基于局部基本解法的声学反问题模拟及Matlab实现

针对柯西声学反问题，即部分边界信息未知的声学问题，本文采用局部基本解法，对基于局部基本解法的声学反问题模拟及Matlab实现进行研究。采用新型半解析无网格配点法，将中心节点处的声压表示成局部支撑域内支撑节点处声压的线性组合，再通过可测边界节点的已知物理量，使内部节点和不可测边界节点的声压值满足控制方程，建立一个大型稀疏线性方程，获得不可测边界的声压值。同时，给出局部基本解法的计算模型及其数值离散格式，并以Matlab为软件平台，设计了声学反问题仿真计算程序，开发了图形用户界面(graphics user interface, GUI)。仿真结果表明，该方法计算精度高，数值稳定，对含有噪声的边界数据可得到较好的反演结果。该研究为声学反问题的数值模拟提供了一种新的思路。     

选择溢流坝反弧尺寸的新方法

在总结现有选择反弧尺寸常用经验公式的基础上，提出了选择合理反弧尺寸的设计准则，并在应用溢流坝等效势流假设的基础上，对多组反弧尺寸进行了数值计算。根据计算结果，作出了在各组反弧尺寸时，挑流出射角θｓ与佛汝德数Ｆｒ的关系曲线，作出了满足设计准则的反弧尺寸与佛当德数的关系曲线，总结出“合理的反弧尺寸只与确定的反弧段弧长有关”的结论。     

立面二维水流数学模型

采用修正Ｋ—ε模型封闭Ｒｅｙｎｏｌｄｓ方程作为紊流控制方程,引入通度概念处理曲面不规则边界,用ＶＯＦ法追踪自由表面,对闸孔出流和溢流坝过坝水流及水跃等一类复杂流速场进行数值模拟。计算结果表明,所建数学模型能够较好地模拟此类水流现象。     

SF6断路器中气流分析的流体网格法

提出了应用于ＳＦ６断路器弧室中复杂流场数值分析的流体网格（ＦＬＩＣ）法，建立了灭弧室气流场的基本控制方程和任意三角形的差分格式，解决了具有任意复杂边界形状的跨音速流的求解问题，给出了用该法计算一台ＳＦ６断路器短路开数据时弧室内热气流流场的应用实例．     

明流隧洞反弧段水力及空化特性研究

明流隧洞反弧段是最容易发生空蚀的部位。本文根据势流理论,运用解析函数的 Riemann—Hilbert 混合边值问题理论,导出了计算二维明流泄洪洞反弧段水力特性的边界积分方程,对反弧段的时均压强,时均流速及水深的分布进行了计算。结合对曲边边界层动量积方程的分析,探讨了反弧末端易于发生空蚀破坏的原因。     

线弹性静力学中的另一类边界积分方程

讨论一类新的边界积分方程，它与经典的Ｒｉｚｚｏ型边界积分方程“共轭互补”探讨了该类边界积分方程数值方法的实现，可望它与经典的Ｒｉｚｚｏ型边界积分方程的恰当组合能导致更有效的边界元法。     

溢流坝反弧水深计算的研究

在消力戽水力设计中,按弧形底板上的水跃计算法和按形成戽内表面旋滚的“临界”水深法都需计算溢流坝反弧段底部的收缩水深h_c(图1)。对于反弧收缩水深的计算,曾经有经验公式,渐变流收缩水深公式。文献[4]指出经验公式缺乏理论依据;渐变流公式不能反映反弧段急变流的流动情况,当水深较大时误差很大。文献[4]中导出了恒定急变流能量方程,并假设反弧段水流线为同心园,采用极坐标,应用恒定急变流能量方程推导出了急变流收缩水深公式。本文应用恒定急变流能量方程,对反弧段水流流线的曲率半径分别采用等半径假设、同心园假设、变半径假设,推导出不同的急变流收缩水深公式。把这些公式的计算值与实验资料比较后,本文认为:采用变半径假设推导的公式适用范围更大。     

弹性介质中SH波传播的三角形格子法

目的提出一种不规则边界非均匀弹性介质中反平面剪切(SH)波传播数值模拟方法,研究反平面剪切波入射时地表起伏及软弱层对场地的影响.方法将实际介质计算区域剖分成三角形网格,构造出控制体,给出积分形式的控制体运动方程;交替运用控制体运动方程和SH波的本构方程,在时间域上递推计算给出被研究区域内各节点的加速度、速度、位移和各格子的应力.结果给出了弹性介质中SH波传播数值模拟三角形格子法.数值算例结果与解析解比较,验证了方法的计算精度和有效性.瞬态反平面剪切波入射时,地表起伏、软弱层会引起场地的运动状态量和应力量的放大,有运动状态量和最大剪应力集中现象.结论SH波传播数值模拟三角形格子法计算精度较高,处理不规则边界非均匀介质波动问题的适应性强,算法实现简单、计算量小.是研究大规模、不规则边界非均匀介质中SH波传播问题的一种有力工具,为岩土动力学中的波动研究提供了一种新的数值方法.     

粘性液体小幅晃动常单元及线性元的分析比较

采用边界元法对容器中粘性、不可压缩液体小幅晃动进行数值分析。从二维线性化的Navier-Stokes方程出发,推导了该问题分析的边界积分方程。结合边界条件建立了问题的一个边界元数值求解过程。数值处理过程中,利用线性元对边界进行离散,对角点进行了有效处理。数值结果与常单元的数值结果比较表明线性元的计算结果有更高的精度。     

分区介质样条边界元位移反分析法

通过改造均质体边界积分方程,对分区粘弹性介质的全定义域建立位移反应分析介积分方程及数值求解格式,其具体做法是：在满足分区介质的边界条件和区界联接条件下,均质体边界积分方程来引入虚拟力影响项,用样条函数把分区介质的边界积分方程离散化,由此简化了分区问题反分析计算程序,使之与求解均质问题的计算方法趋于一体。     

On energy boundary layer equations in power law non-Newtonian fluids

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.     

明渠非恒定流控制方程的求解与应用

本文从物质不灭定律出发导出了明渠非恒定流的连续性方程．把动量变化率和作用于质量的力联系起来，导出了明渠非恒定流的动量方程．对这些很难求解的联立拟线性方程，文中作了一些探讨，在某些条件下，给出了方程的解，并在实测中加以应用．     

Improved Implicit SPH Method for simulating free surface flows of power law fluids

Implicit smoothed particle hydrodynamics method has been proposed to overcome the problem that only very small time steps can be used for high viscosity fluids(such as power law fluids)in order to obtain a stable simulation.However,the pressure field is difficult to simulate correctly with this method because the numerical high-frequency noise on the pressure field cannot be removed.In this study,several improvements,which are the diffusive term in the continuity equation,the artificial viscosity and a simplified physical viscosity term in the momentum equation,are introduced,and a new boundary treatment is also proposed.The linear equations derived from the momentum equation are large-scale,sparse and positive definite but unsymmetrical,therefore,Conjugate Gradient Squared(CGS)is used to solve them.For the purpose of verifying the validity of the proposed method,Poiseuille flows with Newtonian and power law fluids are solved and compared with exact solution and traditional SPH.Drops of different fluid properties impacting a rigid wall are also simulated and compared with VOF solution.All the numerical results obtained by the proposed method agree well with available data.The proposed method shows the higher efficiency than traditional SPH and the less numerical noise on the pressure field and better stability than implicit SPH.     

Similarity solutions to a laminar boundary layer problem in power law fluids

A suitable similarity transformatiopn is introduced to reduce the laminar boundary layer equations of power law fluids to a class of singular nonlinear two-point boundary value problems.The skin friction and shear stress distributions for boundary layer flow over a moving flat plate are investigated by utilizing the shooting technique.Results indicate that for each fixed value of the power law exponent n or the velocity ratio parameter ξ,the skin friction and shear stress decrease with the increasing of n or ξ respectively.     

Slip flow and variable properties of viscoelastic fluid past a stretching surface embedded in a porous medium with heat generation

This study examines theoretically and computationally the non-Newtonian boundary layer flow and heat transfer for a viscoelastic fluid over a stretching continuous sheet embedded in a porous medium with variable fluid properties, slip velocity, and internal heat generation/absorption. The flow in boundary layer is considered to be generated solely by the stretching of the sheet adjacent to porous medium with boundary wall slip condition. Highly nonlinear momentum and thermal boundary layer equations governing the flow and heat transfer are reduced to set of nonlinear ordinary differential equations by appropriate transformation. The resulting ODEs are successfully solved numerically with the help of shooting method. Graphical results are shown for non-dimensional velocities and temperature. The effects of heat generation/absorption parameter, the porous parameter, the viscoelastic parameter, velocity slip parameter, variable thermal conductivity and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction coefficient and Nusselt number are presented. Comparison of numerical results is made with the earlier published results under limiting cases.     

磁流体动力学动量轮的致动特性和影响因素

结合不可压缩流体的纳维?斯托克斯方程和磁流体动力学基本方程,针对电流和电压控制模式下矩形截面环管内金属流体的哈脱曼流动问题建立完整的传递函数模型,深入分析流体中黏滞力项和边界层效应对动量轮输出性能的影响. 通过有限元仿真软件COMSOL对流体运动特性和流场分布进行仿真验证,分析电流、磁场和流体特征参数对动量轮输出指标的影响. 在电流控制模式下,动量轮的角动量输出标度因数约为9.68×10^?5 N·m·s/A,可作为动量轮的设计与优化依据.     

圆顶堰溢流边界层的发展

在总结溢流边界层的有关文献以及采用激光流速仪对圆顶堰模型进行系列试验的基础上,本文研究了圓顶堰外流(势流)区和边界层内的流速分布规律,并且提出了一些经验公式来定量地描述这些规律,经验公式与试验资料尚能吻合。此外,根据在正交曲线坐标系下推导的动量积分方程式,本文计算了圆顶堰溢流边界层的厚度,计算成果与试验资料也基本上相符。最后,本文分析了圆顶堰溢流边界层的发展规律,指出与此规律有关的重要特征参数是上游水头与圓顶堰半径的比值。     

Research of the parameters of SL scaling law

As a universal principle of turbulence cascade,scaling law is important in the research on statistics of turbulence.In the thesis PIV system is used to measure the streamwise velocity vector(u’) and the component of vorti-city (dv’/dx) in order to analyze the parameters of SL scaling law in the boundary layer at Reθ=2694 (Reθ is obtained by the momentum thickness and free flow velocity).The method of wavelet and statistics are used in this paper.Then,the parameters of SL scaling law are fitted with the scaling law of extended self similarity,extended of refined similarity hypothesis and a new form of refined similarity.At different distances from the wall and different scale,the results show that the fitted curves of u’ is in accordance with experimental curves.For dv’/dx,the fitted curves which are fitted with extended of refined similarity hypothesis and a new form of refined similarity is in accordance with experimental curves.     

流体层流横掠多孔介质中等温平板的对流换热积分解

对流体层流横掠多孔介质中等温平板的二维流动应用Brinkman--Forchheime--extended Darcy模型和流体与多孔介质之间局部热平衡的传热理论建立质量方程、动量方程和能量方程,应用数量级分析的方法对方程组进行了简化,并应用积分法得出了边界层内流体的速度分布、温度分布、以及摩擦系数和对流换热系数的理论表达式。结果表明,多孔介质中平板表面的速度边界层厚度与光板时有明显的不同,其在平板前端迅速增长,尔后变得非常平坦并几乎不再增长;而热边界层厚度则和光板时类似,沿着流动方向不断地增长。