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21.
On the basis of the Helmholtz decomposition, a grid‐free numerical scheme is provided for the solution of unsteady flow in hydraulic turbines. The Lagrangian vortex method is utilized to evaluate the convection and stretch of the vorticity, and the BEM is used to solve the Neumann problem to define the potential flow. The no‐slip boundary condition is satisfied by generating vortex sticks at the solid surface. A semi‐analytical regularization technique is applied to evaluate the singular boundary surface integrals of the potential velocity and its gradients accurately. The fast multipole method was extended to evaluate the velocity and velocity gradients induced by the discretized vortex blobs in the Lagrangian vortex method. The successful simulation for the unsteady flow through a hydraulic turbine's runner has manifested the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
22.
In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from the viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex–antivortex pairs taking place at space–time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer degrees of the magnetization vector field around the singularities. Moreover, the change of the topological charge of the system is crucial to vortex core reversal processes in ferromagnetic thin films. With the help of the topological current theory and implicit function theorem, the processes of vortex merging, splitting as well as vortex core reversal are discussed in detail. 相似文献
23.
In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
24.
S. Shanmuganathan D. L. Youngs J. Griffond B. Thornber R. J. R. Williams 《国际流体数值方法杂志》2014,74(5):335-358
At low Mach numbers, Godunov‐type approaches, based on the method of lines, suffer from an accuracy problem. This paper shows the importance of using the low Mach number correction in Godunov‐type methods for simulations involving low Mach numbers by utilising a new, well‐posed, two‐dimensional, two‐mode Kelvin–Helmholtz test case. Four independent codes have been used, enabling the examination of several numerical schemes. The second‐order and fifth‐order accurate Godunov‐type methods show that the vortex‐pairing process can be captured on a low resolution with the low Mach number correction applied down to 0.002. The results are compared without the low Mach number correction and also three other methods, a Lagrange‐remap method, a fifth‐order accurate in space and time finite difference type method based on the wave propagation algorithm, and fifth‐order spatial and third‐order temporal accurate finite volume Monotone Upwind Scheme for Conservation Laws (MUSCL) approach based on the Godunov method and Simple Low Dissipation Advection Upstream Splitting Method (SLAU) numerical flux with low Mach capture property. The ability of the compressible flow solver of the commercial software, ANSYS FLUENT , in solving low Mach flows is also demonstrated for the two time‐stepping methods provided in the compressible flow solver, implicit and explicit. Results demonstrate clearly that a low Mach correction is required for all algorithms except the Lagrange‐remap approach, where dissipation is independent of Mach number. © 2013 Crown copyright. International Journal for Numerical Methods in Fluids. © 2013 John Wiley & Sons, Ltd. 相似文献
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Robert L. Jerrard 《偏微分方程通讯》2015,40(2):135-190
We study dynamics of vortices in solutions of the Gross-Pitaevskii equation i? t u = Δu + ??2 u(1 ? |u|2) on ?2 with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter ?. By carefully tracking errors we allow for asymptotically large numbers of vortices, and this lets us connect the Gross-Pitaevskii equation on the plane to two dimensional incompressible Euler equations through the work of Schochet [19]. 相似文献
27.
本文针对坡莫合金椭圆形盘中的磁涡旋结构, 采用微磁学模拟与傅里叶分析相结合的技术研究了磁涡旋自旋波的本征激发模式. 通过沿样品短轴方向施加一面内方向的脉冲磁场, 观察到一系列方位角自旋波模式. 观察到的自旋波模式具有两重对称性, 可以通过C2群理论来进行类型的划分. 此外, 自旋波模式的频率随着方位角指标的变化而线性增加. 模拟结果显示样品的平均交换能量密度明显的高于平均静磁能量密度; 局域交换能量密度主要集中在涡核初始位置, 而局域静磁能量密度主要分布在长轴附近. 交换作用对受限于铁磁薄膜椭圆盘中的单个涡旋态的能量要起主导作用, 从而导致方位角自旋波模式频率随着方位角指标的增加而增加. 相似文献
28.
Danyang Feng Yangbo Dong Liangliang Zhang Dr. Xin Ge Prof. Wei Zhang Prof. Sheng Dai Prof. Zhen-An Qiao 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2020,132(44):19671-19677
The development of noble-metal-free heterogeneous catalysts is promising for selective oxidation of aromatic alcohols; however, the relatively low conversion of non-noble metal catalysts under solvent-free atmospheric conditions hinders their industrial application. Now, a holey lamellar high entropy oxide (HEO) Co0.2Ni0.2Cu0.2Mg0.2Zn0.2O material with mesoporous structure is prepared by an anchoring and merging process. The HEO has ultra-high catalytic activity for the solvent-free aerobic oxidation of benzyl alcohol. Up to 98 % conversion can be achieved in only 2 h, to our knowledge, the highest conversion of benzyl alcohol by oxidation to date. By regulating the catalytic reaction parameters, benzoic acid or benzaldehyde can be selectively optimized as the main product. Analytical characterizations and calculations provide a deeper insight into the catalysis mechanism, revealing abundant oxygen vacancies and holey lamellar framework contribute to the ultra-high catalytic activity. 相似文献
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30.
The interaction between the film-cooling jet and vortex structures in the turbine passage plays an important role in the endwall cooling design. In this study, a simplified topology of a blunt body with a half-cylinder is introduced to simulate the formation of the leading-edge horseshoe vortex, where similarity compared with that in the turbine cascade is satisfied. The shaped cooling hole is located in the passage. With this specially designed model, the interaction mechanism between the cooling jet and the passage vortex can therefore be separated from the crossflow and the pressure gradient, which also affect the cooling jet. The loss-analysis method based on the entropy generation rate is introduced, which locates where losses of the cooling capacity occur and reveals the underlying mechanism during the mixing process. Results show that the cooling performance is sensitive to the hole location. The injection/passage vortex interaction can help enhance the coolant lateral coverage, thus improving the cooling performance when the hole is located at the downwash region. The coolant is able to conserve its structure in that, during the interaction process, the kidney vortex with the positive rotating direction can survive with the negative-rotating passage vortex, and the mixture is suppressed. However, the larger-scale passage vortex eats the negative leg of the kidney vortices when the cooling hole is at the upwash region. As a result, the coolant is fully entrained into the main flow. Changes in the blowing ratio alter the overall cooling effectiveness but have a negligible effect on the interaction mechanism. The optimum blowing ratio increases when the hole is located at the downwash region. 相似文献