Search results

The central idea of this research article is to examine the characteristics of Clairaut submersions from Lorentzian trans-Sasakian manifolds of type (α, β) and also, to enhance this geometrical analysis with some specific cases, namely Clairaut submersion from Lorentzian α-Sasakian manifold, Lorentzian β-Kenmotsu manifold and Lorentzian cosymplectic manifold. Furthermore, the authors discuss some results about Clairaut Lagrangian submersions whose total space is a Lorentzian trans-Sasakian manifolds of type (α, β). Finally, the authors furnished some examples based on this study.

This research discourse based on classifications of submersion, mainly Clairaut submersions, whose total manifolds is Lorentzian trans-Sasakian manifolds and its all classes like Lorentzian Sasakian, Lorenztian Kenmotsu and Lorentzian cosymplectic manifolds. In addition, the authors have explored some axioms of Clairaut Lorentzian submersions and illustrates our findings with some non-trivial examples.

The major finding of this study is to exhibit a necessary and sufficient condition for a submersions to be a Clairaut submersions and also find a condition for Clairaut Lagrangian submersions from Lorentzian trans-Sasakian manifolds.

The results and examples of the present manuscript are original. In addition, more general results with fair value and supportive examples are provided.

The purpose of this paper is to present a new approach to optimizing the design of 3D magnetic circuits. This approach is based on topology optimization, where derivative calculations are performed using the continuous adjoint method. Thus, the continuous adjoint method for magnetostatics has to be developed in 3D and has to be combined with penalization, filtering and homotopy approaches to provide an efficient optimization code.

To provide this new topology optimization code, this study starts from 2D magnetostatic results to perform the sensitivity analysis, and this approach is extended to 3D. From this sensitivity analysis, the continuous adjoint method is derived to compute the gradient of an objective function of a 3D topological optimization design problem. From this result, this design problem is discretized and can then be solved by finite element software. Thus, by adding the solid isotropic material with penalization (SIMP) penalization approach and developing a homotopy-based optimization algorithm, an interesting means for designing 3D magnetic circuits is provided.

In this paper, the 3D continuous adjoint method for magnetostatic problems involving an objective least-squares function is presented. Based on 2D results, new theoretical results for developing sensitivity analysis in 3D taking into account different parameters including the ferromagnetic material, the current density and the magnetization are provided. Then, by discretizing, filtering and penalizing using SIMP approaches, a topology optimization code has been derived to address only the ferromagnetic material parameters. Based on this efficient gradient computation method, a homotopy-based optimization algorithm for solving large-scale 3D design problems is developed.

In this paper, an approach based on topology optimization to solve 3D magnetostatic design problems when an objective least-squares function is involved is proposed. This approach is based on the continuous adjoint method derived for 3D magnetostatic design problems. The effectiveness of this topology optimization code is demonstrated by solving the design of a 3D magnetic circuit with up to 100,000 design variables.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

This study focuses on the CFD numerical simulation and analysis of the vortex stacking problem at the top of the impeller of a high-speed fuel pump, mainly using LCS and entropy production theory to visualize the vortex at the top of the impeller as well as quantitatively analyzing the energy loss caused by the vortex at the top of the impeller. By combining the two methods, the two are well verified with each other that the stacking problem of the vortex at the top of the impeller and the location of the energy loss caused by the vortex are consistent with the vortex location. Such a method can reveal the problem of vortex buildup at the top of the lobe well, and provide a novel guidance idea for improving the performance of high-speed fuel pumps.

Based on CFD numerical simulation and analysis, this study mainly uses LCS and entropy production theory to visualize the top vortex of the impeller. Through the combination of the two methods, the accumulation problem of the top vortex of the impeller and the location of the energy loss caused by the vortex can be well revealed.

(1) The CFD numerical simulation analysis of the high-speed fuel pump is carried out, and the test is conducted to verify the numerical simulation results. The inlet and outlet pressure difference? P is used as the validation index, and the error analysis shows that the error between numerical simulation and test results is within 10%, which meets our requirements. Therefore, we carry out the next analysis with the help of CFD numerical simulation. By analyzing the full working condition simulation, its inlet and outlet differential pressure? P and efficiency? Are evaluated. It is found that its differential pressure decreases with the flow rate and its efficiency reaches its maximum at Qv = 9.87 L/s with a maximum efficiency of 78.32%. (2) We used the LCS in the analysis of vortices at the top of the impeller blades of a high-speed fuel pump. One of the metrics used to describe the LCS in fluid dynamics is the FTLE. The high FTLE region represents the region with the highest and fastest particle trajectory stretching velocity in the fluid flow. We performed a cross-sectional analysis of the FTLE field on the different height surfaces of the impeller on 25% Plane, 50% Plane, and 75% Plane, respectively. And a quarter turn of the rotor rotation was analyzed as a cycle divided into 8 moments. It is found that on 25% Plane, the vortex at the top of the lobe is not obvious, but there are high FTLE values on the shroud surface. On 50% Plane, the lobe top vortex is relatively obvious and the number of vortices is three. The vortex pattern remains stable with the rotating motion of the rotor. At 75% Plane, the lobe top vortex is more visible and its number of vortices increases to about 5 and the vortex morphology is relatively stable. The FTLE ridges visualize the vortex profile. This is a good guide for fluid dynamics analysis. (3) At the same time, we use the entropy production theory to quantitatively analyze the energy loss, and define the entropy production rate Ep. Through the entropy production analysis of the impeller shroud surface and the suction surface of the pressure surface of the blades at eight moments, we find that the areas of high energy loss are mainly concentrated in the leading and trailing edges of the blades as well as in the shroud surface close to the leading edge of the blades, and the value of the entropy production rate is up to 106 W/m3/K. The areas of high energy loss in the leading edge of the blades as well as the trailing edge show a curved arc, and the energy loss is decreasing as it moves away from the shroud surface and closer to the hub surface. The high energy loss areas at the leading and trailing edges of the blades are curved, and the energy loss decreases as they move away from the shroud surface and closer to the hub surface. The energy loss at the pressure surface of the blade is relatively small, about 5 × 105 W/m3/K, which is mainly concentrated near the leading edge of the blade near the shroud surface and the trailing edge of the blade near the hub surface. Such energy loss corresponds to the vortex LCS at the top of the impeller, and the two mirror each other.

This study focuses on the CFD numerical simulation and analysis of the vortex stacking problem at the top of the impeller of a high-speed fuel pump, mainly using LCS and entropy production theory to visualize the vortex at the top of the impeller as well as quantitatively analyzing the energy loss caused by the vortex at the top of the impeller. By combining the two methods, the two are well verified with each other that the stacking problem of the vortex at the top of the impeller and the location of the energy loss caused by the vortex are consistent with the vortex location. Such a method can reveal the problem of vortex buildup at the top of the lobe well, and provide a novel guidance idea for improving the performance of high-speed fuel pumps.

Under the high-speed operating conditions, the effects of wheelset elastic deformation on the wheel rail dynamic forces will become more notable compared to the low-speed condition. In order to meet different analysis requirements and selecting appropriate models to analyzing the wheel rail interaction, it is crucial to understand the influence of wheelset flexibility on the wheel-rail dynamics under different speeds and track excitations condition.

The wheel rail contact points solving method and vehicle dynamics equations considering wheelset flexibility in the trajectory body coordinate system were investigated in this paper. As for the wheel-rail contact forces, which is a particular force element in vehicle multibody system, a method for calculating the Jacobian matrix of the wheel-rail contact force is proposed to better couple the wheel-rail contact force calculation with the vehicle dynamics response calculation. Based on the flexible wheelset modeling approach in this paper, two vehicle dynamic models considering the wheelset as both elastic and rigid bodies are established, two kinds of track excitations, namely normal measured track irregularities and short-wave irregularities are used, wheel-rail geometric contact characteristic and wheel-rail contact forces in both time and frequency domains are compared with the two models in order to study the influence of flexible wheelset rotation effect on wheel rail contact force.

Under normal track irregularity excitations, the amplitudes of vertical, longitudinal and lateral forces computed by the flexible wheelset model are smaller than those of the rigid wheelset model, and the virtual penetration and equivalent contact patch are also slightly smaller. For the flexible wheelset model, the wheel rail longitudinal and lateral creepages will also decrease. The higher the vehicle speed, the larger the differences in wheel-rail forces computed by the flexible and rigid wheelset model. Under track short-wave irregularity excitations, the vertical force amplitude computed by the flexible wheelset is also smaller than that of the rigid wheelset. However, unlike the excitation case of measured track irregularity, under short-wave excitations, for the speed within the range of 200 to 350 km/h, the difference in the amplitude of the vertical force between the flexible and rigid wheelset models gradually decreases as the speed increase. This is partly due to the contribution of wheelset’s elastic vibration under short-wave excitations. For low-frequency wheel-rail force analysis problems at speeds of 350 km/h and above, as well as high-frequency wheel-rail interaction analysis problems under various speed conditions, the flexible wheelset model will give results agrees better with the reality.

This study provides reference for the modeling method of the flexible wheelset and the coupling method of wheel-rail contact force to the vehicle multibody dynamics system. Furthermore, by comparative research, the influence of wheelset flexibility and rotation on wheel-rail dynamic behavior are obtained, which is useful to the application scope of rigid and flexible wheelset models.

The paper aims to clarify the distribution of excess pore pressure during cone penetration in two-layered clay and its influence on penetrometer resistance.

An arbitrary Lagrangian–Eulerian scheme is adopted to preserve the quality of mesh throughout the numerical simulation. Simplified methods of layered penetration and coupled pore pressure analysis of cone penetration have been proposed and verified by previous studies. The investigation is then extended by the present work to study the cone penetration test in a two-layered clay profile assumed to be homogeneous with the modified Cam clay model.

The reduction of the range of pore pressure with decreasing PF will cause a decrease of the sensing distance. The PF of the underlying soil is one of the factors that determine the development distance. The interface can be obtained by taking the position of the maximum curvature of the penetrometer resistance curve in the case of stiff clay overlying soft clay. In the case of soft clay overlying stiff clay, the interface locates at the maximum curvature of the penetrometer resistance curve above about 1.6D.

The cone penetration analyses in this paper are conducted assuming smooth soil-cone contact.

A simplified method based on ALE in Abaqus/Explicit is proposed for layered penetration, which solves the problem of mesh distortion at the interface between two materials. The stiffness equivalent method is also proposed to couple pore pressure during cone penetration, which achieves efficient coupling of pore water pressure in large deformations.

Through the scientific and reasonable evaluation of the site selection of the emergency material reserve, the optimal site selection scheme is found, which provides reference for the future emergency decision-making research.

In this paper, we have chosen three primary indicators and twelve secondary indicators to construct an assessment framework for the determination of suitable locations for storing emergency material reserves. By mean of the improved entropy weight-order relationship weight determination method, the evaluation model of kullback leibler-technique for order preference by similarity to an ideal solution (KL-TOPSIS) emergency material reserve location based on relative entropy is established. On this basis, 10 regional storage sites in Beijing are selected for evaluation.

The results show that the evaluation model of the location of emergency material reserve not only respects the objective knowledge, but also considers the subjective information of the experts, which makes the ranking result of the location of the emergency material reserve more accurate and reliable.

Firstly, the modification factor is added to the calculation formula of traditional entropy weight method to complete the improvement of entropy weight method. Secondly, the order relation analysis method is used to assign subjective weights to the indicators. The principle of minimum information entropy is introduced to determine the comprehensive weight of the index. Finally, KL distance and TOPSIS method are combined to determine the relative entropy and proximity degree of alternative solutions and positive and negative ideal solutions, and the scientific and effective of the method is proved by case study.

This paper aims to introduce an alternative for modeling levitation forces between NdFeB magnets and bulks of high-temperature superconductors (HTS). The presented approach should be evaluated through two different formulations and compared with experimental results.

The T-A and H-ϕ formulations are among the most efficient approaches for modeling superconducting materials. COMSOL Multiphysics was used to apply them to magnetic levitation models and predict the forces involved.The permanent magnet movement is modeled by combining moving meshes and magnetic field identity pairs in both 2D and 3D studies.

It is shown that it is possible to use the homogenization technique for the T-A formulation in 3D models combined with mixed formulation boundaries and moving meshes to simulate the whole device’s geometry.

The case studies are limited to the formulations’ implementation and a brief assessment regarding degrees of freedom. The intent is to make the simulation straightforward rather than establish a benchmark.

The H-ϕ formulation considers the HTS bulk domain as isotropic, whereas the T-A formulation homogenization approach treats it as anisotropic. The originality of the paper lies in contrasting these different modeling approaches while incorporating the external magnetic field movement by means of the Lagrangian–Eulerian method.