On the stability of gas bubbles oscillating non-spherically in a compressible liquid

Summary This paper describes the non-spherical free and forced oscillations of a gas bubble in a compressible liquid. Generally two different cases of oscillations are possible: spherically radial motion and surface oscillations. The deviation from spherical shape is assumed to be small and is given by a spherical harmonic. Included in the theoretical model are the effect of surface tension, the compressibility of the liquid and the gas. Stability and threshold conditions for the shape oscillations are given.     

On a method for vibration analysis of viscous compressible fluid–structure systems

A fluid–structure interaction formulation for viscous compressible fluid is under consideration. The formulation involves finite element approximation of linearized Navier–Stokes equations and response determination made by means of modal superposition analysis. Standard and simplified schemes of the viscous compressible fluid–structure interaction problem solution are developed. The schemes are based on the frequency condensation method of a complex eigenvalue problem solving. Free and forced oscillations of several fluid–structure systems are studied by the standard and simplified schemes. The analysis of the results obtained shows that the simplified scheme provides a saving of 90% of the computational time required to define oscillation of the structure with viscous compressible fluid in the lowest frequency range. A certain influence of the fluid viscosity on the transient response of the fluid–structure system is also demonstrated. Copyright © 2004 John Wiley & Sons, Ltd.     

高分子材料非线性粘弹性问题的解法

尽管实验限制在小变形范围之内，高分子材料仍表现出明显的非线性粘弹性性能。目前由于分析上的困难，通常只好采用线粘弹性假设。基于前文，提出了一个求解高分子材料物理非线性（含线性）粘弹性问题的新原理，通过对改性聚丙烯材料的实验表明了该原理的正确性和对于此类材料的实用性。     

Chaotic Shape and Translational Dynamics of 2D Incompressible Bubbles under Forced Vibration in Microgravity

Nonlinear shape oscillations of 2D incompressible bubbles in an inviscid fluid, subject to a forced vibration in microgravity, have been studied numerically. Forced vibration induces an oscillatory translational motion as well as shape oscillations. It is shown that for large enough oscillation amplitudes, the coupling between the shape oscillation and the translational motion of a bubble results in a chaotic behaviour. For two-bubble systems, the bubbles may attract each other. The attraction force is stronger at higher Bond numbers. Higher Bond numbers also yield larger bubble deformation.     

Dynamics of the Moving Load Acting on the Hydro-elastic System Consisting of the Elastic Plate,Compressible Viscous Fluid and RigidWall

The subject of the paper is the study of the dynamics of the moving load acting on the hydro-elastic system consisting of the elastic plate, compressible viscous fluid and rigid wall. Under this study the motion of the plate is described by linear elastodynamics, and the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. Numerical results are obtained for the case where the material of the plate is steel, but the fluid material is Glycerin. According to these results, corresponding conclusions related to the influence of the problem parameters, such as fluid viscosity, plate thickness, fluid depth, fluid compressibility and initial stresses on the inter-phase normal stress and normal and tangent velocities of the fluid caused by the load which moves with constant velocity, are made. In particular, it is established that the influence of the fluid viscosity of the aforementioned quantities becomes more considerable under lower velocities of the moving load. Moreover, it is established that there exists a critical velocity of the moving load under which a resonance type event takes place.     

Numerical study on the nonlinear oscillations of a torsion absorber filled with a viscoelastic fluid

Summary. Results are presented concerning the mechanical behavior of a torsion absorber filled with a viscoelastic fluid. As regards the nonlinear constitutive equation of the viscoelastic filling, a multi-mode fluid model is used, leading to a set of coupled ordinary differential equations, which were solved numerically. The influence of different excitation strengths and frequencies on the energy dissipated per cycle in the periodic stage, as well as the resulting shear in the transient and fully developed stages are given and discussed. The findings for small excitation amplitude were compared to those resulting from linear theory.     

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

A Mixed Finite Element (MFE) method for 3D non-steady flow of a viscoelastic compressible fluid is presented. It was used to compute polymer injection flows in a complex mold cavity, which involves moving free surfaces. The flow equations were derived from the Navier-Stokes incompressible equations, and we extended a mixed finite element method for incompressible viscous flow to account for compressibility (using the Tait model) and viscoelasticity (using a Pom-Pom like model). The flow solver uses tetrahedral elements and a mixed velocity/pressure/extra-stress/density formulation, where elastic terms are solved by decoupling our system and density variation is implicitly considered. A new DEVSS-like method is also introduced naturally from the MINI-element formulation. This method has the great advantage of a low memory requirement. At each time slab, once the velocity has been calculated, all evolution equations (free surface and material evolution) are solved by a space-time finite element method. This method is a generalization of the discontinuous Galerkin method, that shows a strong robustness with respect to both re-entrant corners and flow front singularities. Validation tests of the viscoelastic and free surface models implementation are shown, using literature benchmark examples. Results obtained in industrial 3D geometries underline the robustness and the efficiency of the proposed methods.     

Increasing the nonlinear character of microbubble oscillations at low acoustic pressures

The nonlinear response of gas bubbles to acoustic excitation is an important phenomenon in both the biomedical and engineering sciences. In medical ultrasound imaging, for example, microbubbles are used as contrast agents on account of their ability to scatter ultrasound nonlinearly. Increasing the degree of nonlinearity, however, normally requires an increase in the amplitude of excitation, which may also result in violent behaviour such as inertial cavitation and bubble fragmentation. These effects may be highly undesirable, particularly in biomedical applications, and the aim of this work was to investigate alternative means of enhancing nonlinear behaviour. In this preliminary report, it is shown through theoretical simulation and experimental verification that depositing nanoparticles on the surface of a bubble increases the nonlinear character of its response significantly at low excitation amplitudes. This is due to the fact that close packing of the nanoparticles restricts bubble compression.     

Effect of the Compressibility of the Fluid on the Parameters of a Hydraulic Gun

The effect of the compressibility of the fluid on the parameters of a hydraulic gun is evaluated. The quasionedimensional motion of an ideal compressible fluid is described by equations of nonstationary gas dynamics, which are solved numerically according to the algorithm proposed. The numerical solution for a compressible fluid is compared with an analytical solution for an incompressible fluid and with an experiment, which are performed by other authors. From an analysis of the results conclusions are drawn that the compressibility of the fluid can be disregarded. It is proposed that the Mach number the used as a criterion for assessing account for the compressibility of the fluid.