百色水电站尾水隧洞明满交替流动计算研究

百色水电站运行时，尾水隧洞中有可能出现明满交替流动而使尾水系统对电站运行的稳定性和过渡过程都带来复杂的影响，因此建立合理可行的明满交替流动数值模型是完全必要的。针对现有明满交替流动的数值解法中存在稳定性差的缺点，提出了一种新的计算方法——特征隐式格式法，其主要思路是将动量方程和连续方程转化为双曲型方程组的标准形式进行差分，并通过尾水隧洞水工水力学模型试验专门对该方法进行验证，表明该计算方法是正确的。将谊方法应用于百色水电站的尾水系统动态仿真计算中，并对尾水隧洞洞型进行优化，得到了满意的结果。     

带阻尼井的变顶高尾水系统水力过渡过程数值预测及其特性研究

机组及输水系统在暂态过程中性能参数的控制对电站的安全稳定运行具有重要影响。基于瞬变流数学模型和Priessmann假设,对三峡地下电站采用的带阻尼井的变顶高尾水隧洞进行了过渡过程数值预测,并将计算结果与电站现场试验值进行了对比验证,总结了带阻尼井的明满交替流等复杂水力过程的数值预测模型。基于计算结果分析了在大小波动等暂态过程中变顶高尾水系统明满交替流及阻尼井的水力特性,并从水力学和系统稳定性的角度解释了三峡地下电站采用变顶高尾水洞并设置阻尼井能够代替调压室的原因。     

非定常不可压 N-S 方程的一种有效预处理数值方法

本文发展了一非定常不可压流的有效预处理求解方法。应用预处理技术，对不可压N－S方程使用双时间推进法求解。当沿物理时间层推进时，连续性方程和动量方程沿伪时间方向迭代求解。在沿伪时间方向迭代时，设计了一简化的有效标量隐式线（Gauss－Sidel）迭代算法。对流项采用三阶迎几差分法离散，同时对数值通量项进行了预处理。数值分析了预处理对数值解精度和收敛性的影响。对振荡平板的非定常流动及不同Re数下定常、非定常驱动方腔流动的数值模拟结果表明，本文发展的非定常不可压流的预处理求解方法，不但提高了计算效率，而且减小了人工粘性，改善了数值解的精度。     

设置保水堰管涵输水系统的水力瞬变数值仿真

为研究大型调水工程的水力瞬变过程，采用明渠非恒定流方程及Preissiman方法模拟无压管涵非恒定流、有压管涵水击和明满交替流，提出了设置保水堰的长距离管涵输水系统的水力学仿真模型。所建立的数值模型可模拟包括管涵明满交替和保水堰跌水等复杂的水流现象。数值仿真结果表明，在检修闸门和下游管涵之间设置保水堰，可以调节输水管道内的压力，避免紧急启闭时发生液柱分离以及检修闸门突然关闭时因明满流交替而产生强烈的冲击水压。     

绕圆柱非定常周期性涡旋脱落的数值模拟

利用非定常流函数涡量方程数值模拟圆柱突然起动尾流涡旋的形成及周期性脱落过程。对求解的流函数的一阶导数即速度项采用四阶精度的Hermitian公式，而方程的对流项则采用四阶精度的差分格式，并利用ADI方法迭代求解差分方程组。当雷诺数Re不大于40时，圆柱尾流为附体的两个对称涡，为定常解。当Re大于40后流动为非定常及非对称的，圆柱尾流呈现周期性涡旋交替脱落而形成著名的Karman涡街。选择Re=100为例，在初始条件未加任何扰动情况下，成功地模拟了圆柱非定常涡旋形成与脱落的完整过程（无量纲时间算到t=250及以上）。所计算的阻力系数与实验结果及其它数值方法的计算结果一致。约在t=200形成严格的Karman涡街。对涡量方程ADI求解方法的稳定性进行了分析。对流项采用四阶精度差分格式，若应用于定常问题，将极大提高数值求解的精度，若应用于非定常问题的求解，将对求解精度有所改善，其中时间空间两阶混合偏导数的处理是关键，有待进一步的数值实验。     

基于精细积分法的城市配水系统动态建模

基于功率键合图理论,将所研究的城市配水系统的动态结构绘制成功率键合图,从功率键合图推导出系统的非线性状态空间方程.首先通过增维法将非齐次系统方程转化成齐次方程的形式,避免了系统矩阵求逆,节省计算时间,增强了计算稳定性.模型应用精细积分法迭代求解.实例计算表明,模型计算得到的稳态值同EPANET软件的稳态计算结果一致,验证了算法的正确性.     

水生植物对河道形态影响的三维湍流模型

植被是河床和河岸稳定性指标中的一个重要参数,它主要通过影响水流结构进而影响河道的形态。本文建立曲线坐标系下的三维湍流模型研究水生植物对河道形态的影响,在水流控制方程中加入植物阻力项和植物密度项来描述水生植物对水动力特性的贡献,通过泥沙质量守恒方程求解河道变形,在适体网格中求解模型的控制方程。应用该三维模型数值模拟了矩形水槽内两侧交替布置的非淹没刚性植物对水流结构的影响以及梯形河道内两侧交替布置的非淹没刚性植物对河道形态的影响,数值计算结果与实测结果吻合良好。     

基于最小二乘的N-S方程算子分裂有限元法

提出一种新的求解N S方程的有限元法,即基于最小二乘的N S方程算子分裂有限元法。该算法采用算子分裂法将N S方程分解成扩散项和对流项:扩散项时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法;对流项时间离散采用向后差分格式,空间离散采用最小二乘有限元法。应用该算法对方腔流和后台阶流进行数值模拟,方腔流数值计算结果与标准解吻合很好;在后台阶流数值模拟中给出了不同雷诺数下的流场特征和速度对比曲线,所得计算结果与试验结果吻合较好,表明基于最小二乘的N S方程算子分裂有限元法具有较好的收敛性和较高的精度。     

污染物移流扩散方程的高精度分裂格式

提出了污染物移流扩散方程的一种高精度分裂格式, 该格式将多维移流扩散方程分裂为多个一维方程进行求解, 在每个方向上仅涉及三个空间节点而达到空间四阶精度. 采用该格式对几个经典的纯移流、移流扩散问题进行了数值模拟, 数值结果表明, 该格式比经典的移流扩散方程格式的精度要高得多, 此外该格式还具有编程简单、求解十分快速的优点.     

城门洞型输水隧洞明满流计算与试验

无压输水隧洞中受到闸门启闭而引起的明满交替流水力瞬变现象，通常会造成洞内的压力剧增，对工程安全运行造成威胁。为了探究城门洞型隧洞的明满交替流和明流过渡过程，实测了模型隧洞沿线断面水深或压力变化曲线，基于窄缝法原理，使用扩散法对实测工况进行数值模拟计算，将实测数据与计算结果进行了对比分析。研究表明：在下游初始水深逼近城门洞直墙高时，下游闸门突然关闭后，在大来流量下管路中出现压力瞬间陡增的完全明满流现象，水流向上游传播并伴随剧烈的掺气，在小来流量下表现为不掺气压力突升的临界明满交替流，回波造成二次压力剧增，断面压力达到峰值。窄缝扩散法对于从明流完全转化成满流的明满流过渡过程模拟效果较好，而对于临界明满流的模拟有较大的误差。无压流水力过渡过程数值模拟计算结果与实测值基本一致，反映了明渠水力过渡过程数学模型的合理性。研究成果可为深入研究这一复杂水力现象提供借鉴和参考。     

基于明满流瞬变计算方法的大型灌区输水隧洞最优泄水流量计算

为了明确输水隧洞内的明满流水力瞬变过程以及优化泄水闸的泄水流量,介绍了圆形输水隧洞中明满交替水流水力瞬变计算原理和方法。以某大型灌区干渠工程为例,根据窄缝法计算原理,采用显式差分中的扩散法,对圆形输水隧洞中的明满交替水流进行了水力瞬变计算研究。给出了圆形隧洞瞬变流计算的水力要素计算公式,得到了输水流量变化时隧洞不同断面的水深或压力随时间的变化曲线。结果表明:当圆形隧洞水位封顶时,隧洞中的水压力越靠近下游断面,压力突升越剧烈;明流状态下节制闸关闭时间对隧洞内最大水深影响较小,隧洞内的最大水深随着泄水闸泄水流量的增加呈线性减小的趋势,根据数值模拟计算给出了泄水闸合理的设计泄水流量。研究成果可为输水隧洞工程的设计提供借鉴和参考。     

基于非结构化网格上的三维微幅自由表面流动非静压数值模型

建立了基于非结构化网格求解三维微幅自由表面流动非静压数值模型。一种有限差分法和有限体积法相结合的方法被用来在非结构化网格上离散控制方程。模型中采用分步法,以使压力项分解为静水压力项和动水压力项来单独处理。在每一时间步,得到关于水位和由压力泊松方程得到的动水压力的稀疏的线性方程组。模型是质量守恒的和对于重力波速、风应力、底摩阻、垂向黏性无条件稳定的。通过三个非恒定微幅自由表面流动算例的数值解和解析解的比较,验证了本文所建立的模型能够准确有效的预测三维微幅自由表面流动。     

NUMERICAL SIMULATION OF FLOWS FOR SECOND-ORDER VISCOELASTIC FLUID COUPLED WITH HEAT TRANSFER BY DIFFERENTIAL QUADRATURE METHOD

The problem of two-dimensional steady flow of an incompressible second-order viscoelastic fluid coupled with heat transfer between parallel plates was considered. A viscous dissipation function was included in the energy equation.When the elastic property of the fluid is weaker, the zerothorder and first-order approximate governing equations were obtained by means of the perturbation method. To understand the behavior of flow near the tube wall, the half-domain was divided into two sub-domains, in which one is a thin layer near the wall called the inner domain and the remainder is called the outer domain. The governing equations in the inner domain and in the outer domain were discretized respectively by using the Differential Quadrature Method (DQM). The matching conditions at the interface between the inner and outer domains were presented. An iterative method for solving these discretized equations was given in this paper. The numerical results obtained agree with existing results.     

NUMERICAL SOLUTION OF 2D FLOW USING A LOCAL COORDINATE SYSTEM

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A SPLIT-CHARACTERISTIC FINITE ELEMENT MODEL FOR 1-D UNSTEADY FLOWS

An efficient and accurate solution algorithm was proposed for 1-D unsteady flow problems widely existing in hydraulic engineering. Based on the split-characteristic finite element method, the numerical model with the Saint-Venant equations of 1-D unsteady flows was established. The assembled finite element equations were solved with the tri-diagonal matrix algorithm. In the semi-implicit and explicit scheme, the critical time step of the method was dependent on the space step and flow velocity, not on the wave celerity. The method was used to eliminate the restriction due to the wave celerity for the computational analysis of unsteady open-channel flows. The model was verified by the experimental data and theoretical solution and also applied to the simulation of the flow in practical river networks. It shows that the numerical method has high efficiency and accuracy and can be used to simulate 1-D steady flows, and unsteady flows with shock waves or flood waves. Compared with other numerical methods, the algorithm of this method is simpler with higher accuracy, less dissipation, higher computation efficiency and less computer storage.     

Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, , , and , were used to close the non-simplified quasi-three-dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.     

NUMERICAL INVESTIGATION ON THE AEROELASTIC BEHAVIOR OF AN AIRSHIP WITH HULL-FIN CONFIGURATION

Numerical investigation was conducted on an airship of hull-fin configuration for aerodynamic and aeroelastic characteristics in three-dimensional viscous flows. The mathematical model was built and the corresponding numerical code was developed for the fluid-structure interaction problem. The governing equations of the viscous flow with LL-Low Reynolds modified model were solved by the standard SIMPLE algorithm based on the finite volume method. A fluid-structure coupled method was employed to solve the nonlinear aeroelasticity problem for the airship. The computational results of the viscous flow are in good agreement with the experimental measurements. The simulation on the aeroelastic behavior of the airship in a trimmed flight reveals the effect of structure flexibility on the aerodynamic performance.