Toroidal Vessel Research Articles

Burst pressure performance comparison of type V hydrogen tanks: Evaluating various shapes and materials

Hydrogen, as a clean energy carrier, presents a significant step toward sustainable energy solutions but faces challenges in storage due to its low energy density and high volatility. This study addresses the optimization of Type V hydrogen storage tanks by investigating the burst pressure performance of spherical, cylindrical, and toroidal shapes. Using finite element analysis (FEA) and first-order shear deformation theory, we examined how these geometries impact burst pressure outcomes across a range of composite materials and layup configurations. The materials tested included carbon T700/epoxy, Kevlar/epoxy, E-glass fiber/epoxy, and basalt/epoxy. Results demonstrate that the toroidal shape significantly outperforms spherical and cylindrical designs in stress distribution and burst pressure, with basalt/epoxy composites exhibiting superior burst pressure performance (12.7 MPa) compared to Kevlar/epoxy (10.8 MPa), E-glass fiber/epoxy (11.4 MPa), and carbon T700/epoxy (8.9 MPa). Kevlar/epoxy toroidal tanks outperform other materials in weight performance, having a structural performance index of 0.0305 Mpa.m3/kg and hydrogen density per unit mass of 0.0251 kg H2/kg. The stacking sequence [-45/45]s optimized stress distribution for the toroidal shape across all materials. The findings highlight that toroidal designs offer significant advantages for high-pressure hydrogen storage, providing efficient stress management and improved safety. This paper underlines the potential of toroidal vessels for enhancing hydrogen storage efficiency and emphasizes the importance of material selection and stacking sequences in achieving optimal burst pressure performance for international organization for standardization (ISO) certification.

A shell theory approach for the analysis of metal-FRP hybrid toroidal pressure vessels

This study focuses on the analysis of metal-FRP hybrid toroidal pressure vessels (TPV) using shell theory. The analytical approaches for the design of metal-FRP TPVs considering bending effects are currently not available. Invariably the designs are done based on the most simplified approach like linear membrane theory. In this work, a potential energy functional for the metal-FRP TPV considering the membrane and bending deformations is developed using Love's shell theory. The classical laminate theory is employed to determine the stresses/strains throughout the thickness of the FRP laminate. The Rayleigh-Ritz method is adopted to solve the proposed potential energy functional. A finite element analysis (FEA) is conducted using ABAQUS to validate the proposed analytical solution. In addition, a parametric analysis is carried out to understand the influence of various parameters viz. thickness of base metal, thickness of FRP, and ratio between radii of toroid and cross-section on bending deformations in the hybrid TPV. The results from the proposed solution are in good agreement with that from FEA. Therefore, the proposed solution can be used in the analysis and design of the metal-FRP TPV irrespective of any variations in the geometric parameters. It is found that the inclusion of bending deformations can improve the accuracy of solution and the bending deformations in the base metal decreases or become negligibly small with the increase in R/r ratio and thickness of FRP. The orientation of fibers can change the direction of failure in the base metal. The important design parameters that influence the yield pressure are thickness of base metal and FRP, orientation of fibers and R/r ratio.

Efficient Design Methods for Variable-Angle-Tow Composite Toroidal Pressure Vessels

Pressure vessels are widely used in various aerospace and automotive applications. For some applications with limited space, spherical and ellipsoidal shapes are less attractive than toroids. Toroidal shapes can be defined as curved, endless hollow shapes that eliminate the need for end caps when used for pressure vessels. This study presents an analytical formulation using lamination parameters for the novel design of toroidal pressure vessels. The proposed design is based on stiffness tailoring by changing the fiber tow trajectories spatially through the structure to suppress the direct stress and strain gradients in the thickness direction, leading to reduced structural weight, defined as bend-free variable-angle-tow (VAT) toroidal pressure vessels. For a toroidal pressure vessel with a fixed geometry, the VAT distribution through the structure to suppress bending is obtained. Subsequently, the bending stresses and strain levels in the designed VAT toroidal pressure vessels are assessed numerically and compared with those of their isotropic and constant-stiffness composite counterparts. Results show that the designed VAT toroidal pressure vessel generates considerably lower degrees of bending than its corresponding isotropic and constant-stiffness composite counterparts.

Analyzing the Influence of Dean Number on an Accelerated Toroidal: Insights from Particle Imaging Velocimetry Gyroscope (PIVG)

Computational Fluid Dynamics (CFD) simulations were utilized in this study to comprehensively explore the fluid dynamics within an accelerated toroidal vessel, specifically those central to Particle Imaging Velocimetry Gyroscope (PIVG) technology. To ensure the robustness of our simulations, we systematically conducted grid convergence studies and quantified uncertainties, affirming the stability, accuracy, and reliability of our computational grid and results. Comprehensive validation against experimental data further confirmed our simulations’ fidelity, emphasizing the model’s fidelity. As the PIVG is set up to address the primary flow through the toroidal pipe, we focused on the interaction between the primary and secondary flows to provide insights into the relevant dynamics of the fluid. In our investigation covering Dean numbers (De) from 10 to 70, we analyzed diverse aspects, including primary flow, secondary flow patterns, pressure distribution, and the interrelation between primary and secondary flows within toroidal structures, offering a comprehensive view across this range. Our research indicated stability and fully developed fluid dynamics within the toroidal pipe under accelerated angular velocity, particularly for low De. Furthermore, we identified an optimal Dean number of 11, which corresponded to ideal dimensions for the toroidal geometry with a curvature radius of 25 mm and a cross-sectional diameter of 5 mm. This study enhances our understanding of toroidal fluid dynamics and highlights the pivotal role of CFD in optimizing toroidal vessel design for advanced navigation technologies.

Методика расчета параметров равнонапряженной тороидальной оболочки композитного баллона

The paper considers a promising high-pressure toroidal composite cylinder. It proposes a design option, where its load-bearing shell is reinforced with strong fibers along the meridian. Calculated dependences were obtained to determine the shape of the equal-strength toroidal shell generatrix registered by the elliptic integrals. The generatrix consisted of two smooth curves symmetrically located relative to the horizontal axis and intersecting at the acute angle. The annular frame made by the fibers circumferential winding was installed along the circle, where the revolution surfaces formed by the indicated curves intersected; the frame was made by circumferential winding of the fibers. Numerical example is provided, where geometric and mass characteristics of the designed toroidal pressure vessel were calculated.

A theoretical solution for metal-FRP hybrid toroidal pressure vessel based on membrane approach

Metal-FRP (fiber reinforced polymer) hybrid circular toroidal pressure vessel (TPV) can withstand higher internal fluid pressure compared to a metal TPV of the same thickness. The design of hybrid metal-FRP TPV needs prediction of the stresses and strains induced in the base metal and FRP layers. Existing predictive models for metal TPV based on linear membrane theory are inadequate in obtaining non-singular displacements at the apex in the meridian of the TPV. Further, they are not applicable for metal-FRP TPV. Therefore, a theoretical solution based on a modified linear membrane approach is proposed for a metal-FRP hybrid circular TPV subjected to an internal pressure. The proposed solution is validated through numerical simulations based on three-dimensional finite element analysis (FEA). Subsequently, a parametric study is conducted to understand the effect of the CFRP’s modulus and number of layers, thickness of base metal and R/r ratio (radius of the toroid to its cross-section) on the behavior of the aluminium-CFRP hybrid TPV. The comparison of results in an illustrative case and parametric studies show that the predictions from the proposed model are in good agreement with FEA results.

Numerical and Experimental Buckling and Post-Buckling Analyses of Sphere-Segmented Toroidal Shell Subject to External Pressure

This study determined the buckling characteristics of sphere-segmented toroidal shells subjected to external pressure. The proposed toroidal vessel comprises six spheres and six rings. Two laboratory models with the same nominal dimensions were manufactured, measured, tested, and evaluated. To investigate whether sphere-segmented toroidal shells are imperfection-sensitive structures with closely spaced eigenvalues, the subspace algorithm was applied to evaluate the first 50 eigenmodes, and the modified Riks algorithm was used to obtain post-buckling characteristics. The results indicated that the deviation between the results of the experimental and numerical analyses was within a reasonable range. The proposed sphere-segmented toroidal shells were highly imperfection-sensitive structures with closely spaced eigenvalues. Subsequently, imperfection sensitivity analysis confirmed this conclusion. In numerical analyses, the first eigenmode could be considered as the worst eigenmode of sphere-segmented toroidal shells. The trend of the equilibrium path of sphere-segmented toroidal shells was consistent with spherical shells, revealing instability. In addition, ellipticity and completeness exerted a negligible effect on the buckling load of sphere-segmented toroidal shells.

Current quench and vessel currents characterisation at the COMPASS tokamak

The characterisation of plasma current quench and understanding of its underlying physical processes play a crucial role when designing large fusion devices such as ITER. For the first time, an extensive analysis of the COMPASS tokamak disruption database is presented. A unique set of magnetic diagnostics allows the investigation of local toroidal and poloidal vessel currents, including currents flowing along the open magnetic field lines from the plasma to the vacuum vessel (VV) (i.e., halo currents). Area-normalised current quench times are in agreement with the ITPA 1.67 ms m−2 lower limit. Extremely fast I p quench rates of up to 0.6 MA ms−1 are observed during runaway electron campaigns at COMPASS, which are under the ITPA lower limit. Vertical movement of the plasma column is accelerated by the I p quench during major disruptions. Toroidal vessel currents of around 2% – 4% of the predisruptive plasma current are observed during I p quench. Net poloidal eddy currents are obtained by Mirnov coils and diamagnetic loop, reaching 3% of . Using the Mirnov coils it is shown that the halo current magnitude grows and its poloidal profile broadens with increasing plasma current I p . Geometric features of the VV structure and in-vessel component positions on the poloidal vessel current measurements are discussed.

Analytical and numerical approaches for stress and displacement components of pressurized elliptic toroidal vessels

In this paper, an analytical approach using membrane theory to derive the closed-form solution for displacement components of elliptic toroidal vessels under uniform internal pressure is presented. Membrane stress and displacement components at the crest, intrados, and extrados of elliptic toroidal vessels are expressed in the simplest forms, which can be written in terms of non-dimensional parameters with stress and displacement factors. The validation of analytical results is carried out by the finite element procedures based on differential geometry and the principle of virtual work. The effects of increasing radius and load variations on displacement behavior of elliptic toroidal vessels, including many engrossing characteristics obtained from a parametric study, are investigated thoroughly and discussed in detail herein. In addition, this study also provides charts of stress and displacement factors for engineering applications, which are extremely useful for design engineers to easily evaluate stresses and displacements at the point of the crest, intrados, and extrados.

Computer aided path design for filament winding torus

The torus is a promisingly potential alternative to traditionally cylindrical pressure vessels due to its capability to store more hydrogen energy within limited space. Constant angle winding is widely used in practical filament winding. Hence, it is necessary to study constant angle winding on the torus. This paper presents constant winding angle curve on torus, a new winding trajectory, and gives a sufficient and necessary condition that makes it nonslip and non-bridging, and a computational formula for determining the lower bound of the winding angle of stable constant winding angle curve. By combining with semi-geodesics, we propose an integration design method for winding pattern and develop a computer aided path design system for filament winding torus, which can design constant angle winding pattern or approximate equilibrium winding for toroidal composite pressure vessels. Since our approach uses constant winding angle curve and integration trajectories besides semi-geodesics, our method has more design space for optimizing fiber path, and outperforms the existing methods.

Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics

AbstractIn this paper we generalize an equation studied by Mossino and Temam in [7], to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, which were introduced by Harold Grad in [4], to model the behavior of plasma confined in a toroidal vessel called TOKAMAK. We prove existence of a ‐viscosity solution and regularity up to for any (we improve this regularity near the boundary). The difficulty of this problem lies in the right‐hand side which involves the measure of the superlevel sets, making the problem nonlocal. © 2021 Wiley Periodicals LLC.

A study on nuclear analysis of the divertor region of the CFETR

This paper presents the nuclear analysis performance of the Chinese Fusion Engineering Test Reactor (CFETR) divertor region using the MCNP-5 Monte Carlo N-particles code in a 3D geometry model. We assessed the nuclear responses of the divertor region component systems and evaluated their shielding capability, which can support the development strategy of the physical and engineering design of the CFETR. Model specification based on the latest CAD model of the CFETR divertor has been integrated into the CFETR MCNP reference model with a major/minor radius R = 7.2 m/a = 2.2 m in the 22.5° model, and a fusion-power range of around 1–1.5 GW. The nuclear heating and radiation damage of the divertor system are enhanced compared to that of the ITER and the earlier CFETR design. The initial nuclear responses of the toroidal field coil and vacuum vessel systems showed that the shielding of the current divertor design is not sufficient and optimization work has been carried out. We also carried out calculations and analysis using a hypothetical operating scenario of over 14 years. An excellent improvement in the nuclear performance has been obtained by the improved additional shielding block in the divertor region when referring to the ITER design limit, which can support the design of the future update of the divertor region systems of the CFETR.

Тороидальная равнонапряженная оболочка сосуда давления, образованная меридиональной и окружной намоткой нитей

The paper outlines the prospects for the use of composite toroidal high-pressure cylinders for the breathing apparatus of the Ministry of Emergency Situations, fire brigades, industrial workers, which are more ergonomic in comparison with their cylindrical counterparts. Relying on the analytical solution of the equilibrium equations, we determined the shape of the cross-section of toroidal shells reinforced along the meridians and representing intersecting loop-like curves that form an infinitely long corrugated pipe. The study introduces a solution for a toroidal composite pressure vessel formed by the intersection of the upper and lower branches of the shell, reinforced along the meridians, and a profiled ring layer of filaments installed at the point of their intersection. The parameters of the toroidal uniformly stressed pressure vessel shell made by ring and meridian filament winding are calculated.

Design of the toroidal Composite Pressure Vessel Made by Meridional Winding of Fibers

Design of the toroidal Composite Pressure Vessel Made by Meridional Winding of Fibers

Motion of a capsule in a curved tube

Abstract

Buckling of an externally pressurised toroidal shell of revolution with a doubly-symmetric parabolic-ogival cross-section

As part of recent work on the structural behaviour of toroidal shells, this paper presents results of a numerical study on the buckling resistance of a closed toroidal vessel with a doubly-symmetric parabolic-ogival cross-section, subjected to uniform external pressure. The analysis was carried out on both geometrically perfect and imperfect elastic steel shells, and boundary conditions resulting in the lowest buckling pressure were adopted. A range of shell geometries and possible imperfections of the geometry were considered. The study shows that buckling initiates as non-axisymmetric deformations in the weakest zones near the top and bottom edges of the outer segment of the vessel. The buckling strength of the vessel is found to be strongly dependent on the geometrical parameters of the cross-section, and parameters giving the largest buckling resistance of the vessel are identified. While the buckling behaviour is sensitive to initial geometric imperfections in the form of eigenmodes, the vessel is generally stable after bifurcation.

Particle behavior close to the lower wall of a tokamak type geometry during a loss of vacuum accident

The behavior of tungsten and beryllium particles close to the wall of a tokamak type geometry (i.e. a toroidal vacuum vessel) during a loss of vacuum accident (LOVA) is explored in this paper.Values of the flow field and temperature of the air surging into the torus were calculated by Computational Fluid Dynamics (CFD) simulations from an initial low pressure of 1000 Pa by Gelain et al., Fusion Engineering and Design, 100:87–99, 2015. A new CFD calculation is performed here for an initial low pressure of 500 Pa. The aerodynamic forces on particles in rarefied flow are derived from the calculated friction velocity and temperature in the lowest wall region. The focus is on spherical particles, but these values of forces are complemented for comparison with an estimate of the force on an elongated particle following Sentman (1961). Typical particles with diameters of 1, 2, 5, 10, 20 μm are considered. The possibility for particles which are detached from the lower wall to be entrained away the wall is explored. A particle may be detached by the flow field provided it escapes the adhesion force with the wall, which occurs only for a rough wall and large particles. It is then entrained away from the lower part of the wall provided its weight is smaller than the aerodynamic force, which occurs even at low pressure for all sizes of studied beryllium particles and only for specific sizes and a pressure above 1500 Pa for tungsten particles. This key influence of particle weight on the particle dynamics in rarefied gas flow is the focus of the paper. As a result, only particles of intermediate diameters may be resuspended and transferred away from the wall during the whole pressurisation sequence of the vessel. Using the data for the initial low pressure of 500 Pa, these particle diameters are 5, 10 μm for tungsten and 5, 10, 20 μm for beryllium.

Operational and Performance Overview of the 50 kA–35 kV RFX-Mod DC-Current Interruption System

This article investigates the electrical performances of the high direct current (dc) interruption system in use in the reverse field experiment (RFX)-mod experiment. This system, called the energy transfer system (ETS), provides the loop voltage required for plasma breakdown inside the toroidal vacuum vessel, utilizing the interruption of dc currents up to 50 kA, with a recovery voltage of up to 35 kV. The ETS is composed of four identical units, each including the vacuum circuit breaker (VCB, each composed of two Vacuum Interrupters (VIs), in series), a transfer resistor, and an artificial zero current network. The system was designed in the 1980s and upgraded in 2008 to permit reliable operations at the full current of 50 kA. A new auxiliary branch was connected in parallel to each dc-current interruption system and all the VIs have been replaced with units with a larger contact surface. Since this upgrade, the ETS has been working routinely, and so far has performed almost 9000 current interruptions. By taking advantage of the large database of ETS electrical measurements, this article investigates the key waveforms and parameters of each VI (arc U-I characteristic, close-contact resistance, and recovery voltage) and correlates their variation with the fault occurrence and with the aging of the VCB components.

Design and Development of Mirnov Coil Sensor for Eddy Currents Experiment on Toroidal Vessel

Tokamak is a magnetic confinement device that confines hot plasma in the shape of torus during the process of thermonuclear fusion power generation. In tokamak, eddy currents are produced due to change in plasma positions during plasma instabilities that induce electromagnetic forces on interaction with the induced currents. Mirnov coils are widely used in tokamaks to study plasma positions during plasma instabilities. Principle objective of this paper is the design and development of Mirnov coil sensor to find eddy currents on a toroidal vessel. This paper presents an elaborative and practical construction technique of a Mirnov coil. The calibration method of a Mirnov coil is also discussed. Mirnov coils as an eddy current diagnostics are tested and experiments to measure magnetic fields due to induced current on torroidal vessel are performed using the coils.

Nonlinear Free Vibration Analysis of a Toroidal Pressure Vessel under Constrained Volume Condition

This paper focussed on the large displacement nonlinear free vibration of a toroidal pressure vessel in free space under constrained volume condition. Three states of the toroidal pressure vessel surface comprising the initial unstrained surface, reference surface, and vibrating surface were considered in the energy functional of the toroidal pressure vessel system based on the principle of virtual work. For the reference surface, it was assumed that the toroidal pressure vessel has a circular cross-section and is subjected to uniform internal pressure. Nonlinear numerical solutions were obtained utilizing the FEM and a modified direct iteration technique, and compared with those generated by ABAQUS. More importantly, this study showed that the fundamental nonlinear natural frequency of a toroidal pressure vessel under the constrained volume condition was lower than that of the published results for an inflated toroidal membrane and shell.