S型水跃局部水头损失系数与跃后水深计算方法

鉴于水跃跃后水深作为消力池体形设计的重要参数,通过建立水跃区跃前和跃后断面的能量方程,分析了突扩式消力池S型水跃局部水头损失系数和共轭水深比的变化规律。研究发现,S型水跃相对局部水头损失系数是跃前断面弗劳德数函数,并随着弗劳德数的增大而增大;相对局部水头损失系数随跃前断面弗劳德数的变化规律既可用线性公式表示又可用乘幂公式表示;水跃共轭水深比是跃前断面弗劳德数和消力池突扩比的函数。通过能量方程求解的S型水跃跃后水深公式具有较高的计算精度和较好的通用性,且能作为矩形明渠水跃共轭水深的求解公式。     

梯形断面渠道临界水深显式计算

简述了梯形断面渠道临界水深的各种计算方法,提出了一个显式计算公式,经比较证明,其公式简洁、实用、精度高,便于在实际计算中使用.     

梯形渠道水力最佳断面设计的简单方法

根据梯形渠道水力最佳断面的宽深比计算公式及明渠均匀流计算公式 ,推出了水力最佳断面水深的直接求解公式 ,大大减少了计算量     

粒子群优化在临界水深计算中的应用

将临界水深的计算建模为一个非线性约束优化问题,应用新型粒子群优化算法加以求解。通过实例计算以及与文献方法的计算结果对比分析,表明粒子群优化算法求解梯形明渠临界水深适用性强、计算精度高、算法实现简单,同时验证了算法的有效性和正确性,为梯形明渠临界水深问题的求解提供了一条新途径。     

非对称平行水跃水力特性研究

通过两孔平底泄洪闸物理模型试验,对比研究了非对称平行水跃和传统水跃的水跃特性,揭示了非对称平行水跃的消能机理,探究了其能量耗散、共轭水深比、水跃旋滚长度与闸门开度比之间的关系。结果表明,非对称平行水跃中水流横向扩散增大了平行射流面积,除形成大幅度横轴旋滚外,还激起局部立轴旋滚,增强了相邻水股剪切紊动,加剧了能量耗散;相较于传统水跃,非对称平行水跃能显著降低跃后水深及缩短水跃长度;结合试验数据提出共轭水深比、水跃旋滚长度计算经验公式,经验公式拟合效果较好,精度较高,可为同类工程设计提供参考依据。     

折坡扩散消力池水跃共轭水深计算方法及水跃长度、消能率分析

为了解折坡扩散消力池的水跃特性及相关参数、判别其消能效果,通过模型试验的方法对折坡扩散消力池水跃进行了研究,提出了共轭水深计算公式,分析了水跃长度、共轭水深比、消能率等相关水力参数及其变化规律。结果表明,在试验条件下,公式计算结果与实测值相比误差较小,精度较高;水跃长度与共轭水深比、佛劳德数均遵循正比例变化规律;水跃消能率与佛劳德数呈正比。     

二次抛物线形渠道临界水深与共轭水深简化算法

针对目前二次抛物线形断面渠道临界水深与共轭水深计算过程及表达式复杂的问题,推导了抛物线形渠道临界水深的通用直接计算公式,进而推求出二次抛物线形渠道共轭水深的隐性关系式,再采用Matlab仿真平台对抛物线形渠道的共轭水深的高次隐函数方程以实例进行了编程求解。为验证该方法的可靠性与准确性,同时将隐函数方程变形为收敛的迭代公式,通过临界水深选出迭代初值对共轭水深进行迭代求解。对比结果表明,Matlab软件编程法简捷、精确、便于实际应用。     

明渠均匀流弗劳德数随水深的变化规律

弗劳德数(Fr)是判别明渠水流流态的标准,掌握弗劳德数随明渠水深的变化规律,对认识明渠水流的流态特性、指导明渠的设计具有重要意义。从弗劳德数Fr的定义出发,通过理论计算分析明渠均匀流弗劳德数Fr随水深的变化规律,分别揭示了矩形、梯形和圆形断面明渠均匀流弗劳德数Fr极大值的存在条件及变化特征。分别列举算例对计算结果进行验证,为今后工程实际中通过控制断面水深来控制流态提供了依据。     

复式断面共轭水深范围的判定

复式断面因共轭水深范围的不同会有多个水跃方程,为选用正确的水跃方程一般均需进行试算,这个过程异常繁琐。在深入分析复式断面跃前水深与跃后水深二者之间共轭关系的基础上,提出一种直接判定共轭水深取值范围的可靠方法,从而不必反复试算即可直接选用正确的水跃方程。尤其是当大量不同水力参数条件下的共轭水深需要计算时,更可大幅减少试算工作量。     

标准Ⅱ型马蹄形断面正常水深和临界水深的简化计算

马蹄形断面几何形状复杂,正常水深和临界水深的计算需求解超越方程,计算比较麻烦。根据明渠均匀流理论和临界水深理论,研究了马蹄形断面正常水深和临界水深的一般计算方法,并引入无量纲参数和优化拟合理论,得到了标准Ⅱ型马蹄形断面正常水深和临界水深的简化计算公式,公式形式简单,计算方便,精度满足工程设计要求。     

河网非恒定流计算的牛顿迭代解法

对描述河网非恒定流的圣维南方程组进行差分,利用牛顿迭代的数值计算方法建立迭代方程组,并应用一种特殊的高斯消元法来求解此方程组;给出了一维河网非恒定流的一个通用解法;用一个实例验证了此解法的可行性.     

悬链线形渠道正常水深与临界水深的计算方法

基于悬链线形渠道断面几何特点,根据均匀流基本方程推导出了悬链线形渠道正常水深的直接计算公式,并根据临界流方程,通过适当的数学变换,得到了计算悬链线形渠道临界水深的无量纲关系式,从而获得了两种水深的计算方法。采用Matlab语言编程对某悬链线形渠道断面临界水深的计算结果表明,该计算方法简单、结果精确,便于在实际工程中推广应用。     

叶轮强度计算的迭代法

根据离心机械中叶轮轮盘应力计算的基本方程式,导出了用迭代法对叶轮轮盘进行应力计算的迭代公式和求解方法。该方法克服了二次计算法的不足,特别适合编程用计算机计算求解。     

Structured Multiblock Grid Solution of Two-Dimensional Transient Inverse Heat Conduction Problems in Cartesian Coordinate System

ABSTRACT

In this study a structured multiblock grid is used to solve two-dimensional transient inverse heat conduction problems. The multiblock method is implemented for geometric decomposition of the physical domain into regions with blocked interfaces. The finite-element method is employed for direct solution of the transient heat conduction equation in a Cartesian coordinate system. Inverse algorithms used in this research are iterative Levenberg-Marquardt and adjoint conjugate gradient techniques for parameter and function estimations. The measured transient temperature data needed in the inverse solution are given by exact or noisy data. Simultaneous estimation of unknown linear/nonlinear time-varying strengths of two heat sources in two joined surfaces with equal and different heights is obtained for the solution of the inverse problems, and the results of the present study for unknown heat source functions are compared to those of exact functions. This study is an attempt to challenge the goal of combining a multiblock technique with inverse analysis methods. In fact, the structured multiblock grid is capable of providing accurate solutions of inverse heat conduction problems (IHCPs) in industrial configurations, including composite structures. In addition, the multiblock IHCP solver is suitable to estimate unknown parameters and functions in these structures.     

USE OF GCG METHODS FOR THE EFFICIENT SOLUTION OF MATRIX PROBLEMS ARISING FROM THE FVM FORMULATION OF RADIATIVE TRANSFER

Preconditioned generalized conjugate gradient (GCG) iterative methods are applied to the solution of large, sparse, and unsymmetric linear algebraic equations resulting from the application of the finite-volume method to the problem of radiative heat transfer in an absorbing, emitting, and scattering gray medium, with the boundary surfaces reflecting radiation in both diffuse and specular regimes. The governing radiative transfer equation, which is a complicated integro-differential equation, has been discretized using the S N finite-volume method (FVM). Different variants of GCG methods have been tested on a problem of 2-D radiation in a cylinder, and efficiencies of the methods have been compared. Numerical results indicate that preconditioning suggested in the article dramatically improves the performance of the GCG methods. Results on test problems based on S 8 FVM agree well with exact results reported in the literature.     

APPLICATION OF IMPLICIT NUMERICAL TECHNIQUES TO THE SOLUTION OF THE THREE-DIMENSIONAL DIFFUSION EQUATION

Implicit techniques for calculating three-dimensional, time-dependent heat diffusion in a cube are tested with emphasis on storage efficiency, accuracy, and speed of calculation. For this purpose, a tensor product technique with both Chebyshev collocation and finite differences and a generalized conjugate gradient technique with finite differences are used in conjunction with Crank-Nicolson discretization. An Euler explicit finite difference calculation is performed for use as a benchmark. The implicit techniques are found to be competitive with the Euler explicit method in terms of storage efficiency and speed of calculation and offer advantages both in accuracy and stability. Mesh stretching in the finite difference calculations is shown to markedly improve the accuracy of the solution.     

On a Wavenumber Optimized Streamline Upwinding Method for Solving Steady Incompressible Navier-Stokes Equations

A stabilized upwind finite-element model is developed to solve the three-dimensional incompressible steady Navier-Stokes equations. The test function is constructed to have a larger weight on the upstream side. This has been achieved by adding a stabilized term to the shape function so as to optimize the numerical wavenumber for convection terms. To avoid Lanczos or pivoting breakdown while solving the resulting unsymmetric and indefinite mixed finite-element matrix equations iteratively, the finite-element equation has been modified by pre-multiplying it with its transpose. The resulting normalized matrix equation becomes symmetric and positive-definite. We can therefore apply a computationally efficient conjugate gradient Krylov iterative solver to get an unconditionally convergent solution. However, the condition number of the new system becomes the square of the original unsymmetric indefinite system. To fully exploit excellent convergence nature of the conjugate gradient iterative solver, an element-by-element strategy is adopted to avoid assembling of all the stiffness matrices obtained at element level. We alleviate the drawback of slower convergence of the conjugate gradient method due to the increased condition number by preconditioning the positive-definite matrix. The resulting preconditioned matrix equation is solved in a matrix-free manner using the preconditioned conjugate gradient iterative solver. The developed finite-element code is first verified by solving a problem amenable to analytical solution. The benchmark lid-driven cavity problem is also solved in a cube for assessing the three chosen iterative solvers.     

Simultaneous determination of the heat source and the initial data by using an explicit Lie-group shooting method

Abstract

In this article, an explicit Lie-group shooting method (LGSM) is developed to solve the time-dependent heat source and the initial data for backward heat conduction problems. To recover both unknown data simultaneously, it is very difficult to obtain a stable solution by explicit or implicit schemes. To solve these problems by using conventional numerical schemes, numerical iterative regularization techniques and numerical integration techniques are necessary. To avoid these numerical techniques and to increase the computational efficiency, an explicit LGSM is developed. According to the solution of the quadratic equation of the LGSM, the initial condition can be directly obtained by using the final condition and boundary conditions at the initial time and final time. Using the reciprocal relationship of the solutions for the initial condition and the final condition, the proposed algorithm can avoid numerical integration and numerical iteration. Additionally, a closed-form formula from a two-point Lie-group equation can be directly used to calculate the heat source term. To illustrate the effectiveness and accuracy of the proposed algorithm, several benchmarks are tested. The numerical results indicate that the proposed algorithm can achieve an efficient and stable solution, even with noisy measurement data, by comparing the estimation results with the existing literature.