An Experimental Analysis of Gas-Liquid Flow Breakdown in a T-Junction

When a gas-liquid two-phase flow(GLTPF)enters a parallel separator through a T-junction,it generally splits unevenly.This phenomenon can seriously affect the operation efficiency and safety of the equipment located downstream.In order to investigate these aspects and,more specifically,the so-called bias phenomenon(all gas and liquid flowing to one pipe,while the other pipe is a liquid column that fluctuates up and down),laboratory experiments were carried out by using a T-junction connected to two parallel vertical pipes.Moreover,a GLTPF prediction model based on the principle of minimum potential energy was introduced.The research results indicate that this model can accurately predict the GLTPF state in parallel risers.The boundary of the slug flow and the churn flow in the opposite pipe can be predicted.Overall,according to the results,the pressure drop curves of the two-phase flow in the parallel risers are basically the same when there is no bias phenomenon,but the pressure drop in the parallel riser displays a large deviation when there is a slug flow-churn flow.Only when the parallel riser is in a state of asymmetric flow and one of the risers produces churn flow,the two-phase flow is prone to produce the bias phenomenon.

Analytical and Experimental Research on Wave Scattering by an Open-Type Rectangular Breakwater with Horizontal Perforated Plates

This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

Rectangular tunnel heading stability in three dimensions and its predictive machine learning models

Tunnel heading stability in two dimensions(2D)has been extensively investigated by numerous scholars in the past decade.One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization.Nevertheless,it is possible to study the stability of tunnels in three dimensions(3D)with a rectangular shape using finite element limit analysis(FELA)and a nonlinear programming technique.This paper employs 3D FELA to generate rigorous solutions for stability numbers,failure mechanisms,and safety factors for rectangular-shaped tunnels.To further explore the usefulness of the produced results,multivariate adaptive regression spline(MARS)is used for machine learning of big dataset and development of design equations for practical design applications.The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.

Investigating the Effects of Injection Pipe Orientation on Mixing and Heat Transfer for Fluid Flow Downstream a T-Junction

At T-junctions, where hot and cold streams flowing in pipes join and mix, significant temperature fluctuations can be created in very close neighborhood of the pipe walls. The wall temperature fluctuations cause cyclical thermal stresses which may induce fatigue cracking. Temperature fluctuation is of crucial importance in many engineering applications and especially in nuclear power plants. This is because the phenomenon leads to thermal fatigue and might subsequently result in failure of structural material. Therefore, the effects of temperature fluctuation in piping structure at mixing junctions in nuclear power systems cannot be neglected. In nuclear power plant, piping structure is exposed to unavoidable temperature differences in a bid to maintain plant operational capacity. Tightly coupled to temperature fluctuation is flow turbulence, which has attracted extensive attention and has been investigated worldwide since several decades. The focus of this study is to investigate the effects of injection pipe orientation on flow mixing and temperature fluctuation for fluid flow downstream a T-junction. Computational fluid dynamics (CFD) approach was applied using STAR CCM+ code. Four inclination angles including 0 (90), 15, 30 and 45 degrees were studied and the mixing intensity and effective mixing zone were investigated. K-omega SST turbulence model was adopted for the simulations. Results of the analysis suggest that, effective mixing of cold and hot fluid which leads to reduced and uniform temperature field at the pipe wall boundary, is achieved at 0 (90) degree inclination of the branch pipe and hence may lower thermal stress levels in the structural material of the pipe. Turbulence mixing, pressure drop and velocity distribution were also found to be more appreciable at 0 (90) degree inclination angle of the branch pipe relative to the other orientations studied.

Unified Solution Method of Rectangular Plate Elastic Bending

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...

Sensitivity of springback and section deformation to process parameters in rotary draw bending of thin-walled rectangular H96 brass tube

In order to study the effects of the process parameters on springback and section deformation, a sensitivity analysis model was established based on the combination use of the multi-parameter sensitivity analysis method and the springback/section deformation prediction finite element model, and by using this model the sensitivities of the springback and the section deformation to process parameters were analyzed and compared. The results show that the most sensitive process conditions for springback angle are the boost speed and the pressure of pressure die, and the most sensitive process condition for section deformation is the number of cores. When the clamp force, the boost speed and the pressure of pressure die are utilized to control section deformation, the effect of these process parameters on springback should be considered. When the process parameters are mainly used to control springback, the effect of these process parameters on the section deformation should be always considered.

EXPERIMENTAL RESEARCH AND NONLINEAR FINITE ELEMENT ANALYSIS ON NEW TYPE JOINT BETWEEN COLUMN AND STEEL BEAM OF CONCRETE-FILLED RECTANGULAR STEEL TUBULAR

Experimental results of new type joints between the column and the. steel beam of concrete-filled rectangular steel tubular （CFRT） under reversed cyclic loads are presented. The earthquake resistant capacity of the joint is influenced by infilled concrete, stiffener length and relative dimensions of column and beam. It is found that the hysteresis curves obtained in the experiment are full and the joints have a good energy dissipation capacity. The nonlinear finite element models are also used to analyze the hysteresis behavior of the joints under reversed cyclic loads using ANSYS 8.0. The influences of the stiffener length and the infilled concrete are analyzed. Analytical results show that the stiffener length and the infilled concrete are critical for the joints. Furthermore, the skeleton curves of the finite element models are in good agreement with those of experiments.

Yield Modeling of Rectangular Defect Outline

In integrated circuits, the defects associated with photolithography are assumed to be in the shape of circular discs in order to perform the estimation of yield and fault analysis. However,real defects exhibit a great variety of shapes. In this paper,a novel yield model is presented and the critical area model of short circuit is correspondingly provided. In comparison with the circular model corrently available, the new model takes the similarity shape to an original defect, the two-dimensional distributional characteristic of defects, the feature of a layout routing and the character of yield estimation into account. As for the aspect of prediction of yield, the experimental results show that the new model may predict the yield caused by real defects more accurately than the circular model does. It is significant that the yield is accurately estimated and improved using the proposed model.

Finite-difference calculation of traveltimes based on rectangular grid

To the most of velocity fields, the traveltimes of the first break that seismic waves propagate along rays can be computed on a 2-D or 3-D numerical grid by finite-difference extrapolation. Under ensuring accuracy, to improve calculating efficiency and adaptability, the calculation method of first-arrival traveltime of finite-difference is de- rived based on any rectangular grid and a local plane wavefront approximation. In addition, head waves and scat- tering waves are properly treated and shadow and caustic zones cannot be encountered, which appear in traditional ray-tracing. The testes of two simple models and the complex Marmousi model show that the method has higher accuracy and adaptability to complex structure with strong vertical and lateral velocity variation, and Kirchhoff prestack depth migration based on this method can basically achieve the position imaging effects of wave equation prestack depth migration in major structures and targets. Because of not taking account of the later arrivals energy, the effect of its amplitude preservation is worse than that by wave equation method, but its computing efficiency is higher than that by total Green′s function method and wave equation method.

Robot coverage algorithm under rectangular decomposition environment

The environment modeling algorithm named rectangular decomposition, which is composed of cellular nodes and interleaving networks, is proposed. The principle of environment modeling is to divide the environment into individual square sub-areas. Each sub-area is orientated by the central point of the sub-areas called a node. The rectangular map based on the square map can enlarge the square area side size to increase the coverage efficiency in the case of there being an adjacent obstacle. Based on this algorithm, a new coverage algorithm, which includes global path planning and local path planning, is introduced. In the global path planning, uncovered subspaces are found by using a special rule. A one-dimensional array P, which is used to obtain the searching priority of node in every direction, is defined as the search rule. The array P includes the condition of coverage towards the adjacent cells, the condition of connectivity and the priorities defined by the user in all eight directions. In the local path planning, every sub-area is covered by using template models according to the shape of the environment. The simulation experiments show that the coverage algorithm is simple, efficient and adapted for complex two- dimensional environments.

WAVE TRANSFORMATION AND BREAKING OVER A RECTANGULAR STEP

An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.

Laser Doppler Vibrometer Without Directional Ambiguity Using Rectangular Phase Grating

The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scattered laser Doppler vibrometer without directional ambiguity using the single peri- od rectangular phase grating as the beam-combiner described.The principles of this kind of vibrometer are explained in detail,and some experimental re- sults are given.In this kind of vibrometer,the rectangular phase grating, without the zero diffracted order and even orders,is used to eliminate use- less stray light and to combine the useful signal light.Differential electronics is employed to reject signal noise.Therefore,the signal-to-noise ratio of Doppler signals and the measurement accuracy of the instrument are im- proved and the range of application is expanded.

Effects of Perforated Baffle on Reducing Sloshing in Rectangular Tank:Experimental and Numerical Study

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional （3D） rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.

Resonance suppression and electromagnetic shielding effectiveness improvement of an apertured rectangular cavity by using wall losses

The cavity-mode resonance effect could result in significant degradation of the shielding effectiveness （SE） of a shielding enclosure around its resonance frequencies. In this paper, the influence of coated wall loss on the suppression of the resonance effect is investigated. For this purpose, an equivalent circuit model is employed to analyze the SE of an apertured rectangular cavity coated with an inside layer of resistive material. The model is developed by extending Robinson＇s equivalent circuit model through incorporating the effect of the wall loss into both the propagation constant and the characteristic impedance of the waveguide. Calculation results show that the wall loss could lead to great improvement on the SE for frequencies near the resonance but almost no effect on the SE for frequencies far away from the resonance.

Study on Failure Mechanism and Bearing Capacity of Three-Dimensional Rectangular Footing Subjected to Combined Loading

This paper presents two kinematic failure mechanisms of threc-dimensional rectangular footing resting on homogeneous undrained clay foundation under uniaxial vertical loading and uniaxial moment loading. The failure mechanism under vertical loading comprises a plane strain Prandti-type mechanism over the central part of the longer side, and the size of the mechanism gradually reduces at the ends of the longer side and over the shorter side as the corner of rectangular footing is being approached where the direction of soil motion remains normal to each corresponding side respectively. The failure mechanism under moment loading comprises a plane strain scoop sliding mechanism over the central part of the longer side, and the radius of scoop sliding mechanism increases linearly at the ends of the longer side. On the basis of the kinematic failure mechanisms mentioned above, the vertical ultimate bearing capacity and the ultimate bearing capacity against moment or moment ultimate bearing capacity are obtained by use of upper bound limit analysis theory. At the same time, numerical analysis results, Skempton＇ s results and Salgado et al. ＇s results are compared with this upper bound solution. It shows that the presented failure mechanisms and plastic limit analysis predictions are validated. In order to investigate the behaviors of undrained clay foundation beneath the rectangular footing subjected to the combined loadings, numerical analysis is adopted by virtue of the general-purpose FEM software ABAQUS, where the clay is assumed to obey the Mohr-Coulomb yielding criterion. The failure envelope and the ultimate bearing capacity are achieved by the numerical analysis results with the varying aspect ratios from length L to breadth B of the rectangular footing. The failure mechanisms of rectangular footing which are subjected to the combined vertical loading V and horizontal loading H （Vertical loading V and moment loading M, and horizontal loading H and moment loading M respectively are observed in the finite element analysis. ） is explained by use of the upper bound plasticity limit analysis theory. Finally, the reason of eccentricity of failure envelope in H-M loading space is given in this study, which can not be explained by use of the traditional ＇ swipe test＇.

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.

Two-dimensional analyses of delamination buckling of symmetrically cross-ply rectangular laminates

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameterβ defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that （i） when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; （ii） as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter.

Study of the double rectangular waveguide grating slow-wave structure

A slow-wave structure （SWS） with two opposite gratings inside a rectangular waveguide is presented and analysed. As an all-metal slow-wave circuit, this structure is especially suited for use in millimetre-wave travelling wave tubes （TWTs） due to its advantages of large size, high manufacturing precision and good heat dissipation. The first part of this paper concerns the wave properties of this structure in vacuum. The influence of the geometrical dimensions on dispersion characteristics and coupling impedance is investigated. The theoretical results show that this structure has a very strong dispersion and the coupling impedance for the fundamental wave is several tens of ohms, but the coupling impedance for -1 space harmonic wave is much lower than that for the fundamental wave, so the risk of backward wave oscillation is reduced. Besides these, the CST microwave studio is also used to simulate the dispersion property of the SWS. The simulation results from CST and the theoretical results agree well with each other, which supports the theory. In the second part, a small-signal analysis of a double rectangular waveguide grating TWT is presented. The typical small-signal gain per period is about 0.45 dB, and the 3-dB small-signal gain bandwidth is only 4%.