Pressure waves in a tube filled with a bubbly mixture with a nonuniform cross-sectional bubble distribution

The evolution of pressure waves in a tube filled with a gas-liquid medium with a stepped cross-sectional bubble distribution is investigated. The calculations are compared with experimental data. It is shown that in the case of a nonuniform bubble distribution, due to the appearance of transverse flows, the pressure pulse is damped faster than for a uniform distribution. The interaction of pressure waves with a bubble cluster in a tube filled with liquid is also analyzed.     

Motion of a solidcontaininga spherical damper

For the purpose of modeling the motion of a solid with a cavity filled with a viscous fluid, M. A. Lavrent'ev [1] has proposed a model in the form of a solid with a spherical cavity in which another solid, spherical in shape, is enclosed. The sphere is separated from the cavity walls by a small, clearance in which viscous forces act (a lubricating film). This simple model with a finite number of degrees of freedom possesses certain mechanical properties of a solid with a cavity containing a viscous fluid. Study of this model is therefore of interest.The present paper examines certain properties of the model, which will be termed a solid with a damper. It is shown that for a highviscosity lubricant the motion of a solid with a damper can be described by the same equations which pertain to the motion of a solid with a spherical cavity filled with a high-viscosity fluid. Expressions relating the parameters of the systems are obtained. If these relations are fulfilled, the systems become mechanically equivalent.The steady motions of a free solid with a damper and their stability conditions are determined.These motions and stability conditions hold for a body with a cavity filled with a viscous fluid [2].     

Visualisation studies of the transition regime flow in a channel of varying cross section under the influence of Coriolis force

 This paper is a flow visualisation study of the effect of Coriolis force on the flow in the transition regime in a channel with a mild change in cross section. Transition in this flow is found to share a salient gross feature with its counterpart in a rotating channel of uniform cross section, viz. that it takes place at a Reynolds number around two orders of magnitude lower than the critical Reynolds number in a non-rotating system and it is then to a state of flow with highly ordered steady longitudinal vortices. The change in channel cross section has the effect that the longitudinal vortices may arise or be annihilated in neighbouring sub-domains within the flow region. While in a channel of decreasing cross section the flow may undergo transition as it proceeds downstream, it may also revert from the state with vortices to one without in a channel of increasing cross section. Viewed in terms of a stability diagram with local flow parameters alone, the cross-over points from one state to another do not coincide for the two cases, with the reversal of transition exhibiting a kind of “hysteresis”. Received: 21 July 1995/Accepted: 2 November 1996     

Coupled RANS–LPT modelling of dilute,particle-laden flow in a duct with a 90° bend

A dilute, particle-laden flow in a square duct with a 90° bend is modelled using a RANS approach, coupled to a second-moment turbulence closure, together with a Lagrangian particle tracking technique, with particle dispersion modelled using a stochastic approach that ensures turbulence anisotropy. Detailed predictions of mean and fluctuating fluid and particle velocities are validated through comparisons of predictions with experimental measurements made for gas–solid flows in a vertical-to-horizontal flow configuration. Reasonable agreement between predicted first and second moments and data is found for both phases, with the consistent application of anisotropic and three-dimensional modelling approaches resulting in predictions that compare favourably with those of other authors, and which provide fluctuating particle velocities in acceptable agreement with data.     

A Direct theory of viscous fluid flow in channels

This paper deals with an Eulerian formulation of the theory of directed fluid sheets appropriate for incompressible, linear viscous fluid flow in channels with arbitrary shapes for their major boundaries which may be moving or fixed. Special cases of the theory are applied to a number of two-dimensional fluid flow problems and these solutions are in general discussed for unsteady flow. Specific applications include fluid flow in a channel whose boundaries are symmetric with respect to a middle plane in the channel, subjected to time-dependent pressure gradient at one end; and to lubrication problems in a general shaped channel when one of the channel walls is a fixed plane while the other is moving with a constant velocity. Flow of a viscous fluid with a free surface over a fixed boundary is also discussed.Dedicated to J. L. Ericksen on the occasion of his Sixtieth Birthday     

Optimization of the wash process and wash water recycling in the preparation of MgZnAl-CO3 layered double hydroxides

An MgZnAl-CO3 layered double hydroxide (LDH) slurry with Na2 SO4 as the by-product has been prepared by a co-precipitation method.The filtrates in the LDH washing process were collected according to their different levels of salinity.Filtrates with lower salinity can be used to wash a LDH slurry with higher salinity in the next cycle.Only in the final stages is pure water used.Recycling of the wash water in this way has been employed in a commercial production process,resulting in a water-saving of over 80%.The resulting MgZnAl-CO3-LDH product has a well-formed crystalline layered structure with a low content of impurities.     

Magnetoelastic interactions in a soft ferromagnetic body with a nonlinear law of magnetization: Some applications

Linearized equations and boundary conditions of a magnetoelastic ferromagnetic body are obtained with the nonlinear law of magnetization. Magnetoelastic interactions in a multi-domain ferromagnetic materials are considered for magneto soft materials, i.e. the case when the magnetic field intensity vector and magnetization vector are parallel. As a special case, the following two problems are considered: (1) the magnetoelastic stability of a ferromagnetic plate-strip in a homogeneous transverse magnetic field; (2) the stress–strain state of a ferromagnetic plane with a moving crack in a transverse magnetic field. It is shown that the modeling of magnetoelastic equations with a nonlinear law of magnetization provides qualitative and quantitative predictions on physical quantities including critical loads and stresses. In particular, it is shown that the critical magnetic field in plate stability problems found with the nonlinear law of magnetization is in better agreement with the experimental finding than the one found with a linear law. Furthermore, it is also shown that the stress concentration factor around a crack predicted with the nonlinear law of magnetization is more accurate than the one obtained with a linear counterpart. Numerical results are presented for above mentioned two problems and for various forms of nonlinear laws of magnetization.     

A numerical study of two- and three-dimensional detonation dynamics of pulse detonation engine by the CE／SE method

In this paper, the CE/SE method is developed to simulate the two- and three-dimensional flow-field of Pulse Detonation Engine (PDE). The conservation equations with stiff source terms for chemical reaction are solved in two steps. The detailed analysis of computational results of a PDE with a single detonation tube and a PDE with five detonation tubes are given in this paper. Complex wave systems are observed inside and outside a PDE. For a PDE with 5 detonation tubes, there is a big bow shock produced from a number of little shocks near the open ends of tubes. A lot of vortexes interact with shocks and a large expansion wave propagates forward and backward with respect to the PDE in a semi-oval shape.The project supported by the National Natural Science Foundation of China (59906005), the Teaching and Research Award Program for Outstanding Young Teachers in High Education Institutions of MOE, China     

Measuring The Temperature and Density of Secondary Electrons in an Argon Electron-Beam Plasma

The results of temperature and density measurements of secondary electrons in a free jet of argon, activated in an electron beam plasma, carried out using a Langmuir double electrostatic probe. A cold plasmatron prototype with a primary beam energy of 1 keV is used obtain a jet of dense cold plasma with a cross size of approximately 80 mm and parameters with which silicon layers may be deposited with necessary characteristics in a forvacuum pressure range.     

Levitation of Magnets and Paramagnetic Bodies in Vessels Filled with Magnetic Fluid

Formulas are obtained for the forces and moments acting on a spherical body made of a paramagnetic material in an uniform applied magnetic field and a magnet in a spherical vessel filled with magnetic fluid. An approximate formula is found for the force acting on bodies in ellipsoidal and cylindrical vessels or in a plane channel with a magnetic fluid in an uniform magnetic field. An analogy between the forces acting on a magnet and a paramagnetic body is demonstrated. The possibility of levitation of magnets and paramagnetic bodies in a vessel with a magnetic fluid is investigated.     

SPH for 3D floating bodies using variable mass particle distribution

A floating body with substantial heave motion is a challenging fluid–structure interaction problem for numerical simulation. In this paper we develop SPH in three dimensions to include variable particle mass distribution using an arbitrary Lagrange–Eulerian formulation with an embedded Riemann solver. A wedge or cone in initially still water is forced to move with a displacement equal to the surface elevation of a focused wave group. A two‐dimensional wedge case is used to evaluate two forms of repulsive‐force boundary condition on the body; the force depending on the normal distance from the object surface produced closer agreement with the experiment. For a three‐dimensional heaving cone the comparison between SPH and experiment shows excellent agreement for the force and free surface for motion with low peak spectral frequencies while for a higher peak frequency the agreement is reasonable in terms of phase and magnitude, but a small discrepancy appears at the troughs in the motion. Capturing the entire three‐dimensional flow field using an initially uniform particle distribution with sufficiently fine resolution requires an extremely large number of particles and consequently large computing resource. To mitigate this issue, we employ a variable mass distribution with fine resolution around the body. Using a refined mass distribution in a preselected area avoids the need for a dynamic particle refinement scheme and leads to a computational speedup of more than 600% or much improved results for a given number of particles. SPH with variable mass distribution is then applied to a single heaving‐float wave energy converter, the ‘Manchester Bobber’, in extreme waves and compared with experiments in a wave tank. The SPH simulations are presented for two cases: a single degree‐of‐freedom system with motion restricted to the vertical direction and with general motion allowing six degrees‐of‐freedom. The motion predicted for the float with general motion is in much closer agreement with experimental data than the vertically constrained system. Using variable particle mass distribution is shown to produce close agreement with a computation time 20% of that required with a uniformly fine resolution. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimization of cylindrical shells with compliant cores

Thin-walled, cylindrical structures are found extensively in both engineering components and in nature. The weight to load bearing ratio is a critical element of design of such structures in a variety of engineering applications, including space shuttle fuel tanks, aircraft fuselages, and offshore oil platforms. In nature, thin-walled cylindrical structures are often supported by a honeycomb- or foam-like cellular core, as for example, in plant stems, porcupine quills, or hedgehog spines. Previous studies have suggested that a compliant core increases the buckling resistance of a cylindrical shell over that of a hollow cylinder of the same weight. In this paper, we extend the linear-elastic buckling theory by coupling it with basic plasticity theory to provide a more comprehensive analysis of isotropic, cylindrical shells with compliant cores. We examine the optimal design of a thin-walled cylinder with a compliant core, of given radius and specified materials, for a prescribed load bearing capacity in axial compression. The analysis gives the values of the shell thickness, the core thickness, and the core density that maximize the load bearing capacity of the shell with a compliant core over an equivalent weight hollow shell. The analysis also identifies the optimum ratio of the core modulus to the shell modulus and is supported by a Lagrangian optimization technique. The analysis further discusses the selection of materials in the design of a cylinder with a compliant core, identifying the most suitable material combinations. The performance of a cylinder with a compliant core is compared with competing designs (optimized hat-stiffened shell and optimized sandwich-wall shell). Finally, the challenges associated with achieving the optimal design in practice are discussed, and the potential for practical implementation is explored.     

Taylor instability of a fluid film on a body

The Taylor instability develops in a parallel flows when the body force acts in the direction from the heavier fluid toward the lighter [1]. It has been suggested that an increase in flow vorticity may have a stabilizing influence on the Taylor instability [2]. In studying the hydrodynamic stability of a viscous film on a body in a flow of a low-viscosity fluid [3], the author noted some stabilization of the Taylor instability with increase in Reynolds number, and suggested that cases of complete stabilization of the flow with respect to two-dimensional disturbances are possible with some increase in Reynolds number. In the present investigation, calculations revealed cases in which with increase in Reynolds number the Taylor instability goes over into a Helmholtz instability, which increases with increase in Reynolds number, and also cases in which the Taylor instability completely disappears at some value of the Reynolds number before a Helmholtz instability has developed, i.e., cases of complete stabilization of the flow with respect to two-dimensional disturbances as a result of an increase in Reynolds number.     

Transverse galloping of circular cylinders fitted with solid and slotted splitter plates

The galloping response of a circular cylinder fitted with three different splitter plates and free to oscillate transverse to a free stream has been investigated considering variations in plate length and plate porosity. Models were mounted in a low mass and damping elastic system and experiments have been carried out in a recirculating water channel in the Reynolds number range of 1500 to 16 000. Solid splitter plates of 0.5 and 1.0 diameter in length are shown to produce severe galloping responses, reaching displacements of 1.8 diameters in amplitude at a reduced velocity of around 8. Fitting a slotted plate with a porosity ratio of 30% also caused considerable vibration, but with a reduced rate of increase with flow speed. All results are compared with the typical vortex-induced vibration response of a plain cylinder. Force decomposition in relation to the body velocity and acceleration indicates that a galloping mechanism is responsible for extracting energy from the flow and driving the oscillations. Visualisation of the flow field around the devices performed with PIV reveal that the reattachment of the free shear layers on the tip of the plates is the hydrodynamic mechanism driving the excitation.     

Weak–Strong Uniqueness of Dissipative Measure-Valued Solutions for Polyconvex Elastodynamics

For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of a dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same initial data, when such a classical solution exists. As an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution. Also, for a system of conservation laws endowed with a positive and convex entropy, we show that dissipative measure-valued solutions attain their initial data in a strong sense after time averaging.     

Numerical study of spherical blast-wave propagation and reflection

The objective of this study is to understand the flow structures of weak and strong spherical blast waves either propagating in a free field or interacting with a flat plate. A 5th-order weighted essentially non-oscillatory scheme with a 4th-order Runge-Kutta method is employed to solve the compressible Euler/Navier-Stokes equations in a finite volume approach. The real-gas effects are taken into account when high temperature occurs. A shock-tube problem with the real-gas effect is first tested in order to verify the solver accuracy. Moreover, unsteady shock waves moving over a stationary wedge with various wedge angles, resulting in different types of shock wave reflections, are also tested. It is found that the computed results agreed well with the existing data. Second, the propagation of a weak spherical blast wave, created by rupture of a high-pressure isothermal sphere, in a free field is studied. It is found that there are three minor shock waves moving behind the main shock. Third, the problem of a strong blast wave interacting with a flat plate is investigated. The flow structures associated with single and double Mach reflections are reported in detail. It is found that there are at least three local high-pressure regions near the flat plate. Received 27 July 2000 / Accepted 25 January 2002 – Published online 17 June 2002     

Formation of the impermeable layer in the process of methane hydrate dissociation in porous media

The problem of decomposition of methane hydrate coexisting with water in a highpermeability reservoir is considered. The asymptotic solution is obtained for the decomposition regime in the negative temperature domain. Energy estimates presented show that an impermeable layer saturated with a hydrate-icemixture can be formed in reservoirs with initial positive temperature. The mathematical model of the process of hydrate decomposition is formulated under the assumption on the presence of such a layer in a high-permeability reservoir. In this case the problem is reduced to a purely thermal problem with two unknown moving boundaries. The water-ice phase transition takes place on the leading boundary, while hydrate dissociates at negative temperatures on the slower boundary. The conditions of existence of the layer saturated with a hydrate-ice mixture which is implemented in reservoirs with the high hydrate content are investigated.     

Free vibration of a sagged cable with attached discrete elements

An algorithm is presented to analyze the free vibration in a system composed of a cable with discrete elements, e.g., a concentrated mass, a translational spring, and a harmonic oscillator. The vibrations in the cable are modeled and analyzed with the Lagrange multiplier formalism. Some fragments of the investigated structure are modeled with continuously distributed parameters, while the other fragments of the structure are modeled with discrete elements. In this case, the linear model of a cable with a small sag serves as a continuous model, while the elements, e.g., a translational spring, a concentrated mass, and a harmonic oscillator, serve as the discrete elements. The method is based on the analytical solutions in relation to the constituent elements, which, when once derived, can be used to formulate the equations describing various complex systems compatible with an actual structure. The numerical analysis shows that, the method proposed in this paper can be successfully used to select the optimal parameters of a system composed of a cable with discrete elements, e.g., to detune the frequency resonance of some structures.     

Asymptotics for filtration of polydisperse suspension with small impurities

A model for deep bed filtration of a polydisperse suspension with small impurities in a porous medium is considered.Different suspended particles move with the same velocity as the carrier water and get blocked in the pore throats due to the size-exclusion mechanism of particle retention.A solution of the model in the form of a traveling wave is obtained.The global exact solution for a multiparticle filtration with one high concentration and several low concentrations of suspended particles is obtained in an explicit form.The analytic solutions for a bidisperse suspension with large and small particles are constructed.The profiles of the retained small particles change monotony with time.The global asymptotics for the filtration of a polydisperse suspension with small kinetic rates is constructed in the whole filtration zone.