Torispherical Head Research Articles

Pressure Vessel Design by Design by Analysis Route

Pressure vessels are conventionally designed based on the Design by Rule (DBR) approach. Standard vessel geometries are designed using simple formulae and charts, formulated as standards and codes based on the rules proposed in the ASME Boiler and Pressure Vessel Code and the European Standard prEN13445-3. The stress categorization problem faced employing DBR methodology was overcome by employing Limit Load Analysis using the DBA approach. A simple unfired vertical cylindrical pressure vessel with torispherical pressure head and Y-forged skirt support was analyzed for its structural integrity using ANSYS software. The results obtained for two different materials, high strength steel P500-QT and the conventional low strength steel P355 employing DBA approach was compared with the calculated results using the DBR approach. The maximum allowable pressure (PMAX) for P500-QT material was found to be 2.5X the maximum pressure calculated using the DBR approach as per ASME codes and 3X times as per EN13445-3 standard. For P355 material the maximum allowable pressure (PMAX) was found to be 2.32X the maximum pressure calculated using the DBR approach as per ASME codes and 2.6X times as per EN13445-3. The DBR methodology proves to be highly conservative whereas the use of DBA leads to less conservative design parameters.

PROTOTYPE ALAT BEJANA PEMBAKARAN

The process of designing a pyrolysis reactor vessel with an electric heating system is intended to design a pyrolysis reactor vessel functioned as a heating chamber for pyrolysis test materials to convert biomass into energy. The vertically-designed torspherical vessel consists of a torispherical shell and head, with a temperature control system designed using a PID control temperature device as its main controller and uses SSR as a voltage controller actuator and uses thermocouple as its temperature sensor and on its heating system using electric heating element. obtained from the test results is the heating rate obtained is 0.25³C / sec with the maximum temperature obtained 480˚C within 30 minutes and the cost required for a single process of Rp 5,500,

Shakedown analysis of a torispherical head with a piping nozzle under combined loads by the stress compensation method

Shakedown assessment is an important task in determining the load-bearing capacity of structures and evaluating their safety. The traditional shakedown analyses, which are based on the upper or lower bound shakedown theorem to establish the mathematical programming formulation and solve an optimisation problem, are difficult to apply in engineering practice owing to limitations of the computing scale and computational efficiency. In this study, a numerical shakedown analysis using the recently developed stress compensation method (SCM) is performed for a torispherical head with a piping nozzle, which is a typical structural component of pressure vessel equipment. The loads applied to the structural component include an internal pressure, axial force, twisting moment, out-of-plane and in-plane bending moments, and thermal loading, all of which vary independently of each other. Two- and three-dimensional strict shakedown boundaries for the torispherical head under different combinations of these loads are presented and analysed. In addition, the effect of a temperature-dependent yield strength on the shakedown domain is also investigated. These investigations demonstrate that the proposed SCM is capable of solving the practical shakedown problem for structures under complicated combined loads in industrial applications. The obtained results can provide guidance for the safe structural design of torispherical heads with piping nozzles.

Effect of Head Types on the Free Vibration and Fatigue for Horizontal LPG Pressure Vessels

Pressure vessels are the heart of plants and oil refineries stations. In many engineering applications such vessels can be subjected to periodic loading either internally due to the charging and discharging process or externally due to the excitation from other nearby components such as pumps, compressors or from seismic. So that in spite of a good design according static assumption it may be critical in dynamics. In this work a horizontal pressure vessel with accessories subjected to liquefied petroleum gas pressure LPG is considered. Three models of different head types are investigated herein namely; Deep torispherical, Elliptical 2:1 and Hemispherical. The design and material selections are chosen as per ASME. For practical service many accessories are attached to the vessel such as manhole, supports, inlet and outlet opining. Finite Element method via ANSYS R18.2 is introduced for the numerical analysis. The fatigue life in case of fully reversed cyclic loading are estimated and located. Vibration characteristics such as mode shapes and natural frequencies for the lowest five modes are evaluated and compared. It is found that the fatigue life can be increased as higher as 180% for hemi- spherical head as compared with deep torispherical head pressure vessel and the lowest four natural frequencies are nearly identical for all models, however significant change observed in the fifth natural frequency.

Adoption of in-vessel retention concept for VVER-440/V213 reactors in Central European Countries

An in-vessel retention (IVR) concept was proposed for standard VVER-440/V213 reactors equipped with confinement made of reinforced concrete and bubbler condenser pressure suppression system. This IVR concept is based on simple modifications of existing plant technology and thus it was attractive for plant operators in Central European Countries. Contrary to the solution that was adopted before at Loviisa NPP in Finland (two units of VVER-440/V213 reactor with steel confinement equipped with ice condenser), the coolant access to the reactor pressure vessel from flooded cavity is enabled via closable hole installed in the centre of thermal shield of the reactor lower head instead of lowering this massive structure in the case of severe accident. As a consequence, the crucial point of this IVR concept is narrow gap between torispherical lower head and thermal and biological shield. Here the highest thermal flux is expected in the case of severe accident. Thus, realistic estimation of thermal load and corresponding deformations of reactor wall and their impact on gap width for coolant flow are of primarily importance. In this contribution the attention is paid especially to the analytical support with emphasis to the following points:1) ∗Estimation of thermal loads acting on the inner reactor surface;2) ∗Estimation of structural response of reactor pressure vessel (RPV) with emphasis on the deformation of outer reactor surface and its impact on the annular gap between RPV wall and thermal/biological shield;3) ∗Analysis of external reactor vessel cooling. For this purpose the ASTEC code was used for performing analysis of core degradation scenarios, the ANSYS code for structural analysis of reactor vessel subjected to thermal load from corium, and RELAP5 code for assessment of external reactor vessel cooling. Finally, implementation of IVR system in NPPs in Czech Republic and Slovakia is shortly described.

Investigation of the Effects of Geometric and Load Perturbation to Buckling in Multilayered Torispherical Pressure Vessel Heads

The object of this paper is to investigate the effects of geometry and load perturbation to buckling in multilayered pressure vessel heads. The pressure vessel head in concern is thin walled torispherical geometry. Geometric and load perturbation can alter both the critical load for buckling and the buckled shape. Two and three layered torsispherical heads are considered. Two layered models include steel–aluminum and titanium–aluminum configurations and three layered models include copper–steel–copper configuration. Internally pressurized three-dimensional torispherical pressure vessel head model that is previously used in literature is constructed. As a first step eigenvalue solutions are obtained for each model. After this instability solutions with large deformation effects are conducted to obtain more realistic instability pressure values nonlinear. The solution is performed by finite element program ANSYS Workbench. In nonlinear analyses, perfectly plastic material model is used. It is concluded that geometric and load perturbations cause the instability pressure to decrease and cause the structure to buckle at a lower pressure value. It is also observed that for steel-aluminum configuration geometric perturbation is more critical than load perturbation whereas for aluminum-titanium the reverse is valid.

Elastoplastic Analysis of Novel Parabola-Arc-Shaped Head for Internal Pressure Vessel

In this paper, the elastoplastic stress analysis of a novel parabola-arc-shaped head subjected to internal pressure has been carried out using finite element method. Limit loads and burst pressures are obtained for various geometric parameters and compared with the conventional torispherical and ellipsoidal heads. For the same middle diameter and thickness, the novel parabola-arc-shaped head shows better mechanical performance than the torispherical head. The burst pressure is mainly determined by the size of cylinder and the burst always occurs in cylinder. The head can improve the burst load when the cylinder is relatively short. The improvement of the novel parabola-arc-shaped head is almost the same as the ellipsoidal head, while the torispherical head is slightly inferior. As the novel parabola-arc-shaped head can be more easily formed with less material consumed compared to the conventional ones, it should thus be applicable in engineering practice.

Buckling of thin-walled torispherical heads in water heater tanks

The buckling strength of a thin-walled torispherical head in a residential electric water heater tank was investigated by both experimental and finite element analyses. Three water heater tanks pressurized with water were tested, and the strains on the heads and the pressure variations were measured and recorded. Finite element analysis was used to predict the buckling of the torispherical head. The effect of the imperfection induced by the contact nonuniformity between the torispherical head and the shell on the buckling of the structure is included. Good agreement between the test and finite element results shows that finite element models used in this paper are viable to predict the buckling pressure of a thin-walled torispherical head in a water heater tank. The results also show that the contact between the bottom head and the shell has a reinforcing effect on the buckling strength of the head. The contact imperfection will produce a dent adjacent to the knuckle region when the head buckles. The buckling pressure of the head perfectly contacting with the shell is 6.88% higher than that without contacting with the shell. The obtained results provide reference for the design and manufacture of water heater tanks.

Strain-hardening Characteristic and Limit Load Analysis of S30408 Torispherical Head

With the aid of the magnetic measuring instrument FMP30,the deformation induced martensite contents(DIMC) of S30408 plate tensile specimen under different plastic deformation are measured to determine the relationship between the DIMC and the plastic strain.The DIMC of the dished head is measured for the inner vessel of a cryogenic liquid semi-trailer.The DIMC distribution along meridional direction is simplified to correlate with plastic strains in different region of the head due to process history.According to the bygone plastic strain,the stress-strain curve for every region of the head is determined for the ultimate bearing capacity analysis of the structure by nonlinear finite element method.Compared with the results obtained by the two other inelastic modes(considering the strain strengthening characteristics based on the true stress-strain relationship without bygone plastic strain in consideration;Elastic perfect plastic(EPP) mode without strain strengthening in consideration),it is found that,for the dished head made of S30408,the collapse load and the limit load with the strain strengthening characteristics in consideration are greater than that with the EPP model.The strain strengthening characteristics based on process history has little effect on the collapse load,but great effect on the limit load by bitangent method.It can significantly improve the limit load of the structure.

Optimal Design of the Large-Diameter Spinning Torispherical Head

Two important parameters of torispherical head that are (interior radius of spherical crown area) and r (interior radius of transition corner) have been optimized by the module of the large general-purpose finite-element software ANSYS, targeting the strength and stability of the head. This paper provides an optimized torispherical head, which improves the stability of the edge of the head with acceptable strength of the head. The procedure is generally applicable as a design tool for optimal design.

Simulation and experimental work on manufacturing torispherical heads in explosive hydro-forming process

This study presents a numerical investigation on the deformation of the circular blanket against a male die under impulsive loading to form a torispherical heads shape. A finite element model was developed and verified with experimental tests for the explosive forming of the torispherical heads made of AA5083 aluminum alloy in the framework of LS-DYNA crash simulator software. The nature of the deformation was turned from the stretching to the buckling and compression of the specimen by using a male die, which is a novel concept in the high speed forming processes. Johnson-Cook (JC) and Modified Zerilli-Armstrong (MZA) constitutive equations were used to describe the behavior of the specimen in a high strain rate forming process with different stress status. Most of the experimentally observed material behaviors simulated well in pure tension or compression tests, while the transient zone was not adequately described. The predicted width for the transient rim is considerably smaller than experimental measurements. The blast loading process including the underwater detonation and the interaction with the specimen simulated using Arbitrary Lagrangian-Eulerian formulation as well as cavitations and reloading effect. The simulation results for blast loading verified base on Cole’s relation for the underwater detonation of small charges, show a good agreement of 95% accuracy. Key words: Explosive hydro-forming, male die, arbitrary Lagrangian-Eulerian formulation, torispherical head, Johnson-Cook, Zerilli-Armstrong.

Investigation of the effects of perturbation forces to buckling in internally pressurized torispherical pressure vessel heads

The object of this paper is to investigate the effects of perturbation forces to buckling in pressure vessel heads. The pressure vessel heads in concern are confined to torispherical geometry with thin walls. Perturbation forces can alter not only the critical load for buckling but the buckled shape as well. In this paper in addition to previously used perturbation model, three more different perturbation force configurations are applied to the knuckle of the vessel. Internally pressurized three-dimensional torispherical pressure vessel head model that is previously used in literature is constructed and finite element program ANSYS Workbench is used for the solutions. First of all eigenvalue solutions are performed for each model. Then nonlinear instability solutions are conducted to obtain more realistic instability pressure values. For the nonlinear analyses not only large deformation static analyses but also large deformation transient analyses are conducted. For nonlinear analyses, perfectly plastic material model is used. It is concluded that instability pressures obtained by transient analyses are closer to plastic pressure values by PWC and ASME TES criteria and perturbation models increase instability pressure and equivalent plastic strain values.

Stress analyses for reactor pressure vessels by the example of a product line '69 Boiling Water Reactor

Abstract The reactor pressure vessels (RPV) of boiling water reactors (BWR) belonging to the product line '69 have unusually designed heads. The spherical cap-shaped bottom head of the vessel is welded directly to the support flange of the lower shell course. This unusual construction has led repeatedly to controversial discussions concerning the limits and admissibility of stress intensities arising in the junction of the bottom head to the cylindrical shell. In the present paper, stress analyses for the design conditions are performed with the finite element method in order to determine and categorize the occurring stresses. The procedure of stress classification in accordance with the guidelines of German KTA 3201.2 and Section III of the ASME Code (Subsection NB) is described and subsequently demonstrated by the example of a typical BWR vessel. The accomplished investigations yield allowable stress intensities in the considered area. Additionally, limit load analyses are carried out to verify the obtained results. Complementary studies, performed for a torispherical head, prove that the determined maximum peak stresses in the junction between the bottom head and the cylindrical shell are not unusual also for pressure vessels with regular bottom head constructions.

Numerical analysis of the effect of torispherical head on the buckling of pressure vessels

Effect of torispherical head on the buckling of pressure vessels was investigated by finite element (FE) method. The FE method with use of nonlinear buckling analysis was applied to predict the critical buckling Load. The influences of geometrical parameter such as thickness, knuckle radius and diameter of cylindrical part, on the buckling of heads have been studied. The Arc Length method which can control the load level, the length of the displacement increment and the maximum displacement was been used. By verification performed with the European Convention for Constructional Steelwork (ECCS) code, it was confirmed that the nonlinear buckling analysis could assure accurate results for buckling strength. It was shown that geometrical imperfections had little effect on buckling strength.

Stress Classification Using the r-Node Method

The ASME Code Secs. III and VIII (Division 2) provide stress-classification guidelines to interpret the results of a linear elastic finite element analysis. These guidelines enable the splitting of the generated stresses into primary, secondary, and peak. The code gives some examples to explain the suggested procedures. Although these examples may reflect a wide range of applications in the field of pressure vessel and piping, the guidelines are difficult to use with complex geometries. In this paper, the r-node method is used to investigate the primary stresses and their locations in both simple and complex geometries. The method is verified using the plane beam and axisymmetric torispherical head. Also, the method is applied to analyze 3D straight and oblique nozzles modeled using both solid and shell elements. The results of the analysis of the oblique nozzle are compared with recently published experimental data.

Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Element Analyses

The procedures described in this paper for determining a limit load is based on Mura’s extended variational formulation. Used in conjunction with linear elastic finite element analyses, the approach provides a robust method to estimate limit loads of mechanical components and structures. The secant modulus of the various elements in a finite element discretization scheme is prescribed in order to simulate the distributed effect of the plastic flow parameter, μ0. The upper and lower-bound multipliers m0 and m′ obtained using this formulation converge to near exact values. By using the notion of “leap-frogging” to limit state, an improved lower-bound multiplier, mα, can be obtained. The condition for which mα is a reasonable lower bound is discussed in this paper. The method is applied to component configurations such as cylinder, torispherical head, indeterminate beam, and a cracked specimen.

An assessment of ASME III and CEN TC54 methods of determining plastic and limit loads for pressure system components

The paper considers three different pressure system components—a nozzle in a torisphere subjected to moment loading, a piping branch junction subjected to out-of-plane moment loading and an unpierced torispherical head under pressure loading. The results from non-linear, finite element, stress analyses are used to compare the limit and plastic loads obtained using the ASME III twice-elastic-slope and the CEN TC54 tangent intersection definitions. The results highlight the difficulties involved in quantifying limit loads and plastic loads for such components.

Nozzles in the knuckle region of a torispherical head: limit load interaction under combined pressure and piping loads

Limit loads are assessed for a piping nozzle in a Klöpperböden torispherical drumhead. The particular concern is when the nozzle is located in the knuckle region of the head. Individual limit loads for internal pressure and the four nozzle loads are presented. Limit load interaction plots for pressure versus nozzle axial force, in-plane moment, out-of-plane moment and torsion, and for in-plane moment versus out-of-plane moment are also presented. The results are discussed in the light of design code rules for load interaction.

Fully stressed head of a pressure vessel

This work is devoted to a head of a vessel charged with internal uniform pressure. The analysis is aimed at finding a shape of the head that ensures its full charge with stresses. In a classical torispherical or ellipsoidal head the region of its joint with the cylindrical shell is loaded with shear force and bending moment as a result of the forced consistency of displacements of both parts of a vessel. The load causes high bending stresses in the area of the joint. Therefore, a shape of a head meridian is sought for which the shear force and the bending moment approach zero. Only membrane state stresses should occur in such a structure. The mathematical description is based on the theory of shells, taking account of boundary disturbances. The numerical solution determines the sought-after shape of the head and its minimal relative convexity.

Nozzles in the knuckle region of a torispherical head: Stress levels and load interaction effects

The results of a limited parametric study on the stress levels in knuckle encroaching nozzles in a Klöpperböden torispherical head due to pressure and nozzle loads are presented. The results give support to the CEN TC 54 procedure which requires thickening of the knuckle region for such nozzles for pressure loading. Stress levels due to nozzle loads are shown to be of the same order of magnitude as those in the equivalent axisymmetric nozzle. Studies of interaction diagrams have confirmed the CEN TC 54 proposal for combined loading in axisymmetric nozzles but have shown that a linear interaction rule should be recommended for non-axisymmetric nozzles in heads.