Unidirectional flows of binary mixtures within the framework of the Oberbeck–Boussinesq model

Existence conditions are investigated for the unidirectional flows of binary mixtures describable by the equations of motion in the Oberbeck–Boussinesq approximation with account for the thermodiffusion effect. Possible solutions are classified, known and novel classes of exact solutions being distinguished. For the solutions obtained different formulations of boundary-value problems are proposed. Flows between two rigid walls with given heat distribution laws are described.     

An application of the k-ɛ model with variable Prandtl number to heat transfer computations in air flows

The two-equation `low Reynolds number' k-? model of turbulence with a set of universal constants suggested by Launder and Sharma is modified in the present paper. The variability of the turbulent Prandtl number Pr_t in the energy equation is assumed along with a change of a constant in the dissipation term of the turbulent kinetic energy equation. The turbulent heat transfer is computed for an air flow in a circular pipe for the Reynolds number within the range of 10⁴?4. The modification considerably improves the agreement between the numerical results and the experiment data published in the available literature.     

The use of the “trident” model in the analysis of plastic zones near crack tips and corner points

The paper deals with calculation of a plastic zone near a crack tip in a homogeneous elastoplastic solid and near a corner point of the boundary of this solid. The calculations are conducted for a solid subject to plane strain and within the framework of models with plastic strips. It is shown that in comparison with the widely used model with two straight slip-lines, the process of plastic deformation is described by the “trident” model more accurately. The results of calculations of the plastic zone by the “trident” model that correspond to different stages of the development of plastic deformation are given for a crack of normal separation in a quasibrittle material. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 95–100, March, 2000.     

Experimental and numerical study of installing a dune model in a 90° bend in the horizontal-vertical pneumatic conveying system

In the pneumatic conveying process, particles move to the bend under the influence of inertia to form a particle rope, which will cause serious wear between the particles and the pipe wall, and then the dune model is designed and installed in the 90° bend to reduce energy consumption and wear in this study. Firstly, the minimum pressure drop velocity of particles transported by different size dune models was obtained through experimental study. Then the energy saving mechanism of the dune model is studied by CFD-DEM coupling. The experimental results show that the installation of the dune model reduces the minimum pressure drop velocity. The numerical simulation results show that the number of collisions between the particles and the tube wall in the vertical tube decreases after the installation of the dune model, which reduces the energy loss. Moreover, the increasing of tail size of the dune model is beneficial to the diffusion and acceleration of the particles in the vertical tube.     

“Everything flows?”: elastic effects on startup flows of yield-stress fluids

It is now 30 years since Barnes and Walters published a provocative paper in which they asserted that the yield stress is an experimental artifact. We now know that the situation is far more complicated than understood at the time, and that the mechanics of the solid material prior to yielding must be considered carefully. In this paper, we examine the response of a well-studied “simple” yield-stress material, namely a Carbopol gel that exhibits no thixotropy, and demonstrate the significance of the pre-yielding behavior through a number of elementary measurements.     

A compressible two-layer model for transient gas–liquid flows in pipes

This work is dedicated to the modeling of gas–liquid flows in pipes. As a first step, a new two-layer model is proposed to deal with the stratified regime. The starting point is the isentropic Euler set of equations for each phase where the classical hydrostatic assumption is made for the liquid. The main difference with the models issued from the classical literature is that the liquid as well as the gas is assumed compressible. In that framework, an averaging process results in a five-equation system where the hydrostatic constraint has been used to define the interfacial pressure. Closure laws for the interfacial velocity and source terms such as mass and momentum transfer are provided following an entropy inequality. The resulting model is hyperbolic with non-conservative terms. Therefore, regarding the homogeneous part of the system, the definition and uniqueness of jump conditions is studied carefully and acquired. The nature of characteristic fields and the corresponding Riemann invariants are also detailed. Thus, one may build analytical solutions for the Riemann problem. In addition, positivity is obtained for heights and densities. The overall derivation deals with gas–liquid flows through rectangular channels, circular pipes with variable cross section and includes vapor–liquid flows.     

“Leapfrogging” solitons in a system of coupled KdV equations

A system of two KdV equations coupled by small linear dispersive terms is considered. This system describes, for example, resonant interaction of two transverse gravity internal wave modes in a shallow stratified liquid. In the framework of an approach based on Hamilton's equations of motion, evolution equations for parameters of two solitons belonging to different wave modes are obtained in the adiabatic approximation. It is demonstrated that when the solitons' velocities are sufficiently lose, the solitons may form a breather-like oscillatory bound state, which provides a natural explanation for recent numerical experiments demonstrating “leapfrogging” motion of the two solitons. The frequency and the maximum amplitude of the “breather”'s internal oscillations are obtained. For the case when the relative velocity of the solitons is not small, perturbation-induced phase shifts of the two colliding free solitons are calculated. Then emission of radiation (small-amplitude quasilinear waves) by an oscillating “breather,” also detected in the numerical experiments, is investigated in the framework of the perturbation theory based on the inverse scattering transform. The intensity of the emission is calculated. Radiative effects accompanying collision of the free solitons are also investigated.     

Homogenization of the nonlinear Kelvin–Voigt model of viscoelasticity and of the Prager model of plasticity

Denoting by the stress tensor, by the linearized strain tensor, by A the elasticity tensor, and assuming that is a convex potential, the inclusion accounts for nonlinear viscoelasticity, and encompasses both the linear Kelvin–Voigt model of solid-type viscoelasticity and the Prager model of rigid plasticity with linear kinematic strain-hardening. This relation is assumed to represent the constitutive behavior of a space-distributed system, and is here coupled with the dynamical equation. An initial- and boundary-value problem is formulated, and the existence and uniqueness of the solution are proved via classical techniques based on compactness and monotonicity. A composite material is then considered, in which the function and the tensor A rapidly oscillate in space. A two-scale model is derived via Nguetseng’s notion of two-scale convergence. This provides a detailed account of the mesoscopic state of the system. Any dependence on the fine-scale variable is then eliminated, and the existence of a solution of a new single-scale macroscopic model is proved. The final outcome is at variance with the nonlinear extension of the generalized Kelvin–Voigt model, which is based on an apparently unjustified mean-field-type hypothesis.     

Coriolis effects on the stability of pulsed flows in a Taylor–Couette geometry

Results steming from the linear stability of time-periodic flows in a Taylor–Couette geometry with cylinders oscillating in phase or out-of-phase are presented. Our analysis takes into account the gap size effects and investigates the influence of a superimposed mean angular rotation of the whole system.In case of no mean rotation, the finite gap geometry is found to affect the shape of the stability diagrams (critical Taylor number versus the frequency parameter) which consist of two distinct branches as opposed to being continuous in the narrow gap approximation. In particular, in the out-of-phase configuration a new branch for low frequencies was found, thus enabling better agreement with available experimental results.When cylinders are co-rotating and subject to rotation effects, our calculations provide the evolution of the critical Taylor number versus the rotation number for two values of the frequency. The stability curves are found to be in qualitative agreement with available experimental data revealing a maximum of instability for a rotation number of about 0.3.In the high rotation regime, enhancement of the critical Taylor number is investigated through an asymptotic analysis and the value of the rotation number at which restabilization occurs is found to depend on the frequency parameter.A restabilization of the flow also occurs when the rotation number and the gap size are of the same order, a phenomenon already pointed out in the case of steady flows and attributed to the near cancellation of Coriolis and centrifugal effects. Our investigation proves that the same mechanism still holds for time-periodic flows.     

Effect of prestress on the stability of electrode–electrolyte interfaces during charging in lithium batteries

We formulate a model of the growth of electrode–electrolyte interfaces in lithium batteries in the presence of an elastic prestress. The model accounts for the kinetics of Li⁺ transport through a solid electrolyte and, within the interface, for the kinetics of Li⁺ adsorption by the anode, electrostatics, and the elastic field. We specifically account for the effect of the elastic field through an asymptotic analysis of a nearly flat interface between two semi-infinite elastic bodies. We use the model as a basis for assessing the effect of prestress on the stability of planar growth and the potential of prestress as a means of suppressing the formation of deleterious dendrites. We present a linear stability analysis that results in explicit analytical expressions for the dependence of growth rates, and of the critical unstable wavelength for the interfacial roughening, on the state of prestress and on fundamental parameters such as surface diffusivities, surface energy, deposition kinetics, and elastic moduli. Finally, we examine the model in the light of experimental observations concerned with the effect of applied pressure on a lithium/dioxolane-dimethoxy ethane electrolyte systems. With reasonable choices of parameters and some calibration, the model accounts for the observation that a modest applied pressure indeed results in a substantial reduction in the roughening of the lithium surface during cycling.     

On the formation of Taylor–G?rtler vortices in RMF-driven spin-up flows

This paper is concerned with a liquid metal flow driven by a rotating magnetic field inside a stationary cylinder. We consider especially the secondary meridional flow during the time when the fluid spins up from rest. The developing flow is investigated experimentally and by direct numerical simulations. The vertical profiles of the axial velocity are measured by means of the ultrasound Doppler velocimetry. Evolving instabilities in the form of Taylor–G?rtler vortices have been observed just above the instability threshold (Ta ≥ 1.5· Ta ^cr). The rotational symmetry may survive over a distinct time even if a first Taylor–G?rtler vortex pair has been formed as closed rings along the cylinder perimeter. The transition to a three-dimensional flow in the side layers results from the advection or a precession and splitting of the Taylor–G?rtler vortex rings. The predictable behaviour of the Taylor–G?rtler vortices disappears with increasing magnetic field strength. The numerical simulations agree very well with the flow measurements.     

Some issues related to the modeling of interfacial areas in gas–liquid flows,II. Modeling the source terms for dispersed flows

The first part of this paper dealt with the conceptual issues encountered in the definition of the interfacial area and in the derivation of a transport equation. The second part has the following objectives: 1. to address the closure issues for the source terms appearing in the transport equation when dealing with a bubbly flow in a vertical pipe; 2. to provide a list of open questions to be answered before introducing a transport equation for the interfacial area concentration in a thermal–hydraulic computer code.     

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k_SGS, containing a production term proportional to the square root of k_SGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k_SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k_SGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k_SGS transport equation. In the MTS model, the SGS turbulence energy, k_es, estimated by filtering the instantaneous flow field is used. Since the k_es approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional k_SGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.     

Dynamic model of vertical vehicle-subgrade coupled system under secondary suspension

As it is known, track transportation can be divided into track system above and track system below. While the train is moving, the parts above and below are interacted and influenced. Therefore, in fact, the problem of track transportation is the match between the vehicle and the railway line system. In this paper, on a basis of dynamic analysis of the vehicle-subgrade model of vertical coupled system under primary suspension, utilizing track maintenance standard and simulating track irregularity excitation, the dynamic interaction of vehicle-track-subgrade system is researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension is established by compatibility condition of deformation. Even this model considers the actual structure of a vehicle, also considers vibration characteristic of the substructure of track including subgrade and foundation. All these work want to be benefit for understanding and design about the dynamic characters of subgrade in high speed railway.     

Simulating tornado-like flows: the effect of the simulator’s geometry

Meccanica - Within the wind engineering community, a series of physical simulators of differing geometries have been used to investigate the flow-field of tornado-like vortices. This paper examines...     

Opening of a system of cracks—on the mechanism of the cyclic lateral eruption of the St. Helens volcano in 1980

The dynamic behavior of a magma melt filling a slot channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a slug and a system of internal cracks (dikes) near the dome, as well as a crater open into the atmosphere. A two-dimensional model of a slot eruption is constructed with the use of the Iordanskii–Kogarko–van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.     

Criticality of bifurcation in the tuned axial–torsional rotary drilling model

We study the bifurcation characteristics of a lumped-parameter model of rotary drilling with 1:1 internal resonance between the axial and the torsional modes which leads to the largest stability thresholds. For this special case, the two-degree-of-freedom model for the drill-string reduces to an effectively single-degree-of-freedom system facilitating further analysis. The regenerative effect of the cutting action due to the axial vibrations is incorporated through a delayed term in the cutting force with the delay depending on the torsional oscillations. This state dependency of the delay introduces nonlinearity in the current model. Steady drilling loses stability via a Hopf bifurcation, and the nature of the bifurcation is determined by an analytical study using the method of multiple scales. We find that both subcritical and supercritical Hopf bifurcations are present in this system depending on the choice of operating parameters. Hence, the nonlinearity due to the state-dependent delay term could both be stabilizing or destabilizing in nature, and the self-interruption nonlinearity is essential to capture the global behavior. Numerical bifurcation analysis of a global axial–torsional model of rotary drilling further confirms the analytical results from the method of multiple scales. Further exploration of the rotary drilling dynamics unravels more complex phenomena including grazing bifurcations and possibly chaotic solutions.