Axial Leakage Research Articles

A Study on Analysis of Synchronous Reluctance Motor Considering Axial Flux Leakage Through End Plate

This paper discusses the design of a synchronous reluctance motor designed to replace a 5.5 kW industrial induction motor. End plates are axially placed at both ends of an industrial motor to fix the lamination of the rotor. It is manufactured from magnetic materials to ensure manufacturing convenience and price advantage. With its construction from magnetic materials, a lower output of the motor due to axial flux leakage is observed. This paper analyzed the drop in output caused by the axial flux leakage in the end plate constructed of magnetic material and methods to compensate for the said output drop. The first method to improve the output degradation problem was to fabricate the end plate as a non-magnetic material. This, however, was found to be inefficient due to the need for different mass production apparatus for the new material. A new method proposed in this paper involved using the end plate constructed of magnetic material but incorporating a new shape to the end plate with the saliency ratio to resolve the decreased output problem. This method converts the magnetic flux leaked in the axial direction into reluctance torque. The 3-D FEA was performed for the validity of the method, and reliability was verified through the production and testing of the actual models.

Reduction of Torque Ripple in Consequent-Pole Permanent Magnet Machines Using Staggered Rotor

Consequent-pole permanent magnet (CPM) machines have considerable potential for low-cost applications because they can improve the permanent magnet (PM) utilization ratio. However, the phase back electromotive force (EMF) of CPM machines with Ns /( mt ) = odd ( t is the greatest common divisor of the stator slot number Ns and the rotor pole-pair number p , and m is the phase number) is asymmetric, i.e., the phase back EMF has even-order harmonics, which will increase torque ripples. This paper utilized the staggered rotor to eliminate the even-order harmonics and reduce the cogging torque of CPM machines, thereby potentially decreasing torque ripples considerably. The axial flux barrier in the middle of the rotor was used and optimized using three-dimensional finite element (FE) analysis to reduce the axial leakage flux of the CPM machine with the proposed staggered rotor. Furthermore, the axial magnetized PM was embedded in the flux barrier, which improved the flux density of the airgap above the iron-pole and, consequently, further increased the output torque. The electromagnetic performance of the proposed machine, including the open-circuit airgap flux density, back EMF, average torque, torque ripples, and PM utilization, was compared with that of the conventional CPM machine. Results showed that the proposed machine obtained a similar torque and PM utilization ratio but a much lower torque ripple compared with the conventional one.

The Mathematical Model of Coupling Calculation the Electromagnetic Field and Heats of End Zone Powerful Turbogenerator

A quasi-three-dimensional field mathematical model of the electromagnetic field and heat transfer processes in end zone of a powerful turbogenerator has been developed. A model is the intermediate version between two-dimensional and three-dimensional solutions and is based on the numeral calculations in transversal and longitudinal sections of turbogenerator, interconnected by a complex of boundary conditions. On the first stage, a two-dimensional field model of the electromagnetic field in transversal section of central zone of a turbogenerator is considered. Then, taking into account the field distribution in central part, the magnetic field in longitudinal section is simulated. In response to the symmetry of the machine along axial and radial directions, the calculation area of end zone is considered as a half of the rotor section along its axis and the section of the stator core tooth in the tangential direction (circumferentially). Having taken the distribution of electromagnetic parameters obtained in the load mode of the machine as the initial data, the thermal losses in the elements and nodes of the end zone are determined. As a result of solving the joint problem of calculating the electromagnetic field and heat exchange processes, the distribution of heating has been obtained not only on the surface, but also inside the structural parts of the end zone. In particular, it has been found that the maximum temperature of 97.3 °C takes place in the tooth area of the end package of the stator core. This is explained by the combined effect of the main radial field, the axial leakage flux of the frontal portions of the stator and rotor windings, as well as by the “buckling” of a portion of the main flux out of the air gap. In addition, the pressure plate shielding effect is the cause of local field concentration in the toothed zone of the end package. The presented model makes it possible as early as at the design stage to evaluate the efficiency of design solutions for the formation of the end zone of the turbogenerator stator for different load modes of the machine, including the modes of consumption of reactive power.

The Fluid Force on a Whirling Columnar Rotor

In the operation of hydro turbines and pump, self-excited vibration can occur due to fluid force which is generated as a response to the vibration and is called rotordynamic fluid force. The tangential component of rotordynamic fluid force has large impact on the stability of rotors. Characteristics of the tangential fluid force acting on a whirling columnar rotor which is modelled on the front shroud of a Francis turbine during self-excited vibration were investigated in computation in the present study. The angular velocity of the whirling motion of the rotor and the tangential force could be normalized by the axial velocity of axial leakage flow through the clearance between the rotor and the casing and the square of it, respectively. In the range of large whirling velocity, the tangential force was caused by a pressure distribution in the case without axial leakage flow. In the range of small whirling velocity, it is known that the tangential force is generated by the inertia of axial leakage flow. In the range of middle whirling velocity, the tangential force was found to be caused by both effects of whirling motion of the rotor in static fluid and the inertia of axial leakage flow. The pressure distribution without axial leakage flow was due to pressure loss in the wake of the rotor in addition to effects of shear stress and discharge from /suction into the clearance.

누설 유동을 고려한 다단 축류 터빈의 유선곡률해석법에 대한 연구

누설 유동을 고려한 다단 축류 터빈의 유선곡률해석법에 대한 연구

Improved Accuracy in the 2-D/1-D Method with Anisotropic Transverse Leakage and Cross-Section Homogenization

The Two-Dimensional (2-D)/One-Dimensional (1-D) method allows pin-resolved computational transport solutions for large, full-core light water reactor simulations at relatively low computational cost compared to a true three-dimensional (3-D) transport method. The 2-D/1-D method constructs an approximation to the 3-D transport equation with (1) a 2-D transport equation in the radial variables and , discretized on a fine radial spatial grid, and (2) a 1-D transport (or approximate PN) equation in the axial variable , discretized on a radially coarse spatial grid. The 2-D and 1-D equations are coupled through transverse leakage (TL) terms. In this paper, a new 2-D/1-D P3 method with anisotropic transverse leakages and anisotropic homogenized 1-D cross sections (XSs) is proposed to improve the accuracy of conventional 2-D/1-D with pin homogenization. It is shown that only the polar component of the anisotropic homogenized XS has a significant effect on the solution; the azimuthal component is negligible. However, the polar and azimuthal components of the leakage terms are both important. The new method is implemented in the 2-D/1-D code Michigan PArallel Characteristics Transport (MPACT). The method in this paper is shown to achieve nearly 3-D transport accuracy with sufficient refinement in space and angle. The improvement of this new method compared to the previous 2-D/1-D method in MPACT is most notable in problems with strong axial leakage and sharp axial discontinuities, such as control rod tips or part-length rods. The method is computationally more expensive than the existing 2-D/1-D method with isotropic TL and XSs, but this additional cost may be justified when the axial flux shape does not vary smoothly due to axial heterogeneity and needs to be resolved well.

Numerical Investigation of the Fluid Flow Characteristics in the Hub Plate Crown of a Centrifugal Pump

Due to the lack of understanding in the flow mechanism of the hub plate crown, the current calculation of the disc friction loss and the axial thrust in the centrifugal pump often uses empirical formulas. Research on the flow characteristics of the hub plate crown is of practical significance. The shroud and hub cavities are respectively studied with regard to tangential and radial velocities at the four different angular positions (0°, 90°, 180°, and 270°) at the four different operational points (0.6Qsp, 0.8Qsp, 1.0Qsp, and 1.2Qsp). Results indicate that at the same operational point, the smaller the volute chamber sectional area is, the higher the tangential velocity of the fluid core zone of the shroud cavity is. Radial leakage flow from the volute to the seal ring at the same operational point appears in 0° and 90° direction; when the flow is large, the tangential and radial velocities of the shroud and hub cavities with the same radius tend to be equal with axial symmetry. The axial leakage flow through the balance holes significantly affects the radial distribution of both tangential and radial velocities of fluid flow in the hub cavity. The numerical calculation results of fluid leakage through the clearance of back sealing ring are in good agreement with the test results. Accordingly, the magnitude of leakage is closely related to the fluid pressure and velocity distribution in the hub plate crown of the centrifugal pump. The analysis of the flow characteristics in the hub plate crown of the centrifugal pump could reveal the cause of the disc friction loss from the mechanism, providing a significant guidance for improving the accuracy of calculation and balancing the axial thrust in the centrifugal pump.

Validation of in-line inspection data quality and impact on steel pipeline diagnostic intervals

The aim of this research is to evaluate the inaccuracies of pipe wall flaws sizing derived from an axial excitation magnetic flux leakage technology (MFL), in respect to the defect field checking. During direct assessment, construction and metallurgical features such as rolling anomalies and ingot imperfections were discovered on the natural gas pipeline serviced for many years. MFL tool sizing accuracy of pipe wall losses was individually compared with a limited number of excavations. The inspection equipment errors were estimated based on a small-scale of the verified anomalies within tolerances and the correct pipe surface classifications. The quality of diagnostic results and their correspondence to the pipeline maximum admissible operating pressure calculations was highlighted. However, certain flaws on the considered pipeline are not metal loss-type and, for this reason, cannot be assessed by the code based level 1 engineering method. A deterministic approach to the pipeline pigging time intervals was analyzed. The impact of the defect growth rate on the inspection schedule was presented in the current paper in the simplest way. Based on the considered analysis and author's experience, expert judgment guidelines for conducting in-line inspection on underground gas transmission pipelines were formulated in this publication.

Investigating the application of a honeycomb abradable lining in the turbine stage of an aero-engine

Abstract Modern aero-engines use abradable linings to reduce axial gas leakage. In this study the wear performance of a new developed nickel superalloy honeycomb abradable lining was investigated on a novel high-speed test rig, using in-situ measurement techniques, combined with post-test microscopy and X-ray fluorescence based elemental analysis. In particular the effect of changing the nickel-aluminide filler ratio was considered, as well as the impact of thermal ageing of the specimens. Compaction of abradable occurs, resulting in fin wear, along with high forces and temperatures. This wear mechanism is cyclic with debris ejection and sparks. Ageing of the abradable generally leads to an increase in fin wear, with the exception that in one case this lead to improved fracture of the abradable and an improved cutting performance by the fin.

A Study on the Maximum Flux Linkage and the Goodness Factor for the Spoke-Type PMSM

In this paper, we propose a goodness factor that shows how the output density of a Spoke-type permanent-magnet synchronous motor (PMSM) is improved than that of the conventional surface permanent-magnet synchronous motor (SPMSM). The application of the goodness factor, which is defined as the ratio of the total flux between different motor configurations, enables a comparison of the total flux between the SPMSM and spoke-type PMSM. A performance comparison analysis between the two motor configurations with the same rotor diameter, air gap length, stack length, permanent-magnet usage, and materials was performed using the proposed goodness factor. In order to improve the performance prediction accuracy, furthermore, the effect of both the bridge leakage and the axial leakage was included during the analysis process of the spoke-type PMSM. Finally, in order to verify the proposed method, SPMSM and Spoke-type PMSM with the same outer diameter size and permanent-magnet usage were fabricated and evaluated.

Characteristics Analysis of SPMSM Using 2-D Finite-Element Analysis Considering Axial Leakage Flux

In this paper, the characteristics analysis of the surface-mounted permanent-magnet synchronous motor is carried out using the method of reflecting the axial leakage magnetic flux into the 2-D finite-element analysis (2-D FEA), and the result is discussed. For the method of projecting the axial leakage flux on the 2-D plane, the permeance coefficient was introduced. By using the proposed method, the parameters such as d- and q-axes inductance and linkage flux for d- and q-axes equivalent circuit analysis were calculated, and the characteristics analysis was performed. In order to verify the effectiveness of the proposed 2-D FEA, a speed versus torque experiment was performed and compared with the analysis results.

Design Comparison of NdFeB and Ferrite Radial Flux Surface Permanent Magnet Coaxial Magnetic Gears

Magnetic gears promise the benefits of mechanical gears with added advantages from contactless power transfer. Although most of the literature focuses on minimizing the size of magnetic gears, their material costs must also be reduced to achieve economic feasibility. This paper compares the active material costs of NdFeB and ferrite radial flux coaxial magnetic gears with surface permanent magnets through a parametric two-dimensional (2-D) and 3-D finite element analysis study. Differences in optimal design trends such as pole counts and magnet thicknesses are illustrated for the two materials. The results demonstrate that, for most historical price rate scenarios, NdFeB gear designs are capable of achieving lower active material costs than ferrite gear designs, and they are always capable of achieving much higher torque densities. Based on the selected design constraints, relative to a nominal ferrite cost of $10/kg, NdFeB must cost more than $90/kg before ferrite is cost competitive. However, ferrite gears can achieve higher efficiencies than NdFeB gears, especially at high speeds, and generally emit less axial leakage flux. Additionally, contour plots are provided to show the impact of material price rate variation on the cost break points.

Accuracy and analysis of the iteratively coupling 2D/3D method for the three-dimensional transport calculations

The characteristics based coupling method is almost becoming a standard transport solver for the whole-core calculations, which includes the 2D/1D fusion method and the 2D/1D method. Different with the 2D/1D method that utilizes 1D calculation to get the axial leakage, here introduces a 2D/3D coupling method employing the 3D SN method to get the axial leakage. Compared with the 2D/1D method, because of the better axial leakage from the 3D SN method, the 2D/3D could decrease the number of MOC layers while keeping the accuracy. In another word, it could improve the accuracy with the same axial mesh size. In the paper, the theory and leakage analysis of this 2D/3D coupling method is introduced. And a small test problem is given to show the leakage comparison of axial leakage between the 2D/1D method and 2D/3D method. Finally the results of the 3D C5G7 problems are given to demonstrate the accuracy and performance of the 2D/3D method.

Accelerated polynomial axial expansions for full 3D neutron transport MOC in the APOLLO3® code system as applied to the ASTRID fast breeder reactor

In recent years a solver based on the Method of Characteristics (MOC) allowing the treatment of 3D extruded geometries has been developed inside the TDT code of APOLLO3. The standard Step Characteristics (SC) approximation is used and results show an excellent agreement with Monte-Carlo simulations. However a fine mesh refinement is needed to converge axially the strong flux gradients customarily appearing in 3D reactor physics applications. In this paper an improvement of this method is proposed: the results of the previous work show that much of the flux variations are likely to be represented by a polynomial basis along the vertical direction. Since most of the geometrical and physical heterogeneities are radially located, the SC approach is preserved to represent the solution over the radial plane. As a matter of fact the strong irregularities in the geometrical meshes prevent from an efficient use of a polynomial expansion. On the contrary along the axial direction the computational meshes assume a Cartesian shape, well suited for a polynomial representation of sources and fluxes. A convenient polynomial development in this direction allows us to approximate the strong flux slopes without the help of a large number of axial meshes. Finally we will show how synthetic accelerated results for the fourth generation fast breeder reactor ASTRID perform with respect to computational time, memory efficiency and precision against Monte-Carlo calculations. We will consider assembly geometries that span the full-height of the reactor and that are characterized by the strong heterogeneity conceived to enhance the axial leakage which improves the safety features of this new concept, especially under void conditions.

A Novel Approach for 2-D Electromagnetic Field Analysis of Surface Mounted Permanent Magnet Synchronous Motor Taking Into Account Axial End Leakage Flux

This paper proposes a novel approach for electromagnetic field analysis of surface-mounted permanent synchronous machines taking into account axial end leakage flux. In order to calculate the axial end leakage flux using the 2-D finite-element analysis (FEA), the leakage magnetic flux in the axial direction is reflected to the 2-D model by applying the permeability factor into the slot area. The permeability factor is derived by the equivalent magnetic circuit method. At this time, the permeability factor is calculated by considering the main leakage path in the slot and the leakage path in the axial direction of air region. The effectiveness of the proposed method is verified by comparing the results of the proposed method with the experimental results as well as the conventional 2-D FEA results and the 3-D FEA results.

Unsteady Leakage Flow Through Axial Clearance of an ORC Scroll Expander

As the scroll-type expander (STE) becomes an attractive expansion device for small-scale organic Rankine systems, performance enhancement of STE could achieve a further improvement of the energy efficiency of ORC system. The gas leakages through the axial and radial clearances have a great effect on the overall performance of STE. The present work proposed a three-dimensional numerical technique available for modeling the radial leakage flows through the axial clearances at the tip and root of scroll wrap. The radial leakage flow patterns of both axial clearances are investigated. Asymmetrical distribution of the radial leakage flow through the axial clearances at both sides of working chambers are revealed. Leakage flow difference between the top and bottom axial leakage clearances is comparatively discussed. The effects of radial leakage on the flow fields in the working chambers are also analyzed. The results show the radial leakage flows occur at the axial clearances of both the scroll segments between asymmetrical working chambers and those between symmetrical working chambers. Radial leakage flows through the top and bottom axial clearances are approximately symmetrical about the meshing line. Pressure distribution in the axial clearance passage is uneven along the scroll involute direction, especially in the axial clearance passages between asymmetric chambers. Pressure distortion occurs in the downstream of the axial clearance passage between asymmetric working chambers nearby the mesh point of the scroll wraps. Radial leakage flow leads to the secondary vortex flows and non-uniform pressure distributions in the working chambers.

Advanced Burner Reactors with Breed-and-Burn Thorium Blankets for Improved Economics and Resource Utilization

This paper assesses the feasibility of designing seed-and-blanket (S&B) sodium-cooled fast reactor (SFR) cores to generate a significant fraction of the core power from radial thorium-fueled blankets that operate in the breed-and-burn (B&B) mode. The radiation damage on the cladding material in both seed and blanket does not exceed the presently acceptable constraint of 200 displacements per atom (dpa). The S&B core is designed to have an elongated seed (or driver) to maximize the fraction of neutrons that radially leak into the subcritical B&B blanket and reduce the neutron loss via axial leakage. A specific objective of this study is to maximize the fraction of core power generated by the B&B blanket that is proportional to the neutron leakage rate from the seed to the blanket. Since the blanket feed fuel is very inexpensive and requires no reprocessing and remote fuel fabrication, a larger fraction of power from the blanket will result in a lower fuel cycle cost per unit of electricity generated by the SFR core. It is found possible to design the seed of the S&B core to have a lower transuranics (TRU) conversion ratio (CR) than a conventional advanced burner reactor (ABR) core without deteriorating core safety. This is due to the unique synergism between a low CR seed and the B&B thorium blanket. The benefits of the synergism are maximized when using an annular seed surrounded by inner and outer thorium blankets. Two high-performance S&B cores are designed to benefit from the annular seed concept: (1) an ultra-long-cycle core having a CR = 0.5 seed and a cycle length of ~7 effective full-power years (EFPYs) and (2) a high-transmutation core having a TRU CR of 0.0. The TRU transmutation rate of the latter core is comparable to that of the reference ABR with a CR of 0.5, and the thorium blanket can generate close to 60% of the core power. Because of the high blanket power fraction along with the high discharge burnup of the CR = 0 seed, the reprocessing capacity per unit of core power required by this S&B core is only approximately 1/6th that of the reference ABR core with a TRU CR of 0.5. Although the seed fuel CR is nearly zero, the burnup reactivity swing is low enough to enable a cycle length of more than 4 EFPYs. This is attributed to a combination of reactivity gain in the thorium blankets over the cycle and the relatively high heavy metal inventory. Moreover, despite the very low leakage, the S&B cores feature a less positive coolant reactivity coefficient and large enough negative Doppler coefficient even when using nonfertile fuel for the seed, because of the unique physics properties of the 233U and Th in the thorium blankets. With the long cycles, the S&B SFR is expected to have a higher capacity factor, and therefore a lower cost of electricity, than conventional ABRs. The discharge burnup of the thorium blanket fuel is typically 70 MWd/kg such that the thorium fuel utilization is approximately 12 times that of natural uranium in light water reactors. A sensitivity study is subsequently undertaken to quantify the trade-off between the core performances and several design variables: amount of zirconium in the inert matrix seed fuel, active core height, coolant pressure drop, and radiation damage constraint. The effect of the criterion used for quantifying acceptable radiation damage is evaluated as well. It is concluded that a viable S&B core can be designed without significant deviation from typical SFR core design practices.

Theoretical Analysis of the Static Characteristics of the Carbon Segmented Seal

The segmented carbon seal is regularly used for sealing bearing chambers of aeronautical turboengines or as part of a buffer seal in space turbopumps. The seal operates with contaminated air or with an inert gas and is made of many identical carbon segments (generally three or six) with reciprocally overlapping ends. The segments are pressed against the rotor by the pressure difference between the upstream and the downstream chambers and by a circumferential (garter) spring. The pressure difference and an axial spring press the segments also against the stator. The inner cylindrical surface of each segment is provided with pads that create an aerodynamic lift proportional to the rotor speed. Following this lift force, the segments of the seal are pushed away from the rotor and the seal opens. The contact between the rotor and the segments is lost, and an axial leakage path is thus created. Although it was developed since long, a model for calculating the characteristics of the segmented seal is completely absent from the scientific literature. The goal of the present work is to fill this gap at least for the static characteristics (leakage and torque). The analysis is carried out for a single segment of the seal by supposing that all the segments have the same characteristics. Each segment has a planar motion (i.e., three degrees-of-freedom (3DOF)), and therefore the film thickness under each pad is not uniform. Given the stationary operating conditions (pressure difference and rotation speed), the present model calculates the equilibrium position of each segment on the bases of the lift and the friction force acting on the pads, the friction forces acting on the nose of the seal, and the radial and axial springs. Once found the static equilibrium position, the leakage and the torque of the seal are calculated. A parametric study enlightens the importance of the pad waviness, the pocket depth, and the spring forces on the characteristics of the segmented seal.

NEMHEX solution of benchmark problems on thermal and fast breeder reactor cores with hexagonal lattice

This paper gives the solution of some benchmark problems for reactor core calculations in hexagonal geometry using a computer code NEMHEX (Nodal Expansion Method for HEXagonal geometry). The problems cover a wide range of thermal reactor cores including large heavy water, fast breeder and VVER reactors in both two and three dimensional. The code is based on higher order nodal expansion method (NEM) for the solution of the neutron diffusion equation in 3-D hexagonal geometry. In this method, flux in each mesh/node and energy group is expanded in terms of polynomial up to third order in X–Y plane and fourth order in axial direction (Z). Weighted residual method is used to calculate the higher order expansion coefficients of the polynomials. Both the partially integrated radial and axial leakages are approximated by the quadratic polynomial. Higher order polynomial expansion [with respect to the work by Lawrence (DIF3D nodal neutronics option for two-and three-dimensional diffusion theory calculations in hexagonal geometry, 1983)] of flux as well as leakage in each node improves the accuracy in power distribution of VVER-1000 type reactor (which is having large size lattice) in terms of maximum reduction in error from 8 to 2%. The final inhomogeneous response matrix equation involves spatial moments of nodal flux and surface averaged partial currents across the surfaces of node. These equations are solved using conventional fission source iteration. This code is used for calculation of effective multiplication factor, neutron flux and fission power distribution. The results of the analysis establish the adequacy of NEMHEX for thermal as well as fast reactor core calculations in hexagonal geometry.

A Study on Correcting the Nonlinearity Between Stack Length and Back Electromotive Force in Spoke Type Ferrite Magnet Motors

The accurate estimation of the performance change according to variations in stack length of motors is important in related industries. A permanent magnet (PM) motor usually represents a characteristic in which its back electromotive force (EMF) constant (K e ) is linearly proportional to stack length. It is an enormous advantage in designing and estimating the performance of PM motors. However, the linearity cannot be held in spoke-type ferrite magnet synchronous motors (SFMSM) due to the axial leakage magnetic flux that is irrelevant to the stack length. Thus, it is possible to accurately analyze the performance of SFMSM using a 3-D finite-element analysis (FEA) method but this method is very inefficient. In this paper, a new relationship formula that can consider the nonlinearity between stack length and back EMF constant in SFMSM is proposed. This formula can estimate the back EMF constant in a new stack length based on the results of 2-D-FEA and 3-D-FEA in a specific stack length. Finally, the validity of this formula is verified through analyzing its accuracy and testing it according to changes in motor parameters.