Equations Of Incompressible Fluid Research Articles

Non-Newtonian effects of a lubricant flow through a T-shaped microchannel

In this paper, the importance of non-Newtonian effects of a lubricant flow through a T-shaped microchannel with a moving lead are investigated. The lubricant flow isrepresented by Navier-Stokes equation for viscous, incompressible and steady fluid flows.Non-Newtonian characteristics are simulated by FENE-P constitutive equation. Finite Volume method was used to solve the case numerically. PSD distribution for Reynolds number Re=0.01 and Weissenberg number We =1 were compared with Newtonian case. Clear numerical evidence of a higher stresses for non-Newtonian case is discussed.

Systems with strong damping and their spectra

We establish a new method for obtaining nonconvex spectral enclosures for operators associated with second‐order differential equations in a Hilbert space. In particular, we succeed in establishing the existence of a spectral gap, which is the first result of this kind since the seminal results of Krein and Langer for oscillations of damped systems. While the latter and other spectral bounds are confined to dampings D that are symmetric and dominated by A0, we allow for accretive D of equal strength as A0. To achieve these results, we prove new abstract spectral inclusion results that are much more powerful than classical numerical range bounds. Two different applications, small transverse oscillations of a horizontal pipe carrying a steady‐state flow of an ideal incompressible fluid and wave equations with strong (viscoelastic and frictional) damping, illustrate that our new bounds are explicit.

The Initial Value Problem for the Euler Equations of Incompressible Fluids Viewed as a Concave Maximization Problem

We consider the Euler equations of incompressible fluids and attempt to solve the initial value problem with the help of a concave maximization problem.We show that this problem, which shares a similar structure with the optimal transport problemwith quadratic cost, in its "Benamou-Brenier" formulation,always admits a relaxed solution that can be interpretedin terms of $sub-solution$ of the Euler equations in the sense of convex integration theory.Moreover, any smooth solution of the Euler equations can be recovered from this maximization problem, at least for short times.

On the Duhamel’s Solutions to the Null Equations of Incompressible Fluids

On the Duhamel’s Solutions to the Null Equations of Incompressible Fluids

On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows

This paper reports the stability conditions for intense zonal flows (ZFs) and the growth rate γTI of the corresponding “tertiary” instability (TI) within the generalized Hasegawa–Mima plasma model. The analytical calculation extends and revises Kuo's analysis of the mathematically similar barotropic vorticity equation for incompressible neutral fluids on a rotating sphere [H.-L. Kuo, J. Meteor. 6, 105 (1949)]; then, the results are applied to the plasma case. An error in Kuo's original result is pointed out. An explicit analytical formula for γTI is derived and compared with numerical calculations. It is shown that, within the generalized Hasegawa–Mima model, a sinusoidal ZF is TI-unstable if and only if it satisfies the Rayleigh–Kuo criterion (known from geophysics) and that the ZF wave number exceeds the inverse ion sound radius. For non-sinusoidal ZFs, the results are qualitatively similar. As a corollary, there is no TI in the geometrical-optics limit, i.e., when the perturbation wavelength is small compared to the ZF scale. This also means that the traditional wave kinetic equation, which is derived under the geometrical-optics assumption, cannot adequately describe the ZF stability.

Nearshore wave processes numerical study for a better prediction of hydrodynamic loads on coastal structures

Taking into account the sensible approach in the coastal zones, in these types of areas were found different ways of understanding and description of the phenomena occurring during the water wave propagation. The waves hit the zone with a force that can affect the shoreline. Coastal protection measures were implemented, which include the hydrodynamic structures. The hydrodynamic process plays an important role in coastal area which involves the need for knowledge on the prediction of hydrodynamic loading required up to a very detailed level, such as maximum or minimum pressures. In this paper, we will present a study of wave fields that propagates in a simplified, constant-slope coastal model and relations between waves and hydrodynamics structures. The processes of wave fields include dissipative mechanisms such as depth-induced wave breaking, bottom friction and the interaction between wave field and coastal dike. The numerical models were constructed using ANSYS-Fluent program for modelling fluid flow and to solve the unsteady, two dimensional Navier-Stokes equations of incompressible fluid. Water waves are generated in two-phase fluid domain, where Volume of Fluid Model is used for generation of the two-phase flow model - the water-air interaction.

Study on PEFC Gas Diffusion Layer with Designed Wettability Pattern Tolerant to Flooding

For reduction of the cost of a polymer electrolyte fuel cell (PEFC), it is desired to increase the maximum current density. Under high current density operation, it is important to control water drainage for smooth supply of oxygen. A gas diffusion layer (GDL) which is placed between separator and CL plays an important role for the water transport. Therefore, the improvement of GDL design is important to increase the maximum current density. Recently, there is a report which shows that better cell performance was obtained using the GDL with designed hydrophobic and hydrophilic lines (1). However, the water transport in the GDL is still unclear because the detail observation of liquid water behavior in GDL is difficult due to the quite complex structure and the very small pores (pore diameter: approximately 10 mm). Therefore, there is some room for improving the GDL structure. The objective of this study is to investigate the water transport in GDL with designed wettability pattern and to develop the ideal GDL. To evaluate the water transport in the GDL, a lattice Boltzmann method (LBM) is applied. The LBM is a simulation method to analyze the fluid behavior by tracking movements of large number of particle ensembles. The particle density is expressed by distribution functions, and the distribution functions are calculated by a simple law of collision and transition ensuring the continuity equation and the Navier-Stokes equations for incompressible fluids. Due to the simplicity of the algorithm, it has an advantage of adaptability for complex boundary geometries. Therefore, the LBM is suitable model to simulate the water behavior in the GDL. For high speed calculation, the LBM treating two-phases as having the same density is applied in this study although the densities of air and water are very different. The applicability of this LBM model for the simulation in GDL has been confirmed in the previous study (2). The density of the two-phase in the simulation is set identical to water, ρ = 978kg/m3. The interfacial tension between the two-phase is σ = 6.40×10-2N/m, and liquid and gas viscosities are μL = 4.04×10-4Pa∙s and μG = 2.30×10-5Pa∙s respectively. Figure 1 shows the simulation domain and boundaries. The lower half of simulation domain is GDL layer, on which rib and channel space are placed. Size of GDL is 240μm × 240μm × 100μm and the porosity of GDL is 75%. Sizes of rib and channel are both 120μm × 240μm × 160μm. The bottom of the simulation domain is assumed the micro-porous layer (MPL) and it is treated as a solid wall. Commonly, much water stays in the GDL region under rib. Therefore, to focus on the water behavior in GDL under rib, MPL crack as inlet boundary is set at MPL under rib. Top of the channel is outlet boundary. Four side boundaries are solid walls. The contact angle of GDL, MPL and side walls is set 130º. The contact angle of rib is set 50º. Figure 2 shows simulation results of water transport in GDL without designed wettability pattern. In the simulation, the water is transported randomly and water spreads in the x-y plane of GDL. Finally, the water is drained to channel from pores which is slightly away from the rib. Figure 3 shows simulation results of water transport in GDL with designed wettability pattern. The pattern is set in the center of GDL structure and the size is 50μm × 240μm × 100μm. The contact angle of designed wettability pattern is 50º. Here, the GDL structure is same as Fig. 2. In the simulation, the water is accumulated in the designed wettability pattern of GDL and the smooth water transport from the GDL region under rib to the GDL region under channel is achieved. It is known that water tends to retain in the GDL under ribs and smooth removal of the water is important to avoid flooding. In Ref. (1), it seems that the cell performance using the GDL with designed wettability pattern was improved by the smooth water transport from GDL under rib to GDL under channel. In the final full paper, the effect of the structural characteristics of the GDL such as the contact angle of the pattern and the pore distributions will be discussed. Figure 1

On a new type of 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. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we proceed exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids, with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of flow.The main motivation of the current research is the exploring the case when velocity field u is supposed to be perpendicular to the vector ∇α. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained, for which non-stationary helical flow with invariant Bernoulli-function is considered.The spatial part of the pressure field of the fluid flow should be determined via Bernoulli-function, if components of the velocity of the flow are already obtained.

A Preliminary Study on Numerical Waves and Its Impact on Horizontal Plate Based on Fluent

Based on the N-S equations for viscous, incompressible fluid and RNGk − ε turbulence model, a two dimensional Numerical Wave Tank is established, utilizing the secondary development function of Fluent software and the VOF method. A two-dimensional linear regular wave and a random wave are generated by defining the motion of moving boundary and adding wave absorbing zone at the end of the wave tank. The resulting numerical wave shape agreed well with the theoretical shape. The simulated wave spectrum of random wave keeps the original structure of the target spectrum. The impact of waves on the horizontal plate is simulated referring to the existing physical model test. Compared with the physical and the numerical pressure data of 11 pressure points under the horizontal plate, it is found that the two datas fit well, indicating the effectiveness of Fluent in simulating the interaction between waves and structures, which lays a foundation for further exploring the factors that affect the magnitude of the impact pressure on the horizontal plate.

NUMERICAL SIMULATION OF A ELASTO-VISCOPLASTIC FLUID FLOW INSIDE A CAVITY

This article addresses finite element approximations for elasto-viscoplastic flows. Numerical simulations aiming at investigating the role of elasticity for inertialess flows of viscoplastic materials within lid-driven cavity.The mechanical model is made up of the usual governing equations for incompressible fluids coupled with a Oldroyd-B type equation (de Souza Mendes, 2011) modified to incorporate the dependency both of relaxation and retardation time as the viscoplastic viscosity on the strain rate. These parameters depend on the material microstructure, which level is described by an structure parameter . This model is approximated by a multi-field Galerkin least-squares formulation (Behr et al., 1993) in terms of extra-stress tensor, the pressure field and the velocity vector. Results, focused on the determination of yield surface topology, investigate the influence of elastic and viscous governing parameters on the flow pattern.

Assessment of two-equation model for simulation of air pocket advancing into a rectangular duct

ABSTRACTThis research aims to evaluate the influence of air on the water surface and pressure profiles in two-phase (air–water) flow. In previous studies, the authors used the continuity and momentum equations for water in a one-dimensional finite volume model. In the present study, the authors additionally incorporate both the mass conservation and momentum equations for incompressible fluids as basic equations for the air portion. Momentum equations were integrated for the free surface and pressurized flow regions after interface observations made at each time step. To correct velocity and pressure in the pressurized portion, the authors used the highly simplified mark-and-cell method. A pressure drop equation is used at the interface of pressurized and free surface flows to deduce the pressure. The Harten total variation diminishing scheme was used to avoid numerical oscillations. The results were compared with experimental data and numerical simulations without considering the air effect.

NUMERICAL SIMULATION OF UNSTEADY THREEDIMENSIONAL DETACHED FLOW AROUND THE REFERENCE AHMED CAR MODEL

For the numerical simulation of the flow around simplified Ahmed Car type vehicle the Reynolds averaged Navier-Stokes equations of a viscous incompressible fluid were applied. To close the system of equations, the Shear Stress Transport (SST) turbulence model was used. The numerical solution of the governing equations was obtained by the control volume method. The numerical technique is implemented in program-methodical ware, written in the Fortran language. The computational domain around the Ahmed Car body is divided into control volumes by an unstructured hexahedral mesh consisting of 3.5 million cells. Calculations of two variants of the reference geometry - with the rear slant angle of 25° and 35° were carried out. The Reynolds number based on model length was equal to 2.6 million. The calculation results were visualized, analyzed and compared with results of other authors. The distributions of the velocity modulus, the pressure and the streamlines in the Ahmed Car symmetry plane, the distribution of the pressure and friction coefficients along the model surface, the distribution of the velocity vector in the cross section behind the Ahmed Car body were represented. The visualization of the return-flow region behind the rear surface of the model and the trailing vortex obtained by the isosurface of the velocity invariant Q was performed. For comparison, the results of other authors are presented: the velocity distribution in the longitudinal section and the pressure distribution along the Ahmed Car from the work of Banga S., the distribution of the velocity vectors in the cross section behind the Ahmed Car body from the works of Minguez M. and Lienhart H. The simulation results completely reproduce all known features of the flow structure around the Ahmed Car body. The aerodynamic characteristics of Ahmed Car were obtained. The drag coefficient was 0.255 and 0.268 for the rear slant angle of 25° and 35° respectively, which agrees well with the results of other numerical and experimental studies. The obtained results indicate the practical applicability of the chosen method and the developed program-methodical ware for the tasks of the ground vehicle aerodynamics.

The Euler equations of an inviscid incompressible fluid driven by a Lévy noise

Our aim in this article is to show the local existence of pathwise solutions of the Euler equations driven by a general Lévy noise, in all space dimensions and for strictly positive time almost surely. The Euler equations are considered in a regular domain with slip boundary condition, or with periodic boundary conditions or in the whole space. In addition, we prove that when all data are C∞ in space, so is the solution.

Biological reactor retrofitting using CFD-ASM modelling

In recent years, the interest in modelling activated sludge (AS) systems by means of Computational Fluid Dynamics (CFD) techniques has significantly increased. This work shows a successful case study combining CFD hydrodynamics and biokinetic modelling. The hydrodynamics is analysed by using the Reynolds-averaged Navier-Stokes equation for incompressible non-Newtonian fluids and SST turbulence model. Biokinetics has been included in the CFD as transport equations with source and sink terms defined by the Activated Sludge Model n°1 (ASM1). Furthermore, a strategy for reducing the computational cost while maintaining accuracy of the results of these calculations has been proposed. This strategy is based on a two-step solver configuration and the definition of a variable timestep scheme. The resulting CFD-ASM approach permits a proper evaluation of denitrification in the anoxic tanks as well as the reproduction of nitrate and readily biodegradable substrate distributions. To demonstrate the strength of the proposed CFD-ASM, it has been used to evaluate the operation of a full-scale AS system and optimize its performance through changes in the biological reactor anoxic zone. The original configuration has been retrofitted and modified after detecting intrinsic defects in the fluid behaviour within the tank. This study has been assessed by analysing hydrodynamics in detail and validating the simulation results with tracer tests and flow velocity measurements. Substantial variations on the Residence Time Distribution have been confirmed when modifying the internal elements of the tank configuration: the wall-bushing and the stirrer positioning. As a result of this work, an influential short circuiting was corrected improving hydrodynamics and increasing mean residence time, all favouring denitrification efficiency. Outcomes of this study show the benefit of CFD when applied to AS tanks.

Effects of the wind on the breaking of modulated wave trains

The effect of wind on the wave breaking induced by the modulational instability is investigated numerically using the open source software Gerris. The two-phase flow is modelled by the two-dimensional Navier–Stokes equations for a single incompressible fluid and a Volume of Fluid technique is employed to capture the air–water interface. The flow is initialized as a fundamental wave component with two side-band perturbations so that the breaking is induced via the Benjamin–Feir instability mechanism. In order to investigate its effect on the wave evolution and on the breaking process, a uniform wind, twice the phase speed, is assigned in the air phase. The simulation covers the initial development of the wind profile, the growth of the modulational instability, the breaking and post breaking phases. Results show the occurrence of air flow separation from the wave crests shortly after the initial start. Pressure and tangential stress acting on the free surface are computed. It is shown that due to the flow separation there is a favourable pressure gradient about the wave crests whereas the tangential stresses are generally in favour of the wave propagation on the back of the wave but are opposed to the propagation along the forward face and in the wave trough. An initial growth of the energy content in water is observed, followed by a dissipation stage which is not related to the breaking process. In agreement with the experiments, the growth rate of the side-bands is reduced when compared to the corresponding no-wind solution. Because of the slower growth, the limiting condition for the onset of the breaking is reached with some delay. At the end of the breaking process, when the downshift is completed, the amplitude of the left side-band in the wind case is somewhat lower than that for the no-wind case. No substantial differences have been found in terms of the total energy dissipated by the whole breaking process although the dissipation rate for the wind case is noticeably higher. The higher dissipation rate observed in the wind case is found to be related to the larger amount of air entrained by the breaking process.

Coupling immersed method with node-based partly smoothed point interpolation method (NPS-PIM) for large-displacement fluid-structure interaction problems

The newly developed node-based partly smoothed point interpolation method (NPS-PIM) and immersed technique are coupled to simulate fluid-structure interaction (FSI) problems associated with largely deformable solid/structure. Under the framework of immersed method, the governing equations can be decomposed into three components based on fictitious fluid assumption, i.e. equations for incompressible viscous fluid, FSI conditions and nonlinear solid. The semi-implicit characteristic-based split algorithm is used to solve the Navier-Stokes equation of incompressible viscous fluid, and the fictitious fluid domain can be used to calculate the FSI force. Owing to the properly softened stiffness by the node-based partly strain smoothing operation, NPS-PIM can effectively solve the large deformation problem of solids discretized with the simplest linear triangular mesh. The immersed framework makes the present method avoid the troublesome re-meshing process and the triangular mesh further simplifies the preprocessing operation. In comparison with the models using FEM and node-based smoothed point interpolation method (NS-PIM) as solid solver, numerical results have shown that the present method using NPS-PIM can provide more accurate solutions for both steady and transient problems with regard to large-displacement FSI problems.

Decay estimate of solutions to the coupled chemotaxis–fluid equations in [formula omitted

We are concerned with a model arising from biology, which is coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. We study the large time behavior of solutions near a constant states to the chemotaxis-Navier–Stokes system in R3. Appealing to a pure energy method, we first obtain a global existence theorem by assuming that the H3 norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms Ḣ−s(0≤s<32) or homogeneous Besov norms Ḃ2,∞−s(0<s≤32), we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual Lp−L2(1≤p≤2) type of the decay rates without requiring that the Lp norm of initial data is small.

A Riccati-type solution of 3D Euler equations for incompressible flow

In fluid mechanics, a lot of authors have been reporting analytical solutions of Euler and Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we explore the case of non-stationary flows of the Euler equations for incompressible fluids, which should conserve the Bernoulli-function to be invariant for the aforementioned system.We use previously suggested ansatz for solving of the system of Navier-Stokes equations (which is proved to have the analytical way to present its solution in case of conserving the Bernoulli-function to be invariant for such the type of the flows). Conditions for the existence of exact solution of the aforementioned type for the Euler equations are obtained. The restrictions at choosing of the form of the 3D nonstationary solution for the given constant Bernoulli-function B are considered. We should especially note that pressure field should be calculated from the given constant Bernoulli-function B, if all the components of velocity field are obtained.

A quasi-Lagrangian finite element method for the Navier–Stokes equations in a time-dependent domain

The paper develops a finite element method for the Navier–Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form Δt≤C, where C depends only on problem data, and h2mu+2≤cΔt, mu is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced computed tomography images.

Geometric generalised Lagrangian-mean theories

Many fluctuation-driven phenomena in fluids can be analysed effectively using the generalised Lagrangian-mean (GLM) theory of Andrews &amp; McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646) This finite-amplitude theory relies on particle-following averaging to incorporate the constraints imposed by the material conservation of certain quantities in inviscid regimes. Its original formulation, in terms of Cartesian coordinates, relies implicitly on an assumed Euclidean structure; as a result, it does not have a geometrically intrinsic, coordinate-free interpretation on curved manifolds, and suffers from undesirable features. Motivated by this, we develop a geometric generalisation of GLM that we formulate intrinsically using coordinate-free notation. One benefit is that the theory applies to arbitrary Riemannian manifolds; another is that it establishes a clear distinction between results that stem directly from geometric consistency and those that depend on particular choices. Starting from a decomposition of an ensemble of flow maps into mean and perturbation, we define the Lagrangian-mean momentum as the average of the pull-back of the momentum one-form by the perturbation flow maps. We show that it obeys a simple equation which guarantees the conservation of Kelvin’s circulation, irrespective of the specific definition of the mean flow map. The Lagrangian-mean momentum is the integrand in Kelvin’s circulation and distinct from the mean velocity (the time derivative of the mean flow map) which advects the contour of integration. A pseudomomentum consistent with that in GLM can then be defined by subtracting the Lagrangian-mean momentum from the one-form obtained from the mean velocity using the manifold’s metric. The definition of the mean flow map is based on choices made for reasons of convenience or aesthetics. We discuss four possible definitions: a direct extension of standard GLM, a definition based on optimal transportation, a definition based on a geodesic distance in the group of volume-preserving diffeomorphisms, and the ‘glm’ definition proposed by Soward &amp; Roberts (J. Fluid Mech., vol. 661, 2010, pp. 45–72). Assuming small-amplitude perturbations, we carry out order-by-order calculations to obtain explicit expressions for the mean velocity and Lagrangian-mean momentum at leading order. We also show how the wave-action conservation of GLM extends to the geometric setting. To make the paper self-contained, we introduce in some detail the tools of differential geometry and main ideas of geometric fluid dynamics on which we rely. These include variational formulations which we use for alternative derivations of some key results. We mostly focus on the Euler equations for incompressible inviscid fluids but sketch out extensions to the rotating–stratified Boussinesq, compressible Euler, and magnetohydrodynamic equations. We illustrate our results with an application to the interaction of inertia-gravity waves with balanced mean flows in rotating–stratified fluids.