曲线坐标系下平面二维浅水模型的修正与应用

借鉴有关弯道水流流速分布的研究成果,计入弯道环流引起的横向的动量交换,对曲线坐标系平面二维浅水方程做了修正;采用边界处正交的曲线网格生成技术,处理复杂的计算区域边界。采用修正后的模型对90°弯道水流进行了数值模拟,并与原模型的计算结果及实测资料进行了比较,结果表明该模型能够有效地模拟流线弯曲的复杂水流的水力特性。     

弯道水流二维浅水模型的修正研究

借鉴有关弯道水流流速分布的研究成果,计入深度平均流速与真实流流速分布差值引起的扩散效应,在正交曲线坐标系下建立了平面二维浅水模型.采用以标准κ-ε模型为基础的曲率效应修正紊流模型模拟紊动应力项,在一定程度上考虑了流线弯曲水流紊动应力的各向异性.应用控制体积法和交错网格法离散方程,并用SIMPLEC算法求解离散方程;同时采用修正后的模型对90°弯道水流进行了数值模拟,并与原模型的计算结果及实测资料进行了比较,结果表明该模型能够有效地模拟流线弯曲水流的水力特性.     

弯曲渠道中的振荡流和二次流

本文以弯道理想不可压缩流动的流线和等势线为曲线坐标系给出了弯道内不可压缩粘性振荡流动的一阶解以及边界层流型下的二阶解,以直角弯道为例对弯道內的粘性振荡流动以及二次流的影响进行了讨论。     

正交曲线坐标系下紊流数学模型的曲率修正

考虑弯曲边界曲率效应对水流水力特性的影响,建立了正交曲线坐标系下的素流数学模型。通过计算实例说明,该数学模型能够很好地帷有复杂边界的流线弯曲水流的水力特性。     

定床弯道内水沙两相运动的数值模拟

在适体同位网格中采用非正交曲线坐标系下的三维k-ε-kp固液两相双流体湍流模型研究弯道内水流和悬浮泥沙运动,主要计算了试验室S型水槽内清水流动的三维流场、120°弯道内水沙两相流动中底沙与底流的运动轨迹以及S型水槽内水沙两相流动的两相流场和泥沙浓度场. 对于S型水槽内清水流动,数值结果与试验结果吻合良好. 120°弯道内水沙两相流动中固液两相的运动轨迹在弯道直线段基本重合,在弯道内泥沙轨迹逐步偏离水体轨迹,其偏离程度随泥沙粒径增大而增大. 从S型水槽内水沙两相流动计算结果中发现泥沙纵向流速在壁面附近比水流纵向速度大,在远离壁面区域比水流纵向速度小;弯道内泥沙横向流速比水流横向流速小;垂向流速在直线段和泥沙沉速相当,在弯道内受螺旋水流影响而变化;两相流速差别随泥沙粒径增大而变大;泥沙浓度呈现下浓上稀的分布,在弯道内横向断面上呈现凸岸大凹岸小的分布,泥沙浓度随泥沙粒径增大而减小.      

正交数值网格的生成及平面二维流场的数值模拟

提出了一种边界正交曲线网格的生成方法。在内域,求解拉普拉斯方程组生成二维正交曲线网格;在计算域边界,提出了正交曲线网格边界正交化处理的分段拉格朗日插值边界滑动法,并对控制方程N-S方程进行曲线坐标变换,使用SIMPLEC算法求解曲线坐标下的k-ε双方程湍流模型。文中以长江重庆九龙坡弯道河段正态模型为资料进行验证,计算了流场,数值模拟结果与实测结果吻合较好。     

曲线坐标下连通域河道平面二维水流的数值模拟

在边界拟合曲线坐标系下,运用B型交错网格模式和动边界扫描技术建立了基于连通域的二维水流数学模型,并提出了模型中有关参数的处理方法.采用贴体坐标变换将复杂的物理域变换成规则的计算域,在计算域上采用控制容积法离散方程,应用SIMPLEC算法计算速度-压力耦合.研究结果表明:采用控制容积法和SIMPLEC算法离散求解方程,具有良好的守恒性和稳定性; 该模型能够较准确地模拟连通域河段的流场变化、水位变化等过程,可供实际工程应用.     

常曲率弯道二维流动稳定性与非线性演化规律分析

国内外对弯曲河流的研究从线性特性转移到不稳定性与非线性特性上来, 弯曲河流作为一个不稳定的系统, 主要是受到水流和边界的不稳定性的影响.针对弯曲河流中存在的水流动力的不稳定性与非线性特征,利用弱非线性理论与摄动法进行展开, 在微弯条件下建立了时间模式下的常曲率 弯道二维水流扰动幅值与扰动幅角的非线性演化方程.研究了在不同弯曲度下的扰动发展特征,探讨了扰动流场在弯曲度影响下的时空分布的规律,分析了扰动流场中出现的扰动漩涡的运动过程, 阐述了弯曲度对弯曲边界内水流不稳定性的影响, 具体表现为在微弯的情况下, 弯道的弯曲度增大会提高河湾内水流的稳定性, 扰动振幅与扰动幅角会随弯曲度的增大其衰减速度更快, 并且扰动流速的对称性在弯曲度较大时减弱, 逐渐向弯道的凸岸偏斜, 在中性状态附近 的弯道水流动力具有对流不稳定性和非线性衰减的特征.本文的研究成果为构建水流动力非线性与床面形态几何非线性相互作用的模型提供了思路.      

90°弯道明渠横向环流的大涡模拟研究

采用气液两相流大涡模型模拟90°弯道明渠水流的水力特性。使用有限体积法对控制方程进行离散;使用压力隐式算子分裂PISO(Pressure-Implicit with Splitting of Operators)算法求解速度与压力的耦合;采用了VOF(Volume of Fluid)法模拟自由水面。通过计算得到弯道处流速、压强系数、横向环流强度等水力参数的分布规律。分别比较弯道纵向流速与横向流速的模拟值与实验值,二者吻合较好。通过分析弯道环流的流态特征得出:因受重力作用与水流在流经弯道时发生的离心现象的影响,凸岸附近较凹岸存在较大的二次流强度的结果;凸岸与凹岸压强系数均沿程增大,当达到弯顶时,水面横比降达到最大值;弯道横向环流强度随弯道角度增大而逐渐增大,其最大值出现在明渠底部。     

含污染物的弱弯曲明渠弯道湍流数值模拟

建立了可模拟弯道中含污染物湍流的三维部分抛物型代数应力模型。针对左右两岸分别泄放污染物的环流非充分发展弯道流进行了计算。分析了水流结构及污染物浓度分布的特点。     

三维不可压缩边界层分离流的反解法

本文提出了计算具有分离区的三维层流和湍流边界层的一种反解法。计算中采用了半正交曲线坐标系和涡粘性各向异性湍流模型。数值分析中采用了变换域技术和 Keller分块差分格式。用本文方法计算了一个三维边界层分离流实例,计算结果同实验数据吻合得很好。     

Boltzmann equation and moment equations in curvilinear coordinates

Various forms of writing the Boltzmann equation in an arbitrary orthogonal curvilinear coordinate system are discussed. The derivation is presented of a general transport equation and moment equations containing moments of the distribution function no higher than the fourth. For a gas of Maxwellian molecules it is shown that the system of moment equations for flows which differ little from equilibrium flows transforms into the system of hydrodynamic equations. The resulting equations may be useful in solving problems on motions of a rarefied gas by the moment methods. The results are valid for both the Boltzmann equation and model kinetic equations.The author wishes to thank A. A. Nikol'skii for discussions and helpful comments.     

Construction of approximate solutions to two-dimensional potential problems of electrohydrodynamics

After transformation to new variables the system of equations describing planar potential electrohydrodynamic flows with a small interaction parameter is converted to a single equation. The particular solution of this equation, which is the electrohydrodynamic analog of Hamel's solution in the dynamics of a viscous liquid, is found. Two types of flows, described by simplified equations, can be distinguished when certain constraints are imposed on the manner in which the electrical parameters vary along the coordinate lines and the terms of the equation correspondingly estimated. These flows are the jet and quasione-dimensional flows of the charged component in a curvilinear electrostatic field and a supper-posed two-dimensional potential flow of the carrier medium. Solutions to the approximate equations are obtained for certain particular cases.Kiev. Transklated from Izvestiya Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–147, July–August, 1972.     

Equations of viscous supersonic jets with a high degree of overexpansion

A complete system of equations determining a viscous laminar, strongly overexpanded jet is obtained; the system is formed by shortened Navier—Stokes equations, equations for the metric of a coordinate system related with the form of the jet, and equations of transition from curvilinear coordinates to Cartesian. The problem of calculating the jet is formulated as a Cauchy problem for this system. Two- and three-dimensional flows are examined. Possible swirling of the jet is taken into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 137–147, March–April, 1977.     

TVD格式在超音速喷管三维粘性流动求解中的应用

详细给出了任意三维曲线坐标系中Ｎｏｖｉｅｒ－Ｓｔｏｋｅｓ方程的对流项ＴＶＤ格式的构造过程，建立了数值求解三维粘性流动的计算方法，应用该方法对三维超音速喷管中有激波及无激波情况下的两种工况的层流流场进行了数值求解，并与实验做了对比。结果表明本文建立的计算方法具有较高的精度，同时也证明ＴＶＤ格式具有分辩率高，稳定收敛等优点，为进一步开展叶栅流场及紊流的研究打下了基础。     

On general form of Navier-Stokes equations and implicit factored scheme

A general weak conservative form of Navier-Stokes equations expressed with respect to non-orthogonal Curvilinear coordinates and with primitive variables was obtained by using tensor analysis technique, where the contravariant and covariant velocity components were employed. Compared with the current coordinate transformation method, the established equations are concise and forthright, and they are more convenient to be used for solving problems in body-fitted curvilinear coordinate system. An implicit factored scheme for solving the equations is presented with detailed discussions in this paper. For n-dimensional flow the algorithm requires n-steps and for each step only a block tridiagonal matrix equation needs to be solved. It avoids inverting the matrix for large systems of equations and enhances the speed of arithmetic. In this study, the Beam- Warming’s implicit factored schceme is extended and developed in non-orthogonal curvilinear coordinate system.     

三维分区算法在复杂多连域湍流问题中的应用

提出并实现了一种适合于任意曲线坐标系下非交错网格系统的流体力学数值模拟的三维分区算法 ,通过三维立方块绕流问题对其进行了考证和优化工作 ,证明有良好、稳定的工作性能。在此基础上 ,将该算法有效地应用到了具有典型多连域特征的涉及内外流耦合作用的串列双空气冷却塔定常绕流流动问题 ,揭示了横向风对其运行性能产生不利影响的主要原因     

A meshless method for numerical simulation of depth‐averaged turbulence flows using a k‐ϵ model

A three‐dimensional numerical model is developed to analyze free surface flows and water impact problems. The flow of an incompressible viscous fluid is solved using the unsteady Navier–Stokes equations. Pseudo‐time derivatives are introduced into the equations to improve computational efficiency. The interface between the two phases is tracked using a volume‐of‐fluid interface tracking algorithm developed in a generalized curvilinear coordinate system. The accuracy of the volume‐of‐fluid method is first evaluated by the multiple numerical benchmark tests, including two‐dimensional and three‐dimensional deformation cases on curvilinear grids. The performance and capability of the numerical model for water impact problems are demonstrated by simulations of water entries of the free‐falling hemisphere and cone, based on comparisons of water impact loadings, velocities, and penetrations of the body with experimental data. For further validation, computations of the dam‐break flows are presented, based on an analysis of the wave front propagation, water level, and the dynamic pressure impact of the waves on the downstream walls, on a specific container, and on a tall structure. Extensive comparisons between the obtained solutions, the experimental data, and the results of other numerical simulations in the literature are presented and show a good agreement. Copyright © 2015 John Wiley & Sons, Ltd.     

Visualization of three-dimensional incompressible flows by quasi-two-dimensional divergence-free projections in arbitrary flow regions

A visualization of three-dimensional incompressible flows by divergence-free quasi-two-dimensional projections of the velocity field onto three coordinate planes is revisited. An alternative and more general way to compute the projections is proposed. The approach is based on the Chorin projection combined with a SIMPLE-like iteration. Compared to the previous methodology based on divergence-free Galerkin–Chebyshev bases, this technique, formulated in general curvilinear coordinates, is applicable to any flow region and allows for faster computations. To illustrate this visualization method, examples in Cartesian and spherical coordinates, as well as post-processing of experimental 3D-PTV data, are presented.     

Development of an Artificial Compressibility Methodology with Implicit LU-SGS Method

A numerical method has been developed to solve the steady and unsteady incompressible Navier-Stokes equations in a two-dimensional, curvilinear coordinate system. The solution procedure is based on the method of artificial compressibility and uses a third-order flux-difference splitting upwind differencing scheme for convective terms and second-order center difference for viscous terms. A time-accurate scheme for unsteady incompressible flows is achieved by using an implicit real time discretization and a dual-time approach, which introduces pseudo-unsteady terms into both the mass conservation equation and momentum equations. An efficient fully implicit algorithm LU-SGS, which was originally derived for the compressible Eulur and Navier-Stokes equations by Jameson and Toon [1], is developed for the pseudo-compressibility formulation of the two dimensional incompressible Navier-Stokes equations for both steady and unsteady flows. A variety of computed results are presented to validate the present scheme. Numerical solutions for steady flow in a square lid-driven cavity and over a backward facing step and for unsteady flow in a square driven cavity with an oscillating lid and in a circular tube with a smooth expansion are respectively presented and compared with experimental data or other numerical results.