Recognition of gas–liquid two-phase flow patterns based on improved local binary pattern operator

A new method to pattern recognition of gas–liquid two-phase flow regimes based on improved local binary pattern (LBP) operator is proposed in this paper. Five statistic features are computed using the texture pattern matrix obtained from the improved LBP. The support vector machine and back-propagation neural network are trained to flow pattern recognition of five typical gas–liquid flow regimes. Experimental results demonstrate that the proposed method has achieved better recognition accuracy rates than others. It can provide reliable reference for other indirect measurement used to analyze flow patterns by its physical objectivity.     

Thermographical Analysis of Paper During Tensile Testing and Comparison to Digital Image Correlation

The thermal response in paper has been studied by thermography. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of warmer streaks could be observed in the samples. On the same samples digital image correlation (DIC) was used to study local strain fields. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Because of its fibrous network structure, paper has an inhomogeneous micro-structure, which is called formation. It could be shown that the formation was the cause of the inhomogeneous deformations in paper. Finite element simulations was used to show how papers with different degrees of heterogeneity would deform. Creped papers, where the strain at break has been increased, were analysed. For these paper it was seen that an overlaid compaction of the paper was created during the creping process. During tensile testing this was recovered as the paper network structure was strained.     

Galilean-invariant axisymmetric self-similar submodel of gas dynamics without swirling

This paper deals with one insufficiently studied submodel of invariant solutions of rank 1 of the equations of gas dynamics. It is shown that, in cylindrical coordinates, the submodel without swirling reduces to a system of two ordinary differential equations. For the equation of state with additional invariance, a self-similar system is obtained. A pattern of phase trajectories is constructed, and particle motion is studied using asymptotic methods. The obtained solutions describe unsteady flows over axisymmetric bodies with possible strong discontinuities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 46–52, March–April, 2009.     

Motion of two interconnected mass points under action of non-symmetric viscous friction

This paper deals with the analysis of a one-dimensional motion of two mass points in a resistive medium. The force of resistance is described by small non-symmetric viscous friction acting on each mass point. The magnitude of this force depends on the direction of motion. The mass points are interconnected with a kinematic constraint or with an elastic element. Using the averaging method the expressions for the stationary “on the average” velocity of the systems’s motion as a single whole is found. In case of a small degree of non-symmetry an explicit expression for the stationary “on the average” velocity of the system is derived. For the other case we obtained algebraic equations for the corresponding stationary velocity.     

Natural convection in an inclined enclosure with a fluid layer and a heat-generating porous bed

Multiple steady-state solutions of natural convection in an inclined enclosure with a fluid layer and a heat-generating porous bed is investigated numerically by the finite volume method. The conservation equations for the porous layer are based on a general flow model which includes both the effects of flow inertia and friction. The flow in fluid layer is modeled by Navier–Stokes equations. The method of pseudo arc-length continuation is adapted in studying the effects of tilt angle on flow pattern and heat transfer. It is found that, in the whole domain of tilt angle, there exist two groups of solutions with quite different flow pattern and heat transfer behavior. The effects of aspect ratio on flow pattern and heat transfer have also been studied. Received on 04 March 1997     

Pattern selection in a reaction-diffusion equation

This paper studies the pattern selection in a spatially-periodic problem of a simplified reaction-diffusion system described by an evolutionary Duffing equation. Numerical explorations by a pseudo-spectral method reveal the dependence of the pattern formation on the initial profile as well as the parameter. Only patterns with 2 ^m humps are found to be meta-stable in the corresponding parameter ranges. The project supported by Chinese Special Funds for Major State Basic Research Project “Nonlinear Science”, and NSFC (10002002 and 19990510)     

Global Branches of Multi-Bump Periodic Solutions of the Swift-Hohenberg Equation

In this paper we study the existence of single- and multi-bump periodic solutions of a class of fourth order ordinary differential equations arising in problems of pattern formation. Measuring the tendency to form patterns by a parameter q∈ℝ, we view the problem as a nonlinear eigenvalue problem. With the use of analytical as well as numerical methods, branches of periodic solutions are investigated, both locally and globally. Accepted November 1, 2000?Published online May 7, 2001     

Extended thermodynamics – consistent in order of magnitude

It was always known that ordinary thermodynamics requires fairly smooth and slowly varying fields. Extended thermodynamics on the other hand is needed for rapidly changing fields with steep gradients. This notion is made explicit in the present paper by assigning orders of magnitude in steepness to the moments which are the field variables of extended thermodynamics. Once a process is deemed to be steep of O(n), the number of field variables may be read off from a table and the field equations are closed, by omission of all higher order terms. The procedure is demonstrated for stationary one-dimensional heat conduction and for heat conduction and one-dimensional motion. An instructive synthetical case of a “one-dimensional gas” is also treated and it is shown in this case how the hyperbolic equations of extended thermodynamics may be regularized – or parabolized – in a rational manner. The theory of O(n) is fully compatible with the entropy principle of that order, but no entropy postulate is needed here, at least not for closure. The theory can be shown to be compatible with an exponential phase density. Received April 15, 2002 / Published online November 6, 2002 RID="*" ID="*"Communicated by Kolumban Hutter, Darmstadt     

The Motion of a Fluid–Rigid Disc System at the Zero Limit of the Rigid Disc Radius

We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier–Stokes equations and the motion of the rigid body by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate, as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of the Navier–Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory.     

Symmetry Properties of the Elastic Energy of a Woven Fabric with Bending and Twisting Resistance

A woven fabric can be described as a surface made of two families of fibers: in this work we study how the geometry of the weave pattern affects the symmetry properties of the elastic energy of the surface. Four basic symmetry classes of weave patterns are possible, depending on the angle between the fibers and their material properties. The properties of the pattern determine the material symmetry group of the network, under which the elastic energy is invariant. We derive representations for the energy of a woven fabric that are invariant under the symmetry group of the network, and discuss the relation of these invariants with the curvature and twist of the fibers.      

Spatial averaging in the mechanics of heterogeneous and dispersed systems

Spatial averaging of the equations describing two single-phase media is separately considered in this paper regarding the volumes occupied by either phase with allowance for the boundary conditions on phase interfaces. The equations obtained are specialized to describe monodispersed mixtures within a “cellular” scheme. It is shown that it is necessary to consider the average values both over the whole cells and over those intersected by the boundary of a selected mixture volume.The problem of motion in the cell is formulated. Fictitious parameters are introduced at “infinity” for the carrier phase to solve the problem. These parameters do not coincide with the average values for this phase. A closed system of equations is derived for two extreme cases: an ideal incompressible carrier fluid and an extremely viscous incompressible carrier fluid. These are correlative with the inertial and viscous motions in the cell.Various effects are discussed in this paper. These include the radial motion of bubbles, the oriented rotation of dispersed particles (the symmetry and asymmetry of stress tensor), viscosity, phase transitions and the finite volume content of dispersed particles. Some aspects of earlier studies are critically analyzed.     

Network simulation method for solving phase-change heat transfer problems with variable thermal properties

 The transient heat conduction equation in a finite slab undergoing phase change (two-phase problem of melting and solidification), with isothermal, adiabatic or convective boundary conduction is studied by the network simulation method; solid phase conductivity and specific heat are assumed to be dependent on temperature. Ablation, as a particular case, is also analysed. A network model is established for a cell and boundary conditions are added to complete the whole network model. No restrictions exist, as to the kinds of linear and non-linear boundary conditions, Stefan number values or the initial conditions (when hypotheses concern of the Stefan problem, numerical and exact solutions are compared for a large interval of Stefan numbers; simulation values show good agreement). Movement of the solid–liquid boundary and thermal fields are determined in all cases. Received on 10 May 2000 / Published online: 29 November 2001     

Collagen Fiber Network Infiltration: Permeability and Capillary Infiltration

In dentin restoration, collagen fiber network infiltration is an issue. Using data from the literature, we have constructed a relevant numerical geometrical model of the network. The specificity of our model is that the fibers are taken into account implicitly using a regularized Heaviside function. This function is either used to set the viscosity or to localize the contact line where capillary forces are applied. A level set technique with respect to fluid infiltration front tracking in five fiber networks using the level set method and Navier–Stokes equations with capillary terms is used to point out efficient critical infiltration parameters. A variational formulation which can be implemented in a finite elements model is proposed both for the infiltration front and the contact line. Because of lack of knowledge on fiber orientation, different configurations were tested through permeability assessment of the whole network. Fiber orientation, interfibrillar space and contact angle influence were investigated.     

Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network

In this paper a new approach is presented to reduce vibrations for one- and two-dimensional mechanical structures, as beam or thin plates, by means of several piezoelectric transducers shunted with a proper electric network system. The governing equations of the whole system are coupled to each other through the direct and converse piezoelectric effect. More in detail, the mechanical equations are expressed in accordance with the modal theory considering n vibration modes and the electrical equations reduce to the one-dimensional charge equation of electrostatics for each of n considered piezoelectric transducers. In this electromechanical system, a shunting electric device forms an electric subsystem working as multi degrees of freedom (dof’s) damped vibration absorber for the mechanical subsystem. Herein, it is introduced a proper transformation of the electric coordinates in order to approximate the governing equations for the whole shunted system with n uncoupled, single mode piezoelectric shunting systems that can be readily damped by the methods reported in literature. A further numerical optimisation problem on the spatial distribution of the piezoelectric elements allows to achieve a better performance. Numerical case studies of two relevant systems, a double clamped beam and a fully clamped plate, allow to take into account issues relative to the proposed approach. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.     

Flow patterns in vertical two-phase flow

This paper is concerned with the flow patterns which occur in upwards gas-liquid two-phase flow in vertical tubes. The basic flow patterns are described and the use of flow pattern maps is discussed. The transition between plug flow and churn flow is modelled under the assumption that flooding of the falling liquid film limits the stability of plug flow. The resulting equation is combined with other flow pattern transition equations to produce theoretical flow pattern maps, which are then tested against experimental flow pattern data. Encouraging agreement is obtained.     

Design of Coupled Nonlinear Systems for Storage of Prescribed Binary Patterns

In this paper, we investigate synchronization and cluster formation phenomena in two-dimensional arrays of locally interconnected chaotic circuits. We report the existence of an abundance of attractors, for which each cell stores a binary information. We describe a simple method for storing binary patterns in the network. We also address the question which patterns can be successfully stored in the network and discuss problems of pattern stability and influence of parameters mismatch. This research has been supported in part by the European Community research program “COSYC of SENS”, no. HPRN-CT-2000-00158 and by AGH-UST grant 11.11.120.182.     

Global Regularity for a Class of Generalized Magnetohydrodynamic Equations

It remains unknown whether or not smooth solutions of the 3D incompressible MHD equations can develop finite-time singularities. One major difficulty is due to the fact that the dissipation given by the Laplacian operator is insufficient to control the nonlinearity and for this reason the 3D MHD equations are sometimes regarded as “supercritical”. This paper presents a global regularity result for the generalized MHD equations with a class of hyperdissipation. This result is inspired by a recent work of Terence Tao on a generalized Navier–Stokes equations (T. Tao, Global regularity for a logarithmically supercritical hyperdissipative Navier–Stokes equations, arXiv: 0906.3070v3 [math.AP] 20 June 2009), but the result for the MHD equations is not completely parallel to that for the Navier–Stokes equations. Besov space techniques are employed to establish the result for the MHD equations.     

Single-Phase (Brine) and Two-Phase (DNAPL–Brine) Flows in Induced Fractures

This study reports an investigation on the characteristics of single-phase (brine) and two-phase (DNAPL–brine) flows in induced fractures. The fracture aperture and fluid phase distributions were determined using X-ray computer tomography. In the single-phase flow tests, the pressure gradient across the induced fractures increases linearly with increasing flow rate. However, models based on the measured aperture do not yield a consistent match with the experimental data because the effect of pressure losses due to aperture variation and undulation are not taken into account. In the two-phase flow tests, the measured phase distributions reveal that the flow pattern is dominated by a dispersed or mixed flow in which either DNAPL or brine phase is discontinuous. The channel flow pattern, in which DNAPL and brine phases are continuous in the fracture and well represented by the widely used Romm’s relative permeability relationship was not observed in this study. In contrast, a Lockhart–Martinelli-type correlation developed for gas–liquid flow in pipes was found to match the pressure gradient and phase saturation results obtained from the laboratory tests.     

Henry’ Law and Gas Phase Disappearance

In a two-phase (liquid–gas) two-component (water–hydrogen) system we discuss the formulation of the possible dissolution of hydrogen in the liquid phase. We show how Henry’s law fits in a phase diagram and the problem is formulated as a set of nonlinear partial differential equations with complementarity constraints.