Green’s functions for non-self-adjoint problems in heat conduction with steady motion

Heat conduction in a rectangular parallelepiped that is in steady motion relative to a fluid is studied in this paper. The governing equation consists of the standard heat equation plus lower-order derivative terms with the space variables that represent the effects of the solid flow. The presence of the first-order-derivative terms with the space variables renders the spatial part of the governing differenial equation non-self-adjoint and care must be exercised in defining the new Green’s functions to be used in representing the solutions of initial- and boundary-value problems. It is illustrated how the Green’s functions may be constructed and how solutions of initial- and boundary-value problems may be obtained that lead to numerical results. Convergence properties of the solutions are also discussed.     

A time-marching scheme based on implicit Green’s functions for elastodynamic analysis with the domain boundary element method

The present work presents an alternative time-marching technique for boundary element formulations based on static fundamental solutions. The domain boundary element method (D-BEM) is adopted and the time-domain Green’s matrices of the elastodynamic problem are considered in order to generate a recursive relationship to evaluate displacements and velocities at each time-step. Taking into account the Newmark method, the Green’s matrices of the problem are numerically and implicitly evaluated, establishing the Green–Newmark method. At the end of the work, numerical examples are presented, verifying the accuracy and potentialities of the new methodology.     

A new family of time integration methods for heat conduction problems using numerical green’s functions

This paper is concerned with the formulation and numerical implementation of a new class of time integration schemes applied to linear heat conduction problems. The temperature field at any time level is calculated in terms of the numerical Green’s function matrix of the model problem by considering an analytical time integral equation. After spatial discretization by the finite element method, the Green’s function matrix which transfers solution from t to t + Δt is explicitly computed in nodal coordinates using efficient implicit and explicit Runge-Kutta methods. It is shown that the stability and the accuracy of the proposed method are highly improved when a sub-step procedure is used to calculate recursively the Green’s function matrix at the end of the first time step. As a result, with a suitable choice of the number of sub-steps, large time steps can be used without degenerating the numerical solution. Finally, the effectiveness of the present methodology is demonstrated by analyzing two numerical examples.     

Experimental setup for precise measurement of losses in high-temperature superconducting transformer

A simple cryogenic system for testing of the superconducting power transformer was constructed. Thermal shielding is provided by additional liquid nitrogen bath instead of super-insulation. The system, together with use of a precise nitrogen liquid level meter, permitted calorimetric measurements of losses of the 8 kVA HTS transformer with a resolution of the order of 0.1 W.     

The cryogenic system for ITER CC superconducting conductor test facility

This paper describes the cryogenic system of the International Thermonuclear Experimental Reactor (ITER) Correction Coils (CC) test facility, which consists of a 500 W/4.5 K helium refrigerator, a 50 kA superconducting transformer cryostat (STC) and a background field magnet cryostat (BFMC). The 500 W/4.5 K helium refrigerator synchronously produces both the liquid helium (LHe) and supercritical helium (SHe). The background field magnet and the primary coil of the superconducting transformer (PCST) are cooled down by immersing into 4.2 K LHe. The secondary Cable-In-Conduit Conductor (CICC) coil of the superconducting transformer (SCST), superconducting joints and the testing sample of ITER CC are cooled down by forced-flow supercritical helium. During the commissioning experiment, all the superconducting coils were successfully translated into superconducting state. The background field magnet was fully cooled by immersing it into 4.2 K LHe and generated a maximal background magnetic field of 6.96 T; the temperature of transformer coils and current leads was reduced to 4.3 K; the inlet temperature of SHe loop was 5.6 K, which can meet the cooling requirements of CIC-Conductor and joint boxes. It is noted that a novel heat cut-off device for High Temperature Superconducting (HTS) binary current leads was introduced to reduce the heat losses of transformer cryostat.     

Elasticity studies of aluminium-substituted highT c superconducting materials

Longitudinal and shear wave velocities of Al-substituted Bi-Sr-Ca-Cu-O superconducting materials prepared by the ceramic technique were measured by the pulse transmission technique. Using the data, several elasticity parameters like Young’s modulus, rigidity modulus, Poisson’s ratio, Debye temperature etc were evaluated. Variation of elasticity parameters with composition has been explained in terms of binding forces between various atoms of the superconducting materials. Temperature variation of longitudinal wave velocity has also been measured and attempts have been made to explain the anomalies at 200 K.     

Numerical studies on crack problems in three-layered elastic media using an image method

Two-dimensional crack problems in a three-layered material are analyzed numerically under the conditions of plane strain. An image method is adopted to obtain fundamental solutions for dislocation dipoles in trilayered media. The governing equations for equilibrium cracks can be constructed by distributed dislocation technique and their solutions are sought in terms of the displacement discontinuity method (DDM). Comparisons are made with available analytical or reference solutions for several examples at various contrasts of material constants, and good agreements are found. A crack within a brittle adhesive layer joining two semi-infinite blocks can propagate in a variety of ways. In particular, crack paths in the form of sigmoidal waves within the adhesive layer are revisited to reveal the sensitivities of cracking paths to initial crack locations and directions and residual stresses. In addition, Z-shape and H-shape cracks alternating from interface to interface are re-examined to highlight the transition of failure modes and the role of the interlayer thickness.     

First-principles study of repeated current switching in a bimolecular device

Using nonequilibrium Green’s functions in combination with the first-principles density-functional theory, we investigate electronic transport properties of a bimolecular device consisting of two parallel placed phenalenyl molecules. When the two molecules get close enough, the currents of this bimolecular device could switch repeatedly by the mechanical strain. The deeper analysis indicates that the overlapping region size sensibly alters the coupling and charge transfer between the two parallel π-conjugated molecules is a very important factor for this behavior.     

Design and test of a simplified and reliable cryogenic system for high speed superconducting generator applications

Under the contract with Air Force Research Lab (AFRL), General Electric has successfully tested a high speed, superconducting generator for a Multimegawatt Electric Power System (MEPS). As the first successful full-power test of a superconducting generator for the Air Force, the demonstration tested the generator’s load up to 1.3 MW and over 10,000 rpm. A key component of the generator system is a closed loop cryo-refrigeration system to cool the field excitation coil at liquid neon temperature. This paper reports the design and tests of the cryogenic system, including the liquid neon dewar, cryogenic cooling loop for the high temperature superconducting (HTS) field coil and the cryostat. Performance data during both short-term load run and long-term non-load run were presented. Also, some key issues to design a reliable cryogenic system for a superconducting generator were discussed.     

Theoretical Study of Interplay of Superconductivity and Ferromagnetism in Hybrid Rutheno–Cuprate Superconductors RuSr2RCu2O8

We consider the extended two-band s–f model with additional terms, describing intersite Cooper pairs’ interaction between 4f (5f) and conduction electrons. Following Green’s function technique and equation of motion method, self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (m _f ) are derived. The expressions for specific heat, density of states, and free energy are also derived. The theory has been applied to explain the coexistence of superconductivity and ferromagnetism in hybrid rutheno-cuprate superconductors RuSr₂RECu₂O₈ (RE = Gd, Eu). The theory shows that it is possible to become superconducting if the system is already ferromagnetic. A study of specific heat, density of states and free energy is also presented. The agreement between theory and experimental observations is quite satisfactory.      

On conduction-cooling of a high-temperature superconducting cable

Current generation high-temperature superconducting (HTS) power transmission cables use liquid nitrogen as a coolant that circulates along the cable. In this work, the use of axial conduction-cooling in attaining HTS temperatures in transmission lines is proposed. Liquid coolant use is envisioned only at periodic length intervals along the transmission lines, in combination with insulation and copper. The proposed concept is feasible due to the high thermal conductivity of pure copper at cryogenic temperatures. A basic design for the insulated cable is proposed and a detailed numerical simulation of heat transfer in such a cable is carried out for various case studies considering the superconducting materials MgB₂ and BSCCO-2223.     

Comparison study of cable geometries and superconducting tape layouts for high-temperature superconductor cables

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable’s transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.     

Modified Roebuck compression device for cryogenic refrigeration system of superconducting rotating machine

Cryogenic refrigeration system installed on superconducting rotor has the merit that it can eliminate cryogen transfer between rapidly revolving rotor and stationary part and, therefore, the loss generated by it. Nevertheless, such an on-board cryogenic refrigeration system has not been realized yet because of the absence of compression device that can work reliably on rapidly revolving rotor. This paper presents the idea of modified Roebuck compression device as a potential on-board compression device. Although it has the disadvantage that it requires large radial space and external cooling and heating, a modified Roebuck compression device of 14 stages with diameter of 0.80 m mounted on a rotor revolving at 3600 rpm can produce substantially high compression ratio. J-T neon refrigeration system equipped with such a compression device can produce low temperature of 30 K and be useful for cooling superconducting rotor windings made of high temperature superconductor.     

On the existence of periodic solution for equation of motion of thick beams having arbitrary cross section with tip mass under harmonic support motion

A cantilever beam having arbitrary cross section with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Green’s function and employing Schauder’s fixed point theorem. The derived equation of vibration motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for periodic oscillatory behavior of the beam are established. Consequently, the phase domain of periodicity and stability for various values of physical characteristics of the beam-mass system and harmonic base excitation are presented.     

Sound Produced When a Vortex Pair is Swallowed by a Jet

An analysis is made of the sound generated during the high-Reynolds-number convection of a vortex pair in a jet of water exhausting from a large vessel through a slit aperture. The equations of motion are linearized about the classical free-streamline solution describing steady flow through the aperture. It is assumed that the vortex pair is swept through the aperture into the jet by the steady mean flow, with no account taken of the nonlinear influence on the motion of ‘images’ in the boundaries. Additional vorticity is shed from the edges of the aperture in order that the flow should remain smooth and continuous (the Kutta condition). This vorticity is convected away within a sheet of ‘bound’ vorticity on the mean free streamlines of the jet. A strong peak in the bound vorticity is established when the vortex pair enters the aperture. Both the incident and the shed vorticity generate sound, but their respective contributions to the acoustic pressure are of opposite phase. The dominant radiation in the water above the aperture is produced as the vortex enters the jet, and has the form of a pressure pulse of width ~h/M and monopole strength , where h is the width of the aperture, ρ _o the density of the water, v a typical flow velocity, and M is the jet Mach number.     

Heat transfer performance of cryogenic oscillating heat pipes for effective cooling of superconducting magnets

The cryogenic oscillating heat pipe (OHP) for conduction cooling of superconducting magnets was developed and the function was demonstrated successfully. OHP is a highly-efficient heat transfer device using oscillating flow of two-phase mixture. The working fluids that are employed in the present research are Nitrogen, Neon and Hydrogen, and the operating temperatures are 67–91 K, 26–34 K and 17–27 K, respectively. The estimated effective thermal conductivities from the measurement data of the OHP were higher than one of the solids such as copper at low temperature. These results revealed that the cryogenic OHP can enhance the performance of cooling system for magnets.     

Multiplicities and thermal runaway of current leads for superconducting magnets

The multiple solutions of conduction and vapor cooled copper leads modeling current delivery to a superconducting magnet have been numerically calculated. Both ideal convection and convection with a finite heat transfer coefficient for an imposed coolant mass flow rate have been considered. Because of the nonlinearities introduced by the temperature dependent material properties, two solutions exist, one stable and one unstable regardless of the cooling method. The limit points separating the stable form the unstable steady states form the blow-up threshold beyond which, any further increase in the operating current results in a thermal runway. An interesting finding is that the multiplicity persists even when the cold end temperature is raised above the liquid nitrogen temperature. The effect of various parameters such as the residual resistivity ratio, the overcurrent and the variable conductor cross section on the bifurcation structure and their stabilization effect on the blow-up threshold is also evaluated.     

Electromagnetic analysis of a superconducting transformer for high current characterization of cable in conduit conductors in background magnetic field

A large cable-in-conduit-conductor (CICC) test facility has been designed and fabricated at the High Magnetic Field Laboratory of the Chinese Academy of Sciences (CHMFL) in order to meet the test requirement of the conductors which are applied to the future fusion reactor. The critical component of the test facility is an 80 kA superconducting transformer which consists of a multi-turn primary coil and a minor-turn secondary coil. As the current source of the conductor samples, the electromagnetic performance of the superconducting transformer determines the stability and safety of the test facility. In this paper, the key factors and parameters, which have much impact on the performance of the transformer, are analyzed in detail. The conceptual design and optimizing principles of the transformer are discussed. An Electromagnetic-Circuit coupled model built in ANSYS Multiphysics is successfully used to investigate the electromagnetic characterization of the transformer under the dynamic operation condition.     

Sub-cooled nitrogen cryogenic cooling system for superconducting fault current limiter by using GM-cryocooler

The 21st Century Frontier R&D Program was planned to develop and commercialize the inductive Superconducting Fault Current Limiter (SFCL) in Korea until 2011. The 1.2 kV/80 A inductive SFCL was planned to develop at the first year in the first phase (2001-2002) and the 6.6 kV/200 A inductive SFCL for short run operation test was planned to develop at the second and third year in the first phase (2002-2004). The experimental characteristics of conduction-cooled cooling system developed in the first year was very weak from the sudden large thermal disturbance. Therefore, the conduction-cooled cooling system was concluded not appropriate for the cryogenic technology of the application of superconducting fault current limiter. In the third year research, the improved sub-cooled nitrogen cooling system was adopted and investigated.In this paper, the characteristics of each cooling type was compared and the basic deign of ameliorated cooling system was introduced and the total heat load of the cooling system was calculated and compared with the heat load of the cooling system developed at 2nd year research.     

Theoretical Study of Specific Heat,Density of States,Free Energy,and Critical Field of High Temperature Cuprate Superconductors Based on Intra and Interlayer Interactions

The role of attractive interlayer and intralayer interactions in layered high T _c cuprate superconductors have been investigated using a one-band two layer tight binding Hamiltonian. Self-consistent equations for the superconducting order parameter (Δ) and critical temperature (T _c ) are derived using double time Green’s functions and equation of motion method. The expression for excitonic type correlation (γ _c ), specific heat, density of states, free energy, and critical field are obtained. The interlayer interactions play an important role in the enhancement of T _c in layered high T _c cuprates. The oxygen isotope effect is also analyzed. The agreement between theoretical and experimental results for the system YBa_2−x La _x Cu₃O₇ (0≤x≤0.5) is quite satisfactory.