计算二维粘性流动的流线迭代法

本文提出一种利用流线迭代法来计算任意形状流道中定常粘性层流流动的数值方法。通过任意非正交曲线网格中的压力梯度方程、能量方程和熵方程之间的迭代计算,可以得到整个流道中定常粘性可压缩(或不可压缩)流动的数值解。本文导出了二维(包括轴对称)流道中的基本方程,并详细地叙述了本方法的计算步骤。利用本方法对一些流道进行了数值计算,计算结果与其他巳知的数值解符合得很好。     

叶轮机械流道中粘性可压缩流动的数值计算——(Ⅰ)静止叶列中轴对称流动的计算

本文提出一种计算叶轮机械流道中粘性可压缩定常层流问题的数值方法,通过在任意非正交曲线方向上的焓梯度方程、能量方程和熵方程之间的迭代计算,可以得到整个流道中粘性可压缩定常流动问题的数值解。本文首先在静止坐标系中进行分析和讨论,并描述了叶轮机械的静止叶列中轴对称流动的计算方法。计算实例表明,本方法的特点是简单明了,计算速度快,可以广泛地应用于工程设计之中。     

粘性不可压缩流的壁涡数值边界条件

本文对具有固壁边界的二维粘性不可压缩定常流提出了一种四阶壁涡公式,并构造了一类非平凡的精确解。用两种具有代表性的内点差分格式及六种常用的壁涡公式(包括本文提出的一种),对本文所构造的雷诺数直到2000的一系列流动进行了数值求解,并以所构造的精确解为基准,分析和比较了这六种壁涡格式的精度、稳定性和收敛速度。计算结果表明,本文所提出的壁涡公式是这六种公式中最好的一种。本文数值实验中的一些结果对粘性不可压缩流固壁数值边界条件的处理可能具有一定的普遍意义。     

叶轮机械流道中粘性可压缩流动的数值计算——(Ⅱ)旋转叶列中轴对称流动的计算

本文把第一部分中所提出的计算叶轮机械流道中粘性可压缩定常层流问题的数值方法应用到旋转坐标系中。首先导得旋转叶列中粘性可压缩流动所满足的基本方程组,然后通过在任意非正交曲线方向上的焓梯度方程、能量方程和熵方程之间的迭代计算,得到叶轮机械旋转叶列流道中粘性轴对称流动的数值解。     

粘性不可压缩流体定常流动的差分解法

本文研究了定常N-S型方程和压力泊松方程的耦合求解。提出了一种处理压力自洽边界条件的方法,结合文[7]中给出的自调差分格式,可以对一些较复杂的粘性不可压缩流进行数值求解。     

黏弹性流体扩展及收缩流动的格子Boltzmann模拟分析

本文应用格子Boltzmann 方法(LBM)并结合Oldroyd-B 模型,讨论了不可压缩的 Navier-Stokes 方程和平流扩散本构方程的解耦及各自求解方法,以及两类问题的边界处理格式,实现了黏弹性流体在二维1:3 扩展流道以及3:1 收缩流道中的流动的数值模拟．获得了不同雷诺数Re 和维森伯格数Wi 以及黏度vs 下流动的流线分布,计算给出了漩涡的涡心位置和大小,并分析了参数Re、Wi 和vs 对流动特点的影响．模拟结果表明本文所采用模型和边界处理方法具有良好的精度和稳定性．     

可压缩、粘性翼前缘分离涡研究

从N-S方程出发,推得用于描述飞行器分离涡的可压缩、粘性涡核方程,给出了对于亚、跨、超音速都适用的数值解法,它可以计算分离涡或尾迹涡特性。导出了可压缩分离涡的破裂条件,并用于计算破裂位置。得到和分析了压缩性等参数对分离涡运动影响的一系列感兴趣特性。     

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。     

一种用边界元方法求解二维不可压缩粘性流动的方法

本文用边界元方法求解了二维不可压缩粘性流动的涡量——速度方程,利用求解区域边界上的速度法向导数和速度值直接得到了涡量的边界条件,克服了利用涡量方程求解二维不可压缩粘性流动时涡量边界条件(主要是壁面边界条件)难以给定的困难,算例表明:这种方法比较简单且计算结果基本上是令人满意的。     

网格与高精度差分计算问题

研究NS方程差分求解时来流雷诺数、计算格式精度和计算网格之间的关系．给出了判定空间三个方向上的粘性贡献在给定雷诺数、格式精度和网格下是否能够正确计入的估计方法．指出在NS方程的二阶差分方法的数值模拟中,由于物面法向采用了压缩网格技术,物面附近的网格间距很小,该方向上的粘性贡献可被计入．但是如果流向和周向的网格较粗,相应的差分方程中的粘性贡献可能落入截断误差相同的量级,因此在精度上等于仍是求解略去流向和周向粘性项的薄层近似方程．指出,高阶精度的差分计算格式,可以避免对网格要求苛刻的困难．并进一步讨论了建立高阶精度格式的问题,提出了建立高阶精度格式应该满足的原则：耗散控制原则以及色散控制原则．为了避免激波附近可能出现的微小非物理振荡,建议发展混合高阶精度格式,即在激波区,采用网格自适应的NND格式,在激波以外的区域,采用按上述原则发展的高阶格式．     

Flow field calculation and its experimental verification for inertia stage of marine gas turbine air intake filter

A numerical method is presented in this paper for the solution of flow field in marine gas turbine air intake filtration channel. The flow field was successfully calculated by this method, and aerodynamic characteristics were obtained for various types of filtration channels. This work is expected to be of practical importance for the design of such filters. Upstream difference was adopted to discretize the non-conservative type N-S equation for two-dimensional, time-dependnet, viscous and incompressible flow, and the stability, convergence, accuracy and artificial viscosity of the resulting difference equation were examined. This equation can be used to calculate viscous flows with Reynolds number up to tens of thousands. Also presented in this paper is a calculation method for treating wall vortex at boundary inflection points. Careful studies show that calculation based on the difference equational and wall vortex treatment proposed here are in good agreement with experimental results.     

The Integral Formula for Pressure Field in the Nonstationary Barotropic Flows of Viscous Fluid

An integral expression of pressure via dynamical characteristics of the vortex and velocity fields for viscous fluid is presented. This expression may be considered as an analog (or generalization) of the Bernoulli equation for nonstationary vortex flows of ideal or viscous fluids, including the case of an external nonconservative mass force. The presented formulas are useful for calculating the pressure field when meshless vortex methods are applied for the flow simulation.     

分区Lagrangian涡方法及瞬时起动圆柱初期流动的模拟

本文提出一种分区Lagrangian涡方法:将附着流动和分离流动分开处理,在附着区解边界层方层,只在分离区用涡方法解N-S方程。由于将尺度不同的区域分开了,求解分离区流动的涡方法中,每一时间步上物面引出的涡数在较小程度上依赖于Re数。这样,求解高Re数流动时,流场内的涡数,因而计算机内存和时间得以大大减小。用该方法计算了瞬时起动圆柱的初期流动,与实验结果比较相符很好。     

Effect of Volume Energy Supply on the Stability of a Subsonic Vortex Flow

Calculations of the stability of an axisymmetric vortex flow of viscous heat-conducting gas with volume energy supply are presented. The unperturbed axisymmetric vortex flow was found numerically using a quasi-cylindrical approximation of the Navier-Stokes equations under the assumption of constant peripheral-velocity circulation in the ambient co-current flow. The volume energy supply in the viscous vortex core was modeled by an additional source term in the energy equation. The stability characteristics of the viscous vortex flow in a longitudinal vortex with respect to both axisymmetric and non-axisymmetric three-dimensional waves traveling along the vortex axis and corresponding to both positive and negative values of the azimuthal wave number were found using the time-dependent formulation of the linear stability theory for compressible three-dimensional plane-parallel flows.     

Diffusion velocity for a three-dimensional vorticity field

A discussion is presented on the existence of a diffusion velocity for the vorticity vector that satisfies extensions of the Helmholtz vortex laws in a three-dimensional, incompressible, viscous fluid flow. A general form for the diffusion velocity is derived for a complex-lamellar vorticity field that satisfies the property that circulation is invariant about a region that is advected with the sum of the fluid velocity and the diffusion velocity. A consequence of this property is that vortex lines will be material lines with respect to this combined velocity field. The question of existence of diffusion velocity for a general three-dimensional vorticity field is shown to be equivalent to the question of existence of solutions of a certain Fredholm equation of the first kind. An example is given for which it is shown that a diffusion velocity satisfying this property does not, in general, exist. Properties of the simple expression for diffusion velocity for a complex-lamellar vorticity field are examined when applied to the more general case of an arbitrary three-dimensional flow. It is found that this form of diffusion velocity, while not satisfying the condition of circulation invariance, nevertheless has certain desirable properties for computation of viscous flows using Lagrangian vortex methods. The significance and structure of the noncomplex-lamellar part of the viscous diffusion term is examined for the special case of decaying homogeneous turbulence.     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

全附体潜艇粘性流场的RANS模拟及场量和涡量的校验分析

采用相同拓扑结构和相近网格质量的4套网格和5种湍流模型,对全附体Suboff潜艇粘性流场进行RANS模拟,分析了网格密度、节点空间分布规律和湍流模型对计算精度的影响,详细校验了其力积分量、速度场量和涡量特征。结果表明:网格密度最大的G4网格(140万)计算精度最高,总阻力较实验值误差为0.723%,其采用SST湍流模型时最优。计算得到的压力系数和剪切应力系数分布均与实验值吻合很好;桨盘面速度等值线分布计算精度与文献相当,轴向相对速度0.9以上的计算半径稍大于实验值,其余半径与实验吻合较好;桨盘面上0.25倍半径处速度分量沿周向分布计算精度较文献高,轴向分量与实验值吻合较好,径向分量峰值稍小于实验值,但峰值所处周向位置与实验值一致。成功捕捉到了附体端面绕流诱导对旋涡、附体叶根截面下游处项链形涡对、尾翼端面尾缘上方附着涡蹄、附体马蹄涡系、尾翼截面通道流体挤压作用诱导涡以及桨盘面涡量汇集的潜艇涡量场特征,且围壳端面绕流诱导对旋涡沿流动方向持续稳定,不影响桨盘面涡量场,均与文献中由大涡模拟模拟得到的定性结论一致。研究表明,在网格密度较大、节点分布合理、网格质量较高、湍流模型选取适当和壁面函数使用有效的条件下,RANS模拟潜艇粘性流场的场量和涡量特征同样具有很高的计算精度,能够在工程应用中有力支撑新型艇型设计与性能分析。     

Vortex‐in‐cell method combined with a boundary element method for incompressible viscous flow analysis

In this study, an immersed boundary vortex‐in‐cell (VIC) method for simulating the incompressible flow external to two‐dimensional and three‐dimensional bodies is presented. The vorticity transport equation, which is the governing equation of the VIC method, is represented in a Lagrangian form and solved by the vortex blob representation of the flow field. In the present scheme, the treatment of convection and diffusion is based on the classical fractional step algorithm. The rotational component of the velocity is obtained by solving Poisson's equation using an FFT method on a regular Cartesian grid, and the solenoidal component is determined from solving an integral equation using the panel method for the convection term, and the diffusion term is implemented by a particle strength exchange scheme. Both the no‐slip and no‐through flow conditions associated with the surface boundary condition are satisfied by diffusing vortex sheet and distributing singularities on the body, respectively. The present method is distinguished from other methods by the use of the panel method for the enforcement of the no‐through flow condition. The panel method completes making use of the immersed boundary nature inherent in the VIC method and can be also adopted for the calculation of the pressure field. The overall process is parallelized using message passing interface to manage the extensive computational load in the three‐dimensional flow simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

Temporal Evolution of Vortical Structures in the Wall Region of Turbulent Channel Flow

Hairpin-like vortical structures that form in the wall region of turbulent channel flow are investigated. The analysis is performed by following a procedure in which the Navier-Stokes equations are first integrated by means of a computational code based on a mixed spectral-finite difference technique in the case of the flow in a plane channel. A DNS turbulent-flow database, representing the turbulent statistically steady state of the velocity field through 10 viscous time units, is computed and the vortex-detection method of the imaginary part of the complex eigenvalue pair of the velocity-gradient tensor is applied to the velocity field. As a result, hairpin-like vortical structures are educed. Flow visualizations are provided of the processes of evolution that characterize hairpin vortices in the wall region of turbulent channel flow. The relationship is investigated between vortex dynamics and 2nd- and 4th- quadrant events, showing that ejections and sweeps play a fundamental role in the way the morphological evolution of a hairpin vortex develops with time.     

Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

The vortex method is applied to the calculation of a homogeneous shear turbulence, and compared with a finite difference code using identical calculation conditions. The core spreading method with spatial adaptation is selected as the viscous diffusion scheme of the vortex method. The shear rate is chosen so that it matches the maximum value observed in a fully developed channel flow. The isosurface, anisotropy tensors, and joint probability density functions reflect the ability of the present vortex method to quantitatively reproduce the anisotropic nature of strongly sheared turbulence, both instantaneously and statistically. Copyright © 2009 John Wiley & Sons, Ltd.