DISSIPATIVE BOUSSINESQ SYSTEM OF EQUATIONS IN THE BENARD-MARANGONI PHENOMENON

By using the long-wavelength approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a Benard-Marangoni system is obtained. It includes nonlinearity, dispersion, and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained.

The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows

In this paper, the meshless method is introduced to magnetohydrodynamics. A numerical scheme based on the element-free Galerkin method is used to solve the laminar steady-state two-dimensional fully developed magnetohydrodynamic flow in a rectangular duct. Accurate and convergent solutions are achieved for low to moderately high Hartmann numbers.

NONLINEAR SURFACE-WAVE EXCITATIONS IN THE BENARD-MARANGONI SYSTEM

We examine the appearance of surface waves governed by Burgers and Korteweg-de Vries equations in a shallow viscous heated fluid. We consider waves triggered by a surface-tension variation induced by both temperature and concentration gradients. We also establish the range of parameters for which the above-mentioned equations appear.

High-speed cavity preparation techniques with different water flows

Statement of problem. Cavity and tooth preparations generate heat because the use of rotary cutting instruments on dental tissues creates friction. Dental pulps cannot survive temperature increases greater than 5.5degreesC.Purpose. This study evaluated the efficiency of 3 different water flows for 2 different tooth preparation techniques to determine which are safe for use.Material and methods. Thermocouples were placed in the pulpal chambers of 30 bovine teeth, and 1 of 2 tooth preparation techniques was used: a low-load intermittent tooth preparation technique or a high-load tooth preparation technique without intervals. Water flows of 0, 30, and 45 mL/min were associated with each technique, for a total of 6 different groups. The results were analyzed with a 2-factor analysis of variance (P<.05).Results. Temperature increases with the high-load technique were 16.40&DEG;C without cooling (group 1), 11.68&DEG;C with 30 mL/min air-water spray cooling (group III), and 9.96&DEG;C with 45 mL/min cooling (group V). With the low-load tooth preparation technique, a 9.54&DEG;C increase resulted with no cooling (group II), a 1.56&DEG;C increase with 30 mL/min air-water spray cooling (group TV), and a 0.04&DEG;C decrease with 45 mL/min cooling (group VI). The low-load technique was associated with more ideal temperature changes.Conclusion. The results of this study confirm the necessity of using a low-load technique and water coolants during cavity and tooth preparation procedures.

An application of the Adomian's decomposition method to the analysis of MHD duct flows

A new approach is proposed in this work for the treatment of boundary value problems through the Adomian's decomposition method. Although frequently claimed as accurate and having fast convergence rates, the original formulation of Adomian's method does not allow the treatment of homogeneous boundary conditions along closed boundaries. The technique here presented overcomes this difficulty, and is applied to the analysis of magnetohydrodynamic duct flows. Results are in good agreement with finite element method calculations and analytical solutions for square ducts. Therefore, new possibilities appear for the application of Adomian's method in electromagnetics.

Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon

By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed Nonlinear Schrödinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.

Simulations of incompressible fluid flows by a least squares finite element method

In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-ω) and u-p-τ formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-ω and u-p-τ formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature. Copyright © 2005 by ABCM.

The use of molecular spectra simulation for diagnostics of reactive flows

The C 2 * radical is used as a system probe tool to the reactive flow diagnostic, and it was chosen due to its large occurrence in plasma and combustion in aeronautics and aerospace applications. The rotational temperatures of C 2 * species were determined by the comparison between experimental and theoretical data. The simulation code was developed by the authors, using C++ language and the object oriented paradigm, and it includes a set of new tools that increase the efficacy of the C 2 * probe to determine the rotational temperature of the system. A brute force approach for the determination of spectral parameters was adopted in this version of the computer code. The statistical parameter c 2 was used as an objective criterion to determine the better match of experimental and synthesized spectra. The results showed that the program works even with low-quality experimental data, typically collected from in situ airborne compact apparatus. The technique was applied to flames of a Bunsen burner, and the rotational temperature of ca. 2100 K was calculated.

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.

Law of large numbers for certain cylinder flows

We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit a law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a Gaussian distribution.

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic - Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.

Erosion Protection by Calcium Lactate/Sodium Fluoride Rinses under Different Salivary Flows in vitro

This study investigated the effect of a calcium lactate pre-rinse on sodium fluoride protection in an in vitro erosion-remineralization model simulating two different salivary flow rates. Enamel and dentin specimens were randomly assigned to 6 groups (n = 8), according to the combination between rinse treatments - deionized water (DIW), 12 mm NaF (NaF) or 150 mm calcium lactate followed by NaF (CaL + NaF) and unstimulated salivary flow rates - 0.5 or 0.05 ml/min simulating normal and low salivary flow rates, respectively. The specimens were placed into custom-made devices, creating a sealed chamber on the specimen surface connected to a peristaltic pump. Citric acid was injected into the chamber for 2 min, followed by artificial saliva (0.5 or 0.05 ml/min) for 60 min. This cycle was repeated 4x/day for 3 days. Rinse treatments were performed daily 30 min after the 1st and 4th erosive challenges, for 1 min each time. Surface loss was determined by optical profilometry. KOH-soluble fluoride and structurally bound fluoride were determined in specimens at the end of the experiment. Data were analyzed by 2-way ANOVA and Tukey tests (alpha = 0.05). NaF and CaL + NaF exhibited significantly lower enamel and dentin loss than DIW, with no difference between them for normal flow conditions. The low salivary flow rate increased enamel and dentin loss, except for CaL + NaF, which presented overall higher KOH-soluble and structurally bound fluoride levels. The results suggest that the NaF rinse was able to reduce erosion progression. Although the CaL prerinse considerably increased F availability, it enhanced NaF protection against dentin erosion only under hyposalivatory conditions. (C) 2014 S. Karger AG, Basel

Numerical solution of the FENE-CR model in complex flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Application of the PTT Model to Axisymmetric Free Surface Flows

This work is concerned with numerical simulation of axisymmetric viscoelastic free surface flows using the Phan-Thien-Tanner (PTT) constitutive equation. A finite difference technique for solving the governing equations for unsteady incompressible flows written in Cylindrical coordinates on a staggered grid is described. 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 applied. The numerical method is verified by comparing numerical predictions of fully developed flow in a pipe with the corresponding analytic solutions. To demonstrate that the numerical method can simulate axisymmetric free surface flows governed by the PTT model, numerical results of the flow evolution of a drop impacting on a rigid dry plate are presented. In these simulations, the rheological effects of the parameters epsilon and xi are investigated.