ALE finite element method for gas–liquid two-phase flow including moving boundary based on an incompressible two-fluid model

This paper proposes an ALE (Arbitrary Lagrangian–Eulerian) finite element method for gas–liquid two-phase flow, based on an incompressible two-fluid model, to analyze the two-phase flow including moving boundaries. The basic equations are derived by describing the two-fluid model in the ALE form. The solution algorithm is parallel to a fractional step method, and the Galerkin method is employed for the formulation. A quadrilateral element with four nodes is used for the discretization of the computational domain. The present method is also applied to calculate the flow around a circular cylinder, which is forced to oscillate in a quiescent air–water two-phase mixture. The drag coefficients of the cylinder exhibit periodical change in accordance with the variation of the flow around the cylinder. The time variations of the flow field and drag coefficients are discussed in relation to the oscillation of the cylinder.     

复合材料圆管阻尼特性研究

本文采用复模量方法的Timoshenko梁理论和模态应变能法的Love一阶壳理论建立了复合材料圆柱壳动力学方程,进行了相应的模态测试,并与有限元及试验结果进行对比。本文计算结果与有限元及试验结果符合良好。根据所建立的动力学方程,分析了梁理论的局限性,研究了铺层角度、长径比、厚径比、边界条件及环向波数对复合材料圆管阻尼特性的影响。结果表明：壳理论模型能对复合材料圆管的弯振阻尼特性进行准确分析,梁理论模型仅在轴向振动损耗占优的情况下比较准确;一弯模态损耗因子随长径比的增大而减小,在大于10时趋于定值;厚径比对一弯模态损耗因子影响较小;一弯模态损耗因子随铺层角度的增大先减小再增大后轻微减小,在铺层角度<30°和>75°时,双边固支边界的一弯模态损耗因子最大,在30°~75°之间时,悬臂边界的最大。     

Modeling approaches for strongly non-homogeneous two-phase flows

In some situations, two-phase flows exhibit strongly non-homogeneous behaviors like the one where the flow domain is divided into a bubbly region and a droplet region separated by a free surface. In such a situation, the gas bubbles in the bubbly region and the gas sky in the droplet region can exhibit very different fields of velocity and temperature. The same observation can be made for the liquid droplets and the continuous liquid in the bubbly region. The classical ‘two-fluid model’ can be too limited in its capabilities to correctly predict such types of flow, especially in the region around the free surface. In this paper, we analyze three different models more adapted to this kind of situation. The first one is a four-field model where one set of balance equations is written for each of the four fields: continuous liquid, continuous gas, liquid droplets and gas bubbles. This model is particularly heavy since it basically contains 12 balance equations. Therefore, two simplified two-field models have been written by summing the equations of the four-field model two by two, in two different ways. In the first two-field model, the equations are summed by region, giving three balance equations for the bubbly mixture and three balance equations for the droplet mixture. In the second two-field model, the equations are summed by phase, giving a model analogous to the usual two-fluid model, but with additional terms coming from the different fields interactions. The closure problem is discussed for each model and the three models are compared according to several criteria.     

Classification of two-phase flow regimes via image analysis and a neuro-wavelet approach

A non-intrusive method of two-phase flow identification is investigated in this paper. It is based on image processing of data obtained partly from dynamic neutron radiography recordings of real two-phase flow in a heated metal channel, and partly by visible light from a two-component mixture of water and air. Classification of the flow regime types is performed by an artificial neural network (ANN) algorithm. The input data to the ANN are some statistical moments of the wavelet pre-processed pixel intensity data of the images. The pre-processing used in this paper consists of a one-step multiresolution analysis of the 2-D image data. The investigations of the neutron radiography images, where all four flow regimes are represented, show that bubbly and annular flows can be identified with a high confidence, but slug and churn-turbulent flows are more often mixed up in between themselves. The reason for the faulty identifications, at least partially, lies in the insufficient quality of these images. In the measurements with air-water two-component mixture, only bubbly and slug flow regimes were available, and these were identified with nearly 100% success ratio. The maximum success ratio attainable was approximately the same whether the raw data was used without wavelet preprocessing or with a wavelet preprocessing of the input data. However, the use of wavelet preprocessing decreased the training time (number of epochs) with about a factor 100.     

悬臂管在同心套管包围的水中振动特性的研究

对悬臂管在同心套管包围的水中的振动特性作了分析。通过求解二维线性Navier—Stokes方程,得出了计算附加质量系数和粘滞阻尼比的公式。为了验证理论分析结果,对悬臂管在同心套管包围的水中的附加质量系数和粘滞阻尼进行了实验研究。得出了附加质量系数和粘滞阻尼比与套管内径和悬臂管外径之比、悬臂管在同心套管包围的水中振动的固有频率以及Stokes数之间的关系。     

Measurements of void fraction by an improved multi-channel conductance void meter

An improved multi-channel conductance void meter (CVM) was developed to measure a void fraction. Its measuring principle is based upon the differences in electrical conductance of a two-phase mixture due to the variation of void fraction around a sensor. The sensor is designed to be flush-mounted to the inner wall of the test section to avoid flow disturbances. The signal processor with three channels is specially designed so as to minimize inherent bias error due to the phase difference between channels. It is emphasized that the guard electrodes are electrically shielded in order not to affect the measurement of two-phase mixture conductance, but to ensure that the electrical fields are evenly distributed in the measuring volume. Void fraction is measured for bubbly and slug flow regimes in a vertical air–water flow and statistical signal processing techniques are applied to show that CVM has good dynamic resolution which is required to investigate the structural developments of bubbly flow and the propagation of void waves in a flow channel.     

Stability of axially compressed cylindrical shells filled with a fluid

This paper investigates the stability of fluid-filled cylindrical shells. A thin cylindrical shell is filled with an incompressible fluid and is axially compressed. Under a transient disturbance the fluid is assumed to undergo plane motion with the boundary velocity compatible with that of the shell surface. The stability of the shell is investigated by checking the boundedness of the oscillations. Extensive numerical studies are made for a wide range of parameters such as the densities of shell material and fluid, the geometry of the shell and the depth of fluid in the shell.     

摇摆状态下窄矩形通道内两相流流型特性研究

以空气和水为工质,在40mm×1.6mm的窄矩形通道内对竖直状态和摇摆状态下两相流流型进行了研究。流型由拍摄照片辨别,实验通道内观察到的流型有泡状流、弹状流、搅混流和环状流,绘制出窄矩形通道内的流型图,并与常规尺寸圆管内两相流型进行了对比。摇摆对窄矩形通道内流型的影响与常规尺寸圆管相似,但由于狭小空间的限制及表面张力的作用,摇摆对两相流动并无明显影响。     

Discontinuity stress analysis of pressure vessels using the finite element method

In pressure vessels the centre lines of the cylinder and dome portions often do not coincide thereby leading to a discontinuity at their junction. Structural analysis of such a structure assuming the centrelines of the cylinder and dome portions to be coincident leads to an incorrect estimation of stress and displacement distributions around the discontinuity. To predict accurately the stress and displacement distributions around the discontinuity, an iterative finite element scheme is developed in this paper using a conical shell finite element. The method is applied to two typical pressure vessels, one with hemispherical end domes and the other with ellipsoidal end domes. It is found that the solution converges in a few iterations.     

Measurement System of Bubbly Flow Using Ultrasonic Velocity Profile Monitor and Video Data Processing Unit

The authors have been developing a measurement system for bubbly flow in order to clarify its multi-dimensional flow characteristics and to offer a data base to validate numerical codes for multi-dimensional two-phase flow. In this paper, the measurement system combining an ultrasonic velocity profile monitor with a video data processing unit is proposed, which can measure simultaneously velocity profiles in both gas and liquid phases, a void fraction profile for bubbly flow in a channel, and an average bubble diameter and void fraction. Furthermore, the proposed measurement system is applied to measure flow characteristics of a bubbly countercurrent flow in a vertical rectangular channel to verify its capability.     

Transient film boiling under transient conditions related to vapor explosion (effects of transient flow and fragmentation under a shock pressure)

Two fundamental phenomena are significant when a shock pressure interacts with the large scale coarse mixing state. One is an intensive flow and the other is the surface area enhancement due to the disintegration of the hot drops. The effects of these phenomena on the transient heat transfer and behavior of vapor film under a shock pressure are investigated. Transient heat transfer of film boiling from an electrically heated platinum ribbon 2.5 mm wide and 0.15 mm thick was measured immediately after passage of a shock pressure from 0.1 to 0.7 MPa. The heater was set horizontally in a vertical shock tube which was filled with vapor liquid bubbly mixture and kept initially in the film boiling state. That is, the heater corresponds to a typical hot drop and the bubbles around it correspond to the coarse mixture around the drop. The liquid was Freon-113 with an initial void fraction in the range from 0 to 3%. When the shock wave arrives at the heater, intensive transient flow occurs due to collapse of bubbles around the heater. First, the effects of the initial void fraction, the intensity of the shock and the heated wall temperature on the transient heat fluxes and collapse of the vapor film were investigated experimentally and analytically under the shock pressure. Compared with a heated wall in the liquid alone, the transient heat flux at the heated wall increases and the collapse of the vapor film becomes easier in the bubbly mixture due to the transient flow. Effects of surface enhancement during the fragmentation process on the heat transfer rate and transient behavior of vapor film are investigated analytically by application of the newly proposed surface stretch model. It is made clear when the surface area is increasing, the vapor film is apt to collapse and the transient heat transfer is enhanced by the surface stretch.     

Seismic analysis of cracked reactor vessels

This paper deals with the dynamic response of a thin finite, elastic circular cylindrical shell representing a reactor vessel to time-dependent loadings symmetrical with respect to the axis of the cylinder. The shell contains an axial through-crack of length 2c. The dynamic counterpart of Donnell's shell equations are used in this investigation. Extensive numerical results are presented for stress intensity factors in aluminum and steel vessels and results are discussed.     

宏观-微观模型和朗之万方法在低能核裂变研究中的应用

基于三维朗之万模型对低能核裂变动力学过程和断点构型进行了研究,其中位能曲面采用基于双中心壳模型和有限程液滴模型的宏观 微观模型计算得到,质量张量和黏滞张量分别采用Werner Wheeler方法和墙加窗一体模型得到。以14 MeV中子诱发235U裂变为例,分别研究了拉长形变空间和壳衰减因子对裂变碎片质量分布、总动能分布及断点处核拉长与质量非对称度关联的影响,确定了模型计算中拉长形变空间边界至少应为35R0（R0为球形核半径）,以及壳衰减因子的合理取值为60 MeV。基于该模型,计算得到了14 MeV中子诱发233,235U裂变碎片质量分布,与ENDF/B Ⅷ0评价数据符合较好,说明该模型具有定量计算裂变碎片质量分布的能力。     

Wave propagation in isotropic- or composite-material piping conveying swirling liquid

An analysis is presented for the propagation of free harmonic waves in a thin-walled, circular cylindrical shell of orthotropic or isotropic material conveying a swirling flow. The shell motion is modeled by using the dynamic orthotropic version of the Sanders improved first-approximation linear shell theory and the fluid forces are described by using inviscid incompressible flow theory. Frequency spectra are presented for pipes made of isotropic material and composite materials of current engineering interest.     

Two-phase flow in an annulus with a rotating inner cylinder (flow pattern in bubbly flow region)

The two-phase flow pattern in a concentric annulus with a rotating inner cylinder have been investigated experimentally. The observed flow patterns were dispersed bubbly, ring-form, single-spiral, double-spiral, triple-spiral flows and transition regions. When the rotational speed was at a relatively low level, the buoyancy effect of bubbles dominated the flow field and a dispersed bubbly flow was formed. On the other hand, when the rotational speed was at a high level, the vortex motion induced by the rotation dominated the flow field and ring-form and spiral flows were formed.     

A numerical study on turbulence attenuation model for liquid droplet impingement erosion

The bent pipe wall thinning has been often found at the elbow of the drain line and the high-pressure secondary feed-water bent pipe in the nuclear reactors. The liquid droplet impingement (LDI) erosion could be regarded to be one of the major causes and is a significant issue of the thermal hydraulics and structural integrity in aging and life extension for nuclear power plants safety. In this paper two-phase numerical simulations are conducted for standard elbow geometry, typically the pipe diameter is 170 mm. The turbulence attenuation in vapor-droplets flow is analysed by a damping function on the energy spectrum basis of single phase flow. Considering the vapor turbulent kinetic energy attenuation due to the involved droplets, a computational fluid dynamic (CFD) tool has been adopted by using two-way vapor-droplet coupled system. This computational fluid model is built up by incompressible Reynolds Averaged Navier–Stoke equations using standard k–ε model and the SIMPLE algorithm, and the numerical droplet model adopts the Lagrangian approach, a general LDI erosion prediction procedure for bent pipe geometry has been performed to supplement the CFD code. The liquid droplets diameter, velocity, volume concentration are evaluated for the effects of carrier turbulence attenuation. The result shows that carrier turbulence kinetic energy attenuation is proved to be an important effect for LDI erosion rate when investigating the bent pipe wall thinning phenomena.     

Sloshing effect on the dynamic behavior of horizontal cylindrical shells

The present study investigates the effect of free surface motion of a fluid on the dynamic behavior of thin-walled cylindrical shells. This paper outlines a semi-analytical approach to dynamic analysis of a fluid-filled horizontal cylindrical shell taking into account free surface motion; sloshing. The aim of the method is to provide a general approach that can be used for both analysis and synthesis of fluid/structure interaction problems in horizontal cylindrical shells focusing on the dynamic interaction between a flexible structure and incompressible and inviscid flow. The approach is very general; it allows dynamic analysis of both uniform and non-uniform cylindrical shells and considers the fluid forces and includes the sloshing effect exerted on the structure. The hybrid method developed in this work incorporates a combination of the classic finite element approach and thin shell theory to determine the specific displacement functions. Mass and stiffness matrices of the shell are determined by precise analytical integration. A potential function is applied to develop the dynamic pressure due to the fluid. The kinetic and potential energies are evaluated for a range of fluid heights to find the influence of the fluid on the dynamic responses of the structure. The influence of physical and geometrical parameters on the fluid-structure system has been considered in the numerical solutions. When these results are compared with corresponding results available in the literature, both theoretical and experimental, very good agreement is obtained.     

A calculation methodology proposed for liquid droplet impingement erosion

Bent pipe wall thinning has been often found at the elbow of the drain line and the high-pressure secondary feed-water bent pipe in nuclear reactors. Liquid droplet impingement (LDI) erosion could be regarded as one of the major causes and is a significant issue of the thermal hydraulics and structural integrity in aging and life extension for nuclear power plant safety. In this paper a computational methodology is established for simulation of LDI erosion using computational fluid dynamics (CFD) simulation and theoretical calculation. Two-phase flow numerical simulations are conducted for standard elbow geometry, typically with the pipe diameter of 170 mm. This computational fluid model is built up by incompressible Reynolds Averaged Navier–Stoke equations using standard k–? turbulence model and the SIMPLE algorithm, and the numerical droplet model adopts the Lagrangian approach. The turbulence damping in vapor–droplets flow is theoretically analyzed by a damping function on the energy spectrum basis of single phase flow. Locally, a droplet impact angle function is employed to determine the overall erosion rate. Finally, the overall and local investigations are combined to purpose a general methodology of LDI erosion prediction procedure, which has been complemented into CFD code. Based on our more physical computational results, comparison with an available accident data was made to prove that our methodology could be an appropriate way to simulate and predict the bent pipe wall thinning phenomena.