An enhanced pipe elbow element—application in plastic limit analysis of pipe structures

In this paper, we present a new pipe elbow element based on a previous simplified model proposed by Bathe and Almeida [1, 2] and modified by Militello and Huespe [3]. It is really a beam‐type element but it describes the ovalization, warping, radial expansion and non‐symmetric deformation of cross‐section of curved pipe with Fourier series. Therefore, it could model precisely enough a real pipe elbow structure but remains simple. The extensive loading cases are effectively implemented by the proposed numerical techniques and displacement model. The developed element is used in this paper in plastic limit analysis of pipe elbow structures. This is realized by means of a direct mathematical programming technique. Various elastic and plastic limit state analyses of straight pipes and elbow structures are presented, which illustrates the efficiency of the element and the numerical method. Copyright © 1999 John Wiley & Sons, Ltd.     

大型弯头无模整体液压胀形新工艺的实验研究

提出了一种旨在用于大型管路系统的无模整体液压胀形制造弯头新工艺，成功地获得了一个厚度3．0mm，口径531．0mm，弯曲半径1310．0mm 的45．0°弯头实验件，其材料为Q235A该弯头初始结构为截面为正六边形的焊接扇形环壳结构，成形压力约为2．5MPa，实验表明，无模整体液压胀形法制造大型弯头造价低廉，简单可行。     

Analysis and mechanical properties characterization of operated gas main elbow with hydrogen assisted large-scale delamination

The pipe elbows with hydrogen assisted large-scale delamination revealed in 40-years operated lateral pipelines located behind the compressor station were investigated. The crack on the external surface of the pipe elbow above the delamination was observed. The causes of the material degradation were studied by non-destructive testing using ultrasound thickness meter, microstructure observing, hydrostatic pressure testing, and mechanical properties characterization. The degradation degree of the pipe elbow steel was higher than of the straight pipe steel regardless of a section was tensioned or compressed. Basing on the tensile tests carried out on the cylindrical standard smooth and proposed circular notched specimens it was established that the plasticity of the operated steel could be measured correctly only on the specimens with a notch due to localisation of deformation in the cross section. The limitations in using elongation and reduction in area for characterization of plasticity of the pipe steel with extensive delamination were established. A special short transverse specimen for impact toughness measurement of pipelines steels was designed, fracture plane in which was parallel to the delamination plane. The extremely low KCV values were obtained under designed specimens testing, which correctly characterized brittle fracture resistance of material along structure fibers and a sensitivity of pipe steel to delamination as well. The two stages of in-service degradation of metal, deformation aging and multiple damaging, were analysed, and two substages of the second one were distinguished: dissipated disoriented damaging and damaging oriented in rolling direction.     

高精度弯管流量计的理论研究和实验验证

通过求取N-S方程数值解的方法对弯管流量计进行理论研究,得出其测量准确度不仅与传感器自身的管径、曲率半径、弯径比、压力测点位置等几何结构尺寸的准确度有关,而且还与测量使用的条件有关。特别是弯管流量计与前后直管段产生的安装偏转角、直管段管径与其自身管径的一致性等环境应用条件会对弯管流量计的高精度使用产生影响。针对上述影响因素,通过对用整体数控加工的、自身带有直管段的弯管流量计进行反复实验, 结果表明:在2σ准则下,弯管流量计可以达到0.5%的测量准确度水平;不同管径情况下,流量系数也具有良好的一致性。     

Investigation on flow characteristics of ice slurry in horizontal 90° elbow pipe by a CFD-PBM coupled model

Elbow pipes are important components for ice slurry pipeline transport. However, the flow characteristics of ice slurry in elbow are far from fully being understood, especially the influence of ice particle kinetics on ice particle size distribution (PSD). This study is intended to provide a better understanding of the behavior of ice slurry flow in elbow pipe. A CFD-PBM coupled model is employed to investigate the flow characteristics of ice slurry in horizontal 90° elbow pipe. The quadrature method of moments is utilized to solve the population balance equations. Based on the revised model, the flow characteristics of ice slurry in the horizontal 90° elbow pipe are investigated. The simulation results show that in the range of calculations, the pressure drop of elbow pipe is increased with the increase of velocity and ice packing fraction (IPF). An adverse pressure gradient is formed due to the change in flow direction. The emergence of secondary flow is caused by the centrifugal force. It makes the ice particles gather on the outer wall of the elbow section. The ice diameter increases along the flow direction due to the aggregation. The evolution of particle size distribution (PSD) is not significant. However, aggregation and stratification cannot be ignored in the process of long distance transport of ice slurry. The results are of significance for guiding the safety design and operation of ice slurry transportation.     

Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic–plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic–plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.     

Liquid metal flow through a thin walled elbow in a plane perpendicular to a uniform magnetic field

This paper presents analytical solutions for the liquid-metal flow through two straight pipes connected by a smooth elbow with the same inside radius. The pipes and the elbow lie in a plane which is perpendicular to a uniform, applied magnetic field. The strength of the magnetic field is assumed to be sufficiently strong that inertial and viscous effects are negligible. This assumption is appropriate for the liquid-lithium flow in the blanket of a magnetic confinement fusion reactor, such as a tokamak. The pipes and the elbow have thin metal walls.The flow tends toward the inside surface of the elbow, approaching a vortex about the center of curvature of the elbow. This flow migration away from the uniform fully developed flow in the pipes leads to voltage variations along the pipes. These voltage variations drive four electric current circulations in planes perpendicular to the magnetic field. These current circulations produce significant pressure variations in the cross sections of the pipes and elbow. A long length of pipe is required on both sides of the elbow for the completion of the circuits for these electric current circulations and for the decay of the disturbances to the fully developed flow in the straight pipes. All pressure drops and rises due to the three-dimensional electric current circulations cancel. The total pressure drop is the same as that for fully developed flow in a single straight pipe with the same length. While the analysis treats pipes and elbows with circular cross sections, the absence of a pressure drop in addition to that for fully developed flow is true for any smooth elbow.     

Effect of nonuniform conduit section on waterhammer

Summary Fundamental equations for studying transient flows in conduits with variable cross sections are reviewed. The flow is assumed to be quasi-one-dimensional provided the variation in the pipe cross section is mild. The set of equations is then integrated by a numerically implemented characteristics method. A benchmark case is investigated through which the effect of contraction and expansion of pipe cross section on the waterhammer phenomenon (pressure surge) is addressed and discussed. The result shows a shift of pressure fluctuation from low frequency mode to high frequency mode as the pipe alters from a necking to a bulging configuration.     

New unloading compliance correlation for throughwall circumferentially cracked pipe to measure crack growth during fracture tests

Crack growth is generally measured during fracture experiment of specimen or component. The unloading compliance technique is commonly used for this purpose because of its simplicity. It infers the crack length from unloading compliance of cracked component. The pre‐requisite of this technique is the availability of an equation that correlates crack length with unloading compliance. While such correlations are available for compact tension and three‐point bend specimens, it is not available for big components such as pipe or pipe bend. Development of such a correlation for throughwall circumferentially cracked (TCC) straight pipe under bending, therefore, forms the objective of the present study. However, the challenge to develop such correlation for TCC pipe is that the equation should contain not only crack length as a function but also the current deformation or load level as a parameter. This is attributed to the fact that the circular cross section of the pipe ovalizes during deformation leading to change of bending stiffness of the cracked body. New compliance correlations have been proposed for TCC pipe under bending load considering these complexities. Elastic‐perfectly plastic material behaviour has been assumed to characterize the material stress–strain response. However, it has been shown that error due to this approximation with respect to the actual stress–strain behaviour is negligible if one chooses flow stress equal to average of yield and ultimate strength. The proposed correlations are expressed in terms of normalized parameters to make them independent of specific values of geometric dimensions such as radius, thickness and span length of four‐point bending loading system. Effectiveness of this normalization has also been verified by carrying out a sensitivity study.     

大型弯头液压成形的理论分析与实验研究

针对现有弯头制造中存在的问题 ,提出了用环壳液压胀形工艺制造弯头的方法 ,分析了环壳的应力特点 ,并给出了其最后的成形压力 .通过实验研究了环壳胀形过程中位移、应变的变化规律及成形后壳体的几何尺寸 ,并对其成形过程中的起皱进行了分析 .研究表明用液压液压胀形工艺制作弯头是可行的 .     

管道内冰浆流动压降特性模拟和实验研究

本文采用以颗粒相动力学为基础的Euler-Euler模型,利用FLUENT研究冰浆在水平直管、90°弯管和T型管中的流动压降特性(计算过程不考虑相变)。模拟结果显示,在管道入口处压降较明显,90°弯管拐弯后内侧压力小于外侧,T型管在分流直角拐角处出现压力最高点和最低点。冰浆流动实验发现,冰浆单位压降随流速和含冰率的增加而增大,且3种管型中直管压降最小,T型管压降最大。对比实验与模拟结果,单位压降随流速的变化趋势一致,且误差在20%以内,但在大流速时,模拟值大于实验值。     

Generalized similarity of laminar nonisothermic flows of a viscous gas in thin pipes of variable cross section

The method of generalized similarity of the boundary-layer theory is applied to the problem of laminar flow of a viscous gas in thin circular pipe with cross section which varies along the length of the pipe.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 2, pp. 285–289, February, 1982.     

弯管元件机械阻抗研究

管路元件阻抗是管路系统振动和声学特性的表征，在管路系统减振降噪设计和计算中具有重要的用途。文章从弯管的振动方程出发，推导了弯管的阻抗计算表达式，并通过给定尺寸的弯管元件阻抗数值计算，分析了弯管相对于直管的机械阻抗差异以及参数变化对机械阻抗的影响。     

Modeling of viscoplastic rate-dependent hardening-softening behavior of hot mix asphalt in compression

The objective of this paper is to model viscoplastic rate-dependent hardening-softening behavior that is experimentally observed from hot mix asphalt (HMA) under repetitive creep and recovery loading in compression. A differential equation is utilized to incorporate the effects of the stress history into yield stress, and an internal variable representing rate dependence in the equation is set as a function of the viscoplastic strain rate to address the change in rate dependence of the material due to gradual hardening. Also, a separate rate-dependent function concept is adopted to describe the difference in rate dependence of the yield stress during unloading and loading. The developed viscoplastic model is applied using the time–temperature superposition principle and shows good agreement with the measured viscoplastic responses of HMA under repetitive creep and recovery loading with various load levels and rest periods.     

Turbulent flow of a fibrous suspension in a pipe

The Henky-Ilyushin equations are used to describe the steady turbulent flow of an incompressible viscoplastic fluid in a pipe. A fibrous suspension is examined as the fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 2, pp. 223–229, February, 1990.     

Comparison of cavern formation in massive salt blocks with single-well and two-well systems

The authors of this article have conducted a comparison study to investigate the construction characteristics of both single-well and two-well systems; two model experiments were conducted using large-size moulded rock salt specimens. An experimental platform was designed to simulate the process of leaching and a theoretical equation of calculating and predicting the cavern volume was derived. The experimental results illustrate that the variation trend of brine instantaneous concentration for single-well and two-well systems is identical, and an equilibrium state appears at last. Moreover, the equilibrium is reached early, after 5–8 pumping cycles. The construction rate in the two-well system is faster than the single-well system, and this phenomenon is observed mainly in the early periods (1–3 pumping cycles). Besides, the cavern shapes for the two construction methods are also found to be distinctive. The cavern of the single-well system has a circular cross section and an axisymmetric profile while that of the two-well system has an ovular cross section and a non-axisymmetric profile.     

Computing the limiting state of banded pipes

The mathematical model of a rectilinear segment of a petroleum pipeline, banded on the outside by a high-strength section wound perpendicular to the generatrix of the pipe is proposed. The mathematical model accounts for stretching of the pipe, which occurs as the section is tensioned during fabrication of the arrangement. The equation and approximate analytical formula for a parameter of the pipe's stressed state are derived with allowance for preliminary stretching of the pipe and deformation due to internal pressure. The equation and recurrent relationship for calculating extremal internal pressure and deformation are obtained. The discrepancy between the computed data and experimental data obtained during fullscale tests of pipes 1220 mm in diameter is 2%.Translated from Problemy Prochnosti, No. 1, pp. 76–81, January, 1990.     

Das Strahlrohrvakuumsystem des HERA-Protonenringes

The beam pipe vacuum system of the HERA proton ring has a length of 6.3 km. During operation of the superconducting magnets the beam pipe is at the temperature of liquid helium over about 5.5 km. There are no detectable leaks within this critical section. The operational pressure is below 10^?12 mbar. The round beam tubes with length up to 10 m are coated with copper of good electrical conductivity from the inside. The remaining 800 m of the system are at ambient temperature. The chambers have different complicated cross sections produced with high precision. Inspite of limited space in certain areas, bakeout up to 300°C is possible in situ.     

弯管后均速管流量计输出特性数值模拟

采用数值模拟方法对处在弯管附件后均速管流量计的输出特性进行了研究.计算中采用k-ε湍流模型,应用有限体积法对控制方程进行离散.计算得到了弯管后管道中不同位置处流量计采用平行、垂直、45°(相对于弯管平面)三种安装方式情况下的差压输出,结合管道及流量计内部流场分布对流量计输出特性进行了分析.结果表明,数值计算结果与实测结果具有很好的一致性.对比三种安装方式的误差,流量计采用垂直于弯管平面的安装方式最优.     

A generalization of Gittus’ viscoplastic “mechanical equation of state” to multiaxial stress states

In this paper, a multiaxial generalization of the viscoplastic “mechanical equation of state” (MEOS) by Gittus is proposed that preserves the physical soundness of the theory. The concept of forward and backward mobility of dislocations is generalized to a concept of directional mobility by splitting the mobile dislocation density in an isotropic and a tensorial part, similar to the approach used in the Bodner unified viscoplastic model. It is shown that the formulation is equivalent to the original MEOS in the case of uniaxial loadings. The approach is easily applied to any uniaxial viscoplastic material model.