Dished End Research Articles

Application and accuracy of shell theory in the analysis of stress and deformations in cylindrical pressure vessels

The presented study focusses on the application of the analytical shell theory to the problems of stresses and deformations in cylindrical pressure vessels. Two standard types of dished ends are investigated, torispherical and ellipsoidal. To solve the problem the membrane theory and edge effect theory is applied. The equations of deformations are formulated to calculate the forces in the shells junction. The orthotropic material model is taken into account. Two known solutions of the homogeneous Reissner– Meissner differential equations are studied. The resolved stress and deformation are compared with the numerical results of the finite element method. The accuracy of the analytical solution is highly dependent on the thickness of the pressure vessel, as well as on the shape of the dished end. According to the results discussed, the solution for the structure with torispherical dished ends is accurate only for exceptionally small thickness, beyond the typical values for industrial pressure vessels. This shortcoming has been proven to be the result of the limitations of the membrane theory, despite the thin-walled nature of the shells studied.

Study of dished end forming by hot forming Vs fully machining method

Hemispherical dished end by fully machining from hollow forging instead of conventional process like hot forming, cold forming, deep drawing, flanging and dishing. For bulk and mass production of dished ends conventional method used. But for each and every dished end with different material and different size we go for fully machining from hollow forging material. Economically, cycle time and equivalent strength to compare to conventional method.

Experimental and numerical verification of stress distribution in additive manufactured cylindrical pressure vessel — A continuation of the dished end optimization study

The presented paper refers to the recent study of shape optimization of dished ends with the aim of reducing the maximum von Mises stress. An adequate method is sought to manufacture pressure vessel models with optimized dished end. Following the results of the static tensile test, Multi Jet Fusion technology is selected to manufacture the models. After evaluating the mechanical properties of PA12 material, the dished end shape is reoptimized. Manufactured models are pressurized and strain gauge measurements are taken. Finally, the optimized stress distribution is compared with the numerical and experimental results, indicating a good agreement between them.

Stress distribution optimization in dished ends of cylindrical pressure vessels

The standard geometries of dished ends of cylindrical pressure vessels were developed at the beginning of the last century. Among them, there are ellipsoidal and torispherical geometries characterized by disadvantageous stress distribution, which is the primary determinant when designing shell structures. This paper focuses on shape optimization of dished ends with the depth equivalent to the standard ones, with the intent to minimize the maximum von Mises stress in a cylindrical pressure vessel. Referring to the Bézier curve (BC), a unique geometry of arbitrary order is developed to describe the parametric shape of the dished end. The optimization is implemented using two approaches. Initially, the fitness function is obtained analytically through the membrane theory (MT). A deterministic optimization algorithm is adopted to complete the procedure. Further, the optimization method is modified to obtain the fitness function using the finite element method (FEM). To process the solution, a genetic algorithm (GA) is employed. The obtained improvement of stress distribution is compelling while maintaining the manufacturability of the shell structure.

Evaluation of DBA-L pressure vessel design method by 2D and 3D solid models

The pressure vessel design method base on elastic analysis in ASME design code includes a stress categorization procedure. It is not obvious to distinguish the primary and secondary stresses, especially in geometric discontinuities. The DBA-L method has been proposed recently to avoid stress categorization. In this paper, the effectiveness of the DBA-L pressure vessel design method is assessed by comparing with other design methods through three vessels: a cylindrical vessel with thick flat end under internal pressure, a dished end with nozzle in knuckle region under pressure and a cylindrical-nozzle intersection. It is found that the DBA-L method successfully predicted reasonable allowable loads and can be used as an alternative method to stress categorization method.

Technological Challenges in Manufacturing of over Dimensional Stainless Steel Components of PFBR

Prototype Fast Breeder Reactor (PFBR) is liquid sodium cooled, pool type nuclear reactor with generating capacity of 1250 MWt / 500MWe. Reactor assembly consists of many large dimensional components made of special grade austenitic stainless steel material. Safety vessel and Main vessel are torispherical dished end vessels with overall height of 12.8 m and 13.4/12.9 m diameter with thickness ranging from 20 to 40 mm. Vessels approx. 111 / 135 MT with running weld length of 500 & 540 m. Inner vessel and thermal baffles are the internals of reactor assembly made of SS 316LN. Forming of dished end petals, weld overlay on the inside surface, circumference matching between the cylindrical shells, cylindrical shell to dished portion was achieved within the tolerances specified. Due to limitations of transportation, these large sized components were manufactured at PFBR site. This paper discusses the experiences gained during the manufacturing of such over dimensional components at PFBR site in meeting the stringent tolerances on various dimensions and NDE requirements.

CANISTER TESTING CHAMBER DESIGN & ANALYSIS USING FEM

Canister is used for carrying, storing and launching of missile. During this process,it is subjected to an internal pressure of 45 kg/cm 2 and external pressure of 9 kg/cm 2 . A canister testing chamber is used to test the canister for both internal and external pressures. This testing chamber is one of the most critical components in defence organisations. For testing the canister its both ends shall be closed by dummy dished ends. Testing chamber is tested for any leakages through the hinged dished end. Analysis of contact gap between this dished end and the shell of the chamber is carried using finite element method in ANSYS.

Design of pressure vessels using shape optimization: An integrated approach

Previous papers related to the optimization of pressure vessels have considered the optimization of the nozzle independently from the dished end. This approach generates problems such as thickness variation from nozzle to dished end (coupling cylindrical region) and, as a consequence, it reduces the optimality of the final result which may also be influenced by the boundary conditions. Thus, this work discusses shape optimization of axisymmetric pressure vessels considering an integrated approach in which the entire pressure vessel model is used in conjunction with a multi-objective function that aims to minimize the von-Mises mechanical stress from nozzle to head. Representative examples are examined and solutions obtained for the entire vessel considering temperature and pressure loading. It is noteworthy that different shapes from the usual ones are obtained. Even though such different shapes may not be profitable considering present manufacturing processes, they may be competitive for future manufacturing technologies, and contribute to a better understanding of the actual influence of shape in the behavior of pressure vessels.

Assessment of creep-fatigue damage at main vessel triple point of Prototype Fast Breeder Reactor after core disruptive accident

The main vessel (MV) carries all the major reactor components including core and liquid sodium filled to 12.4 m height. The reactor core along with the inner vessel is placed on the grid plate, which is supported on the core support structure (CSS). The CSS is supported on the MV through a support shell, welded to the dished end at the point where crown and knuckle joins. The CSS support shell to MV joint is called as triple point and damage at this point is of concern. The core catcher (CC) is placed below the CSS and is also supported on the CSS support shell. The triple point is subjected to a dead load of 920 t. During the unlikely event of core disruptive accident (CDA) a high dynamic pressure will act on the core catcher (CC), which in turn exerts a high load on the triple point. Also the hot molten core debris will come to the CC, which is close to the MV dished end. This will result in increase of temperature in the cold pool, which will cause significant creep damage at triple point during post accident heat removal phase. As the triple point is the only junction, which is supporting the reactor core and CC through CSS support shell, its failure can cause serious consequences to the integrity of MV. Hence, triple point is analysed to ensure its integrity during the transient pressure loading and subsequent post accident heat removal (PAHR) phase of CDA. The stress intensities during transient pressure are found to be within the limits. The subsequent creep damage during post accident heat removal (PAHR) phase is also assessed. Based on the apportioned creep damage of 0.4 for category 4 events, the triple point can be kept at a temperature of 923 K (650°C) or 973 K (700°C) effectively for a period of 1.2 × 104 h (500 days) or 662 h (27.6 days) respectively which are acceptable with comfortable margin. More details are presented in the paper.

Leak-before-break analysis of Prototype Fast Breeder Reactor main vessel

In Prototype Fast Breeder Reactor, the core is immersed in a sodium pool contained within the main vessel (MV). There is an argon cover gas space over the sodium. Top Shield supports the control plug which houses important components such as Control and Safety Rod Driving Mechanism. A core support structure welded to the bottom of MV carries the Grid plate which in turn supports the fuel subassemblies. MV is a cylindrical shell with a bottom dished end and supported at the top. Double ended guillotine rupture of MV will lead to downward movement of the core, which is in effect equivalent to withdrawal of control and safety rod and thus causing a series safety concern. It is essential to demonstrate Leak Before Break (LBB) argument for MV. LBB argument is justified if leak detection is ensured with adequate margin on critical crack length corresponding to failure by tearing instability. The material of construction of MV is SS316 LN. Towards assuring the justification of LBB argument, an isolated 5 mm deep X 200 mm long semi elliptical flaw is taken as the initial flaw and analysed under fatigue loading. A through wall crack in the argon space can be detected by sampling the nitrogen in the annular space between MV and safety vessel surrounding it. Accordingly the detectable crack length is arrived at. The critical crack length is obtained considering stable tearing. More details of the analysis and justification of LBB argument as per RCC-MR Appendix A16 are presented in the paper.

Salvation of S. S. Surge Tank for HTHP Loop

As constituents of nuclear industry, we all know the significance of the stringent specification to the practical level on the manufacture of nuclear components. More so for the primary system of High Temperature High Pressure Loop (HTHP) situated at Water & Steam Chemistry Division (WSCD). The pressurizing of the system is done by heating through immersion heaters provided in the surge tank. The surge tank, at its rated condition, has steam on the top, above the water level. The surge tank has got a l5 0 NB size nozzle at the bottom dished end. A 1500 # flange is welded to this nozzle. The heater unit of the surge tank is connected to this flange. The heater unit consists of a 150 NB, 1500 # blind flange (tube sheet) with eight number of SS U-type immersion heater pins welded to it. Welding of stainless steel heater pin is a demanding task. The task becomes even greater when the job involves welding of 16 pins with a triangular pitch of 25 mm, such as those for the high temperature & pressure loop. Actually, the tank was manufactured by a private firm. During final leak testing, it was found that there were leaks through the heater pins to sleeve welding in three of the heater pins. They could not rectify the leak. Subsequently, the rectification of the weld was referred to CWD. A novel technique was developed and due care was taken to weld the heater pins. The tank was successfully salvaged and tested hydrostatically at 170 bars and pneumatically at 7 bars. The method of fabrication of heater assembly, problems anticipated, problems encountered and measures taken to solve them are dealt with.

Performance of TMCP steel with respect to mechanical properties after cold forming and post-forming heat treatment

The paper describes the results of work done in the Finnish part of the ECOPRESS project on the mechanical properties of pressure vessels made from the TMCP steel grade P420ML2. Dished end (DE)-cylinder assemblies with diameters of 2500 mm and thicknesses of 15 and 30 mm have been examined using DE in both the cold-formed (CF) and CF and post-forming heat treated conditions. The blanks for the DEs contained welds to enable the effect of cold forming on weld metal to be evaluated. Cold forming increases both the transition temperature and the strength of the DEs. Nevertheless, toughness against brittle fracture in the CF state is good for all parts of the DEs and girth weld with T 27J<−50 °C in the absence of blank welds and <−20 °C when blank welds are present. For PFHT DEs T 27J<−50 °C even for the blank welds. T 27J was found to correlate with the fracture toughness reference temperature T 0 which can be used to determine the minimum operating temperature. The impact toughness of the CF DE can be determined by compressing plate specimens 15% and ageing 30 min at 250 °C. Such a procedure can form the basis for an additional requirement on PxxxM/ML grades when high cold forming strains are involved in vessel manufacture. Ductile fracture is not of concern, as upper shelf toughness remains high in all parts of the DE. The yield and tensile strengths of a CF DE are much greater than those of the cylinder, whereas the membrane stresses on the cylinder are greater than those on the DE. Consequently, design can be safely based on the properties of the nominally unformed cylinder. Furthermore, tensile instability will be first reached in the cylinder before it is reached in the DE, even though Y/ T is at its lowest in the cylinder. Secondary bending stresses are greatest at the DE knuckle, but the CF DE has more than sufficient ductility in bending to accommodate the bending strain. The high Y/ T of CF DE is combined with high material ductility and is therefore fully acceptable.

On the shakedown analysis of nozzles using elasto-plastic FEA

The performed shakedown calculations of a dished end with a nozzle in the knuckle region with varying internal pressure load, and two cylinder–cylinder intersections with constant moment load and varying internal pressure load are example cases for the application of the check against progressive plastic deformation as stated in the new European UFPV standard, Annex 5.B: “Direct route for design by analysis” (DBA). To calculate the shakedown limits, Melan's (lower bound) shakedown theorem is used. In this context, the usage of the deviatoric maps of stress states to obtain proper self-equilibrating stress fields is shown. Furthermore, some problems and corresponding possible solutions for performing the shakedown check using a finite element model with shell elements are stated and shown in the examples.

Failure analysis of an ammonia refrigerant condenser tube

A detailed failure analysis was conducted on an ammonia refrigerant condenser tube component that failed catastrophically during its initial hours of operation. Evidence collected clearly demonstrated that the weld between a pipe and a dished end contained a sharp unfused region at its root (lack of penetration). Component failure had started from this weld defect. The hydrogen absorbed during welding facilitated crack initiation from this weld defect during storage of the component after welding. Poor weld toughness at the low operating temperature facilitated crack growth during startup, culminating in catastrophic failure as soon as the crack exceeded critical length.

Nondestructive technique for identification of the dished end of nuclear fuel pellets

Use of an infrared technique for identifying the dished/flat ends of nuclear fuel pellets for PHWR is suggested. The studies show that this method can be used for on-line checking of the orientation of the pellets.

Using upsetting blanks of the dished end type with subsequent final stamping for increasing the quality of semifinished products

Using upsetting blanks of the dished end type with subsequent final stamping for increasing the quality of semifinished products

Stress state and rational design of spherical dished ends with nozzles

1. The structures of the nodal sections of the dished ends designed in accordance with the compensation principle and design restrictions of the standards are charcterized by the permissable level of the maximum working stresses. 2. In varying the fraction of the reinforcing metal of the nozzle section situated in the wall of the dished end from 50 to 80% the level of the maximum stresses in the section changes only slightly. 3. The structures containing 70–80% of reinforcing metal in the wall of the nozzle are more rational from the viewpoint of reducing the metal requirement and have sufficient strength at the same time. 4. The permissible value of the ratio d/D specified by the standards can be increased from 0.3 to 0.5 without reducing the strength of the nozzle section.

Optimizing the engineering planning of dished end production on rolling machines

Optimizing the engineering planning of dished end production on rolling machines

The strength and deformations of torispherical ends for glass-reinforced plastic pressure vessels—Part 2: Effect of torisphere geometry for ends of fixed head height

Four further glass-reinforced plastic cylindrical pressure vessels with torispherical dished ends have been tested to destruction. Together with two vessels already reported on in Part 1 of this paper, these specimens form part of a group with the same head height of 0·25 m but with three different torus radii of 0·1 m, 0·146 m and 0·188 m, giving crown radii of 0·71 m, 0·8 m and 1·0 m, respectively (two vessels of each geometry were tested). As in Part 1, results from the tests were compared with those suggested by the current UK design code (BS 4994) and the predictions of a computer-based elastic stress analysis (BOSOR 4). In contrast to BS 4994, BOSOR 4 indicates that there is little difference in strength between dished ends with the two larger knuckle radii. A torus radius of 0·1 m, however, does produce a significant increase of maximum stress and strain. In fact, of the four additional vessels tested, only those two of this latter geometry ultimately failed in the dished end, those of knuckle radius 0·146 m rupturing in the cylinder.

Elasto-plastic analyses of cylindrical pressure vessels with reversed dished ends

Finite element stress analyses are presented which allow for elastic and elasto-plastic material behaviour for axisymmetric problems of pressure vessels using isoparametric quadrilateral elements with linear, parabolic and cubic displacements. The traditional method of analysis and design of cylindrical pressure vessels with reversed dished ends is based on the well known British Standard BS 5500 Code. 1 The stresses and displacements, especially at and near the junctions, are of great interest to designers. In view of the immense usefulness of such containers, a detailed post yield study has been made based on the stress-strain idealisation for isotropic strain hardening materials—H′= 0·0047E and Von Mises and Tresca yield criteria. The basis for the prediction of load increment sizes for the elasto-plastic analysis and the upper bound for collapse pressure are presented, as well as the excessive deformation and shakedown criteria suitable for the design of reversed dished end containers.