Showing papers on "Shell balance published in 2012"

Global classical large solutions to a 1D fluid-particle interaction model: The bubbling regime

Abstract: This paper is concerned with the 1D fluid-particle interaction model in the so-called bubbling regime which describes the evolution of particles dispersed in a viscous compressible fluid. The model under investigation is described by the conservation of fluid mass, the balance of momentum and the balance of particle density. We obtained the global existence and uniqueness of the classical large solution to this model with the initial fluid density ρ0 admitting vacuum.

Global weak solutions for an incompressible Newtonian fluid interacting with a linearly elastic Koiter shell

Abstract: In this paper we analyze the interaction of an incompressible Newtonian fluid with a linearly elastic Koiter shell whose motion is restricted to transverse displacements. The middle surface of the shell constitutes the mathematical boundary of the threedimensional fluid domain. We show that weak solutions exist as long as the magnitude of the displacement stays below some (possibly large) bound which is determined by the geometry of the undeformed shell.

Global weak solutions for an incompressible, generalized Newtonian fluid interacting with a linearly elastic Koiter shell

Abstract: In this paper we analyze the interaction of an incompressible, generalized Newtonian fluid with a linearly elastic Koiter shell whose motion is restricted to transverse displacements. The middle surface of the shell constitutes the mathematical boundary of the three-dimensional fluid domain. We show that weak solutions exist as long as the magnitude of the displacement stays below some (possibly large) bound which is determined by the geometry of the undeformed shell.

Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

Abstract: The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.

Distribution of fluid pressure along the length of a finite cylindrical oscillating shell

Abstract: An algorithm and program to calculate the pressure distribution on the surface of a cylindrical oscillating shell immersed into a fluid with a given form of its oscillations have been developed. Pressure calculation examples are presented.

Chapter 2 – Fundamentals of Fluid Mechanics

Abstract: Publisher Summary This chapter focuses on the fundamentals of fluid mechanics. A fluid is defined as any material that deforms continually under the application of a shear stress, which is a stress directed tangentially to the surface of the material. Fluid mechanics is the study of fluids at rest and at motion and can be divided into two main categories, which are static fluid mechanics and dynamic fluid mechanics. In static fluid mechanics, the fluid is either at rest or is undergoing rigid-body motion. In dynamic fluid mechanics, the fluid may have an acceleration term and can undergo deformations. Five relationships are the most useful in fluid mechanics problems, which include kinematic, stresses, conservation, regulating, and constitutive. The analysis of fluid mechanics problems can be significantly altered depending on the choice of the system of interest and the volume of interest. Most fluids, under normal conditions can be considered Newtonian fluids. A Newtonian fluid is classified by a constant dynamic viscosity under any shear rate. Similar to a purely elastic material, these fluids have a linear relationship between shear stress and shear rate. However, many fluids do not exhibit Newtonian properties and, therefore, are termed “non-Newtonian” fluids. A fluid can undergo four general motions, which are useful in defining the position of fluid packets, the velocity, and the acceleration of the fluid. A two-phase flow consists of a fluid in both a gas and liquid phase, or two fluids with different viscosities within the same flow conditions. Fluid structure interaction modeling is also important if the fluid can affect and cause a deformation on the flow boundary. This is especially important in the cardiovascular system, in which the blood vessel wall is deformable and cellular matter can interact with the wall.

Application Of Optimal Homotopy Asymptotic Method For Non- Newtonian Fluid Flow In A Vertical Annulus

Abstract: In this paper, the flow of an incompressible non Newtonian fluid in a vertical annulus is considered. The fluid is governed by Sisko fluid model and is assumed to flow upwards under the influence of the pressure gradient and gravity. The non linear momentum equation is then solved using the optimal Homotopy asymptotic method (OHAM). The effect of the power index n, the material parameter and the pressure gradient on the velocity and the stress are explored and presented. It is well known that the momentum flux changes its sign at the same value of the non dimensional radius for which the velocity is maximum. The same has been observed in the present study for Sisko fluids. Further, it is also observed that for negative pressure gradient, the influence of g is more on the shear thinning fluids than that of Newtonian and shear thickening fluids. Thus the second degree approximation of the solution obtained using OHAM is suffice to find analytical solutions to the above mentioned category of problems.