Hoop Force Research Articles

Design and Qualification of ITER CS and TF Cooling Inlets

In the ITER superconducting magnets, the CIC conductors cooling is insured by supercritical helium forced flow in the central and annular parallel channels. In the Central Solenoid, with a thick square jacket conductor, the helium inlet is in the highest field region at the inner bore pancake joggle, and it has to support the high hoop force stress level with a very low stress concentration factor. In the TF magnets, a thin jacket circular conductor is wound in double pancakes, inserted into radial plates, stacked and embedded into a steel case. The helium inlets are located at the inner bore, in the limited space between the radial plates and the coil casing. The PF coils helium inlets, not studied here, are similar to the CS ones, but with a lower stress level. A complete qualification work on the CS and TF helium inlets is presented. A design optimization was performed, by FEM analysis, resulting in acceptable stress level for both helium inlets. The welding procedure was qualified and specific fatigue life mock-ups were designed, analyzed and manufactured using representative jacket materials. Fatigue life qualification at 4 K was performed in the FZK test facility applying the relevant loading and number of cycles. Hydraulic mock-ups were manufactured and qualified in the CEA test facility using GN2 at relevant Reynolds number. Pressure drop as well as flow repartition inside the conductors' petals were measured. The mechanical and hydraulic results are presented

Optimization of the IGNITOR operating scenario at 11MA

Several endeavours have been made, in the frame of the IGNITOR design, in order to minimize technological problems, reducing electromagnetic loads, power supply requirements while avoiding the use of not completely proven materials. The present design modifications comprise both the operating scenario for the poloidal field (PF) currents and the PF coils geometry. The new scenario and a relevant simulation of a related typical fast vertical disruption, in the most dangerous plasma conditions in IGNITOR, have been simulated with the MAXFEA code. In order to reduce the EM loads on plasma chamber and the related stresses due to plasma disruptions, a new approach has been investigated based on the possibility of mitigating these loads by using copper toroidal layers added to the plasma chamber in proper positions. We found that this expedient could be quite effective not only in increasing the time constant of the plasma displacement but even in reducing the vertical force and its combined effect with hoop force on the vessel during a vertical displacement event (VDE).

Improved structure and long-life blanket concepts for heliotron reactors

New design approaches are proposed for the LHD-type heliotron D–T demo-reactor FFHR2 to solve the key engineering issues of blanket space limitation and replacement difficulty. A major radius of over 14 m is selected to permit a blanket-shield thickness of about 1 m and to reduce the neutron wall loading and toroidal field, while achieving an acceptable cost of electricity. Two sets of optimization are successfully carried out. One is to reduce the magnetic hoop force on the helical coil support structures by adjustment of the helical winding coil pitch parameter and the poloidal coils design, which facilitates expansion of the maintenance ports. The other is a long-life blanket concept using carbon armour tiles that soften the neutron energy spectrum incident on the self-cooled flibe-reduced activation ferritic steel blanket. In this adaptation of the spectral-shifter and tritium breeder blanket (STB) concept a local tritium breeding ratio over 1.2 is feasible by optimized arrangement of the neutron multiplier Be in the carbon tiles, and the radiation shielding of the superconducting magnet coils is also significantly improved. Using constant cross sections of a helically winding shape, the ‘screw coaster’ concept is proposed to replace in-vessel components such as the STB armour tiles. The key R&D issues for developing the STB concept, such as radiation effects on carbon and enhanced heat transfer of Flibe, are elucidated.

Spontaneous Formation of Spherical Tokamak by ECH on LATE

Spontaneous formation of spherical tokamak is observed during a microwave discharge at the electron cyclotron resonance (ECR) under a steady vertical magnetic field. In the course of slow plasma current increase, a fast rise of current (usually within several ms) occurs and the magnetic field topology changes drastically from open field type to closed one. After this current jump, a steady plasma current is maintained. The plasma current in the steady stage is proportional to the strength of the vertical field which balances the outward hoop force of the plasma current and maintains the MHD equilibrium. When a 5GHz, 130kW, 60ms microwave power is injected at 85G vertical field, plasma current of 6.8kA is obtained.

Lateral meniscal root tears associated with anterior cruciate ligament injury: classification and management (SS-70)

Objective: The purpose of this study was to define the incidence of posterior horn lateral meniscal root tears, classify the tear patterns, correlate these findings with the preoperative MRIs, and describe a technique for repair. Methods: The operative notes from 298 consecutive ACL reconstructions (1999–2001) were reviewed to identify associated posterior lateral meniscal root tears. These tears were defined as ones that occurred within one centimeter from the posterior bony insertion of the lateral meniscus. This tear pattern was identified in 37 (12.4%) patients. Two surgeons and one musculoskeletal radiologist performed an independent review of the MRIs, operative records, and arthroscopic pictures. Associated injuries and tear patterns were identified. An arthroscopic classification system and a technique for repair was developed. Results: Preoperative MRIs were available for review in 30 of the 37 patients. MRI findings included abnormal gray signal at the root insertion on the T1 images in 26 (87%) patients. T2 signal changes at the root were much less frequent, occurring in only 57% of patients. Lateral and medial compartment edema was present in 83% and 74% of the patients, respectively. MCL injury was present in 48% of the patients, and partial PCL injury was seen in 30%. Medial meniscal tears and additional lateral meniscal tears were identified in 43% and 22% of the patients, correspondingly. An arthroscopic classification system was developed based on three typical tear patterns. Type I injuries were root avulsions. Type II tears were isolated radial split tears within one centimeter from the root insertion, and type III injuries were complex root tears with radial and longitudinal components. The type I and III tears were amenable to arthroscopic repair using a trans-osseous tunnel technique. Conclusions: The association of lateral meniscal tears with ACL injuries is well documented. However, limited data is available on posterior lateral root tears. The mechanism, incidence, natural history, and associated injuries of lateral root tears is unknown. By disrupting the hoop forces, root tears can potentially have a detrimental effect on the lateral compartment biomechanics. This study has helped to define the incidence of concomitant ACL and lateral root tears, associated injuries, and treatment options.

Thermoelectric rotating torus for fusion.

A plasma toroid is rotated toroidally to supersonic speeds by external means. The input power maintains the rotation and also heats the plasma. The thermoelectric effect from the resulting temperature gradient creates and maintains a poloidal magnetic field against resistive decay, confining the plasma in steady state. The shear in the rotation keeps the plasma stable to MHD kinks and interchanges. Such a system has two novel advantages as a fusion device: there are no strong electromagnets needed to create the confining magnetic field, and there is effectively no limit on the field strength and, hence, no limit on the plasma pressure contained. The system has to be of a large aspect ratio, to minimize centrifugal effects, and a weak, external vertical magnetic field is needed to balance the radial hoop force.

Development of Helically Winding Machine for Force-Balanced Coil and Winding Technique

Strong electromagnetic force caused by high magnetic fields and coil current is a serious problem in Superconducting Magnetic Energy Storage (SMES) systems and magnetically confined fusion devices. In facing this problem, we proposed the concept of Force-Balanced Coil (FBC) applied to SMES and fusion devices. The FBC is a helically wound toroidal coil which balances the centering force with the hoop force. The helical winding of the FBC is modulated in order to reduce the torsional force. However, the winding of the FBC is a three-dimensional complex shape so that it may be difficult to manufacture the modulated helical windings. To overcome this difficulty, we developed a helically winding machine. In this paper, we discuss the winding techniques by using the winding machine and improve the shape of the helical windings from the view point of the reduction of the time consumed in winding the coil.

Spheromaks, solar prominences, and Alfvén instability of current sheets

Three related efforts underway at Caltech are discussed: experimental studies of spheromak formation, experimental simulation of solar prominences, and Alfven wave instability of current sheets. Spheromak formation has been studied by using a coaxial magnetized plasma gun to inject helicity-bearing plasma into a very large vacuum chamber. The spheromak is formed without a flux conserver and internal λ profiles have been measured. Spheromak-based technology has been used to make laboratory plasmas having the topology and dynamics of solar prominences. The physics of these structures is closely related to spheromaks (low β, force-free, relaxed state equilibrium) but the boundary conditions and symmetry are different. Like spheromaks, the equilibrium involves a balance between hoop forces, pinch forces, and magnetic tension. It is shown theoretically that if a current sheet becomes sufficiently thin (of the order of the ion skin depth or smaller), it becomes kinetically unstable with respect to the emission of Alfven waves and it is proposed that this wave emission is an important aspect of the dynamics of collisionless reconnection.

Construction of 320 kJ superconducting force-balanced coil

Strong electromagnetic force caused by high magnetic fields and coil current is a serious problem in superconducting magnetic energy storage (SMES) systems. To cope with this problem, we propose the concept of force-balanced coil (FBC) applied to SMES. The FBC is a helical-winding torus coil that balances the centering force with the hoop force, both of which are exerted in the major radius direction. In the case of FBC, the toroidal current distribution is modulated so that one of the magnetic surfaces coincides with the torus surface in order to reduce the torsional force. This current distribution can be achieved by varying the helical winding pitch. However, the smaller the aspect ratio (major radius/minor radius), the more difficult it becomes to manufacture the varying helical windings. To overcome this difficulty, we developed a winding machine which can modulate the helical winding. We also designed an experimental superconducting FBC which is being manufactured using the winding machine.

Experiment of force-balanced coil for magnetic energy storage

Higher magnetic field is of great advantage to superconducting magnetic energy storage because it promises a compact device. However, it does not affect the serious problem of huge electromagnetic forces caused by high magnetic fields and large coil current. Electromagnetic stresses, reaching as much as several hundred bars, thus become a major factor in determining whether a large-size strong magnetic field system can be established. In order to solve this problem, we have proposed the force-balanced coil (FBC) concept that reduces the huge centering electromagnetic forces by balancing them with the hoop forces caused by the toroidal current. Then we designed and fabricated a small-size superconducting FBC system to demonstrate the FBC concept. It was successfully excited up to near rated current. It is shown that the FBC system has the potential for simplifying the supporting structures and making the facility compact. © 1999 Scripta Technica, Electr Eng Jpn, 128(3): 82–91, 1999

Force-balanced coil for large scale SMES

In large scale SMES, huge electromagnetic force caused by high magnetic fields and coil currents is a serious problem. In order to solve this problem, we propose a concept of force-balanced coil (FBC) applied to the SMES. The FBC balances the centering force with the hoop force, both of which are exerted in the major radius direction. Moreover, for the optimization of large aspect ratio superconducting coils, we propose a stress-balanced coil (SEC) concept, improving the concept of FBC, which balances magnetic pressures at the coil nose part where the produced magnetic field reaches its maximum value. Comparing the toroidal magnetic field coil (TFC) and FBC with SEC, the last can reduce coil stresses and obtain large stored energy with shorter length conductors and/or lower magnetic fields.

Hyperbolic Cooling Towers with Bulge Imperfections

Owing to the large expanse of cooling towers, it is not possible to maintain the exact shape of a tower during construction. Alterations in shape also occur due to secondary effects like shrinkage and cracking. These alterations cause the failure of some towers. This paper deals with the application of semiloof shell elements in the analysis of towers with bulge imperfections for both dead and wind loads. Four parameters, namely, (1) radial error amplitude, ζ\im, (2) vertical location of bulge, \iZ\i\dm, (3) vertical extent of bulge, \ih, and (4) angular extent of bulge, Θ\i\dm, have been identified as responsible in influencing the behavior of imperfect towers. Their influence has been studied in detail and most critical geometry of the tower has been arrived at. The behavior of a tower with most critical geometry has also been studied. Analysis suggests that the effect of bulge imperfections on stress resultants is localized, the development of hoop tension in the imperfection zone is of primary concern, and stress changes induced are greater if the imperfection is located closer to the base. Shorter wavelength of an imperfection is more severe since curvature error is significantly high for low wavelength. With increase in angular extent, the change in hoop force is maximum for axisymmetric imperfection. Critical hoop stresses develop around the 70° meridian, where high hoop tension and high meridional moments develop that can induce yielding of hoop reinforcement and consequent failure.

Experiment of Force-balanced coil for Magnetic Energy Storage

Higher Magnetic field is of great advantage to Superconducting Magnetic Energy Storage because it promises a compact device. However, the serious problem of huge electromagnetic forces caused by high magnetic fields and large coil current, still remains. Electromagnetic stresses, reaching as much as several hundred bars, thus become a major factor in determining whether a large sized strong magnetic field system could be established. In order to solve this problem, we propose the force-balanced coil (FBC) concept that reduces the huge centering electromagnetic forces by balancing it with the hoop forces caused by toroidal current. Then we designed and fabricated a small size superconducting FBC system to demonstrate the FBC concept. It was successfully excited up to near rated current. It is shown that the FBC system has a potential for simplifying the supporting structures and making the facility compact.

Finite element analysis of column supported hyperbolic cooling towers using semi-loof shell and beam elements

In most of the early works related to the analysis of hyperbolic cooling towers, under either dead or the wind loads, only the tower shell was considered in the analysis and a continuous boundary condition in the form of fixity of the base of the shell was considered. However, the tower shell is supported by columns in the form of A-frames. In order to consider realistic boundary conditions, it is essential to consider the supporting columns in the analysis along with the shell. The present study considers this problem and an attempt has been made to represent the tower shell by semi-loof shell elements and the supporting columns by semi-loof beam elements. The column ends are assumed to be fixed at their bases. The analysis has been carried out for only the dead load. The results have been found to compare with those of Gould ‘ Finite Element Analysis of Shells of Revolution’, Pitman, London, 1984, and lyer and Appa Rao ‘Studies of stress concentration at shell-column junctions of hyperboloid cooling towers’, Comp. Struct., 1990, 34, 191-20. Hoop forces have been found to have altered significantly in the lower portion of the shell near the column-shell junction. Moreover, the proposed model gives a better physical representation of a column supported hyperbolic cooling tower.

Study on coil winding configuration for Superconducting Magnetic Energy Storage

Superconducting Magnetic Energy Storage (SMES) is very promising for the future power storage system because of fast response, low loss and high efficiency. Strong magnetic field is very favorable for SMES because it promises a compact device. However, the huge electromagnetic forces caused by strong magnetic fields and coil current becomes a serious problem. We propose the Force-balanced Coil (FBC) concept for the SMES which drastically reduces the huge centering forces by balancing it with the hoop forces induced by the toroidal current. Superconductor stress, length, maximum field and stored energy were surveyed. The results were compared with the toroidal type configuration and ordinary helical type one, It is shown that Force-balanced Coil is more compact than the others in view point of electromagnetic force and per-unit length stored energy of the superconductor and has a potential for simplifying the supporting structure, making the facility compact.

Detailed finite element analysis of the winding pack of a cased ITER toroidal field coil

The ITER toroidal field coil system generates a toroidal field in the plasma region of an intensity of 5.7 T. During operation the toroidal field coils experience an electromagnetic load toward the machine axis. This load is resisted by the central structure. The in-plane hoop forces of the coils are carried by a winding pack and case. This paper concentrates on a calculation of the local stress distribution in the insulation, conductor jacket, and steel structure in the most highly stressed region of the winding pack.

On toroidal equilibrium of non-neutral plasma

The equilibrium of a non-neutral cloud in a toroidal magnetic field is analyzed. In the zero mass limit it is shown that, because of plasma diamagnetism and electrostatic hoop force, there is a net force on the cloud along the major radius. In a large-aspect-ratio conducting vessel, this force is balanced by image charges that produce a compensating force toward the major axis. As a result, shift of potential minimum (or maximum) from the geometric center of the vessel (in the poloidal plane) is toward the major axis. A partial differential equation governing the two-dimensional axisymmetric equilibrium is obtained and solved in the large-aspect-ratio limit. Further, it is shown that modification of this equilibrium owing to first-order guiding center drifts is small, i.e., drift surfaces are still closed, however, they are further displaced toward the major axis from the potential surfaces by a small distance. Finally, a brief comparison of the properties of the equilibrium of neutral and non-neutral plasma is given.

Elastic stability of buried elliptical tubes

When a metal culvert is buried under a railway or road embankment, large compressive thrusts can develop in the structure as a result of loads from traffic and from the embankment itself. Culverts are liable to elastic buckling failure, because their flexural stiffness is usually low. This technical note reports a study, whose objectives are to: (1) investigate the elastic stability of elliptical tubes: (2) extend the parametric solution, already available for cylindrical tubes, to the behaviour of elliptical tubes. Using a linear finite element analysis for flexible culvert buckling, it is found that the linear buckling strength of an elliptical tube is approximated well by that of a circular tube of the same circumference. Published results for circular tubes buried near the ground surface can also be used for shallow buried elliptical tubes having the same ratio of cover depth to half-span. For non-uniformly loaded circular tubes, maximum hoop force can be used to calculate a conservative factor of safety relative to the critical hoop force for uniformly stressed structures. Both experimental and theoretical researches support the finding that linear buckling is a useful estimate of metal culvert elastic buckling strength. (Author/TRRL)

Static Response of Deeply Buried Elliptical Tubes

A parametric study of elliptical tubes deeply buried in uniform elastic ground is reported. The static tube response is determined using both analytical and numerical methods for a range of tube geometries and ground and interface conditions. The structural response is evaluated for both rigid structures and structures that are flexible in bending. The solutions are presented in a series of figures, and a simple procedure is developed for calculating distributions of hoop force, bending moment, and radial deflection by means of simple hand calculations. An example problem is included to demonstrate the effectiveness of the simplified analysis.

Tower silo design: Principles and computer implementation

Farm tower silo design in Canada is changing from the use of strictly empirical formulae to analytical methods. This means that several types of structures and a variety of silage materials at a range of moisture contents can be accomodated. This paper attempts to summarize the wall pressures caused by whole plant materials in bottom and top unloading silos. Both dry and wet silages are considered. Guidelines are provided also for determining pressures from high moisture grains. The determination of internal hoop tensile forces is also discussed. A design aid is provided for bottom unloading silos where the internal hoop tensile forces are difficult to calculate. A computer program was developed using the various algorithms to aid in the rapid determination of a pressure diagram and of the resulting hoop forces, given the silo geometry and the specification of the material intended to be stored.