Theoretical analysis of the onset of gas entrainment from a stratified region through multiple branches

A theoretical analysis has been developed to predict the critical height of the onset of gas entrainment (OGE) during dual and triple discharge from a stratified two-phase region. The two and three discharge branches are mounted on a circular wall, resembling a circular reservoir of a CANDU header–feeder configuration. A point sink model has been developed to predict the critical height and to map the velocities and acceleration flow fields during OGE. The model was verified by comparing the theoretically predicted critical height with the available experimental results. The theoretically predicted critical height is found to be a function of the branch Froude number, the location of the secondary branch with respect to the primary branch, and the angle between the branches. The effect of these variables on the predicted OGE height was investigated and is presented in this paper. Predictions of the critical height were shown to be within 25% of experimental values in both dual and triple discharge.     

Experimental investigation of the onsets of gas and liquid entrainment from a small branch mounted on an inclined wall

The phenomena of the onsets of liquid entrainment and gas entrainment were investigated experimentally for the case of a flat plane with a circular outlet branch of diameter d (=6.35 mm) at the plane centre. This flat plane was situated in a large tank containing a stratified mixture of air and water under pressure (317 kPa for most experiments and 520 kPa for a few experiments) and at room temperature. The plane was inclined through various angles (θ) in increments of 30°, from the outlet branch orientation being vertically upward through the horizontal to vertically downward. For both onsets the vertical distance between the centre of the outlet branch and the undisturbed gas–liquid interface (h) was measured for various angles of inclination and Froude numbers. Both onsets were observed visually through a large viewing part of the test section. It was found that for both onsets there is a range of inclination angles where the onset h depended on θ and a range where the onset h essentially did not depend on θ. The data were correlated in terms of onset h/d, Froude number, and θ where there was dependence of onset h on the angle of inclination.     

Study of gas-sheared liquid film in horizontal rectangular duct using high-speed LIF technique: Three-dimensional wavy structure and its relation to liquid entrainment

The flow of a liquid film sheared by high velocity gas stream in a horizontal rectangular duct was investigated using a high-speed laser-induced fluorescence technique. Measurements of local film thickness were resolved in both longitudinal and transverse coordinates with high spatial and temporal resolution. It was found that the generation of fast and slow ripples by the disturbance waves was qualitatively the same as it was observed earlier in completely different conditions. The transverse size and curvature of the disturbance waves and ripples were measured. A relationship between the three-dimensional structure of ripples on top of disturbance waves and the two mechanisms of liquid entrainment, known as ‘bag break-up’ and ‘ligament break-up’, is proposed.     

Numerical study of elbow erosion due to sand particles under annular flow considering liquid entrainment

Sand particle erosion is always a challenge in natural gas production. In particular, the erosion in gas–liquid–solid annular flow is more complicated. In this study, a three-phase flow numerical model that couples the volume of fluid multiphase flow model and the discrete phase model was developed for prediction of erosion in annular flow. The ability of the numerical model to simulate the gas–liquid annular flow is validated through comparison with the experimental data. On the basis of the above numerical model, the phase distribution in the pipe was analyzed. The liquid entrainment behavior was reasonably simulated through the numerical model, which guaranteed the accuracy of predicting the particle erosion. Additionally, four erosion prediction models were used for the erosion calculation, among them, the Zhang et al. erosion model predicted the realistic results. Through the analysis of the particle trajectory and the particle impact behavior on the elbow, the cushion effect of the liquid film on the particles and the erosion morphology generation at the elbow were revealed.     

Experimental investigation and theoretical modeling of liquid entrainment in a horizontal tee with a vertical-up branch

This article describes a comprehensive literature review of liquid entrainment in horizontal pipes with vertical-up branches. Deficiencies in the available data and correlations were identified. The Air–water Test Loop for Advanced Thermal–hydraulic Studies (ATLATS) was constructed and entrainment onset and steady-state data were collected for a wide range of flow conditions. Using new insights gained from experimental testing, the authors developed a model for predicting the onset of entrainment and steady-state entrainment rate. Previously published correlations, along with the new model, are compared against all available data. The new model shows very good agreement with the onset data, but is not very good at predicting branch quality at high liquid flow rates.     

Numerical simulation for the air entrainment of aerated flow with an improved multiphase SPH model

Aerated flow is a complex hydraulic phenomenon that exists widely in the field of environmental hydraulics. It is generally characterised by large deformation and violent fragmentation of the free surface. Compared to Euler methods (volume of fluid (VOF) method or rigid-lid hypothesis method), the existing single-phase Smooth Particle Hydrodynamics (SPH) method has performed well for solving particle motion. A lack of research on interphase interaction and air concentration, however, has affected the application of SPH model. In our study, an improved multiphase SPH model is presented to simulate aeration flows. A drag force was included in the momentum equation to ensure accuracy of the air particle slip velocity. Furthermore, a calculation method for air concentration is developed to analyse the air entrainment characteristics. Two studies were used to simulate the hydraulic and air entrainment characteristics. And, compared with the experimental results, the simulation results agree with the experimental results well.     

A numerical method for the computation of the effects of an air vessel on the pressure surges in pumping systems with air entrainment

This paper describes an improved numerical method and computational procedure for the implementation of typical air vessel responses and their influence on the pressure transient for unsteady flow in a pipeline system with air entrainment. The proposed numerical method and computational procedure is without the necessity of an excessive iterative procedure as required previously by the conventional approach. The effects of air in the transient fluid system with the air vessel were then studied through the improved numerical computational method. Free and dissolved gases in the transported fluid, and cavitation at vapour pressure, are included. © 1998 John Wiley & Sons, Ltd.     

气泡夹带对壁面油膜流动特性的影响

油-气润滑系统工作过程中,润滑油膜受微油滴冲击和压缩空气扰动影响易形成气泡夹带现象,气泡夹带行为将对壁面润滑油膜层的形成及流动过程产生重要影响。基于VOF数值模拟方法,对含气泡油膜沿倾斜壁面的流动行为进行研究,考察了气泡的存在对油膜形态和流动速度的影响规律,以及气泡破裂阶段空腔邻域内流体压力变化特性。研究表明,油膜夹带气泡的形变和迁移诱发气泡周围微流场的速度扰动现象,导致气液界面处产生非均匀速度梯度分布,进而引发油膜表面的形态波动。气泡发生破裂时,油膜空穴部位发生明显的正负压力波动现象,气泡附近壁面将承受一定的交变载荷作用。     

一种新型MOEMS陀螺的提出及理论分析

提出一种新型的光路结构，构成利用空间光路的干涉式MOEMS陀螺。介绍了此种陀螺的基本原理，并从提高基本探测极限的角度，对此种空间光路的各种参数进行了理论分析，提出了设计思路和方法。指出了此种陀螺的特点及其应用领域。     

ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH

The special case of a crack under mode III conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor (SIF) results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.     

Theoretical and computational aspects in the shakedown analysis of finite elastoplasticity

A fully nonlinear shakedown analysis is considered for structures undergoing large elastic-plastic strains. The underlying kinematics of finite elastoplasticity are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. It is Shown that the notion of a fictitious, self-equilibrated residual stress field of Melan's linear shakesdown theorem has to be replaced by the notion of real, self-equilibrated residual state. Path-dependent and path-independent shakedown theorems are presented that can be realized in an incremental step-by-step procedure using Finite Element codes. The numerical implementation is considered for highly nonlinear truss structures undergoing large cyclic deformations with ideal-plastic, isotropic and kinematic hardening material behavior. Path-dependency of the residual states in the case of non-adaptation and path-independency in the case of shakedown are shown, and the shakedown domain is determined taking into account also the stability boundaries of the structure.     

The onset of convection in a viscoelastic liquid saturated anisotropic porous layer

The linear stability of a viscoelastic liquid saturated horizontal anisotropic porous layer heated from below and cooled from above is investigated by considering the Oldroyd type liquid. A generalized Darcy model, which takes into account the viscoelastic properties, the mechanical and thermal anisotropy is employed as momentum equation. The critical Rayleigh number, wavenumber, for stationary and oscillatory states and frequency of oscillation are determined analytically. It is shown that oscillatory instabilities can set in before stationary modes are exhibited. The effect of the viscoelastic parameter, the mechanical and thermal anisotropy parameters and specific heat ratio on the linear stability of the system is analyzed and presented graphically.     

液封液桥内热毛细对流的数值模拟

建立了液封液桥(不相溶混的双层同轴液柱)内热毛细对流的物理数学模型,采用涡量-流 函数法、利用有限差分格式对微重力条件下液封液桥内热毛细对流进行了数值模拟,得到了 双层液柱主流区的温度场和流场,证实了液封技术能削弱液桥主流区的热毛细对流,从而提 高浮区晶体生长质量,找出了液封厚度以及内、外层流体物性参数比对液桥内热毛细对流的 影响规律.     

Numerical study on the effects of air valve characteristics on pressure surges during pump trip in pumping systems with air entrainment

An improved numerical model and computational method are proposed here for the study of the effects of air valve characteristics on pressure surges during pump trip in fluid systems with air entrainment. Numerical experiments have shown that air valves with higher inflow characteristics installed at peak locations of a fluid system may reduce the magnitude of the extreme negative pressure surges. However, for near zero air entrainment levels in the fluid system, air valves with higher outflow characteristics tend to result in higher positive pressure surges. The results of the numerical simulations seem to be in qualitative agreement with available field observations [T.S. Lee and H.F. Cheong, Teck Hock Pumping Station: Flow Rate and Pressure Transient Measurements, Johnson Pacific, Singapore, 1994]. Copyright © 1999 John Wiley & Sons, Ltd.     

Theoretical analysis on hydraulic transient resulted by sudden increase of inlet pressure for laminar pipeline flow

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.     

Propagation of liquid surface waves over finite graphene structured arrays of cylinders

Based on the multiple scattering method, this paper investigates a benchmark problem of the propagation of liquid surface waves over finite graphene (or honeycomb) structured arrays of cylinders. Comparing the graphene structured array with the square structured and with triangle structured arrays, it finds that the finite graphene structure can produce more complete band gaps than the other finite structures, and the finite graphene structure has less localized ability than the other finite structures.     

Fractal analysis of atomizing liquid flows

The work reported in this paper questions the relevance of using fractal concept to study liquid primary atomization process by characterizing the shape of the continuous liquid flow from the nozzle exit to the end of the atomization process. First, three fractal methods were tested on synthetic images in order to define the best adapted protocol to the objective of the study. It appeared that the Euclidean distance mapping was the best appropriate method. Second, this technique was applied to analyze series of images of atomizing liquid flows obtained for several working conditions. This application demonstrates that atomizing liquid flows are fractal objects and that primary atomization can be reasonably seen as fractal processes. The appropriateness of fractal concept was also demonstrated by the fact that fractal characteristics such as textural or structural fractal dimension and inner cutoff scale are physically representative of the process investigated here.     

Interpretation of atomization rates of the liquid film in gas-liquid annular flow

For vertical gas-liquid annular flow the fraction of the liquid in the gas is controlled by the rate of atomization of the liquid film flowing along the wall and the rate of deposition of droplets entrained in the gas. Measurements of the rate of atomization are interpreted by a Kelvin-Helmholtz mechanism. Small wavelets on the liquid film are visualized to be entrained when wave-induced variations in the gas pressure cannot be counterbalanced by surface tension effects.