PZT (adjacent) becomes the sensor. Using this methodology, this paper presents one case of damage detection considering the aluminum plate in the free-free-free-free boundary condition. The damage was simulated by adding additional mass on the plate. It is proposed two damage detection indexes obtained from the experimental signal, involving the Fast Fourier Transform (FFT) and the power spectral density (PSD) that were computed using the output signal. The results show the viability of the presented methodology to damage detection in smart structures

Propagation of ship waves on a sloping bottom

The numerical model FUNWAVE was adapted in order to simulate the generation and propagation of ship waves to shore, including phenomena such as refraction, diffraction, currents and breaking of waves. Results are shown for Froude numbers equal to 0.8, 1.0 and 1.1, in order to verify the refraction of the wave pattern, identify breaking conditions and to investigate the wave generation scheme as a moving pressure at the free surface. © 2009 World Scientific Publishing Co. Pte. Ltd.