Axial Leakage Research Articles

GENESIS: A Three-Dimensional Heterogeneous Transport Solver Based on the Legendre Polynomial Expansion of Angular Flux Method

A heterogeneous transport solver in three-dimensional (3-D) geometry, GENESIS, is developed incorporating recent developments in the method of characteristics (MOC) in 3-D geometry. The Legendre Polynomial Expansion of Angular Flux (LEAF) method is implemented in the GENESIS code, in which neutron transport is calculated in two-dimensional (2-D) characteristics planes rather than in one-dimensional characteristics lines adopted in the conventional approach of 3-D MOC. Unlike the planar MOC method that combines 2-D MOC calculations through axial leakages, the GENESIS code explicitly considers angular and spatial dependence of outgoing and incoming angular fluxes between axial planes. Thus, the GENESIS code eliminates a crucial approximation used in the planar MOC method: No approximation is used for axial leakage treatment. The GENESIS code can handle flexible shapes of objects in rectangular or hexagonal geometry. A two-level, multigroup generalized coarse mesh rebalance acceleration method is adopted for efficient convergence of neutron transport calculation. Performance of the GENESIS code is verified through various benchmark calculations. The calculation results indicate the fidelity of the GENESIS code based on the LEAF method.

A 2-D/1-D Transverse Leakage Approximation Based on Azimuthal, Fourier Moments

The MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport–based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial SN solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The work here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D–Method of Characteristics calculations.These new capabilities are demonstrated for the rodded Takeda light water reactor benchmark problem and the extended C5G7 benchmark suite. Results with heterogeneous pins, as in the C5G7 benchmark, indicate that cancelation of error between the angular and spatial representation of the transverse leakages may be a factor in the results obtained. To test this, an alternative C5G7 problem has been formulated using homogenized pin cells to reduce the errors introduced by assuming that the axial transverse leakage is spatially flat. In both the Takeda and C5G7 problems with homogeneous pins, excellent agreement is observed at a fraction of the run time and with notable reductions in memory footprint.

Axial Magnetic Fields, Axial Force, and Losses in the Stator Core and Clamping Structure of a Synchronous Generator with Axially Displaced Stator

Axial displacement of the stator in a synchronous machine gives rise to axial magnetic field both at the ends and deep inside the stator. The axial magnetic field causes losses. This article contains results from two studies with an axially displaced stator. In the first study, axial magnetic leakage fields in the ends of a small synchronous generator at load and no load were measured and simulated. In the second study, axial force and iron losses at no load were calculated with non-linear materials and a three-dimensional, time-stepped finite element method. For some machines with vertical shafts, the sum of iron losses and thrust bearing losses can be reduced if the rotor is lowered or the stator raised, whichever is best.

Leakage reconstruction method for 2D/1D fusion transport calculations

The 2D/1D fusion method (2D/1D method) is becoming a standard transport method for whole-core calculations, which reduces the group condense and assembly homogenization approximations in the conventional two-step reactor physics calculations. In most 2D/1D codes, a pin is chosen as a 1D calculation domain, which assumes that the axial leakage of the pin is flat on top/bottom surfaces. Similar to the axial leakage, the radial leakage of every 2D plane also introduces several approximations along axial direction for the 1D calculation. This paper studied the error introduced by both axial and radial leakages, and proposed a leakage reconstruction method according to the error analysis for the 2D/1D fusion method, in which MOC is applied to the radial 2D calculation and the Sn diamond difference method is used for the axial 1D calculation. Several cases are tested to show the performance of this leakage reconstruction method especially when the leakage term is significant.

Analysis on Axial End Flux Leakage and Resonance Characteristic of TFPM Linear Generator for Thermoacoustic Electric Generation System

According to 3-D magnetic circuit of the transverse flux permanent magnet linear generator (TFPMLG), the area of end flux leakage is divided into several zones, and the analytical expression of axial end flux leakage is derived through conformal transformation. The linear machine equivalent stiffness factor is derived through the calculation of detent force. Combining the linear machine with mechanical resonance property of thermoacoustic electric generation system, the computing method on resonance spring parameters of the system is provided. A 3-D finite-element model of TFPMLG is built to analyze the flux leakage distribution. The experimental results of the linear machine verified the validity of detent force and stiffness factor theoretical derivation; the research on axial end flux leakage and resonance spring parameters provides a valuable reference to other types of linear machines.

A three-dimensional nodal neutron kinetics code with a higher-accuracy algorithm for reactor core in hexagonal-z geometry

A nodal neutron kinetics model with a higher-accuracy algorithm for three-dimensional multi-group neutron diffusion calculation is developed for transient analysis of reactor core in hexagonal-z geometry. The spatial discretization technique is based on a high order nodal expansion method for hexagonal-z geometry. In this method, one dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four order polynomial expansion respectively. The partially-integrated radial and axial leakages are both approximated by the quadratic polynomial. The time discretization technique is based on a fully implicit scheme combined with a Runge-Kutta method for solving the neutron flux and delayed neutron precursor equations. A flux weighting method is adopted to calculate homogenized multi-group cross sections for transient analysis of control rod ejection accident. The described numerical methods are implemented into the computer code HNHEXK. This code is tested with one static benchmark problem and several kinetic benchmark problems. The numerical results show that the current method has a good agreement with the reference.

Investigation of the operating characteristics of a 12 stepped-cavity relativistic magnetron with axial extraction driven by an “F” transparent cathode using particle-in-cell simulations

We explore the performance of a 12 stepped-cavity relativistic magnetron with axial extraction (12 stepped-cavity RMDO) driven by an “F” transparent cathode (the “F” transparent cathode is a coaxial transparent cathode with two azimuthal periods of increased thickness and which looks like the letter “F,” so we call it “F” transparent cathode) through particle-in-cell (PIC) simulations. It is shown that using the “F” transparent cathode, an electronic efficiency of 70% with gigawatt output power is obtained while reducing the axial leakage current by about 50% compared to using the usual transparent cathode. Further PIC simulations demonstrate that frequency bifurcation occurs and mode switching can be achieved using several hundred kilowatts input RF power in the 12 stepped-cavity RMDO driven by an “F” transparent cathode. For example, it was found that using an applied driver power of 180 kW for 10 ns, the operating TE31 mode can be switched to the TE41 mode. It is also found that the secondary electron and backscattered electron emission and axial leakage current were two disturbing factors for the 12 stepped-cavity RMDO when it works at a stable operation mode but when the 12 stepped-cavity RMDO works near the critical magnetic field at the boundary between two modes, these two factors would lead to the operation modes changing.

Dipole Model to Predict the Rectangular Defect on Ferromagnetic Pipe

Dipole model based analytical expression is proposed to estimate the length and depth of the rectangular defect on ferromagnetic pipe. Among the three leakage profiles of Magnetic Flux Leakage (MFL), radial and axial leakage profiles are considered in this work. Permeability variation of the specimen is ignored by considering the flux density as close to saturation level of the inspected specimen. Comparing the profile of both the components, radial leakage profile furnishes the better estimation of defect parameter. This is evident from the results of error percentage of length and depth of the defect. Normalized pattern of the proposed analytical model radial leakage profile is good agreement with the experimentally obtained profile support the performance of proposed expression.

Pulse-Shortening in a Relativistic Magnetron: The Role of Anode Block Axial Endcaps

A six-vane relativistic magnetron with a single radial output slot is studied by 3-D particle in cell simulations without the presence of plasma. We find that when the six radial slots in the anode block are closed at their axial ends by conducting endcaps, the power flow behaves in a way different from that when they are not. When there are no endcaps, microwave power pulse-shortening is the result of the magnetron impedance being undermatched to the pulsed-power generator, and it cancels when the magnetron impedance is increased sufficiently. The axial electron current flowing in the downstream cavity reduces to negligible values and plays no part in the power flow. When anode block endcaps are added, this axial leakage current is significant and the downstream cavity acts as a second load attached in parallel to the magnetron. For pulse-shortening to cancel, the magnetron impedance needs to increase, which can be achieved by reducing the downstream axial section impedance. We demonstrate this by increasing the axial current. Between the parameter regions where pulse-shortening exists and where it does not, there is a metastable transition region where there is mode competition resulting in a beating pattern separating two regions each characterized by a single mode.

Method for Calculating the Neutron Diffusion Coefficient in a Nuclear Reactor Cell

An approach to solving the three-dimensional transport equation is described. Directional probabilities, which make it possible to analyze axial leakage numerically, are defined. The problems of modeling the boundary conditions for the neutron flux under ordinary operating conditions of reactors and under the conditions of dewatering are discussed. The results obtained show that if the effect of the spectrum of the two-dimensional problem of a VVER cell is taken into account, then the axial leakage changes, especially near the reflector. The axial leakage also increases if the cell contains dewatered channels, but only if the boundary conditions are modeled in the form of mirror reflection on a real hexahedral boundary. This effect vanishes if the equivalent cylindrical cell approximation is used and the boundary conditions are modeled in the form of isotropic reflection.

Investigation of the operating characteristics of a 12-cavity rising-sun relativistic magnetron with diffraction output using particle-in-cell simulations

We report on the performance of a 12-cavity rising-sun relativistic magnetron with diffraction output (12-cavity rising-sun RMDO). Particle-in-cell simulations show an electronic efficiency of 70% for a gigawatt output power 12-cavity rising-sun RMDO with a transparent cathode operating in the π mode for an applied voltage of U∼400 kV ±50 kV. When the RMDO is driven by the “F” transparent cathode, which is a coaxial transparent cathode, the axial leakage current can be reduced by about 50%.

Symmetrical component filter based on line condition monitoring instrumentation system for mine winder motor

As the capital investment in underground coal mining is huge enough by the standards of any conventional industry hence coal production process has to be very efficient to make commercially viable. In a situation of intensive and massive investment, the economics of production would primarily depend on machine utilization indicated by machine availability. Thus machine available time i.e. the time that a machine is available to do productive work, has to be maximized, for best returns on capital invested and utilization of manpower.In this present research work an online condition monitoring instrumentation system has been developed for condition monitoring of mine winder motor. The instrumentation system has been developed based on current monitoring technique. The symmetrical current component present in the unbalanced motor current is sensed with the help of current transformer, current to voltage converter, all pass filters and adders. Any electrical fault in mine winder motor will produce unbalancing in the motor circuit and will cause for the development of symmetrical current component. The type of electrical fault can be determined by sensing the symmetrical current component. One important advantage of this condition monitoring technique is that the instrument can be made hand held and the same hand held instrument may be used for the fault diagnosis of other motors also.A novel condition monitoring instrumentation system based on symmetrical component filter has been developed for on-line condition monitoring of mine winder motor. The instrumentation system would be able to diagnose various incipient faults of mine winder motor and will increase the safety as well as availability of mine winder.The result obtained from symmetrical current component filter based motor diagnostic technique has been verified with the result obtained by axial leakage flux based motor diagnostic technique for similar simulated motor fault condition to pinpoint the exact faulty of condition of the model mine winder motor.

Development and Validation of a Three-Dimensional Diffusion Code Based on a High Order Nodal Expansion Method for Hexagonal-zGeometry

A three-dimensional, multigroup, diffusion code based on a high order nodal expansion method for hexagonal-zgeometry (HNHEX) was developed to perform the neutronic analysis of hexagonal-zgeometry. In this method, one-dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four-order polynomial expansion, respectively. The approximations for one-dimensional radial and axial spatially flux both have second-order accuracy. Moment weighting is used to obtain high order expansion coefficients of the polynomials of one-dimensional radial and axial spatially flux. The partially integrated radial and axial leakages are both approximated by the quadratic polynomial. The coarse-mesh rebalance method with the asymptotic source extrapolation is applied to accelerate the calculation. This code is used for calculation of effective multiplication factor, neutron flux distribution, and power distribution. The numerical calculation in this paper for three-dimensional SNR and VVER 440 benchmark problems demonstrates the accuracy of the code. In addition, the results show that the accuracy of the code is improved by applying quadratic approximation for partially integrated axial leakage and four-order approximation for one-dimensional axial spatially flux in comparison to flat approximation for partially integrated axial leakage and quadratic approximation for one-dimensional axial spatially flux.

A Novel Unsymmetrical Multi-Segment Concentric Winding Scheme for Electromagnetic Force and Leakage Flux Mitigation in HTS Power Transformers

The high axial and radial forces caused by short circuits can be very detrimental to high-temperature superconductor (HTS) windings of HTS transformers. Axial forces above the HTS winding critical value cause irreversible effects on the critical current reduction of an HTS tape. Such forces can disrupt the normal performance of HTS transformers and lead to quench phenomenon and insulation breakdown. Accordingly, any optimization in the design of HTS transformers that decreases the leakage flux and electromagnetic forces is very significant. This paper presents a novel method for reduction of leakage flux and thereby electromagnetic force in the windings of an HTS power transformer. First, concentric primary and secondary windings are subdivided into certain number of segments. In the next step, the proposed method, which is based on selecting the optimum distributive ratios for the created subwindings, is applied to the windings. In order to verify the effectiveness of the proposed method, an advanced finite-element method has been used. The method uses accurate and nonlinear $E{-}J$ power law for defining the superconductivity characteristic. The results showed the efficiency of the applied method to mitigate the radial and axial leakage flux and thereby electromagnetic forces in the windings of the HTS transformer.

Optimization of Distributive Ratios of Apportioned Winding Configuration in HTS Power Transformers for Hysteresis Loss and Leakage Flux Reduction

In recent years, using high-temperature superconductor (HTS) transformers in transportation and electrical power systems has attracted much interest. The major advantages of HTS transformers compared with conventional ones are much smaller size and volume and lighter weight in confined spaces of urban areas or transportation devices. One of the most critical parameters to design, fabricate, and commercialize HTS transformers is hysteresis loss in HTS tapes. Using numerical methods, the accurate value of hysteresis loss and efficiency can be calculated or estimated in HTS transformers. In this paper, two innovative techniques to reduce the leakage flux and thereby hysteresis loss in HTS transformers have been proposed. In the first technique, the concentric windings of HTS transformer are apportioned into a certain number of sub-windings. In the second one, with optimizing the distributive ratios of sub-windings, the windings become unsymmetrical. In order to demonstrate the effectiveness of proposed techniques, an accurate and advanced numerical method based on finite element analysis has been used to design four symmetrical and unsymmetrical primary (P)-secondary (S)-P-S-P and P-S-P-S-P-S-P winding schemes. The simulation results prove the effectiveness of both techniques in reducing the radial and axial leakage flux magnitudes and thereby hysteresis loss in HTS windings.

Effects of winding angle on the behaviour of glass/epoxy pipes under multiaxial cyclic loading

The effects of winding angle on the behaviour of glass/epoxy composite tubes under multiaxial cyclic loading were investigated. The performance of such composite tubes was studied using an indigenous automated test procedure that is compatible with the internal qualification requirements of the composite pipe manufacturers. Glass fibre reinforced epoxy (GRE) composite pipes with three winding angles, namely, [±45°]4, [±55°]4, and [±63°]4, were tested. A novel automated test rig was fabricated to accommodate five stress ratios, ranging from pure axial to pure hoop loadings. The cyclic pressure test was conducted until droplets of water were seen on the outer surface of the pipe. Failure envelopes were then constructed based on the first ply failure (FPF) points determined from the axial stress to hoop strain response at five stress ratios. Three functional failure modes, namely, tensile axial, weepage, and local leakage failures, were observed during the tests. The results indicate that each winding angle dominates a different optimum pressure loading condition, namely, [±55°]4 for pure hydrostatic loading, [±45°]4 for hoop to axial loading, and [±63°]4 for quad hoop to axial loading. The envelopes show a strong dependence on the stress ratio and winding angle.

A new approach to reduce the leakage flux and electromagnetic force on distribution transformer under unbalanced faults based on finite element method

Summary The short-circuit capacity design of a transformer is one of the most significant and challenging criteria. Electromagnetic forces in transformer winding regions are produced by interaction between the leakage flux and current density. Under short circuit condition when currents increase to 20 times, windings are exposed to very high electromagnetic force. This paper is focused on the reduction of leakage flux and electromagnetic force under fault condition of distribution transformer. This article is composed of two parts. First, Finite Element Methods (FEM) that improved in Ansoft-Maxwell has been used to investigate the leakage flux and electromagnetic forces of three-phase, three leg, 10/0.4-kV, 1000-kVA distribution transformer. Then, to optimal design of transformer under single phase to ground short circuit condition two auxiliary winding was chosen as an active shielding to reduce the radial and axial leakage flux. According to Lenz's law this windings produce a magnetic flux that is the apposite of the leakage flux from an iron-core system. Results indicate that the proposed auxiliary winding remarkably decreased the leakage flux and electromagnetic force in the winding regions. It should be noted that the resultant of main flux is not affected by auxiliary winding. Copyright © 2015 John Wiley & Sons, Ltd.

Study on Design of Rotor Profile for the Twin Screw Vacuum Pump with Single Thread Tooth

The trapezoidal profile is always used as part of tooth profile in the screw vacuum pump. However, interferential phenomenon occurs when using trapezoidal tooth profile. The arc is added to the trapezoidal profile to obtain the self-conjugate curve. The geometric characters of new profiles are compared with the old ones from view point of area of leakage triangle, length of contacting line, area utility coefficient, and etc. The rotor with the selfconjugate curve has characteristics of the small axial leakage area. Radial leakage from the carryover was within the same volume and would not influence the mass flow rate of the vacuum pump. High ultimate vacuum can be reached by utilizing this profile.

Improved Flow Rate in Electro-Osmotic Micropumps for Combinations of Substrates and Different Liquids With and Without Nanoparticles

A new design for an electro-osmotic flow (EOF) driven micropump was fabricated. Considering thermal management applications, three different types of micropumps were tested using multiple liquids. The micropumps were fabricated from a combination of materials, which included: silicon-polydimethylsiloxane (Si-PDMS), Glass-PDMS, or PDMS-PDMS. The flow rates of the micropumps were experimentally and numerically assessed. Different combinations of materials and liquids resulted in variable values of zeta-potential. The ranges of zeta-potential for Si-PDMS, Glass-PDMS, and PDMS-PDMS were −42.5–−50.7 mV, −76.0–−88.2 mV, and −76.0–−103.0 mV, respectively. The flow rates of the micropumps were proportional to their zeta-potential values. In particular, flow rate values were found to be linearly proportional to the applied voltages below 500 V. A maximum flow rate of 75.9 μL/min was achieved for the Glass-PDMS micropump at 1 kV. At higher voltages nonlinearity and reduction in flow rate occurred due to Joule heating and the axial electro-osmotic current leakage through the silicon substrate. The fabricated micropumps could deliver flow rates, which were orders of magnitude higher compared to the previously reported values for similar size micropumps. It is expected that such an increase in flow rate, particularly in the case of the Si-PDMS micropump, would lead to enhanced heat transfer for microchip cooling applications as well as for applications involving micrototal analysis systems (μTAS).

Methods for reconstruction of the density distribution of nuclear power

In analytical reconstruction method (ARM), the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G) and homogeneous nodes with dimensions of a fuel assembly (FA). The solution employs a 2D fourth-order expansion for the axial leakage term. The Nodal Expansion Method (NEM) provides the solution average values as the four average partial currents on the surfaces of the node, the average flux in the node and the multiplying factor of the problem. The expansion coefficients for the axial leakage are determined directly from NEM method or can be determined in the reconstruction method. A new polynomial reconstruction method (PRM) is implemented based on the 2D expansion for the axial leakage term. The ARM method use the four average currents on the surfaces of the node and four average fluxes in corners of the node as boundary conditions and the average flux in the node as a consistency condition. To determine the average fluxes in corners of the node an analytical solution is employed. This analytical solution uses the average fluxes on the surfaces of the node as boundary conditions and discontinuities in corners are incorporated. The polynomial and analytical solutions to the PRM and ARM methods, respectively, represent the homogeneous flux distributions. The detailed distributions inside a FA are estimated by product of homogeneous distribution by local heterogeneous form function. Moreover, the form functions of power are used. The results show that the methods have good accuracy when compared with reference values and the ARM method is more accurate than the PRM method. The largest errors are in the peripheries of FAs, near the reflector, reinforcing the fact that these errors are associated with the homogenization process.