一类有理函数的不定积分

目的为了简单地求解有理函数P(x)/Q(x)的积分;方法对∫P(x)/(x-a)mdx∫,P(x)/(x-a)m(x-b)ndx型有理函数的积分给出一般计算公式;结果通过实例说明该公式简捷、对称,避免以往待定系数法带来的诸多不便;结论具有较强的实用性。     

PLC仿真软件在涡流探伤电气系统设计中的应用

分析了涡流探伤系统和工艺流程,介绍了在涡流探伤电气系统中PLC输入输出信号地址的分配情况,然后基于对S7-PLCSIM界面的描述,利用S7-PLCSIM仿真实际的S7-300 PLC。实例表明：仿真结果与涡流探伤中实际的PLC运行一致,因此在电气系统设计过程中可利用S7-PLCSIM来查看程序的运行状况。     

Numerical investigation of unsteady vortex breakdown past 80°/65° double-delta wing

An improved delayed detached eddy simulation （IDDES） method based on the k-x-SST （shear stress transport） turbulence model was applied to predict the unsteady vortex breakdown past an 80o/65o double-delta wing （DDW）, where the angles of attack （AOAs） range from 30° to 40°. Firstly, the IDDES model and the relative numerical methods were validated by simulating the massively separated flow around an NACA0021 straight wing at the AOA of 60°. The fluctuation properties of the lift and pressure coefficients were analyzed and compared with the available measurements. For the DDW case, the computations were compared with such mea-surements as the mean lift, drag, pitching moment, pressure coefficients and breakdown locations. Furthermore, the unsteady properties were investigated in detail, such as the frequencies of force and moments, pressure fluctuation on the upper surface, typical vortex breakdown patterns at three moments, and the distributions of kinetic turbulence energy at a stream wise section. Two dominated modes are observed, in which their Strouhal numbers are 1.0 at the AOAs of 30°, 32° and 34° and 0.7 at the AOAs of 36o, 38° and 40°. The breakdown vortex always moves upstream and downstream and its types change alternatively. Furthermore, the vortex can be identified as breakdown or not through the mean pressure, root mean square of pressure, or even through correlation analysis.     

基于当地流动结构的RANS/LES混合模型

针对传统雷诺平均Navier-Stokes/大涡模拟(RANS/LES)混合模型固有的RANS和LES区域衔接难题,借鉴Vreman提出的亚格子(SGS)模型,提取其中描述流动状态的判断函数,利用不可压缩槽道湍流标定模型系数,构造了一个新的RANS/LES混合模型。评估算例包括不可压缩槽道湍流、稳态超声速平板边界层、NACA4412翼型绕流和亚临界雷诺数圆柱绕流。该模型作为壁面模化LES,解决了传统RANS/LES方法中速度型偏离对数律(LLM)的缺陷,且拓宽了原Vreman模型在粗糙网格上的适用性,具有较高精度。该模型同时解决了模化应力折损问题,且对大尺度分离流动的模拟精度相较传统的RANS/LES混合模型如脱体涡模拟(DES)有进一步提升。     

A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow

It is of great significance to improve the accuracy of turbulence models in shock-wave/ boundary layer interaction flow. The relationship between the pressure gradient, as well as the shear layer, and the development of turbulent kinetic energy in impinging shock-wave/turbulent boundary layer interaction flow at Mach 2.25 is analyzed based on the data of direct numerical simulation(DNS). It is found that the turbulent kinetic energy is amplified by strong shear in the separation zone and the adverse pressure gradient near the separation point. The pressure gradient was non-dimensionalised with local density, velocity, and viscosity. Spalart–Allmaras(S–A) model is modified by introducing the non-dimensional pressure gradient into the production term of the eddy viscosity transportation equation. Simulation results show that the production and dissipation of eddy viscosity are strongly enhanced by the modification of S–A model. Compared with DNS and experimental data, the wall pressure and the wall skin friction coefficient as well as the velocity profile of the modified S–A model are obviously improved. Thus it can be concluded that the modification of S–A model with the pressure gradient can improve the predictive accuracy for simulating the shock-wave/turbulent boundary layer interaction.     

旋转状态气膜换热机理的数值研究

大涡模拟研究了旋转对单孔平板气膜冷却的影响,气膜出流的雷诺数为2600,吹风比为0.5,计算了静止和旋转数为0.02两种状态的流动和换热,从湍流结构演化的角度讨论了旋转状态气膜换热的机理.结果表明:①发卡涡是决定气膜换热的主要湍流结构,旋转状态发卡涡的形状和运动规律主要受哥氏力的影响;②气膜在哥氏力作用下向高半径方向偏...     

惯性量的几何求法及截面特殊点讨论

本文提出计算截面惯性矩、惯性积和几何方法－作惯性圆法，该法具有直观、方便、简洁的优点。讨论了惯性圆退化一点的特点情形，就任意截面特殊点的位置。     

台劳公式的新证明及其推广

中值定理及其台劳公式的证明一般采用构造辅助函数的方法。利用行列式构造了一个统一格式的辅助函数,利用该辅助函数可以证明各中值定理及台劳公式,而且很容易得出台劳公式的推广形式。     

求极限的若干技巧

在求极限基本方法的基础上，阐述了运用泰勒公式，导数定义，定积分先化简等技巧来求极限。     

一个新的向量等式

给出一个新的向量恒等式，首先采用函数论方法严格证明了该恒等式，其次从向量分析角度指出该恒等式与向量加法的三角形法则之间的密切联系，最后从质量守恒的观点给出该恒等式的一种物理解释。