Information Preservation (IP) Method in Simulation

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

LOCAL BENDING OF THIN FILM ON VISCOUS LAYER

Effects of deposition layer position and number/density on local bending of a thin film are systematically investigated. Because the deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the so-called local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection case. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.

Effects of buoyancy on Langmuir circulation

Based on the Navier-Stokes equation, an equation describing the Langmuir circulation is derived by a perturbation method when the influences of Coriolis force and buoyancy force are both considered. The approach used in the analysis is similar to the works carried out by Craik and Leibovich [J. Fluid Mech. 73 (1976) 401], Leibovich [J. Fluid Mech. 79 (1977) 715] and Huang [J. Fluid Mech. 91 (1979) 191]. Potential applications of the equation proposed are discussed in the area of Antarctic circumpolar current.

Flow stabilization with active hydrodynamic cloaks

We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5-119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder. © 2012 American Physical Society.

A domain decomposition algorithm for viscous/inviscid coupling

In fluid mechanics, it is well accepted that the Euler equation is one of the reduced forms of the Navier-Stokes equation by truncating the viscous effect. There are other truncation techniques currently being used in order to truncate the Navier-Stokes equation to a reduced form. This paper describes one such technique, suitable for adaptive domain decomposition methods for the solution of viscous flow problems. The physical domain of a viscous flow problem is partitioned into viscous and inviscid subdomains without overlapping regions, and the technique is embedded into a finite volume method. Some numerical results are provided for a flat plate and the NACA0012 aerofoil. Issues related to distributed computing are discussed.

Thermoelectric MHD in dendritic solidification

The effects of a constant uniform magnetic field on dendritic solidification were investigated using an enthalpy based numerical model. The interaction between thermoelectric currents on a growing crystal and the magnetic field generates a Lorentz force that creates flow. The need for very high resolution at the liquid-solid boundary where the thermoelectric source originates plus the need to accommodate multiple grains for a realistic simulation, make this a very demanding computational problem. For practical simulations, a quasi 3-dimensional approximation is proposed which nevertheless retains essential elements of transport in the third dimension. A magnetic field normal to the plane of growth leads to general flow circulation around an equiaxed dendrite, with secondary recirculations between the arms. The heat/solute advection by the flow is shown to cause a change in the morphology of the dendrite; secondary growth is promoted preferentially on one side of the dendrite arm and the tip velocity of the primary arm is increased. The degree of approximation introduced is quantified by extending the model into 3-dimensions, where the full Navier-Stokes equation is solved, and compared against the 2-dimensional solution.

Detection of improper installation from the sensor signal of vortex flowmeters

Effects of inappropriate installation can bias the measurements of flowmeters. For vortex flowmeters, a method is proposed to detect inappropriate installation of the flowmeter from the oscillatory signal of the vortex sensor. The method is based on assuming the process of vortex generation to be a generic, noisy, nonlinear oscillation, describable by a noisy Stuart-Landau equation, with a corresponding sensor signal that also contains higher harmonic excitations. By making use of the scaling properties of the Navier-Stokes Equation, the method was designed to be robust with respect to uncertainties in the fluid properties. The diagnostic functionality is demonstrated on measurement data. In the experiments, installation effects that lead to more than 0.5% error in the output of the flowmeter could clearly be detected. (C) 2003 Elsevier Ltd. All rights reserved.

Numeric simulation of pollutant dispersion by a control-volume based on finite element method

The dispersion of pollutants in the environment is an issue of great interest as it directly affects air quality, mainly in large cities. Experimental and numerical tools have been used to predict the behavior of pollutant species dispersion in the atmosphere. A software has been developed based on the control-volume based on the finite element method in order to obtain two-dimensional simulations of Navier-Stokes equations and heat or mass transportation in regions with obstacles, varying position of the pollutant source. Numeric results of some applications were obtained and, whenever possible, compared with literature results showing satisfactory accordance. Copyright (C) 2010 John Wiley & Sons, Ltd.

Abordagem matemática de roll waves em escoamentos hiperconcentrados com superfície livre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Simulação numérica de escoamentos de fluídos pelo método de elementos finitos baseado em volumes de controle com a técnica de passo fracionado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estabilidade de métodos numéricos LCR para a simulação de escoamento

Pós-graduação em Matematica Aplicada e Computacional - FCT

Uso das ondas de Lamb e Scholte para caracterização de líquidos

Pós-graduação em Engenharia Elétrica - FEIS

On the radial expansion of tubular structures in a quark-gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes. (C) 2012 Elsevier B.V. All rights reserved.

Meccanismi di formazione dei tubi di lava

Two analytical models are proposed to describe two different mechanisms of lava tubes formation. A first model is introduced to describe the development of a solid crust in the central region of the channel, and the formation of a tube when crust widens until it reaches the leve\'es. The Newtonian assumption is considered and the steady state Navier- Stokes equation in a rectangular conduit is solved. A constant heat flux density assigned at the upper flow surface resumes the combined effects of two thermal processes: radiation and convection into the atmosphere. Advective terms are also included, by the introduction of velocity into the expression of temperature. Velocity is calculated as an average value over the channel width, so that lateral variations of temperature are neglected. As long as the upper flow surface cools, a solid layer develops, described as a plastic body, having a resistance to shear deformation. If the applied shear stress exceeds this resistance, crust breaks, otherwise, solid fragments present at the flow surface can weld together forming a continuous roof, as it happens in the sidewall flow regions. Variations of channel width, ground slope and effusion rate are analyzed, as parameters that strongly affect the shear stress values. Crust growing is favored when the channel widens, and tube formation is possible when the ground slope or the effusion rate reduce. A comparison of results is successfully made with data obtained from the analysis of pictures of actual flows. The second model describes the formation of a stable, well defined crust along both channel sides, their growing towards the center and their welding to form the tube roof. The fluid motion is described as in the model above. Thermal budget takes into account conduction into the atmosphere, and advection is included considering the velocity depending both on depth and channel width. The solidified crust has a non uniform thickness along the channel width. Stresses acting on the crust are calculated using the equations of the elastic thin plate, pinned at its ends. The model allows to calculate the distance where crust thickness is able to resist the drag of the underlying fluid and to sustain its weight by itself, and the level of the fluid can lower below the tube roof. Viscosity and thermal conductivity have been experimentally investigated through the use of a rotational viscosimeter. Analyzing samples coming from Mount Etna (2002) the following results have been obtained: the fluid is Newtonian and the thermal conductivity is constant in a range of temperature above the liquidus. For lower temperature, the fluid becomes non homogeneous, and the used experimental techniques are not able to detect any properties, because measurements are not reproducible.