Equations Of Incompressible Fluid Research Articles

Numerical Investigation of Wind Effects on the Perforated Structures

The paper deals with a numerical analysis of wind effects on structures with perforated surfaces. The solution based on FEM model is governed by the stabilized Navier-Stokes equations for incompressible fluid. Special attention is given to perforated surface. Such a partly resistance barrier always introduces considerable numerical difficulties resulting from the complexity of a flow distortion when the fluid is passing through. For simplification, the barrier is assumed as a thin screen with specific resistance parameters where the fluid flow mechanism needs not be resolved. The general influence of the barrier on the flow field is a loss in the normal momentum component and the change in the flow direction. On the other hand, the authentic simulation of the fluid mechanics requires specifying the relevant input parameters that can be determined by an experiment or by using a corresponding handbook.

Non-stationary helical flows for incompressible 3D Navier–Stokes equations

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier–Stokes equations, even for 3D case of compressible gas flow. But there is an essential deficiency of non-stationary solutions indeed.In our derivation, we explore the case of non-stationary helical flow of the Navier–Stokes equations for incompressible fluids at any given initial conditions for velocity fields (it means an open choice for the space part of a solution).Such a non-stationary helical flow is proved to be decreasing exponentially in regard to the time-parameter, the extent of time-dependent exponential component is given by the coefficient of kinematic viscosity, multiplied by the square of the coefficient of proportionality between the vorticity and velocity field.

Velocity estimation of glaciers with physically-based spatial regularization — Experiments using satellite SAR intensity images

Abstract Glaciers are an important climate indicator due to their sensitive dependence upon local and regional climate variables, which makes them worthwhile research subjects. A comprehensive description of the glaciers' interaction with the environment and their dynamical behavior requires complex physical models and the measurement of relevant parameters. In-situ data acquisitions are costly and often spatially sparse due to the large extent of glaciers; however, satellite-based sensors offer timely data with complete ground coverage, making them a good choice for continuous monitoring of glaciers. Synthetic aperture radar (SAR) allows a nearly weather-independent monitoring of glacier motion, which is beneficial for often cloudy regions like Alaska or Patagonia. This paper presents a new workflow for the automatic extraction of glacier surfaces from SAR intensity images and the determination of their velocities involving a fluid mechanics model. An initial motion estimation is obtained from intensity tracking on SAR image pairs and subsequently corrected by a physics-based spatial regularization. The surface velocity is approximated by the two-dimensional Navier–Stokes equation for incompressible fluids. The regularization is formulated as a data assimilation problem in which the final solution is a proper solution of the Navier–Stokes equation and simultaneously fitted to the observed velocity. This partial differential equation (PDE) constrained optimization is solved with adjoint models using finite element methods. The proposed method is evaluated on the Taku Glacier, AK, an outlet glacier of the Juneau Icefield. Our presented approach is independent from the type of sensor as long as initial velocity estimates can be obtained. The final results can be used as input to methods estimating ice volume and thickness.

A 3D vortex formed by trajectories of the Navier–Stokes equation

.The 3D Navier–Stokes equation for incompressible fluid is resolved by using the Lie group analysis method. The solution shows a spiral vortex structure and some strange related aspects. There are two running modes of the vortex, up-spiral or down-spiral, and the modes are determined by the viscosity of fluid. The calculated z-directional curl of the velocity presents a zero-piercing, which indicates that the variation from the up-spiral structure to the down-spiral may correspond to the state change of the fluid from gas to liquid. In the corresponding parameter region, there is likely a so-called two-phase-coexistence of gas and liquid. Within the vortex, the dependence of the angle velocity of a mass particle on its radial position is dominated by a Gaussian-like curve in the plane of angle velocity versus radial position. This work provides a vivid description of the vortex that is in accordance with a real vortex structure.

Electroosmotic flow and Joule heating in preparative continuous annular electrochromatography.

An openFOAM "computational fluid dynamic" simulation model was developed for the description of local interaction of hydrodynamics and Joule heating in annular electrochromatography. A local decline of electrical conductivity of the background eluent is caused by an electrokinetic migration of ions resulting in higher Joule heat generation. The model equations consider the Navier-Stokes equation for incompressible fluids, the energy equation for stationary temperature fields, and the mass transfer equation for the electrokinetic flow. The simulations were embedded in commercial ANSYS Fluent software and in open-source environment openFOAM. The annular gap (1mm width) contained an inorganic C8 reverse-phase monolith as stationary phase prepared by an in situ sol-gel process. The process temperature generated by Joule heating was determined by thermal camera system. The local hydrodynamics in the prototype was detected by a gravimetric contact-free measurement method and experimental and simulated values matched quite well.

Elementos finitos mixtos estabilizados para flujos confinados de Bingham y de Herschel-Bulkley. Parte I: Formulación

This work presents a methodology for the solution of the Navier-Stokes equations for Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. The theoretical formulation is developed and implemented in a computer code.Viscoplastic fluids are characterized by a minimum shear stress called yield stress. Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a quasi-rigid body, with zero strain-rate.First, the Navier-Stokes equations for incompressible fluid are presented. A review of the viscoplastic rheological models is included, with a detailed description of these models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed as an alternative to the models commonly used.The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization method, the Orthogonal Subgrid Scale (OSS) method and the split orthogonal subscales method are introduced.The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry.

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier–Stokes equations for incompressible fluids is Chorin's projection method [1], whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. We highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.

Standing jumps in shallow granular flows down smooth inclines

The shapes of standing jumps formed in shallow granular flows down an inclined smooth-based chute are analysed in detail, by varying both the slope and mass discharge. Laboratory tests and analytic jump solutions highlight two important transitions. First, for dense flows at high mass discharge, we observe a transition between steep jumps and more diffuse jumps. The traditional shallow-water equation offers a valid prediction for the thickness of the steep water-like jumps. Diffuse frictional jumps require a more general equation accounting for the forces acting inside the jump volume. Second, moving from dense to dilute flows produces another transition between incompressible and compressible jumps. The observed jump height decrease may be reproduced for a more dilute incoming flow by including experimentally measured density variation in the jump equation. Finally, we briefly discuss the likely relevance to avalanche protection dam design that currently utilises traditional shock equations for incompressible frictionless fluids.

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation. The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.

Inertial Deposition of Aerosol Particles in a Periodic Row of Porous Cylinders

The aerosol flow through a periodic row of parallel porous cylinders is investigated. The air flow field outside the cylinders is described by the Navier–Stokes equations of viscous incompressible fluid. The extended Darcy–Brinkman equations are used to calculate the flow velocity inside a porous cylinder. The dependence of the efficiency of the deposition of aerosol particles by inertial impaction and interception on the Stokes number for various values of the Darcy number is studied. Comparison of the results obtained from the numerical model and an approximate analytical model is given. The combined approximate formula for the deposition efficiency of a cylindrical fiber in a parallel array proposed by Müller et al. (2014) is extended for the porous cylindrical fiber. The aerosol flow through the porous body composed by a random array of cylinders is calculated to estimate the interior deposition.Copyright 2015 American Association for Aerosol Research

Dynamic stiffness method for free vibrations analysis of partial fluid-filled orthotropic circular cylindrical shells

Free vibrations of partial fluid-filled orthotropic circular cylindrical shells are investigated using the Dynamic Stiffness Method (DSM) or Continuous Element Method (CEM) based on theFirst Order Shear Deformation Theory (FSDT) and non-viscous incompressible fluid equations. Numerical examples are given for analyzing natural frequencies and harmonic responses of cylindrical shells partially and completely filled with fluid under various boundary conditions. The vibration frequencies for different filling ratios of cylindrical shells are obtained and compared with existing experimental and theoretical results which indicate that the fluid filling can reduce significantly the natural frequencies of studiedcylindrical shells. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of orthotropic cylindrical shells. The advantages of this current solution consist in fast convergence, low computational cost and high precision validating for all frequency ranges.

Variable-focus liquid lens simulation

A numerical study of liquid–based variable lenses is presented in this paper. The effect of applied voltage and the contact angle of the surface are taken into account. The conservation of mass and the Navier–Stokes equations for a Newtonian incompressible fluid were solved to model the fluid flow both inside and outside the droplet. The electrohydrodynamic equations have been solved using the commercial software COMSOL MULTIPHYSICS™ based on the finite element method. It was found that by increasing the viscosity ratio, the time response decreases which can be suitable for camera purposes.

Numerical Examination of Wave-induced Coupling Roll Motion and Fluid Resonance between twin Floating Barges in Proximity

Coupling effects of roll motion and fluid resonance between twin rectangular barges subjected to incident waves normal to the spanwise of the narrow gap are investigated employing a two-dimensional numerical wave flume based on a CFD package OpenFOAM. The governing equations for the fluid flow are the Navier-Stokes equations of incompressible Newtonian fluid. The interface between water and air phases is captured by a VOF (volume of fluid) method. The fluid-structure interaction (FSI) is treated with moving meshes in the Arbitrary Lagrangian-Eulerian frame. The present numerical model is validated against wave generation and propagation over a flat bed and the decay of a free rolling rectangular barge in still water. The comparisons with available numerical results show that the present numerical wave flume works well. It is then used to investigate the roll response of the twin floating barges in proximity. The numerical results of this work show that the resonant frequency of the fluid oscillation in the narrow gap between twin rolling barges is smaller than that between twin fixed barges. However, the resonant wave height in the gap between twin rolling barges is observed to be in the same magnitude as that between twin fixed barges. Moreover, the present numerical results indicate that the maximum rolling amplitudes of the twin barges are close to each other, and they appear at the same resonant frequency of the fluid oscillation in the narrow gap. At the low frequency band, the amplitude of the rear barge is larger than that of the leading one. Otherwise, in the frequency band higher than the resonant conditions, the leading barge has a larger response. The present numerical solutions also suggest that the twin barges roll in anti-phase.

Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains

We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier–Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary

Numerical resolution of Euler equations through semi-discrete optimal transport

Geodesics along the group of volume preserving diffeomorphisms are solutions to Euler equations of inviscid incompressible fluids, as observed by Arnold. On the other hand, the projection onto volume preserving maps amounts to an optimal transport problem, as follows from the generalized polar decomposition of Brenier. We present, in the first section, the framework of semi-discrete optimal transport, initially developed for the study of generalized solutions to optimal transport and now regarded as an efficient approach to computational optimal transport. In a second and largely independent section, we present numerical approaches for Euler equations seen as a boundary value problem: knowing the initial and final positions of some fluid particles, reconstruct intermediate fluid states. Depending on the data, we either recover a classical solution to Euler equations, or a generalized flow for which the fluid particles motion is non-deterministic. See Minimal Geodesics along Volume Preserving Maps, through Semi-Discrete Optimal Transport, Merigot and Mirebeau 2015, for the proofs of the results presented in these proceedings.

Effects of Green Roof on the Wind Field of a Low-rise Building

A three dimensional numerical wind tunnel based on the Navier-Stokes equations for viscous, incompressible fluid and LES method is established. Incoming wind field is generated based on the AIJ guidelines (2004). The numerical wind tunnel is validated against experimental results. A low-rise building with green roof is tested in the numerical wind tunnel. The results show that the green roof reduces the drag force of the building, cuts down the fluctuation near the roof, but has insignificant effect on the time-averaged velocity field.

On the uniqueness of the solution of the flow problem with a given vortex

For the two-dimensional nonstationary Euler equations of an ideal incompressible fluid, the flow problem with a given vortex is considered. The uniqueness of the solution is proved.

Applying shear stress to endothelial cells in a new perfusion chamber: hydrodynamic analysis.

Perfusion bioreactors have been proved to be an impartible part of vascular tissue engineering due to its broad range of applications as a means to distribute nutrients within porous scaffold along with providing appropriate physical and mechanical stimuli. To better understand the mechanical phenomena inside a bioreactor, computational fluid dynamics (CFD) was adopted followed by a validation technique. The fluid dynamics of the media inside the bioreactor was modeled using the Navier-Stokes equation for incompressible fluids while convection through the scaffold was described by Brinkman's extension of Darcy's law for porous media. Flow within the reactor determined the orientation of endothelial cells on the scaffold. To validate flow patterns, streamlines and shear stresses, colorimetry technique was used following attained results from CFD. Our bioreactor was modeled to simulate the optimum condition and flow patterns over scaffold to culture ECs for in vitro experimentation. In such experiments, cells were attached firmly without significant detachment and more noticeably elongation process was triggered even shortly after start up.

The Special Form of Second Order Accuracy N-S Equations for Incompressible Fluid

Classic N-S equation has first order accuracy in both of time and space. It has only the terms of first order, without the terms of second or higher order. These terms are relative in time and space steps. The time and space steps, as basic elements of fluid research, should be only some finite quantities and not be infinitely near to zero as defined in mathematics. If the terms of second or higher order can be ignored depends on the value of the corresponding derivative multiplied. Compared with terms of first order, the terms of second or higher order can be ignored under the condition of laminar flow. However, under the condition of turbulent flow, these can’t be ignored yet. When turbulent flow develops fully, the terms of first order, compared with terms of second order, can be ignored. So, it is why classic N-S equations aren’t closed when they are used to analyze turbulent flow. On the basic, many different special forms of the second order accuracy N-S equations of incompressible fluid are derived.