Showing papers on "Shell balance published in 2008"

Stability and acoustic scattering in a cylindrical thin shell containing compressible mean flow

Abstract: We consider the stability of small perturbations to a uniform inviscid compressible flow within a cylindrical linear-elastic thin shell. The thin shell is modelled using Flugge's equations, and is forced from the inside by the fluid, and from the outside by damping and spring forces. In addition to acoustic waves within the fluid, the system supports surface waves, which are strongly coupled to the thin shell. Stability is analysed using the Briggs–Bers criterion, and the system is found to be either stable or absolutely unstable, with absolute instability occurring for sufficiently small shell thicknesses. This is significantly different from the stability of a thin shell containing incompressible fluid, even for parameters for which the fluid would otherwise be expected to behave incompressibly (for example, water within a steel thin shell). Asymptotic expressions are derived for the shell thickness separating stable and unstable behaviour.We then consider the scattering of waves by a sudden change in the duct boundary from rigid to thin shell, using the Wiener–Hopf technique. For the scattering of an inbound acoustic wave in the rigid-wall section, the surface waves are found to play an important role close to the sudden boundary change. The solution is given analytically as a sum of duct modes.The results in this paper add to the understanding of the stability of surface waves in models of acoustic linings in aeroengine ducts. The oft-used mass–spring–damper model is regularized by the shell bending terms, and even when these terms are very small, the stability and scattering results are quite different from what has been claimed for the mass–spring–damper model. The scattering results derived here are exact, unique and causal, without the need to apply a Kutta-like condition or to include an instability wave. A movie is available with the online version of the paper.

Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid

Abstract: We consider a finite element algorithm intended to study the dynamic behavior of an elastic cylindrical shell filled with an immovable or flowing fluid. To describe the fluid, we use the perturbed velocity potential whose equations with the corresponding boundary conditions are solved by the Bubnov-Galerkin method. To describe the shell, we use the variation principle, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure acting on the shell on the side of the fluid. Solving the problem is reduced to calculating and analyzing the eigenvalues of the coupled system of equations obtained as a result of combining the equations for the perturbed velocity potential and the shell displacements. We consider several test problems in which, along with the comparison of the computational results with the earlier published experimental, analytic, and numerical data, we also study the dynamic behavior of the “shell-fluid” system for various boundary conditions for the perturbed velocity potential.

Modelling of Plates Subjected to Flowing Fluid Under Various Boundary Conditions

Abstract: Elastic structures subjected to fluid flow undergo a considerable change in their dynamic behavior and can lose their stability. In this article we describe the development of a fluid-solid finite element to model plates subjected to flowing fluid under various boundary conditions. The mathematical model for the structure is developed using a combination of the hybrid finite element method and Sanders’ shell theory. The membrane displacement field is approximated by bilinear polynomials and the transversal displacement by an exponential function. Fluid pressure is expressed by inertial, Coriolis and centrifugal fluid forces, written respectively as function of acceleration, velocity and transversal displacement. Bernoulli’s equation for the fluid-solid interface and partial differential equation of potential flow are applied to calculate the fluid pressure. An impermeability condition ensures contact between the system of plates and the fluid. Mass and rigidity matrices for each element are calcul...

On-line method for estimating kinematic viscosity of fluid flowing through system, involves determining absolute viscosity of fluid at section A in system

Abstract: The on-line method involves determining an absolute viscosity of the fluid at a section A in the system (1) and measuring a characteristic of the fluid in the system. A virtual temperature of the fluid is determined with section A using the measured characteristic of the fluid with a relationship, which correlates the characteristic of the fluid with the virtual temperature of the fluid with section A.

Momentum Balance for Two-Phase Horizontal Pipe Flow Part 2: Testing of Models

Abstract: Momentum balance models were tested against reliable data for both holdup and pressure drop. The best prediction performance was achieved using a model that considered the actual shape of the liquid phase in the pipe. In such circumstances the momentum balance calculation tended to under predict both the holdup and pressure drop for some of the annular and stratified regimes. Suggestions are made for improvements in the momentum balance approach.