On Plane-Parallel Separated Flows of an Incompressible Fluid near Flat Boundaries

On the basis of Stokes separated flows, examples of separated flows described by the Navier-Stokes equations of a viscous incompressible fluid are constructed. These flows are represented by series convergent in a certain non-zero neighborhood of a flat contour immersed in the flow. In this neighborhood, the series have the same structure as those for the basic Stokes flows. Examples of the regions in which the series segments chosen give only a slight deviation from the numerical solutions of the Navier-Stokes equations are presented. The comparison between inviscid separated flows (without the no-slip condition on the contour) and viscous flows of the same structure (with the no-slip condition) shows that the viscosity does not play a decisive role in the formation of separation or the type of streamline approach to or departure from the contour.     

分离流动数值模拟的几个问题

介绍了分离流动现象.给出了三维定常粘性流动分离识别准则,研究了分离流动的性态.给出了应用于分离流动的六种模型及有关的控制方程.讨论了求解NS方程的数值方法和数值模拟的前景.特别研究了应用于分离流动的Eulcr方程的数值模拟问题.      

粘流-无粘干扰流动(IF)理论

对不可压缩层流二维干扰流动,本文提出一个干扰流动(IF)理论。IF理论要点为:1)干扰流动沿主流的法向被分为三层即粘性层、干扰层和无粘层,引进了法向动量交换为主导过程的干扰层概念。2)利用力学守恒律、三层匹配关系及文中引进的干扰模型,把三层的空间尺度及惯性-粘性诸力的数置级表示为单参数m的函数,m<1/2·3)导出描述各层流动的控制方程、导出描述全城流动的控制方程为简化Navie-Stokes(SNS)方程。IF理论适用于不存在分离的附着干扰流动以及存在分离的大范围干扰流动,经典边界层(CBL)理论和流动分离局部区域Triple-Deck(TD)理论分别是本文理论在参数m=O和1/4时的两个特例,本文理论容易推广到可压缩、三维及湍流流动。     

高雷诺数流动的基本控制方程体系和扩散跑物化Navier-Stokes方程组的意义和用途

在计算机发达的时代, 高雷诺($Re$)数绕流计算中有无必要使用简化NS方程组, 本文讨论这个问题. 主要内容如下: (1)高$Re$数绕流包含3种基本流动: 所有方向对流占优流动、所有方向对流扩散竞争流动和部分方向对流占优部分方向对流扩散竞争流动(简称干扰剪切流动), 3个基本流动的特征彼此不同且在流场中所占领域大小彼此相差悬殊, NS方程区域很小,它们的最简单控制方程组Euler、Navier-Stokes (NS)和扩散抛物化(DP) NS方程组的数学性质彼此不同, 因此利用Euler-DPNS-NS方程组体系分析计算高$Re$数绕流流动就是一个合乎逻辑的选择, 该法与利用单一NS方程组的常用方法可以彼此检验和补充. (2)流体之间以及流体与外界的动量、能量和质量交换, 流态从层流到湍流的演化主要发生在干扰剪切流动中, 干扰剪切流及其最简单控制方程------DPNS方程组具有基础意义; DPNS方程组笔者在1967年已提出. (3)诸简化NS方程组: DPNS、抛物化(P)NS、薄层(TL)NS、黏性层(VL)NS方程组的发展、相互关系, 它们的历史贡献和今后的用途; 它们的数学性质均为扩散抛物型, 但它们包含的黏性项彼此有所不同; 从流体力学角度来看, 它们中只有DPNS方程组能够准确描述干扰剪切流动. 提出把诸简化NS方程组统一为DPNS方程组的建议. (4)干扰剪切流------DPNS方程组与无干扰剪切流------边界层方程组之间的关系以及进一步研究干扰剪切流的意义.      

弯度翼型大迎角时分离涡流场的多平衡态现象

基于kω的SST两方程湍流模型,在时间域求解雷诺平均Navier-Stokes方程,模拟弯度翼型大迎角时的分离流动。通过给翼型施加一定形式的扰动,重点关注了翼型弯度对大迎角分离涡流场平衡态转移的影响。研究结果表明:与相同厚度20%以上的对称翼型相比,2%弯度的翼型出现分离涡流场平衡态转移的起始迎角变小2°左右,迎角区间变宽约1°;在厚度相对较小的NACA2416翼型上也发现上述分离涡平衡态转移现象。由此说明翼型弯度在一定程度上促使了分离涡平衡态的转移。     

Navier-Stokes equations with imposed pressure and velocity fluxes

Boundary value problems for Stokes and Navier-Stokes equations with non-standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non-standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier-Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiological flows.     

Calculation of laminar flow of compressible gas in the presence of heat transfer in two-dimensional curvilinear channels

Numerical solution of the complete system of Navier-Stokes equations is used to investigate laminar (Re ? 1000) subsonic flows of a compressible gas in the presence of heat transfer (cooled walls) in two-dimensional channels containing a bend section (for different curvature parameters). The appearance of closed separation regions of the flow on the channel walls, their deformation as the parameters of the problem are changed, and the loss of pressure are studied. The sections of the channel walls with maximal and minimal heat fluxes are determined, and the connection between these sections and the separation regions is elucidated.     

分离流动物理特性研究进展

分离流问题的研究在当前流体力学中占有十分重要的地位。它不仅具有重要的理论意义并且具有广泛的应用价值。本文着重评述三维分离流中的基本物理特性和它的流动结构。重点讨论了三维定常分离的两种模式及其判别准则;在三维分离流中应用奇点拓扑理论的定性分析;按照流动的物理特性对三维分离的分类;分离面的物理特性。最后简单介绍了目前在研究湍流边界层分离方面的进展。      

A practical implementation of turbulence models for the computation of three-dimensional separated flows

An upwind MUSCL-type implicit scheme for the three-dimensional Navier-Stokes equations is presented and details on the implementation for three-dimensional flows of a ‘diagonal’ upwind implicit operator are developed. Turbulence models for separated flows are also described with an emphasis on the numerical specificities of the Johnson-King non-equilibrium model. Good predictions of separated two- and three-dimensional flows are demonstrated.     

预处理方法在全速度流场中的应用研究

应用预处理方法求解二维可压缩Navier-Stokes方程,发展出一套既适用于低速流动,也可用于可压缩流动的全速度流场解算方法.空间格式选用Ausm类格式,并采用多步Runge-Kutta时间推进方法.数值模拟了鼓包(Bump),RAE2822翼型,多段高升力翼型的不同速度绕流流场,并与实验数据进行了对比.结果表明预处...     

Numerical study of self-sustained oscillatory flows and heat transfer in channels with a tandem of transverse vortex generators

A numerical investigation was conducted into channel flows with a tandem of transverse vortex generators in the form of rectangular cylinders. The oscillatory behavior of the flow is studied. Data for heat transfer and flow losses are presented for 100≤Re≤400 and cylinder separation distances 1≤S/H≤4. The results are obtained by numerical solution of the full Navier-Stokes equations and the energy equation. Self-sustained flow oscillations are found for Re>100. Alternate and dynamic shedding of large vortex structures from the cylinders is observed by visualization of the numerically determined flow field. A heat transfer enhancement up to a factor 1.78 compared to plane channel flow is observed. Received on 16 July 1997     

Transonic viscous-inviscid interaction by a finite element method

A method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.     

Regimes of laminar lateral flow separation due to jet exhaust

Numerical simulation of the separation flow on the lateral surface of an aircraft due to interaction between the engine exhaust plume and the external air-stream is carried out on the basis of the full Navier-Stokes equations. Three separated flow regimes are revealed, namely, closed, open and periodic. The conditions under which each of these three regimes may exist are determined. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 132–138, January–February, 1994.     

Stagnation flow towards a shrinking sheet

The stagnation flow towards a shrinking sheet is studied. A similarity transform reduces the Navier-Stokes equations to a set of non-linear ordinary differential equations which are then integrated numerically. Both two-dimensional and axisymmetric stagnation flows are considered. It is found that solutions do not exist for larger shrinking rates and may be non-unique in the two-dimensional case. The non-alignment of the stagnation flow and the shrinking sheet complicates the flow structure. Convective heat transfer decreases with the shrinking rate due to an increase in boundary layer thickness.     

Numerical investigation of flow past a system of two sweptback compression wedges

Supersonic flow past a three-dimensional configuration consisting of two neighboring wedges with sweptback leading edges mounted on a preliminary compression surface is numerically investigated. The case of sweptback wedges is considered, when their beveled surfaces deflect the compressed flows to opposite directions. The calculations are carried out on the basis of the averaged Navier-Stokes equations, together with the SST k-? turbulence model, at the freestream Mach number M = 6. The results obtained are compared with the data for inviscid flow calculated using the Euler equations. The flow pattern features, due to the interaction in the plane of symmetry between the shocks formed by the wedges and the shock-induced three-dimensional quasiconical separations of the turbulent boundary layer on the preliminary compression surface along the swept leading edges, are established. Within these separation zones the flow is directed away from the plane of symmetry of the configuration and is characterized by considerably greater values of the transverse velocity component, as compared with the flow outside of the separation zone.     

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.     

Separation of chemical elements in the discharge channel of an inductive plasma gun

Zones of separation of chemical elements in the air plasma flow in the discharge channel of the VGU-4 100-kW inductive plasma gun with a sonic nozzle of the Institute for Problems in Mechanics of the Russian Academy of Sciences are determined from an analysis of numerical solutions obtained within the framework of the Navier-Stokes equations. The occurrence of these zones and their possible influence on heat transfer to bodies in underexpanded jet flows in physical experiments are explained.     

Navier-Stokes analysis of a circulation control airfoil

The two-dimensional, compressible, mass-averaged Navier-Stokes equations are used to investigate flows about a typical circulation control airfoil. The governing equations are solved using the implicit approximate-factorization algorithm of Beam-Warming with a modified algebraic eddy viscosity model. Results are compared with experimental data, and excellent agreement is obtained. The effects of different jet momentum coefficients and angles of attack on the flow are studied. The mechanism of genenating large lift by circulation control is discussed.     

Vortex Formations in Plane Flows of Viscous and Ideal Fluids

An analytic representation of individual vortex formations with different cross-sections is obtained for plane-parallel flows of viscous and ideal fluids. A flow in which one of the streamlines has cusp is also found. In these flows the vorticity is constant; therefore, the solutions obtained for the equations describing the kinematic variables in ideal fluid flows must simultaneously satisfy the Navier-Stokes equations.