Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

Weakly dissipative solutions and weak–strong uniqueness for the Navier–Stokes–Smoluchowski system

This article deals with a fluid–particle interaction model for the evolution of particles dispersed in a fluid. The fluid flow is governed by the Navier–Stokes equations for a compressible fluid while the evolution of the particle densities is given by the Smoluchowski equation. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually. The existence of weakly dissipative solutions is established under reasonable physical assumptions on the initial data, the physical domain, and the external potential. Furthermore, a weak–strong uniqueness result is established via the relative entropy method yielding that a weakly dissipative solution agrees with a classical solution with the same initial data when such a classical solution exists.     

On boundary layer flow of a Sisko fluid over a stretching sheet

Abstract

In this paper, the steady boundary layer flow of a non-Newtonian fluid over a nonlinear stretching sheet is investigated. The Sisko fluid model, which is combination of power-law and Newtonian fluids in which the fluid may exhibit shear thinning/thickening behaviors, is considered. The boundary layer equations are derived for the two-dimensional flow of an incompressible Sisko fluid. Similarity transformations are used to reduce the governing nonlinear equations and then solved analytically using the homotopy analysis method. In addition, closed form exact analytical solutions are provided for n = 0 and n = 1. Effects of the pertinent parameters on the boundary layer flow are shown and solutions are contrasted with the power-law fluid solutions.     

Couette flow of a third grade fluid with rotating frame and slip condition

An incompressible third grade fluid occupies the porous space between two rigid infinite plates. The steady rotating flow of this fluid due to a suddenly moved lower plate with partial slip of the fluid on the plate is analysed. The fluid filling the porous space between the two plates is electrically conducting. The flow modeling is developed by employing a modified Darcy’s law. A numerical solution of the governing problem consisting of a non-linear ordinary differential equation and non-linear boundary conditions is obtained and discussed. Several limiting cases of the arising problem can be obtained by choosing suitable parameters.     

Effects of partial slip on the steady Von Kármán flow and heat transfer of a non-Newtonian fluid

The steady Von Kármán flow and heat transfer of a non-Newtonian fluid is extended to the case where the disk surface admits partial slip. The constitutive equation of the non-Newtonian fluid is modeled by that for a Reiner-Rivlin fluid. The momentum equations give rise to highly nonlinear boundary value problem. Numerical solutions for the governing nonlinear equations are obtained over the entire range of the physical parameters. The effects of slip and non-Newtonian fluid characteristics on the velocity and temperature fields have been discussed in detail and shown graphically.     

Peripheral layer viscosity effects on periodic blood flow through rigid tube of thin diameter

A mathematical model has been presented for periodic blood flow in a rigid circular tube of thin diameter. Blood is presented as a 3-layered fluid by considering core fluid as a casson fluid which is covered by a thin layer of Newtonian fluid (plasma). The energy integral method has been used to obtain the unsteady pressure gradients as suggested by Elkouh [2]. The results obtained for velocity profiles have been compared with the experimental results of Bugliarello and Sevilla (Biorheology 7 (1970), 85). The effects of various parameters on wall shearing stress has also been brought out and discussed.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

Fluid approximation for generalized Jackson network with vacations

Using a bounding technique, we prove that the fluid model of generalized Jackson network (GJN) with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence rate are embodied by the queue length, workload, and busy time processes.     

Magnetohydrodynamics flow of a Burgers’ fluid in an orthogonal rheometer

The magnetohydrodynamics flow of an electrically conducting, incompressible Burgers’ fluid in an orthogonal rheometer is investigated. An exact solution is obtained. The effects of various dimensionless parameters existing in the model on the velocity field, vorticity and traction are studied graphically. It is noted that boundary layers form for a variety of reasons. It form as the Reynolds number increases. Also, as the Weissenberg number increases a distinct boundary layer formation is observed. It can develop at low Reynolds number provided the Weissenberg number is sufficiently high, however, it is not possible in the case of a Newtonian fluid. It is shown that no torque is exerted by the fluid on one of the disks. Results are compared with Oldroyd-B fluid.     

Symmetry breaking of melt flow typically encountered in a Bridgman configuration heated from below

A computational model is developed to investigate three-dimensional fluid flow instability and transition to unsteadiness. The simulated domain corresponds to a parallelepiped configuration which is a restriction to the fluid phase of commonly used configurations in crystal growth (viz. Bridgman configuration). In the present work, this problem is studied using three-dimensional simulations and focuses on symmetry breaking and transition to unsteadiness occurring for a low Prandtl number fluid (Pr = 0.01).     

On the unbounded increase in vorticity and velocity circulation in stratified and homogenous fluid flows

We consider the Oberbeck-Boussinesq system without dissipation (ideal convection) in a horizontal layer and in a “barrel” with flat bottom and flat cover. It is shown that the velocity circulation along a fluid contour consisting of two fluid curves on the bottom and on the cover connected by two isothermic fluid curves can be calculated explicitly and is a linear function of time. The serre result stating that the azimuthal component of vorticity in rotationally symmetric ideal fluid flows between coaxial cylinders increases linearly is generalized to the case of stratified fluids. It is proved that all plane and axially symmetric isothermic flows in a layer or in a barrel are unstable with respect to nonisothermic perturbations and in the case of a homogenous fluid all axially symmetric flows between coaxial cylinders are unstable in the sense of Lyapunov with respect to perturbations of the azimuthal component of the velocity in any metric including the maximum of magnitude of vorticity. Translated fromMaternaticheskie Zametki, Vol. 68, No. 4, pp. 627–636, October, 2000.     

Energy decay and global solutions for a damped free boundary fluid–elastic structure interface model with variable coefficients in elasticity

ABSTRACT

We study a free boundary fluid-structure interaction model. In the model, a viscous incompressible fluid interacts with an elastic body via the common boundary. The motion of the fluid is governed by Navier–Stokes equations while the displacement of the elastic structure is described by variable coefficient wave equations. The dissipation is placed on the common boundary between the fluid and the elastic body. Given small initial data, the global existence of the solutions of this system is proved and the exponential decay of solutions is obtained.     

Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate

The effect of temperature-dependent density on MHD mixed convection flow of power-law fluid past a moving semi-infinite vertical plate for high temperature differences between the plate and the ambient fluid is studied. The fluid density is assumed to decrease exponentially with temperature. The usual Boussinesq approximations are not considered due to the large temperature differences. The surface temperature of the moving plate was assumed to vary according to a power-law form, that is, T_w(x) = T_∞ + Ax^γ. The fluid is permeated by a uniform magnetic field imposed perpendicularly to the plate on the assumption of small magnetic Reynolds number. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. The effects of various parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number are presented graphically and in the tabular form. The results show that application of Boussinesq approximations in a non-Newtonian fluid subjected to high temperature differences gives a significant error in the values of the skin-friction coefficient and the application of an external magnetic field reduces this error markedly in the case of shear-thickening fluid.     

Vibration analysis of rectangular plates coupled with fluid

The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders’ shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli’s equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.     

Fluid analysis of an input control problem

A two-station network with controllable inputs and sequencing control, proposed by Wein (Oper. Res. 38:1065–1078, 1990), is analyzed. A control is sought to minimize holding cost subject to a throughput constraint. In a Lagrangian formulation, input vanishes in the fluid limit. Several alternative fluid models, including workload formulations, are analyzed to develop a heuristic policy for the stochastic network. Both the fluid heuristic and Wein’s diffusion solution are compared with the optimal policy by solving the dynamic program. Examples with up to six customer classes, using Poisson arrival and service processes, are presented. The fluid heuristic does well at sequencing control but the diffusion gives additional, and better, information on input control. The fluid analysis, in particular whether the fluid priorities are greedy, aids in determining whether the fluid heuristic contains useful information.     

A model of fluid injection into the spinal disc

This paper presents an analytical model of the stress–strain response of intervertebral disc to fluid injection. The disc has nonlinear properties and collagen fibres play a significant role in sustaining strain. Each fibre is modeled as a flexible, helical string inclined at ∼30° to the horizontal plane. The tensile stress in the fibres is obtained from a nonlinear stress–strain law that has been determined by experiment. An asymptotic approximation of the model equations based on the ratio of the fluid injected to the initial volume of fluid in the disc is developed and its solution obtained. Some quantitative predictions are made by considering a hypothetical value of the amount of fluid injected and some material values of discs at different levels of the spine. Numerical simulations show that the model compare reasonably well with some experimental observations for discs of the lumbar region.     

A model for fluid flow in non-fully filled tribological interfaces – Part 1: Basics and Numerics

In literature, most contributions on starved lubrication focus on the occurring pressures in macroscopic devices. Hereby, usually the Reynolds equation is modified in different ways. In contrast to this proceeding, this paper's intention is the general investigation of this tribological regime to get a fundamental comprehension on the transition from boundary lubrication to mixed lubrication. The respective model describes the flow of the fluid through two rough surfaces moving relative to each other. The lack of fluid is regarded by the fact that elements may not be fully filled with the fluid. Only elements where the fluid fully fills the gap, generate a pressure. This effect is considered by a type of unilateral constraint in combination with a penalty function. The fluid flow is computed according to the Navier-Stokes equation. In combination with the continuity equation, a set of implicit nonlinear equations has to be solved. Its potential and basic application fields are finally discussed. A further paper will show applications of the algorithm towards different scenarios. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid-structure interaction of an elastic pipe immersed in a coaxial rigid pipe: a model for the Tullio Phenomenon

An axisymmetric, elastic pipe is filled with an incompressible fluid and is immersed in a second, coaxial rigid pipe which contains the same fluid. A pressure pulse in the outer fluid annulus deforms the elastic pipe which invokes a fluid motion in the fluid core. It is the aim of this study to investigate streaming phenomena in the core which may originate from such a fluid-structure interaction. This work presents a numerical solver for such a configuration. It was developed in the OpenFOAM software environment and is based on the Arbitrary Lagrangian Eulerian (ALE) approach for moving meshes. The solver features a monolithic integration of the one-dimensional, coupled system between the elastic structure and the outer fluid annulus into a dynamic boundary condition for the moving surface of the fluid core. Results indicate that our configuration may serve as a mechanical model of the Tullio Phenomenon (sound-induced vertigo). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weakly coupled analysis of a blade in multiphase mixing vessel

Two or more physical systems frequently interact with each other, where the independent solution of one system is impossible without a simultaneous solution of the others. An obvious coupled system is that of a dynamic fluid-structure interaction. [8] In this paper a computational analysis of the fluid-structure interaction in a mixing vessel is presented. In mixing vessels the fluid can have a significant influence on the deformation of blades during mixing, depending on speed of mixing blades and fluid viscosity. For this purpose a computational weakly coupled analysis has been performed to determine the multiphase fluid influences on the mixing vessel structure. The multiphase fluid field in the mixing vessel was first analyzed with the computational fluid dynamics (CFD) code CFX. The results in the form of pressure were then applied to the blade model, which was the analysed with the structural code MSC.visualNastran forWindows, which is based on the finite element method (FEM). (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)