Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Crack extension and kinking in laminates and bicrystals

Singular fields at the tip of an interface crack in anisotropic solids are reviewed with emphasis on establishing a framework to quantify fracture resistance under mixed mode conditions. The concepts of mode mixity and surface toughness are unified by using generalized interface traction components. The similarity between the anisotropic theory and existing isotropic theory is shown. Explicit formulae are given for misoriented orthotropic bimaterials with potential applications envisioned including composite laminates and semiconductor crystals. Competition between crack extension along the interface and kinking into the substrate is investigated using a boundary layer formulation. Several case studies reveal the role of anisotropy. An explicit complex variable representation for orthotropic materials and a solution to a dislocation interacting with a crack are presented in two self-contained Appendices.

Thermophoretic deposition of particles onto cold surfaces of bodies in two-dimensional and axisymmetric flows

The problem of thermophoretic deposition of small particles onto cold surfaces is studied in two-dimensional and axisymmetric flow fields. The particle concentration equation is solved numerically together with the momentum and energy equations in the laminar boundary layer with variable density effect included. It is shown explicitly to what extent the particle concentration and deposition rate at the wall are influenced by the density variation effect for external flow past bodies. The general numerical procedure is given for two-dimensional and axisymmetric cases and is illustrated with examples of thermophoretic deposition of particles in flows past a cold cylinder and a sphere.

Simplified Navier-Stokes equations (SNSE)

Ten kinds of the simplified Navier-Stokes equations (SNSE) are reviewed and also used to calculate the Jeffery-Hamel flow as well as to analyze briefly the seven kinds of flows to which the exact solutions of the complete Navier-Stokes equations (CNSE) have been found. Analysis shows that the actual differences among the solutions of the different SNSE can go beyond the range of the order of magnitude of Re-1/2 and result even in different flow patterns, therefore, how to choose the viscous terms included in the SNSE is worthy of notice where Re=S∞u∞ L/μ∞ is the Reynolds numbers. For the aforesaid eight kinds of flows, the solutions to the inner-outer-layer-matched SNSE and to the thin-layer-2-order SNSE agree completely with the exact solutions to CNSE. But the solutions to all the other SNSE are not completely consistent with the exact solutions to CNSE and not a few of them are actually the solutions of the classical boundary layer theory. The innerouter-layer-matched SNSE contains the shear stress causing angular displacement of the inormal axis with respect to the streamwise axis and the normal stress causing expansion-contraction in the direction of the normal axis and the viscous terms being of the order of magnitude of the normal stress; and it can also reasonably treat the inertial terms as well as the relation between the viscous and inertial terms. Therefore, it seems promising in respects of both mechanics and mathematics.

Additional response: Additional discussion of “Mixed mode ductile fracture using the strain energy density criterion”

boundary-layer flows, the skin friction and wall heat-transfer are higher and the

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made.

含尘大气近地层流底层流动特性及其摩阻系数

采用双向耦合的双流体模型，了大气悬浮沙尘的存在对大气边界层中流底层流动特性及摩阻系数的影响，计算并讨论了不同沙尘含量下含尘大气相对于无尘大气摩阻系数的变化，结果表明，摩阻系数的变化取决于悬浮沙尘的初始运动状态和质量载荷率。

高超声速边界层流动转捩研究

针对高超声速飞行器前体预压缩性所需求的气动构型,开展了具有一级压缩效果的压缩面边界层的流动稳定性分析.采用有限体积法数值求解NS方程组得到基本流场,应用当地局部平行流假设和线性稳定性理论求解了扰动波参数的特征值问题.分析了来流马赫数M∞=6情况下二维扰动波的演化规律,并进一步关联扰动的空间放大率,结合EN方法进行了转捩预测.

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<boundary layer were solved numerically. The pressure distributions and local coefficients of skin friction on the wall are given. The numerical results obtained by the multiscale-domain decomposition algorithm are well agreement with those by NS equations. Comparing with the usual method of solving the Navier-Stokes equations in the whole flow, under the same numerical accuracy, the present multiscale domain decomposition method decreases CPU consuming about 20% and reflects the physical mechanism of practical flow more accurately.

郭永怀文集

郭永怀先生诞辰九十周年纪念文集

目录

力学2000

本书收录关于力学领域的论文301篇。内容包括：回顾20世纪力学在中国的发展，描绘了2000年中国和世界在力学各主要领域的发展现状；展望力学在21世纪的发展方向，探论新世纪中可能面临的新的重大力学等问题。

谈镐生文集

本文集收入了著名力学家、应用数学家、中国科学院院士谈镐生先生在流体力学、稀薄气体动力学和应用数学研究领域的论文和研究报告26篇，谈镐生先生倡导和支持力学基础研究的有关文章和论述21篇，谈先生的学术活动和生活图片多幅，以及谈镐生先生生平，最后附有谈先生生平年表。

 

 

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

MHD控制激波诱导边界层分离的机理

激波边界层相互作用是高超声速飞行器面临的重大问题,激波入射到平板引起的边界层分离是其中最具代表性的一种.用加权的3阶ENN格式计算了小磁雷诺数近似的MHD方程,研究了 MHD控制层流边界层分离的机理.数值结果显示,通过局部电离空气并施加洛伦兹力,能使分离点向下游移动,分离区尺寸减小,从而抑制和缓解由于激波-边界层相互作用而引起的分离.