Ellipsoidal Heads Research Articles

A new analytical tool for the elastic/plastic buckling design of pressure vessels subjected to external pressure

This paper deals with the elastic/plastic buckling design of pressure vessels under external pressure loading. The objective is to build a simple analytical tool devoted to the elastic and elastoplastic buckling analysis of pressure equipments. This tool is aimed to provide the critical external pressure of cylindrical pressure vessels with ellipsoidal (or possibly hemispherical) heads. Depending on the geometry of the equipment and material parameters, the first buckling pressure may involve either the cylindrical shell or the closure ends, in the elastic or plastic range. The calculation tool will be thus based on a series of exact or approximate analytical solutions of the critical pressure of each part of the considered equipment. In this paper, the elementary shell structures involved in such pressure equipments are first individually examined. The fundamental critical pressures for each of them are recalled or introduced, both in elasticity and plasticity. The new solutions are validated against reference numerical results obtained through finite element computations. Then, approximate solutions of the critical pressure are derived for the same shells, taking account of specific boundary conditions (and not idealized ones, as before) due to the presence of the remaining part of the equipment. In the end, a VBA Excel software is developed. It is able to provide the mappings of the buckling mode type and the corresponding critical pressures for large ranges of geometric and material parameters in a very efficient way. These analytical solutions are finally confronted to numerical calculations performed on complete pressure equipments and they are shown to give quite reliable results. A discussion is also initiated on the use of such a program to update the current design rules in this scope of application.

Research on failure model and safety boundary of ellipsoid lower head for SMR

In this paper, the common ellipsoidal lower head in SMR is taken as the research object, the original hemispherical lower head model is improved and developed, and the ellipsoidal lower head geometric model is established. Based on the failure mechanism of the ellipsoidal lower head, the stress failure model is established, and the accuracy of the model is verified by OLHF-1 experiment. Blackout accident and LOCA as the research objects of high pressure meltdown and low pressure meltdown respectively, the failure characteristics of ellipsoidal lower head in the late stage of severe accidents were analyzed, focusing on the stress, strain and temperature variation characteristics of lower head, and the safety boundary of head failure under typical accidents was calculated. Through the research of this paper, the technical problem of the lack of modeling ability of the ellipsoid lower head in the integrated program of severe accidents is solved, which lays a technical foundation for the design and development of the ellipsoid lower head and the coping strategy of the lower head failure.

Design and simulation of 30 000 tons per year of cumene plant from natural gas field

Abstract The research considers the design and simulation of 30 000 tons per year of cumene plant using Aspen HYSYS as the simulation tool. The feed (material content) used is the characterized natural gas from Utorogu Gas Field with composition of 0.9019 methane, 0.0694 ethane, 0.0209 propane, 0.00361 n-butane, 0.00414 i-butane, 0.00005 n-pentane and 0.00007 i-pentane. The cumene plant consist of the cryogenic distillation column, de-hydrogenator (Continuous Stirred Tank Reactor), Alkylator (Plug Flow Reactor), storage tanks, separators, pumps, heat exchanger and mixers. The size/design models of basic plant units such as de-hydrogenator, alkylator, separators, storage tanks and distillation column were developed using the principles of mass and energy balance. The result of design or size specifications in terms of equipment diameter of basic plant units obtained from HYSYS simulation are 0.8 m and 0.319 m for the cryogenic and cumene columns; 1.931 m, 2.244 m and 1.366 m for the propane, propene and cumene storage tanks; 1.868 m and 2.076 m for the de-hydrogenator and alkylator; 1.931 m and 2.146 m for propene and cumene separators respectively. The power or capacity of propane and propene pumps configured in the plant are 0.02 kW and 0.005 kW respectively. The result of the reactor and distillation column thickness specification to withstand corrosion, pressure or stress during plant operation in terms of cylindrical shell and ellipsoidal doomed head are 17.36 mm and 4.31 mm respectively. The economic evaluation (overall cost) including the cost of utilities, catalyst, operating, and maintenance for entire plant is $ 3.004 M.

Design of continuous transition line pattern between layers of composite pressure vessel

To realize efficient and stable continuous transition between different winding process layers of composite pressure vessels. This article uses the non-geodesic winding equation to propose a transition layer design method for composite pressure vessel shells with circular cross-section core molds and ellipsoidal heads. Firstly, the fourth-order Runge–Kutta method is used to solve the non-geodesic stabilized winding pattern and then analyze different regions’ transition ability. Established a calculation model to determine the corresponding transition winding trajectory according to the known core mold shape and fiber position and carried out computer image simulation of different modes of transition layer patterns, and finally carried out experimental verification of 35 MPa composite pressure vessel based on the simulation. The results show that different regions of the core mold have different abilities to change different starting winding angles, and the design of the transition process layer based on this law can save the area needed for transition. This method realizes the smooth transition of different process layers; the fiber of the transition layer does not slip in the actual winding process, and the actual pattern of the winding is consistent with the simulation results, which saves 20.8% of the winding time, and effectively improves the automation of the composite pressure vessel winding process.

Optimization and experimental validation of reinforcing fibers winding pattern for carbon/carbon composite crucible preform

In order to address the problem of transition slip between the cylindrical segment and the ellipsoidal head segment of the carbon/carbon composite crucible preform with asymmetrical structure during the winding process, a winding pattern combining geodesic and non-geodesic is presented innovatively. Firstly, the formulae for the winding angle and the winding central rotation angle of the crucible cylindrical segment and the ellipsoidal head segment are established, and the fourth-order Runge-Kutta numerical method is employed for parametrical design. The two-tangent point winding path is determined by analyzing the effect of the cylindrical segment’s winding pitch, different ellipsoidal head segment heights, and slip coefficient on the winding angle. Secondly, the needle disk winding method is proposed to address the slight winding angle at the open end of the cylinder, making it easier to hang the yarn. Finally, the experiment on dry yarn winding of 3k carbon fiber (linear density: 198 g/km) is carried out. The results indicate that the relative error rate between the actual winding angle and the theoretical design angle differs by no more than 1.66%, demonstrating that carbon fibers can be stably and uniformly wound onto the surface of the carbon/carbon composite crucible preform. Compared to the traditional manual winding method, the winding pattern enhances winding efficiency, ensures carbon fibers’ uniformity and structural stability, and provides a new technological approach to producing high-performance composite materials.

Libanophlebotomites ramyi, a new genus and species of phlebotomine sandflies from Lower Cretaceous Lebanese amber (Diptera: Psychodidae: Phlebotominae)

Libanophlebotomites ramyi gen. et sp. nov. is characterised, illustrated, and described from the lower Barremian amber of Qanat Bakish (Baskinta, Lebanon). It represents the first phlebotomine fly with slightly ellipsoid head without bump on occiput, round wing tip, and legs very slightly shorter than body length. The discovery of this Cretaceous psychodid fly improves our knowledge of the palaeobiodiversity of sandflies.

The sizing and suitability of nonspherical ellipsoid humeral heads for total shoulder arthroplasty

Total shoulder arthroplasty (TSA) implants have evolved to include more anatomically shaped components that better replicate the native state. The geometry of the humeral head is nonspherical, with the frontal diameter of the base of the head being up to 6% larger than the sagittal diameter. Despite this, most TSA humeral head implants are spherical, meaning that the diameter must be oversized to achieve complete coverage, resulting in articular overhang, or portions of the resection plane will remain uncovered. It is suggested that implant-bone load transfer between the backside of the humeral head and the cortex on the resection plane may yield better load-transfer characteristics if resection coverage were properly matched without overhang, thereby mitigating proximal stress shielding. Eight paired cadaveric humeri were prepared for TSA by an orthopedic surgeon who selected and prepared the anatomic humeral resection plane using a cutting guide and a reciprocating sagittal saw. The humeral head was resected, and the resulting cortical boundary of the resection plane was digitized using a stylus and an optical tracking system. To simulate optimal sizing of both circular and elliptical humeral heads, both circles and ellipses were fit to the traces. Two extreme scenarios were also investigated: upsizing until 100% total coverage and downsizing until 0% overhang. By switching from a spherical (circular) to an ellipsoid (elliptical) humeral head, a small, 2.3%±0.3% increase in total coverage occurred (P<.001), which led to a large, 19.5%±1.3% increase in cortical coverage (P<.001). Using a circular head resulted in 2.0%±0.1% greater overhang (P<.001), defined as a percentage of the total enclosed area that exceeded the bounds of the humeral resection. As a result of increasing the head size until 100% resection coverage occurred, the ellipse produced 5.4%±3.5% less overhang than the circle (P<.001). When the head size was decreased until 0% overhang occurred, total coverage was 7.5%±2.8% greater for the ellipse (P<.001) and cortical coverage was 7.9%±8.2% greater for the ellipse (P=.01). Cortical coverage was greater for circular heads when the head size was shrunk below -2.25% of the optimal fitted size. Reconstruction with ellipsoid humeral heads can provide greater total resection and cortical coverage than spherical humeral heads while avoiding excessive overhang; however, cortical coverage can be inferior when undersized. These initial findings suggest that resection-matched humeral heads may yield benefits worth pursuing in the next generation of TSA implant design.

Strength of a cylindrical pressure vessel with individual ellipsoidal dished heads

The paper is devoted to the static stress analysis of a cylindrical tank closed with two non-classical dished heads. The description of the geometry of the dished head in the form of super-ellipsoid is provided containing two dimensionless parameters to control the depth and curvature of the ellipsoid. The equivalent stress distribution along the meridian of the head is calculated analytically and numerically with the use of the finite element method. Based on the analysis of the stress in the whole tank it can be concluded that the replacement of the classical ellipsoidal head with the super-ellipsoidal one may decrease the edge effect at the junction of the two shells. This positive effect increases with the increase of the depth of the head.

Single pressure transducer probe for 3D flow measurements

A new method of measuring 3D flow with a single pressure transducer mounted inside the head of a single probe is presented in this paper. The 3D flow field around the hemispherical or ellipsoidal probe head is used to derive the 3D flow vector in virtual 5-sensor mode. A pressure tap located in the vicinity of the probe head connects the instantaneous pressure of the measurement volume to the pressure transducer. By turning the probe to five different positions around the axis of the stem, a set of five pressures is formed. The relevant flow parameters such as total and static pressure, yaw and pitch angle as well as Mach number are derived from these five pressures using the proposed calibration model. A selection of six different probe head geometries with different pressure tap positions have been manufactured and calibrated in a free jet facility in order to find the ideal probe geometry. The results of the steady probe calibration showed that the probe captures 3D flow at a slightly higher error band compared to other probe techniques such as pneumatic multiple hole probes. A summary of the achieved model accuracy for each probe is given. Finally, the calibration model can be extended to any single sensor cylindrical probe, provided that the pressure coefficient shows a measurable variation with pitch angle.

Residual-stress relaxation mechanism and model description of 5052H32 Al alloy spun ellipsoidal heads during annealing treatment

Marginal-restraint mandrel-free spinning is an advanced technology for manufacturing ellipsoidal heads with large diameter-thickness ratios. Nevertheless, the spinning-induced residual stress, which greatly influences the in-service performance of spun heads, should be removed. In this study, the effects of annealing on the residual-stress relaxation behavior of 5052H32 aluminum alloy spun heads were investigated. It is found that the residual stress first rapidly decreases and then remains steady with the increase in annealing time at the tested annealing temperatures. The relaxation of the residual stress becomes increasingly obvious with the increase in annealing temperature. When the annealing temperature is less than 220 °C, there are no obvious changes in grain size. Moreover, the spinning-induced dislocations are consumed by the static recovery behavior, which decreases the residual stress during annealing. When the annealing temperature is approximately 300 °C, the broken grains transform into equiaxed grains. In addition, static recrystallization and recovery behaviors occur simultaneously to promote the relaxation of the residual stress. Considering the different stress relaxation mechanisms, a model based on the Zener-Wert-Avrami equation was established to predict the residual-stress relaxation behavior. Finally, the optimized annealing temperature and time were approximately 300 °C and 30 min, respectively.

Effect of Nucleation Density Model on CHF of Curved Surface

In the event of a serious accident, external cooling can be applied to the lower head of the reactor pressure vessel (RPV) in order to reduce the possibility of damage to the lower head. However, there will be great heat flow surrounding the lower head of the RPV, so external cooling may cause subcooled boiling, which gathers bubbles and deteriorates heat exchange, even burns out. This research uses ANSYS Fluent to calculate the critical heat flux (CHF) for external cooling of the RPV, and it is found that the nucleation density model studied by Basu Warrier and Dhir can be well applied to the calculation of CHF on the spherical surface. By comparing the CHF of the spherical and ellipsoidal lower head, it is believed that the CHF characteristics of the ellipsoidal lower head are completely different from the spherical structure. The experimental and calculation results of the spherical structure cannot be used to infer the numerical value and variation of the ellipsoidal structure.

Design of externally pressurized ellipsoidal heads with variable wall thicknesses

This study focused on the buckling and strength of ellipsoidal heads with variable wall thicknesses under uniform external pressure. The wall thickness of ellipsoidal heads was designed according to the isostrength principles. The wall thickness distribution of revolution for thin shells were proposed, and the effect of the thickness distribution on the strength of the ellipsoidal head is explored. The buckling of the ellipsoidal heads with variable thicknesses and constant thicknesses were evaluated numerically using the modified Riks method, and the effect of the ellipticity on the buckling performance of the ellipsoidal head was explored and the optimal ellipticity was presented. The results revealed that the buckling load of the ellipsoidal head with variable wall thickness was approximately 17% higher than that of the ellipsoidal head with constant wall thickness, while the volume decreased by 5%. This study can guide the structural design of ellipsoidal heads with variable wall thicknesses.

Comparison of Ellipsoidal and Equivalent Torispherical Heads Under Internal Pressure: Buckling, Plastic Collapse and Design Rules

Abstract Ellipsoidal and torispherical heads, whose geometric shapes are close, are usually used as end closures of internally pressurized vessels. In pressure vessel codes, for example, ASME BPVC Section VIII and EN13445-3, ellipsoidal heads are designed as torispherical heads using geometric equivalency approaches. However, the difference between ellipsoidal and equivalent torispherical heads has not been studied in detail. In this paper, we first investigate shape deviation between the two types of heads. Then we compare elastic–plastic behaviors between ellipsoidal and equivalent torispherical heads as well as their failure modes, i.e., buckling and plastic collapse (bursting). It is found that ellipsoidal heads have more buckling resistance than equivalent torispherical heads, indicating that the current design rules for buckling of ellipsoidal heads based on the geometric equivalency approaches result in uneconomical design. In addition, experimental and numerical results show that such heads experience geometric strengthening. The finite element (FE) method considering the effect of geometric strengthening provides a good prediction of plastic collapse pressure. However, the current design equation for bursting does not consider the effect of geometric strengthening, also leading to uneconomical design. Therefore, in order to avoid uneconomical design, we recommend that (1) with respect to buckling of ellipsoidal heads, a new design equation be proposed rather than implementing the geometric equivalency approaches, and (2) the current design equation for bursting be deleted, and a new design equation, considering the effect of geometric strengthening, be proposed for bursting of ellipsoidal and torispherical heads.

Effects of spinning parameters on microstructures of ellipsoidal heads during marginal-restraint mandrel-free spinning

Marginal-restraint mandrel-free spinning is an advanced technology for manufacturing ellipsoidal heads with large diameter-thickness ratios. The effects of spinning parameters on the forming accuracy of ellipsoidal heads have been studied, and optimized spinning parameters have been obtained. The microstructure evolution of a workpiece is usually very complicated in the spinning process. In this work, the influence of spinning parameters on the microstructures of two-pass spun ellipsoidal heads is studied. It is found that the forming angle and feed rate of the first pass, angle between passes, and feed rate of the second pass significantly affect the microstructures. Meanwhile, the evolution rule of the microstructures near the inner and outer surfaces of the spun parts is almost consistent. A large forming angle, large angle between passes, or large feed rate of the second pass are beneficial to obtain uniform microstructures. A small or large feed rate of the first pass reduces the microstructure uniformity. To improve the microstructure uniformity between the inner and outer surfaces, the optimized spinning parameters are determined.

A simple formula for prediction of plastic collapse pressure of steel ellipsoidal heads under internal pressure

Plastic collapse is a critical failure mode considered in the design of ellipsoidal heads under internal pressure. It is significant to develop a formula to calculate plastic collapse pressure of ellipsoidal heads. First, we use a finite element method to calculate plastic collapse pressure, taking into account the effects of strain hardening and geometric strengthening. Second, we investigate the effects of material and geometric parameters on plastic collapse pressure. Based on parametric study, a simple formula is proposed for predicting plastic collapse pressure of ellipsoidal heads. Finally, in order to verify the accuracy of the proposed formula, a series of burst experiments are performed on full-scale ellipsoidal heads which cover various geometric parameters, various material types, and various manufacturing methods. Comparison between the predictions of the proposed formula and the experimental results of 33 full-scale ellipsoidal heads shows that the proposed formula provides a good prediction of plastic collapse pressure of steel ellipsoidal heads under internal pressure.

Marginal-restraint mandrel-free spinning process for thin-walled ellipsoidal heads

Metal sheet spinning is an advanced near-net forming technology for the manufacture of thin-walled ellipsoidal heads. The exact control of dimensional accuracy, however, is a considerable problem for spinning thin-walled parts with large diameter-to-thickness ratios. In this work, a marginal-restraint mandrel-free spinning process with two passes is proposed for the fabrication of thin-walled ellipsoidal heads without wrinkling. A finite element model is established and verified to study the influences of spinning parameters on the dimensional precision of thin-walled ellipsoidal heads. It is found that the spinning parameters considerably influence the deviations of wall thickness and contour characteristics. A small forming angle or small roller fillet radius during the first pass spinning, as well as the small angle between passes or high feed ratio during the second pass spinning, can improve the wall thickness precision. Meanwhile, as the forming angle or feed ratio is increased during the first pass spinning, the contour precision initially increases and then decreases. During the second pass spinning, the contour precision can be improved at a small angle between passes, whereas it deteriorates at a larger roller installation angle. The optimized spinning parameters are obtained and verified by experiments.

Effects of solution time and cooling rate on microstructures and mechanical properties of 2219 Al alloy for a larger spun thin-wall ellipsoidal head

The effects of solution time and cooling rate on microstructures and mechanical properties of 2219 Al alloy for a larger spun thin-wall ellipsoidal head are investigated. It is found that the Al2Cu phases are greatly affected by the solution time. The content of Al2Cu phases first decreases and then stabilizes with increasing the solution time. Moreover, the effects of solution time on the transformation of precipitates are obvious. As the solution time is increased from 35 min to 60 min, almost all the precipitates transfer from GP zones to θ′′ phases. When the solution time is further increased to 110 min, some θ′ phases appear. Meanwhile, the size of θ′′ phases increases, while the density of θ′′ phases drops. These microstructure changes greatly influence the mechanical properties, i.e., the hardness and tensile strengths first increase and then slightly decrease with the continuous increase of the solution time. In addition, if the cooling rate is decreased, the precipitation of coarse equilibrium θ phases is enhanced, but the precipitation of strengthening phases (θ′′, θ′) is restricted. It significantly deteriorates the mechanical properties. Based on the comprehensive analysis, the suitable solution time and cooling method are about 60 min and water cooling.

A new formula to predict buckling pressure of steel ellipsoidal head under internal pressure

Abstract Buckling is a critical failure mode of ellipsoidal head under internal pressure. This study focuses on the prediction of buckling pressure of steel ellipsoidal heads subjected to internal pressure. First, finite element model of ellipsoidal head is generated, taking into account the effects of material and geometrical nonlinearity. The plastic bifurcation buckling pressure of ellipsoidal head is determined by nonlinear FEM. Second, we study the effects of diameter-thickness ratio, radius-height ratio, yield strength, strain hardening and attached cylinder on buckling pressure. Based on FE results of the models with elastic-perfectly plastic material, we propose a formula to predict buckling pressure of perfect ellipsoidal head. In addition, we summarize experimental results on the buckling of twenty-one ellipsoidal heads which cover different geometrical parameters, material types, and methods of fabrication. Eleven out of twenty-one ellipsoidal heads were tested by the authors recently. Finally, based on the formula for perfect ellipsoidal heads, a new formula is developed for the buckling pressure of actual ellipsoidal heads after considering a reduction factor that accounts for the effect of initial shape imperfection. The reduction factor depends on the methods of head fabrication, i.e. whether cold pressing and spinning or assembly of formed segments. It is shown that the new formula has comprehensive advantage in accuracy and applicability in comparison with other formulae.

On One Imperfection Estimation Method for Thin Shell Buckling in the Design Code RCC-MR

The thin shell design code RCC-MR is used for sodium-cooled fast breeder reactor components operating at high temperatures. Thin shells from such applications can be designed using linear elastic buckling analysis, following procedures given in RCC-MR. For human safety, such procedures can and should be examined by the broader scientific community. Among such procedures, RCC-MR provides three alternative methods to quantify an imperfection value; and that value is used in subsequent calculations to determine safe loads. Of these methods, the third seems potentially nonconservative for some situations. Here, we examine that third method using detailed numerical examples. These examples, found by trial and error, are the main contribution of this paper. The first example is a nonuniform cylindrical shell closed with a spherical endcap under external pressure. The second is a cylinder with an ellipsoidal head under internal pressure. The third is an L-shaped pipe with an end load. In all three cases, the new computed imperfection quantity is found to be surprisingly small compared to the actual value used for computations (e.g., 25 times smaller), and in two cases, the result is insensitive to the actual imperfection. We explain how the three examples “trick” the imperfection quantification method in three different ways. We suggest that this imperfection quantification method in RCC-MR should be re-examined. The primary value of our paper lies not in new mechanics, but in identifying unexpected ways in which a particular step in shell design using RCC-MR could be potentially nonconservative.

Novel simulations to determine the impact of superficial perineal structures on vaginal delivery.

This study's aim was to determine whether the inclusion of superficial perineal structures in a finite-element simulation of vaginal delivery impacts the pubovisceral muscle and perineal body, two common sites of birth-related injury. The hypothesis, inferred from prevailing literature, was that these structures would have minimal influence (differences less than ±10%). Two models were made using the Visible Human Project's female cadaver to create a rigid, fixed pelvis, musculature held by spring attachments to that pelvis, and a rigid, ellipsoidal fetal head prescribed with an inferior displacement to simulate delivery. Injury site stretch ratios and fetal head and perineal body displacements and angles of progression were compared between the Omitted Model (which excluded the superficial perineal structures as is common practice) and the Included Model (which included them). Included Model stretch ratios were +107%, -9.84% and -14.6% compared to Omitted Model perineal body and right and left pubovisceral muscles, respectively. Included Model peak perineal body inferior displacement was +72.5% greater while similar anterior-posterior displacements took longer to reach. These results refute our hypothesis, suggesting superficial perineal structures impact simulations of vaginal delivery by inhibiting perineal body anterior-posterior displacement, which stretches and inferiorly displaces the perineal body.