Some recent developments on integrity assessment of pipes and elbows. Part I: Theoretical investigations

Integrity assessment of piping components is very essential for safe and reliable operation of power plants. Over the last several decades, considerable work has been done throughout the world to develop a system oriented methodology for integrity assessment of pipes and elbows, mainly for application to nuclear power plants. However, there is a scope of further development/improvement of issues, particularly for pipe bends, that are important for accurate integrity assessment of pipings. Considering this aspect, a comprehensive Component Integrity Test Program was initiated in 1998 at Reactor Safety Division (RSD) of Bhabha Atomic Research Centre (BARC), India in collaboration with MPA, Stuttgart, Germany through Indo-German bilateral project. In this program, both theoretical and experimental investigations were undertaken to address various issues related to the integrity assessment of pipes and elbows. The important results of the program are presented in this two-part paper. In the part I of the paper, the theoretical investigations are discussed. Part II will cover the experimental investigations. The theoretical investigations considered the following issues: new plastic (collapse) moment equations of defect-free elbow under combined internal pressure and in-plane closing/opening moments; new plastic (collapse) moment equations of throughwall circumferentially cracked elbow, which are more accurate and closer to the test results; new ‘η_pl’ and ‘γ’ functions of pipes and elbows with various crack configurations under different loading conditions to evaluate J–R curve from test data; and the effect of deformation on the unloading compliance of TPB specimen and throughwall circumferentially cracked pipe to measure crack growth during fracture experiment. These developments would also help to study the effect of stress triaxiality in the transfer of material J–R curve from specimen to component.     

深海保温输油管后屈曲及屈曲传播的有限元分析

本文运用ABAQUS有限元软件模拟深海输油管道的后屈曲及屈曲传播现象．将深海输油管道视为内、外层为合金钢材,夹心为聚氨酯泡沫的输油管道．采用线弹性-线性硬化的本构关系,运用Riks分析法获得后屈曲平衡路径,以此模拟管道中的屈曲传播过程,并获得屈曲传播压力．通过数值算例,综合讨论了不同初始缺陷、不同径厚比、不同夹层与夹心厚度比对、不同的材料弹性模量对屈曲传播过程和压力的影响．最后将输油管退化为单层管,将传播压力的有限元结果与实验结果、 Palmer理论解比较．结果表明有限元值、实验结果、理论值三者比较吻合．验证了有限元分析的正确性．     

Internal ring buckle arrestors for pipe-in-pipe systems

A new buckle arrestor concept for pipe-in-pipe systems is introduced and the results of a systematic study of its performance is presented. The concept involves either one single ring or a number of closely packed narrow rings placed in the annulus between the two pipes. Its effectiveness has been studied through a combination of experiments and analyses. The experiments involved two inch carrier tubes of three different D/t values and internal rings of various dimensions. A number of experiments were first conducted using pipe-in-pipe systems. It was found that the inner tube had only a small effect on the crossover pressure of this arrestor and, as a result, in many of the following experiments inner tubes were not included.The crossover pressure of the ring arrestors was studied by varying their length, wall thickness and yield stress. Other parameters varied were the dimensions and properties of the two tubes and the gap between the arrestor and the carrier tube. The process resulted in an empirical design formula for the arresting efficiency expressed as a function of the key nondimensional variables of the problem. Large-scale finite element models which simulate the buckle crossover process have also been developed. They have been shown capable of reproducing experiments accurately. Such models can be used to prove an arrestor design developed through the empirical process described in the report.     

On the effect of corrosion defects on the collapse pressure of pipelines

The loss of metal in a pipeline due to corrosion usually results in localized pits with various depths and irregular shapes on its external and internal surfaces. The effect of corrosion defects on the collapse pressure of offshore pipelines was studied through the combination of small-scale experiments with nonlinear numerical analyses based on the finite element method. After calibrated based on the experimental results, the model was used to determine the collapse pressure as a function of material and geometric parameters of different pipes and defects. An extensive parametric study using 2-D and 3-D numerical models was carried out encompassing different defect geometries and their interaction with pipe ovalization.     

Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers

Fully resolved direct numerical simulations (DNSs) have been performed with a high-order spectral element method to study the flow of an incompressible viscous fluid in a smooth circular pipe of radius R and axial length 25R in the turbulent flow regime at four different friction Reynolds numbers Re _τ ?=?180, 360, 550 and $1\text{,}000$ . The new set of data is put into perspective with other simulation data sets, obtained in pipe, channel and boundary layer geometry. In particular, differences between different pipe DNS are highlighted. It turns out that the pressure is the variable which differs the most between pipes, channels and boundary layers, leading to significantly different mean and pressure fluctuations, potentially linked to a stronger wake region. In the buffer layer, the variation with Reynolds number of the inner peak of axial velocity fluctuation intensity is similar between channel and boundary layer flows, but lower for the pipe, while the inner peak of the pressure fluctuations show negligible differences between pipe and channel flows but is clearly lower than that for the boundary layer, which is the same behaviour as for the fluctuating wall shear stress. Finally, turbulent kinetic energy budgets are almost indistinguishable between the canonical flows close to the wall (up to y ^?+??≈?100), while substantial differences are observed in production and dissipation in the outer layer. A clear Reynolds number dependency is documented for the three flow configurations.     

复杂载荷下双金属复合管的屈曲失效研究

本文采用有限元方法系统地研究了复杂载荷下双金属复合管的屈曲失效，三维有限元数值模型考虑了双金属复合管的准静态复合成型制造过程中产生的残余应力，分析了外基管直径、内衬管壁厚、内外管初始间隙、内衬管屈服强度、内压等因素对双金属复合管屈曲失效的影响。结果表明，加载路径、复合管的几何尺寸及内衬管的屈服强度对双金属复合管的屈曲性能均有较大影响，内充压力可以延迟内衬管的屈曲失效。     

Ratcheting and wrinkling of tubes due to axial cycling under internal pressure: Part I experiments

Under compression, pressurized tubes thick enough to deform plastically buckle into an axisymmetric wrinkling mode. The wrinkle amplitude is initially small but with persistent compression grows inducing a gradual reduction in axial rigidity and eventually causing a limit load instability, which is followed by collapse. The onset of buckling and collapse can be separated by a strain level of a few percent. This work investigates whether a tube that develops small-amplitude wrinkles can be subsequently collapsed by persistent axial cycling. Part I presents the results from a set of experiments on super-duplex tubes with D/t of 28.5 loaded as follows. A tube is pressurized and then compressed into the plastic range to a level that initiates wrinkling. It is then cycled under stress control about a compressive mean stress while the pressure is kept constant. The combined loads cause simultaneous ratcheting in the hoop and axial directions as well as a gradual growth of the wrinkles. At some stage the amplitude of the wrinkles starts to grow exponentially with the number of cycles N leading to localization and collapse. The rate of ratcheting and the number of cycles to collapse depend on the initial compressive pre-strain, the internal pressure, and the stress cycle parameters all of which were varied sufficiently to generate an adequate data base. Interestingly, in all cases collapse was found to occur when the accumulated average strain reached the value at which the tube localizes under monotonic compression. A shell model coupled to a specially calibrated plasticity model that can reproduce the biaxial ratcheting exhibited in the problem are presented in Part II. The model is first evaluated by comparison to the experiments and then used to study parametrically cyclic loading histories seen in buried pipelines.     

On the effect of Lüders bands on the bending of steel tubes. Part I: Experiments

In several practical applications hot-finished steel pipe that exhibits Lüders bands is bent to strains of 2–3%. Lüders banding is a material instability that leads to inhomogeneous plastic deformation in the range of 1–4%. This work investigates the influence of Lüders banding on the inelastic response and stability of tubes under rotation controlled pure bending. Part I presents the results of an experimental study involving tubes of several diameter-to-thickness ratios in the range of 33.2–14.7 and Lüders strains of 1.8–2.7%. In all cases the initial elastic regime terminates at a local moment maximum and the local nucleation of narrow angled Lüders bands of higher strain on the tension and compression sides of the tube. As the rotation continues the bands multiply and spread axially causing the affected zone to bend to a higher curvature while the rest of the tube is still at the curvature corresponding to the initial moment maximum. With further rotation of the ends the higher curvature zone(s) gradually spreads while the moment remains essentially unchanged. For relatively low D/t tubes and/or short Lüders strains, the whole tube eventually is deformed to the higher curvature entering the usual hardening regime. Subsequently it continues to deform uniformly until the usual limit moment instability is reached. For high D/t tubes and/or materials with longer Lüders strains, the propagation of the larger curvature is interrupted by collapse when a critical length is Lüders deformed leaving behind part of the structure essentially undeformed. The higher the D/t and/or the longer the Lüders strain is, the shorter the critical length. Part II presents a numerical modeling framework for simulating this behavior.     

Experimental study of wall pressure fluctuations in rigid and elastic pipes behind an axisymmetric narrowing

Wall pressure fluctuations, p_t, in rigid and elastic pipes behind a local axisymmetric narrowing are studied. A sharp increase in their rms level in a finite region immediately downstream of the narrowing, leading up to a pronounced maximum upstream of the point of jet reattachment, is found. Approximate estimates both for the distance from the narrowing to the point of maximum rms pressure and for the rms magnitude at this point are obtained. Inspection of the wall pressure power spectrum, P, reveals the presence of low-frequency maxima. The maxima are found to be associated with the large-scale eddies in the regions of separated and reattached flow, and their frequencies are close to the characteristic frequencies of the eddies’ formation. These maxima are the main distinguishing features of the spectrum under investigation compared to the power spectrum of the wall pressure fluctuations in a fully-developed turbulent flow in a pipe without narrowing. A comparative analysis of the data for rigid and elastic pipes shows that changes in the pipe wall bending stiffness cause alterations in the flow structure near the wall and the corresponding redistribution of flow energy among the vortices. This results in an increase in the wall pressure amplitude and the low-frequency level of the wall pressure power spectrum, as well as the appearance of new frequency components in this domain.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

Some recent developments on integrity assessment of pipes and elbows. Part II: Experimental investigations

Integrity assessment of piping components is very essential for safe and reliable operation of power plants. Over the last several decades, considerable work has been done throughout the world to develop a methodology for integrity assessment of pipes and elbows, appropriate for the material involved. However, there are scope of further development/improvement of issues, particularly for pipe bends, that are important for accurate integrity assessment of piping. Considering this aspect, a comprehensive Component Integrity Test Program was initiated in 1998 at Reactor Safety Division (RSD) of Bhabha Atomic Research Centre (BARC), India in collaboration with MPA, Stuttgart, Germany through Indo-German bilateral project. In this program, both theoretical and experimental investigations were undertaken to address various issues related to the integrity assessment of pipes and elbows. The important results of the program are presented in this two-part paper. In the part II of the paper, the experimental investigations are discussed. Part I covered the theoretical investigations. Under the experimental investigations, fracture mechanics tests have been conducted on pipes and elbows of 200–400 mm diameter with various crack configurations and sizes under different loading conditions. Tests on small tensile and three point bend specimens, machined from the tested pipes, have also been done to evaluate the actual stress–strain and fracture resistance properties of pipe/elbow material. The load–deflection curve and crack initiation loads predicted by non-linear finite element analysis matched well with the experimental results. The theoretical collapse moments of throughwall circumferentially cracked elbows, predicted by the recently developed equations, are found to be closer to the test data compared to the other existing equations. The role of stress triaxialities ahead of crack tip is also shown in the transferability of J–resistance curve from specimen to component.     

Water hammer with column separation: A historical review

Column separation refers to the breaking of liquid columns in fully filled pipelines. This may occur in a water-hammer event when the pressure in a pipeline drops to the vapor pressure at specific locations such as closed ends, high points or knees (changes in pipe slope). The liquid columns are separated by a vapor cavity that grows and diminishes according to the dynamics of the system. The collision of two liquid columns, or of one liquid column with a closed end, may cause a large and nearly instantaneous rise in pressure. This pressure rise travels through the entire pipeline and forms a severe load for hydraulic machinery, individual pipes and supporting structures. The situation is even worse: in one water-hammer event many repetitions of cavity formation and collapse may occur.This paper reviews water hammer with column separation from the discovery of the phenomenon in the late 19th century, the recognition of its danger in the 1930s, the development of numerical methods in the 1960s and 1970s, to the standard models used in commercial software packages in the late 20th century. A comprehensive survey of laboratory tests and field measurements is given. The review focuses on transient vaporous cavitation. Gaseous cavitation and steam condensation are beyond the scope of the paper.     

Flow patterns of n-hexadecane–CO2 liquid–liquid two-phase flow in vertical pipes under high pressure

To promote a better understanding of liquid–liquid two-phase flow behavior, particularly under high pressure, flow patterns of n-hexadecane–CO₂ liquid–liquid two-phase upward flow in vertical stainless steel pipes were experimentally investigated. Observations were made in two 0.0015 m I.D. pipes of different lengths (0.068 m and 0.5 m) under high pressure varying from 10.3 to 29.6 MPa using a high pressure visualization system. The total flow rate was fixed at 2.0 × 10⁻⁶ m³/min, while the flow rate ratio (φ) varied from 0.05 to 19. Bubbly flow, plug flow, slug flow, annular flow, and near-one-phase flow regions were found in both pipes, while stratified flow was observed only in the 0.068 m pipe. Flow pattern maps were constructed in the flow rate ratio versus pressure graph, which demonstrates significant impacts of flow rate ratio, pipe length, and pressure on flow patterns. These impacts are discussed in detail. To the authors’ best knowledge, this work is the first attempt to observe complex liquid–liquid two-phase flow behavior with flow pattern transitions under high pressure, and contributes to a better understanding of liquid–liquid two-phase flow behavior.     

Buckling and postbuckling of concentric cylindrical tubes under external pressure

The problem considered involves a structure composed of two concentric and bonded tubes subjected to external and uniform pressure. Compression tests are conducted using structures formed by a thin-walled internal rubber tube and a thick-walled external foam tube. Experimental results are plotted under the form of a bifurcation diagram representing the inner cross-sectional area of the thin tube as a function of pressure. The buckling pressure P_b and the contact pressure P_co are determined from this non linear diagram. A numerical computation by the Finite Element Method (FEM) is used in order to calculate the Euler buckling pressure P_b and the results are compared with experimental data. It is shown that the buckling pressure and the associated buckling mode n, strongly depend upon the elastic and geometrical parameters of both the tubes. The experimental and numerical investigations are also extended to postbuckling behaviour. The contact between the opposite sides of the inner wall is occured with a buckling mode index n = 2, 3. This contact phenomenon is given rise to the discontinuity of a previous diagram and was characterized by the contact pressure P_co.     

加工后的双壁金属换热管在升温-降温过程中受到的力学影响

铅冷钠冷快堆核电设备中的蒸汽发生器,有着在液态金属和水之间进行热交换的作用,其换热部分由排列的换热管组成。贴合式的双壁管是一种具有高换热效率及抵抗管裂纹扩展的管材,适合于这种应用环境。这种管材的内外管间存在残余压力,这是内外管紧贴的标志。然而在经历升至高温又降温的过程后,内外管间残余压力有可能消失引起两管脱开。为了得知温度对贴合式双壁金属管的具体影响,本文设计了一种拉伸法来制备双壁管,并同时采用有限元数值模拟管的加工制备过程并得到了内外管间的残余应力,再对加温后降温的过程进行模拟,分析换热管残余应力和应变状态进行了分析的变化,并通过初步试验来进行验证。通过研究,结果表明温度变化引起的塑性变形是管间残余压力变化的主要原因。通过控制管的加工过程来控制管材加工程度的方法,可望应对温度变化对管稳定性的影响。     

Analysis model to simulate the cracked pipe buried in soil

This paper describes the use of the finite element method to simulate crack propagation in a pipeline in the presence of soil backfill. Since typical values for soil modulus are known, a spring element can be used to simulate the effects of backfilled soil on crack propagation. This consists of the relationship between the soil property and the stiffness of the spring element, and the effect of backfill depth on the crack propagation in the pipes. By equating crack driving force,G, in the presence of soil, to the dynamic fracture toughness of the pipeline material, a theoretical predictive capability is obtained for the first time for the gas transmission and distribution pipelines. Numerical calculations have also been carried out for the cracked pipe with backfill and without backfill.     

管系内一维可压缩流动数值建模与特性分析

针对复杂管系内可压缩流体,基于有限体积法,采用HLLC(Harten-Lax-van Leer Contact)格式和黎曼求解器构建了有限控制体数值离散方法,引入虚拟节点用于连接有限控制体,借助虚拟节点给出控制体之间数值通量的计算格式,发展了一种管道内一维流动数值建模方法.针对含有分支管路的管系,在管道连接部位构建了分...     

On the axial propagation of kink bands in fiber composites : Part ii analysis

A new micromechanical model is presented to simulate the steady-state axial propagation of kink bands investigated experimentally in the accompanying paper (Part I) . The fibers are in a hexagonal array and are assumed to be isotropic and linearly elastic, while the matrix is modeled as an elastic-powerlaw viscoplastic solid. Matrix properties for the model are determined from shear tests on the composite and compression tests on neat PEEK. The model is used to predict the propagation stress (σ_P) of the AS4⧹PEEK composite and to investigate the sensitivity of σ_P to band inclination, matrix properties, and loading rate. A simple model recently reported in the literature is calibrated to the current material system and compared with the present experimental data and model predictions. The micromechanical model is found to predict the propagation stress reasonably well and to capture the rate dependence of the composite. The simple model is found to capture the trends of the behavior.     

力-热载荷下双金属复合管的屈曲失效研究

采用有限元方法研究了力-热载荷下双金属复合管的屈曲失效行为,通过三维有限元建模考虑了双金属复合管的准静态复合成型制造过程中产生的残余应力,分析了温度及内压两个主要参数对双金属复合管屈曲失效的影响。结果表明,高温导致材料发生软化,抑制了双金属复合管的屈曲;弯矩、内压及热载荷联合作用下,复合管内介质温度降低,复合管弯矩达到最大值对应的曲率减小,而弯曲承载能力增大,外基管的椭圆率也增大;内压变化对复合管的弯曲承载能力和外基管的椭圆率影响较小。     

Modelling of the moisture concentration field due to cyclical hygrothermal conditions in thick laminated pipes

The paper presents a new method to calculate the moisture concentration field induced by cyclical environmental conditions in thick laminated pipes. The solution which is obtained is composed of a transient solution over the interior of the pipe wall and a fluctuating solution within two thin regions, close to the inner and outer lateral surfaces of the pipe wall. The thickness of these two regions is depending on both materials and frequency conditions. The transient solution is determined by using an analytical method based on the solving in average of the field equation. The fluctuating solution is derived from a finite difference scheme. It is shown that after some period of time the transient solution tends towards a permanent time independent solution. In that case, the fluctuating solution becomes a periodic solution which is conditioned by the cyclical boundary conditions. Finally, the effect of particular cyclical conditions on the moisture concentration in thick wall pipes will be tackled.