Dynamics of cavitation–structure interaction

Cavitation–structure interaction has become one of the major issues for most engineering applications. The present work reviews recent progress made toward developing experimental and numerical investigation for unsteady turbulent cavitating flow and cavitation–structure interaction. The goal of our overall efforts is to(1) summarize the progress made in the experimental and numerical modeling and approaches for unsteady cavitating flow and cavitation–structure interaction,(2) discuss the global multiphase structures for different cavitation regimes, with special emphasis on the unsteady development of cloud cavitation and corresponding cavitating flow-induced vibrations,with a high-speed visualization system and a structural vibration measurement system, as well as a simultaneous sampling system,(3) improve the understanding of the hydroelastic response in cavitating flows via combined physical and numerical analysis, with particular emphasis on the interaction between unsteady cavitation development and structural deformations. Issues including unsteady cavitating flow structures and cavitation–structure interaction mechanism are discussed.     

Dynamics of worm-like micelles: the Cox–Merz rule

The viscoelastic behaviour of worm-like micelles in small-amplitude oscillatory, steady simple shear and uniaxial extensional flows are analyzed with a model that couples the Oldroyd-B constitutive equation with a kinetic equation that accounts for the structural changes induced by the flow. In some cases, the constitutive equation predicts a viscoelastic behaviour that is consistent with the Cox–Merz rule. Departures from this rule are also predicted. Experimental data obtained for two worm-like micellar systems indicate that in these solutions, the Cox–Merz rule is not usually followed, in agreement with the predictions of our model. In uniaxial extensional flow, the model predicts a strain hardening in the extensional viscosity at low extensional rates and a strain-thinning at high extensional rates.     

Bilinear form and soliton interactions for the modified Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

In this paper, we investigate the modified Kadomtsev–Petviashvili (mKP) equation for the nonlinear waves in fluid dynamics and plasma physics. By virtue of the rational transformation and auxiliary function, new bilinear form for the mKP equation is constructed, which is different from those in previous literatures. Based on the bilinear form, one- and two-soliton solutions are obtained with the Hirota method and symbolic computation. Propagation and interactions of shock and solitary waves are investigated analytically and graphically. Parametric conditions for the existence of the shock, elevation solitary, and depression solitary waves are given. From the two-soliton solutions, we find that the (i) parallel elastic interactions can exist between the (a) shock and solitary waves, and (b) two elevation/depression solitary waves; (ii) oblique elastic interactions can exist between the (a) shock and solitary waves, and (b) two solitary waves; (iii) oblique inelastic interactions can exist between the (a) two shock waves, (b) two elevation/depression solitary waves, and (c) shock and solitary waves.     

Dynamics of stochastic Lorenz–Stenflo system

This paper discusses the Lorenz–Stenflo system under the influence of L \(\acute{\hbox {e}}\) vy noise. We find conditions under which the solution to stochastic Lorenz–Stenflo system is exponentially stable. We then investigate the estimation of the global attractive set and stochastic bifurcation behavior of the stochastic Lorenz–Stenflo system. Results show that the jump noise can make the solution stable, the bounds and bifurcation to undergo change under some conditions. Numerical results show the effectiveness and advantage of our methods.     

Stability of the Camassa–Holm Multi-peakons in the Dynamics of a Shallow-Water-Type System

Consideration herein is the stability issue of a variety of superpositions of the Camassa–Holm peakons and antipeakons in the dynamics of the two-component Camassa–Holm system, which is derived in the shallow water theory. These wave configurations accommodate the ordered trains of the Camassa–Holm peakons, the ordered trains of Camassa–Holm antipeakons and peakons as well as the Camassa–Holm multi-peakons. Using the features of conservation laws and the monotonicity properties of the local energy, we prove the orbital stability of these wave profiles in the energy space by the modulation argument.     

Fluid–structure interaction in water-filled thin pipes of anisotropic composite materials

The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small.     

Homogenization of rectangular cross-section fibre-reinforced materials: bending–torsion effects

We study the homogenization of an elastic material in contact with periodic parallel elastic rectangular cross-section fibres of higher rigidity. The interactions between the matrix and the fibres are described by a local adhesion contact law with interfacial adhesive stiffness parameter depending on the period. Assuming that the Lamé constants in the fibres and the stiffness parameter have appropriate orders of magnitude, we derive a class of energy functionals involving extension, flexure and torsion terms.     

Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate

A general diffusive predator–prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator–prey models and give some ranges of parameters where complex pattern formation cannot occur.     

Status of the Navier–Stokes Equations in Gas Dynamics. A Review

The existing ideas on the status of the Navier–Stokes equations are changed in taking into account the following facts: generally speaking, the terms of these equations neglected in the boundary layer equations are of the order of certain Burnett terms in the conservation equations; the Navier–Stokes equations cannot be used to describe slow nonisothermal gas flows since in this case it is necessary to take the Burnett temperature stresses into account; and in the transport relations the Burnett terms determine certain effects (for example, the mechanocaloric effect).     

Thermo–elasto–plastic stresses in functionally graded materials under consideration of the fabrication process

Summary  The present study analyzes elasto–plastic thermal stresses in some particle-reinforced functionally graded material plates (FGP) by taking into consideration residual stresses of the fabrication process. For the FGP, the region near the cooling metal surface consists of distributed ceramic particles in a metal matrix, while the region near the heating ceramic surface contains distributed metal particles in a ceramic matrix. We use the thermo–elasto–plastic constitutive equation of a particle-reinforced composite, taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Elasto–plastic thermal stresses are discussed here with the goal of reducing the thermal stresses. Two kinds of particle-reinforced FGP are considered: the first kind (FGP1) represents distributed ceramic particles in the metal matrix, and the second one (FGP2) represents distributed metal particles in the ceramic matrix. We modify the thermo–elasto–plastic constitutive equation of a particle-reinforced composite for the FGP2 by taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Using the temperature-dependent material properties, three cases of temperature conditions are studied. The first one is the cooling from the fabrication temperature to the room temperature, the second one is the heating from the room temperature, and the last one is the heating after cooling from the fabrication temperature. The particle volume fraction is assumed to vary according to a power function in the thickness direction of the FGPs. Using the finite element method, the effects of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix and the stress in the particle in the FGPs are discussed. Also, the effects of the particle volume fraction and the fabrication temperature on the maximum tensile matrix stress are discussed. Received 22 November 2000; accepted for publication 24 April 2001     

Homogenization of elastic–viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes

This paper deals with the prediction of the macroscopic behavior of a multiphase elastic–viscoplastic material. The proposed homogenization schemes are based on an interaction law postulated by Molinari et al. [Molinari, A., Ahzi, S., Kouddane, R. 1997. On the self-consistent modelling of elastic–plastic behavior of polycrystals. Mech. Mater., 26, 43–62]. Self-consistent schemes are developed to describe the behavior of disordered aggregates. The Mori-Tanaka approach is used to capture the behavior of composite materials, where one phase can be clearly identified as the matrix. The proposed schemes are developed within a general framework where compressible elasticity and anisotropy of the materials are taken into account. Inclusions can have various shapes and orientations. Illustrations of the homogenization procedure are given for a two-phase composite materials. Comparisons between results of the literature and predictions based on the interaction law are performed and have demonstrated the efficiency of the proposed homogenization schemes.     

Shock–vortex interactions in a soap film

This work experimentally visualizes the interaction of a quasi-one-dimensional moving shock wave with a two-dimensional vortex in a soap film for the first time. A vertical soap film shock tube was used to generate a quasi-one-dimensional moving shock wave and a NACA-0012 airfoil intruded into the soap film was towed to shed the starting vortex. The interesting interaction phenomena were then visualized using a traditional high-speed flash photography. The concentration of sodium dodecyl sulfate (SDS) used was 0.5 CMC (critical micelle concentration) to keep the surfactant molecules behave as two-dimensional gases. A sequence of pictures shows that the shock is distorted non-symmetrically as it passes through the spiral vortex flow field and the vortex structure is compressed in the direction normal to the shock. These flow features observed in soap films are qualitatively similar to their counterparts in gases. In addition, the visualization of the interactions of a quasi-one-dimensional moving shock wave with a Kármán vortex street are presented.      

Dynamics and pattern formation of a diffusive predator–prey model in the presence of toxicity

Nonlinear Dynamics - In this paper, we develop a diffusivepredator–prey model with toxins under the homogeneous Neumann boundary condition. First, the persistence property and global...     

Local instability of plates with pressed–in annular inclusions at the elastoplastic behavior of materials

The local instability of plates with annular inclusions is studied within the framework of exact three–dimensional equations. A numerical experiment is performed for the case where two rings are pressed in a plate made of the same material as the rings. The effect of the physicomechanical parameters of a medium on the critical contact pressures is studied.     

Some Aspects of the Asymptotic Dynamics of Solutions of the Homogeneous Navier–Stokes Equations in General Domains

In the first part of the paper we study decays of solutions of the Navier–Stokes equations on short time intervals. We show, for example, that if w is a global strong nonzero solution of homogeneous Navier–Stokes equations in a sufficiently smooth (unbounded) domain Ω ⊆ R³ and β ∈[1/2, 1) , then there exist C₀ > 1 and δ₀ ∈ (0, 1) such that

Pore-Scale Imaging and Modelling of Reactive Flow in Evolving Porous Media: Tracking the Dynamics of the Fluid–Rock Interface

Transport in Porous Media - Fluid–mineral and fluid–rock interfaces are key parameters controlling the reactivity and fate of fluids in reservoir rocks and aquifers. The interface...     

Dynamics of annular gas–liquid two-phase swirling jets

The dynamics of annular gas–liquid two-phase swirling jets have been examined by means of direct numerical simulation and proper orthogonal decomposition. An Eulerian approach with mixed-fluid treatment, combined with an adapted volume of fluid and a continuum surface force model, was used to describe the two-phase flow system. The unsteady, compressible, three-dimensional Navier–Stokes equations have been solved by using highly accurate numerical methods. Two computational cases have been performed to examine the effects of liquid-to-gas density ratio on the flow development. It was found that the higher density ratio case is more vortical with larger spatial distribution of the liquid, in agreement with linear theories. Proper orthogonal decomposition analysis revealed that more modes are of importance at the higher density ratio, indicating a more unstable flow field. In the lower density ratio case, both a central and a geometrical recirculation zone are captured while only one central recirculation zone is evident at the higher density ratio. The results also indicate the formation of a precessing vortex core at the high density ratio, indicating that the precessing vortex core development is dependent on the liquid-to-gas density ratio of the two-phase flow, apart from the swirl number alone.