关于绕任意机翼非常流动的一种无条件稳定的欧拉方程解

本给出了绕二维与三维刚性或弹性振动机翼非定常无粘流动的欧拉方程解。首先利用Ｊａｍｅｓｏｎ的有限体积方法建立了求解欧拉方程的Ｒｕｎｇｅ－Ｋｕｔｔａ方法，为了提高受Ｒｕｎｇｅ－Ｋｕｌｔｔａ法稳定性限制的时间步长，中采用了变系数的残值光顺方法，该方法避免了常系数残值光顺引起局部流场损失较大的问题。同时可在保证原计算格式精度要求下，大幅度提高计算时间步长，从而提高了计算效率。中以二维与三维矩形机翼为     

绕振动机翼非定常气动力迟滞特性的模拟研究

利用数值模拟方法开展了机翼在不同条件下,由于俯仰振动引起的非定常气动力迟滞特性的模拟计算研究.根据有限体积方法对非定常欧拉方程进行数值求解,以确定相应问题的流场及气动力特性;同时,分别以具有NACA-0012翼型的矩形机翼和带有65°后掠角的三角翼为例,研究了机翼绕不同转轴或以不同频率振动的非定常气动力迟滞特性.     

圆柱振荡绕流的三维不稳定性研究

通过数值求解三维不可压缩Navier-Stokes方程,研究了振荡圆柱绕流的旋涡不稳定性.研究表明,在一定的参数范围内,由于旋涡不稳定性,振荡流动由二维演化成三维流动,并沿圆柱轴向形成交错排列的三维涡结构.数值计算合理地预测了三维涡结构的空间失稳波长,并与实验测试值相符很好.文中还进一步研究了圆柱的受力特性,通过求解Morison方程,计算了圆柱的阻力和惯性力特性,其计算结果与已有的实验数据相吻合.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

三维弹性管的涡致振动特性分析

采用有限体积法联合大涡模拟方法求解三维湍流流场,采用有限元法离散弹性管结构,对Re=1.35×104的湍流流动作用下三维弹性管的涡致振动进行了数值模拟,结构的动力学响应用Newmark算法来求解,管的运动采用基于扩散光顺方法的动网格模型来实现.利用建立的数值模型,分析了升力系数、阻力系数、位移、涡脱频率、相位差随频率比的变化特征,成功扑捉到锁定、相位开关,并联合运动轨迹、相图及Poincaré截面映射,研究了升力系数与横向位移的极限环与分叉等非线性特性.研究结果表明,在阻力系数的最小值处,横向振幅达到最大值,同时,横向响应的"锁定"也始于阻力系数最小值处;在"锁定"范围内,横向振幅随着频率比的增大而逐渐减小;在升力系数的最小值处,升力系数与位移间的相位由反相变为同相;在均匀湍流流动作用下,三维弹性管的升力与横向位移并未出现周期解的分叉.     

沉浮,俯仰及控制面振动引起的跨音速非定常气动载荷计算

本文将文献[9]提出改进的通量分裂方法,应用于随时间变化的贴体网格中,建立了可用于求解非定常Euler方程的通量分裂方法.该方法是以连续的特征值分离为基础,它具有方法简单,便于推广使用的特点.同时克服了Steger-Warming通量分裂方法存在的问题.对通量分裂后的Euler方程.利用MUSCL型迎风差分建立了具有二阶精度的有限体积方程.文中以NACA64A—10翼型为例,对其在跨音速流场中进行沉浮、俯仰及带有振动控制面引起的非定常气动载荷进行了计算.部分计算结果与相应的实验结果进行了比较,吻合良好     

迎风紧致格式与驱动方腔流动问题的直接数值模拟

本文给出了一种求解不可压缩流动问题的高精度差分格式,即迎风紧致格式.出发方程采用二维非定常原始变量Naiver-Stokes方程组.在差分方程中,对流项采用三阶精度的迎风紧致差分,其余空间导数项采用四阶紧致差分.本文利用该差分格式在等距网格上数值模拟了驱动方腔流动中的分离涡运动.在257×257的细网格上,Re数最高计算到10000.Re≤5000时的计算结果与前人结果符合得很好.当Re≥7500时发现流动不存在定常层流解而为非定常周期性解,并首次给出了非定常解的结果。     

三维振荡机翼含激波跨声速非定常绕流广义变分原理的普遍形式及其派生族

本文在文献[1,2]基础上,建立了作任意周期性振荡的三维机翼含激波非定常跨声速绕流的广义变分原理普遍形式及其派生族。为了便于数值处理及捕获未知间断面,文中运用变域变分工具将振荡的激波及自由尾涡面上的间断条件(包括Rankine-Hugoniot激波关系)以及几乎全部边界条件都转化成自然界面条件,并兼顾了翼面吸(喷)气的作用。本文为引进有限元法等变分解法提供一更普遍、完善的理论基础,并可再推广到三维机翼-机身组合体和三维旋转叶栅上去。     

钝体绕流非定常解

本文结合目前流场显示的研究课题,对方块物体和山形物体的钝体绕流在起动阶段的运动情况,进行相应的数值模拟.并用有限差分方法求解二维不可压缩流体运动的N-S方程的非定常解.对差分格式中的显式,隐式和交替方向隐式几种格式进行了讨论.最后用显式和交替方向隐式方法计算了山形物体和方块物体在起动阶段的运动情况.     

透平机械内部三维可压缩Navier-Stokes方程的流面方法和维数分裂算法

在这篇文章中,运用经典的张量分析方法,把流动区域用-个二维流形序列分割成一系列流层之并,推得在流层内半测地坐标之下的Navier-Stokes方程,在流形的法线方向应用向后Euler差分,推导了两维流形上的可压缩Navier-Stokes方程,和流函数满足的方程.在这个基础上,提出了一种维数分裂法的新算法.这种方法不同于区域分解法.对于三维问题,在区域分解法中我们必须在每个子区域上仍解三维问题,但是在这种新方法中,只需要在每个子区域上求解二维问题,不过是几个二维流形上的NS方程.文中还给出了-个透平机械内部流动的数值计算实例.     

Numerical simulation of unsteady flows with transient regimes

Self-oscillatory flows in aerodynamics and astrophysics are studied. The two-dimensional compressible gas equations are solved using the implicit Runge-Kutta scheme of the third order with respect to the inviscid terms and of the second order with respect to the viscous terms. An algebraic Cebeci-Smith turbulence model is used. Weakly unsteady and strongly unsteady flow regimes are observed. The former occur in a supersonic flow past a cylinder with a front projection and in the heliosphere. Such flows became stable when the turbulent diffusion is taken into account. The latter flows occur when a supersonic jet meets an obstacle and when such a jet penetrates a cavity. In these flows, the amplitude of oscillations slightly decreases when the turbulent diffusion is taken into account.     

On some unsteady flows of a non-Newtonian fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows impulsively started from rest by the motion of a boundary or two boundaries or by sudden application of a pressure gradient. Flows considered are: unsteady flow over a plane wall, unsteady Couette flow, flow between two parallel plates suddenly set in motion with the same speed, flow due to one rigid boundary moved suddenly and one being free, unsteady Poiseuille flow and unsteady generalized Couette flow. The results obtained are compared with those of the exact solutions of the Navier–Stokes equations. It is found that the stress at time zero on the stationary boundary for the flows generated by impulsive motion of a boundary or two boundaries is finite for a fluid of second grade and infinite for a Newtonian fluid. Furthermore, it is shown that for unsteady Poiseuille flow the stress at time zero on the boundary is zero for a Newtonian fluid, but it is not zero for a fluid of second grade.     

超声速、高超声速粘性气体分离流动的显隐式差分解法

本文利用反扩散的两步显、隐式差分方法,求解了超声速、高超声速粘性气体绕二维、三维压缩拐角的层流和湍流分离运动.结果表明,它既能获得很好的精度,又能大大缩短计算机时.     

NEW METHOD FOR IMPROVED CALCULATIONS OF UNSTEADY COMPLEX FLOWS IN LARGE ARTERIES

Using an improved computational fluid dynamics (CFD) method developed for highly unsteady three-dimensional flows, numerical simulations for oscillating flow cycles and detailed unsteady simulations of the flow and forces on the aortic vessels at the iliac bifurcation, for both healthy and diseased patients, are analyzed. Improvements in computational efficiency and acceleration in convergence are achieved by calculating both an unsteady pressure gradient which is due to fluid acceleration and a good global pressure field correction based on mass flow for the pressure Poisson equation. Applications of the enhanced method to oscillatory flow in curved pipes yield an order of magnitude increase in speed and efficiency, thus allowing the study of more complex flow problems such as flow through the mammalian abdominal aorta at the iliac arteries bifurcation. To analyze the large forces which can exist on stent graft of patients with abdominal aortic aneurysm (AAA) disease, a complete derivation of the force equations is presented. The accelerated numerical algorithm and the force equations derived are used to calculate flow and forces for two individuals whose geometry is obtained from CT data and whose respective blood pressure measurements are obtained experimentally. Although the use of endovascular stent grafts in diseased patients can alter vessel geometries, the physical characteristics of stents are still very different when compared to native blood vessels of healthy subjects. The geometry for the AAA stent graph patient studied in this investigation induced flows that resulted in large forces that are primarily caused by the blood pressure. These forces are also directly related to the flow cross-sectional area and the angle of the iliac arteries relative to the main descending aorta. Furthermore, the fluid flow is significantly disturbed in the diseased patient with large flow recirculation and stagnant regions which are not present for healthy subjects.     

Long Eddies in Sheared Flows

The characteristic feature of the wide variety of hydraulic shear flows analyzed in this study is that they all contain a critical level where some of the fluid is turned relative to the ambient flow. One example is the flow produced in a thin layer of fluid, contained between lateral boundaries, during the passage of a long eddy. The boundaries of the layer may be rigid, or flexible, or free; the fluid may be either compressible or incompressible. A further example is the flow produced when a shear layer separates from a rigid boundary producing a region of recirculating flow. The equations used in this study are those governing inviscid hydraulic shear flows. They are similar in form to the classical boundary layer equations with the viscous term omitted. The main result of the study is to show that when the hydraulic flow is steady and contained between lateral boundaries, the variation of vorticity ω(ψ) cannot be prescribed at any streamline which crosses the critical level. This variation is, in fact, determined by (1) the vorticity distribution at all streamlines which do not cross the critical level, by (2) the auxiliary conditions which must be satisfied at the boundaries of the fluid layer, and by (3) the dimensions of the region containing the turned flow. If at some instant the vorticity distribution is specified arbitrarily at all streamlines, generally the subsequent flow will be unsteady. In order to emphasize this point, a class of exact solutions describing unsteady hydraulic flows are derived. These are used to describe the flow produced by the passage of a long eddy which distorts as it is convected with the ambient flow. They are also used to describe the unsteady flow that is produced when a shear layer separates from a boundary. Examples are given both of flows in which the shear layer reattaches after separation and of flows in which the shear layer does not reattach. When the shear layer vorticity distribution has the form ωαyⁿ, where y is a distance measure across the layer, the steady flows are of Falkner-Skan type inside, and adjacent to, the separation region. The unsteady flows described in this paper are natural generalizations of these Falkner-Skan flows. One important result of the analysis is to show that if the unsteady flow inside the separation region is strongly sheared, then the boundary of the separation region moves upstream towards the point of separation, forming large transverse currents. Generally, the assumption of hydraulic flow becomes invalid in a finite time. On the other hand, if the flow inside the separation region is weakly sheared, this region is swept downstream and the flow becomes self-similar.     

浅水方程组的数值方法

构造了浅水方程组的二阶精度的TVD格式。格式由简单的TVD Runge-Kutta型时间离散和有坡度限制的空间对称离散格式组成。数值耗散项用局部棱柱化河道流的特征变量构造。格式的主要优点是能够计算天然河道中浅水方程组的弱解并且构造简单。格式能够求出天然河道或非平底部渠道中的精确静水解。给出了渠道溃坝问题数值解与解析解的比较,验证格式精度高。实际天然河道型梯级水库溃坝的数值实验表明格式稳定,适应性强。     

Numerical solution of laminar incompressible generalized Newtonian fluids flow

This paper deals with the numerical solution of laminar viscous incompressible flows for generalized Newtonian fluids in the branching channel. The generalized Newtonian fluids contain Newtonian fluids, shear thickening and shear thinning non-Newtonian fluids. The mathematical model is the generalized system of Navier-Stokes equations. The finite volume method combined with an artificial compressibility method is used for spatial discretization. For time discretization the explicit multistage Runge-Kutta numerical scheme is considered. Steady state solution is achieved for t → ∞ using steady boundary conditions and followed by steady residual behavior. For unsteady solution a dual-time stepping method is considered. Numerical results for flows in two dimensional and three dimensional branching channel are presented.     

Towards optimal Runge-Kutta smoothers for multigrid methods for unsteady flow problems

We consider Runge-Kutta smoothers in a dual time stepping multigrid method for unsteady flow problems. These smoothers are easily parallelizable and Jacobian-free, making them very attractive for 3D calculations. Existing methods have been designed for steady flows, leading to slow convergence for unsteady problems. Here we determine the free parameters of the smoother to provide optimal damping for high frequency components for the unsteady linear advection equation. This is compared with an RK smoother designed for steady state problems, as commonly used in CFD codes. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some exact solutions of an elastico-viscous fluid

The exact solutions for the unsteady flow of an elastico-viscous fluid caused by general periodic oscillations are obtained. Further, the plate is assumed to be rigid as well as porous executing periodic rotary oscillations. The velocity field and shear stress are established.