The effect of bi-directional loading on fatigue assessment of pressurized piping elbows with local thinned areas

An elastic–plastic finite element study is conducted to determine the effect of bi-directional loading on the fatigue characteristics of pressurized 90° piping elbows with local thinned areas. The analysis is conducted on pressurized piping elbows considered previously in the literature, but analyzed only for in-plane loading. Considering also the out-of-plane loading the present analysis seeks to simulate simultaneous horizontal and vertical seismic actions. A validation study is first conducted in which the present results obtained for in-plane loading are compared with previous results. Comparisons are made for deformation patterns, hoop strain histories, and reaction forces. The relative in-plane to out-of-plane load intensities to be adopted for the combined loading case is determined next. Results considering bi-directional loadings are then found for the pressurized piping elbow for a total of 23 cases of local area thinning. Finally conclusions are drawn about the significance of considering the additional out-of-plane loading.     

Toroidal elastic stress fields for pressurized elbows and pipe bends

The zero order and first order stress fields are determined by toroidal elasticity methods for an elbow or pipe bend subjected to internal pressure. The methods of toroidal elasticity, first introduced in 1980 at London, England are here made explicit. These methods formed the basis for the numerical results presented in the earlier paper.

The problem considered in this paper is one of the more difficult of the ten unit problems for a pressurized elbow or curved pipe acted upon by end loads and seismic accelerations. All of these ten unit problems have now been solved. The present paper complements the earlier paper. The solution presented here was initially completed in 1978.     

Experimental study of low-cycle fatigue of pipe elbows with local wall thinning and life estimation using finite element analysis

Low-cycle fatigue tests were conducted using elbow specimens with local wall thinning. Local wall thinning was machined on the inside of the elbow in order to simulate metal loss from erosion corrosion. The local wall thinning was located in three different areas known as the extrados, crown and intrados. The elbow specimens were subjected to cyclic in-plane bending under displacement control without internal pressure. In addition, three-dimensional elastic-plastic analyses were also carried out using the finite element method. As a result, the crack penetration area and the crack growth direction were successfully predicted by the analyses. The fatigue lives estimated by the analyses were close to those obtained by the experiments.     

Three-dimensional stress analyses of mitred elbows

Three-dimensional elastic stress analyses of a mitred elbow have been performed by the application of the MARC finite element program. Seven basic unit load cases have been considered. Results of these reference load cases may be applied in any combination to stress analyses of the same elbow subjected to more complicated loading conditions.

According to results from these analyses, when a mitred bend is subjected to in-plane loads, it exhibits behaviour similar to that of a smooth elbow under the same loading conditions. Results from out-of-plane load cases show some deviation from the behaviour of a smooth bend. These discrepancies cast some doubts on the conventional method of stress analysis of a mitred bend.     

The integrally hydro-forming process of pipe elbows

In this paper, a hydro-bulging technology for manufacturing pipe elbows is proposed to overcome difficulties in manufacturing large diameter elbows using traditional technology. The section profile variation of the toroidal shell during the forming process is discussed. It is demonstrated experimentally that manufacture of a pipe elbow using integrally hydro-bulging technology is feasible.     

Initial yielding in elbows and curved tubing

Cross-section flattening of a piping elbow or curved thin-walled tube may be described by four plastic hinges. The present paper presents an analysis of the plastic hinge formation using the methods of toroidal elasticity. This enables one to identify the location of first yielding which generally, but not necessarily, occurs on the inner surface of the elbow.The mechanism of initial yielding is plastic deformation caused by the vertical component of the axially directed bending stress of a curved pipe. The location of the initial yielding appears to shift both in location and from the inner surface to the outer surface as the curved tube becomes thin.The present paper extends and revises an earlier paper.⁶ It includes an approximate equation which defines the transition curve between the two locations of initial yielding.     

Plastic hinge formation in elbows and curved tubing

Cross-section flattening of a piping elbow or curved thin-walled tube may be described by four plastic hinges. The present paper presents an analysis of the plastic hinge formation using the methods of toroidal elasticity. This enables one to identify the location of first yielding which generally, but not necessarily, occurs on the inner surface of the elbow.Two mechanisms of first yielding occur. The first of these is yielding due to circumferential stress on the inner surface of the elbow. The second mechanism is yielding due to meridional stress which appears to dominate when a thin-walled tubing geometry is considered. An approximate equation is developed which defines the transition curve between the two yield mechanisms.     

Analysis and experiments on the plastic limit pressure of elbows

This paper discusses the plastic limit pressure of elbows without defects and with local thinned area in the extrados. Finite element analysis (FEA) and experiments have been used. The results of FEA show that the limit load of elbows under internal pressure increases with increasing wall thickness and bend radius of the elbow. The results are consistent with the calculated results by the Goodall formula, the maximum error is 6.58%. By data fitting of FEA, an empirical formula for the limit load of elbows with local thinned area in the extrados has been proposed, which is validated by experiments.     

Pressure of Newtonian fluid flow through curved pipes and elbows

Under conditions of high temperature and high pressure, the non-uniformity of pressure loads has intensified the stress concentration which impacts the safety of curved pipes and elbows. This paper focuses on the pressure distribution and flow characteristic in a curved 90 o bend pipe with circular cross-sections, which are widely used in industrial applications. These flow and pressure characteristics in curved bend pipes have been researched by employing numerical simulation and theoretical analysis. Based on the dimensionless analysis method a formula for the pressure of Newtonian fluid flow through the elbow pipes is deduced. Also the pressure distributions of several elbows with different curvature ratio R/D are obtained by numerical methods. The influence of these non-dimensional parameters such as non-dimensional curvature ratio, Reynolds number and non-dimensional axial angle α and circumferential angle β on the pressure distribution in elbow pipes is discussed in detail. A number of important results have been achieved. This paper provides theoretical and numerical methods to understand the mechanical property of fluid flow in elbow pipes, to analyze the stress and to design the wall thickness of elbow pipes.     

Numerical study of shock waves propagating through right angled multiple elbows

Introduction The elbow is one of the important elements used in pipe lines, and it is very important to clarify the propagating phenomena of shock waves through the elbow for engineering applications. Although some investigations of the propagating shock in the single and double elbows have been carried out[1?The working gas is air. The numbers of the grid in the computational domain are 251·(a) Type 4-1 (b) Type 4-2 Fig.3 Pressure distributions on each wall the merging with the 2nd shock…     

Elementary solutions for the propagation of ovalization along straight pipes and elbows

This paper presents an extension of the classical Von Karman's theory for the calculation of the flexibility factor of a pipe bend terminated by a straight pipe or a flange. The analysis is restricted to the linear elastic deformation behavior under in-plane bending, for elbows with specific geometric features. The propagation of ovalization is investigated both in the straight part and in the elbow. The results are presented in terms of global as well as local flexibility factors. They have been compared with computational results and other published theories.     

Nonlinear analysis and plastic deformation of pipe elbows subjected to in-plane bending

The purpose of this study is to investigate the large strain and stress analysis for pipe elbows subjected to in-plane bending moments. A finite element model for the bend was constructed and loaded taking geometric and material nonlinearities into account using (ABAQUS) nonlinear finite element code. The initiation of yielding for the opening and closing cases appears at the inside surface of the elbow crown. However, further loading causes a significant difference in strain distribution and deformed shapes. The limit moment for the opening cases is higher than that for closing due to the geometric stiffening effects.     

The interaction of pressure, in-plane moment and torque loadings on piping elbows

This study concerns the load interaction behaviour of 90° smooth piping elbows with circular cross-section and long straight tangent pipes. The finite element method is used for stress analysis of elbows having a wide range of bend and pipe factors. The main aim of the study is to establish the first yield interaction behaviour when an elbow is subjected to a combination loading of in-plane bending, torsion and internal pressure. The study shows that load interaction is influenced by pipe factor, bend radius and load coupling effect, with thinner elbows being affected to a larger degree.     

Soot oxidation kinetics under pressurized conditions

The oxidation kinetics, under different pressures, of soot samples obtained from different liquid fuels and two standards (a commercial black carbon sample and a reference diesel soot) was studied. Soot samples were generated in a flat-flame, premixed burner under heavily-sooting conditions and captured on a water-cooled stabilization plate located above the burner surface. The collected soot was oxidized using a high-pressure thermogravimetric analyzer (HTGA). TGA operation was optimized to reduce mass transfer effects by adjusting the oxidizer flow rate and initial sample mass. Further corrections for mass transfer were accomplished by computing the effectiveness factors for intraparticle, interparticle, and external mass transfer. Two pressures were evaluated (1 and 10 atm) and O₂ concentration was varied between 10 and 21%.     

Shakedown limit loads for elbows under internal pressure and cyclic in-plane bending

This paper presents elastic, shakedown and plastic limit loads for 90° elbows under constant internal pressure and cyclic in-plane bending, via finite element (FE) analysis. Effects of the elbow geometry (the bend radius to mean radius ratio and the mean radius-to-thickness ratio) and of the large geometry change are systematically investigated. By normalizing the in-plane bending moment by the plastic limit load solution of Calladine, the shakedown diagram is found to be close to unity up to a certain value of normalized pressure (normalized with respect to the limit pressure) and then to decrease almost linearly with increasing normalized pressure. The value up to which shakedown limit loads remain constant depends on the elbow geometry and the large geometry change effect. Effects of the elbow geometry and the large geometry change on shakedown diagrams are discussed.     

金属管式承压空气吸热器实验研究

对内径为6 mm,壁厚为2 mm的太阳能热发电用金属管式承压空气吸热器的热性能进行了实验研究,分析了太阳法向直接辐照度(DNI),金属管式承压空气吸热器内空气质量流量对该吸热器出口空气温度的影响。实验结果表明:在空气质量流量相同的条件下,DNI越高,金属管式承压空气吸热器出口空气温度越高,该吸热器获得的热功率越大,吸热器内空气粘性越高,吸热器内空气压力损失也越大;随着金属管式承压空气吸热器内空气质量流量逐渐减小,该吸热器出口空气温度逐渐升高;随着金属管式承压空气吸热器内空气质量流量逐渐增大,该吸热器内空气压力损失逐渐增大;金属管式承压空气吸热器热效率受DNI和空气质量流量的综合作用,且该吸热器热效率的最大值出现在DNI较低处;当金属管式承压空气吸热器内空气压力损失较大时,应增大吸热管的管径或缩小吸热管单管的管长。     

Stress intensification factors in elbows subjected to in-plane bending moments at elevated temperature

This paper reports the results of a static stress analysis in piping elbows, either with or without stiffening effects due to the sectional ovalization restraint provided by tangent straight pipes. The physical and geometrical aspects together with the loading conditions used in this study are typical of those of pipings for main cooling systems of Liquid Metal Fast Breeder Reactors (LMFBR). The aim of the study is directed towards comparing stress intensification factors in elbows subjected to pure in-plane bending moments obtained by experimental, analytical (using the ASME Section III Subsection NB 3685 detailed analysis procedures) and numerical tests. The numerical calculation was performed taking into account some nonlinearity effects due to the particular geometry of sections or load-induced phenomena, and neglecting the plastic response of the material (elastic behaviour).     

Experimental study of pressurized gas-fluidized bed heat transfer

This paper reports on an experimental study of the influence of operating pressure, in the range 150-1100 kPa, on wall-to-bed heat transfer coefficient in a bubbling fluidized bed. Both Geldart Group A and B solids were studied and the fluidizing gases were air and superheated steam. Fluidizing velocities were in the range 1-33 U_mf and wall temperatures in the range 125-275°C. Wall-to-bed heat transfer coefficients were found to increase steadily with increasing fluidizing gas velocity and not to pass through a maximum. Increase in operating pressure was found generally to result in an increase in wall-to-bed heat transfer coefficient, although the effect is probably non-linear. In the bubbling regime, the wall-to-bed heat transfer coefficient was found to change with vertical position in the bed. Wall-to-bed heat transfer coefficients decreased when the bed entered the slugging regime.     

Characterizing the crack initiation load in circumferentially through-wall cracked elbows under bending load

Ductile fracture assessments of circumferentially through-wall cracked elbows, based on the elastic–plastic J-integral concept, are discussed with particular interest in its ability and accuracy to predict experimental results corresponding to the initiation of stable crack growth. 3D non-linear finite element analysis is backed up with experimental results to determine the crack initiation load. Non-linear finite element analyses were performed considering both material and geometrical non-linearity using the advanced fracture analysis code WARP3D. Numerical analyses have been carried out to understand the role of crack tip constraint in standard specimens and the elbow component. An attempt has been made to obtain a unique multiaxiality quotient (q) for evaluation of the level of constraint. The work provides benchmark data to assist in the engineering treatment of cracked piping elbows.     

Thermal-hydraulic modeling and transient analysis of pressurized water reactors

This paper examines a new dynamic moving boundary thermal-hydraulic fuel pin model (FUELPIN) for the transient analysis of a pressurized water reactor (PWR). FUELPIN is developed to accommodate the reactor core thermal-hydraulic model of the fuel pin and adjacent coolant flow channel, with detailed thermal conduction in fuel elements. Transient analyses using a known thermal-hydraulic analysis code, COBRA, and FUELPIN linked with a PWR system analysis code show that the thermal margin gains more by a transient MDNBR approach than the traditional quasi-steady methodology for a PWR. The studies of the nuclear reactor system show that moving boundary formulation is highly suitable for the transient thermal-hydraulic analysis of PWRs.