适应复杂外形的三维粘性混合网格生成算法

提出一类适应复杂外形的粘性混合网格生成算法。表面网格由前沿推进三角形曲面网格程序获得,边界层布置各向异性的三棱柱体网格,远物面区域采用Delaunay方法生成四面体网格。针对模型的复杂几何特征,综合采用了各种网格处理技术,以保证边界层网格的质量,并避免算法失效问题。网格实例及计算结果表明了本文算法的实用性及和效性。     

黏性边界层网格自动生成

高雷诺数黏性流动在壁面附近存在边界层,在计算模拟中自动生成可靠且有效的计算网格仍然是计算流体力学存在的瓶颈.三棱柱/四面体混合网格技术在一定程度上缓解了这个困难.然而,对于复杂外形的情况,在边界层内自动高效生成高质量的三棱柱单元仍然十分困难.常用的层推进法在凹凸区域及角点处生成的边界层网格单元质量较差,边界层网格最外层尺寸不均匀.针对这些问题,发展了一种黏性边界层网格自动生成方法,通过顶点周围边的二面角识别物面网格特征确定多生长方向,预估并调整生长高度处理相交情况.同时提出一种三维前沿尺寸调节方式,提高了边界层网格单元的正交性,保证了边界层网格与远场网格尺寸的光滑过渡.通过ONERA M6翼型以及带发动机短舱的DLR-F6翼身组合体等外形的网格生成实例及绕流数值模拟,将计算值与标准实验值进行对比,结果表明:该方法能够自动高效地生成满足数值计算需求的混合网格.     

A family of multi‐point flux approximation schemes for general element types in two and three dimensions with convergence performance

A family of flux‐continuous, locally conservative, control‐volume‐distributed multi‐point flux approximation (CVD‐MPFA) schemes has been developed for solving the general geometry‐permeability tensor pressure equation on structured and unstructured grids. These schemes are applicable to the full‐tensor pressure equation with generally discontinuous coefficients and remove the O(1) errors introduced by standard reservoir simulation schemes when applied to full‐tensor flow approximation. The family of flux‐continuous schemes is characterized by a quadrature parameterization. Improved numerical convergence for the family of CVD‐MPFA schemes using the quadrature parameterization has been observed for structured and unstructured grids in two dimensions. The CVD‐MPFA family cell‐vertex formulation is extended to classical general element types in 3‐D including prisms, pyramids, hexahedra and tetrahedra. A numerical convergence study of the CVD‐MPFA schemes on general unstructured grids comprising of triangular elements in 2‐D and prismatic, pyramidal, hexahedral and tetrahedral shape elements in 3‐D is presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Octree partitioning of hybrid grids for parallel adaptive viscous flow simulations

A parallel finite volume method for the Navier–Stokes equations with adaptive hybrid prismatic/tetrahedral grids is presented and evaluated in terms of parallel performance. A new method of domain partitioning for complex 3D hybrid meshes is also presented. It is based on orthogonal bisection of a special octree corresponding to the hybrid mesh. The octree is generated automatically and can handle any type of 3D geometry and domain connectivity. One important property of the octree-based partitioning that is exploited is the octree's ability to yield load-balanced partitions that follow the shape of the geometry. This biasing of the octree results in a reduced number of grid elements on the interpartition boundaries and thus fewer data to communicate among processors. Furthermore, the octree-based partitioning gives similar quality of partitions for very different geometries, while requiring minimal user interaction and little computational time. The partitioning method is evaluated in terms of quality of the subdomains as well as execution time. Viscous flow simulations for different geometries are employed to examine the effectiveness of the octree-based partitioning and to test the scalability of parallel execution of the Navier–Stokes solver and hybrid grid adapter on two different parallel systems, the Intel Paragon and the IBM SP2. © 1998 John Wiley & Sons, Ltd.     

A high‐order element based adaptive mesh refinement strategy for three‐dimensional unstructured grid

Adaptive mesh refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR, better prediction can be obtained with much less labor work and cost compared to manually remeshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh, which is heavily used in the high‐Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high‐order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last, the mesh suitable for the solver is output. Generating refined elements in the parametric space with high‐order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, 3‐dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the 2‐dimensional airfoil and 3‐dimensional full aircraft, the current AMR method proves to be accurate, simple, and robust.     

Effect of ion‐slip current on the thermal instability of mixed connection in a boundary layer flow

Effect of ion‐slip current on the thermal instability in a boundary layer is studied. The criterion on the position marking the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, the Reynolds number, the wave number, the Hall parameter, the ion‐slip parameter, and the Hartmann number. The flow becomes more stable as the magnetic field increases. However, the destabilizing effects are found on the flow when the Hall and ion‐slip currents are presented. The results of the present numerical prediction show reasonable agreement with the experimental data in the case of zero Hartmann number, ion‐slip parameter, and Hall parameter in the open literature. Copyright © 2011 John Wiley & Sons, Ltd.     

四面体模型质量度量准则及其之间的关系

四面体模型质量度量准则是评价网格模型质量的标准,但长期以来,对四面体单元质量的度量和评价并没有公认的标准。因此,本文对常用的四面体网格模型质量度量准则进行总结,并从理论上证明了各质量度量准则之间的关系,同时通过实验分析各质量度量准则之间的这种关系是否成立。分析认为在优化四面体模型时,不能仅仅采用某一种度量标准来评价网格的质量,应根据不同的四面体类型,采用不同的准则或将几种准则联合起来对四面体模型质量进行度量。     

Method of fundamental solutions for partial‐slip fibrous filtration flows

In this study a Stokeslet‐based method of fundamental solutions (MFS) for two‐dimensional low Reynolds number partial‐slip flows has been developed. First, the flow past an infinitely long cylinder is selected as a benchmark. The numerical accuracy is investigated in terms of the location and the number of the Stokeslets. The benchmark study shows that the numerical accuracy increases when the Stokeslets are submerged deeper beneath the cylinder surface, as long as the formed linear system remains numerically solvable. The maximum submergence depth increases with the decrease in the number of Stokeslets. As a result, the numerical accuracy does not deteriorate with the dramatic decrease in the number of Stokeslets. A relatively small number of Stokeslets with a substantial submergence depth is thus chosen for modeling fibrous filtration flows. The developed methodology is further examined by application to Taylor–Couette flows. A good agreement between the numerical and analytical results is observed for no‐slip and partial‐slip boundary conditions. Next, the flow about a representative set of infinitely long cylindrical fibers confined between two planar walls is considered to represent the fibrous filter flow. The obtained flowfield and pressure drop agree very well with the experimental data for this setup of fibers. The developed MFS with submerged Stokeslets is then applied to partial‐slip flows about fibers to investigate the slip effect at fiber–fluid interface on the pressure drop. The numerical results compare qualitatively with the analytical solution available for the limit case of infinite number of fibers. Copyright © 2008 John Wiley & Sons, Ltd.     

Hierarchical structure observation and nanoindentation size effect characterization for a limnetic shell

In the present research, hierarchical structure observation and mechanical property characterization for a type of biomaterial are carried out. The investigated biomaterial is Hyriopsis cumingii, a typical limnetic shell, which consists of two different structural layers, a prismatic "pillar"structure and a nacreous "brick and mortar" structure. The prismatic layer looks like a "pillar forest" with variationsection pillars sized on the order of several tens of microns.The nacreous material looks like a "brick wall" with bricks sized on the order of several microns. Both pillars and bricks are composed of nanoparticles. The mechanical properties of the hierarchical biomaterial are measured by using the nanoindentation test. Hardness and modulus are measured for both the nacre layer and the prismatic layer, respectively.The nanoindentation size effects for the hierarchical structural materials are investigated experimentally. The results show that the prismatic nanostructured material has a higher stiffness and hardness than the nacre nanostructured material.In addition, the nanoindentation size effects for the hierarchical structural materials are described theoretically, by using the trans-scale mechanics theory considering both strain gradient effect and the surface/interface effect. The modeling results are consistent with experimental ones.     

Crystal-plasticity finite-element analysis of inelastic behavior during unloading in a magnesium alloy sheet

A crystal-plasticity finite-element analysis of the loading-unloading process under uniaxial tension of a rolled magnesium alloy sheet was carried out, and the mechanism of the inelastic response during unloading was examined, focusing on the effects of basal and nonbasal slip systems. The prismatic and basal slip systems were mainly activated during loading, but the activation of the prismatic slip systems was more dominant. Thus the overall stress level during loading was determined primarily by the prismatic slip systems. The prismatic slip systems were hardly activated during unloading because the stress level was of course lower than that during loading. On the other hand, because the strength of the basal slip systems was much lower than that of the prismatic slip systems, the basal slip systems would be easily activated under the stress level during unloading in the opposite direction when their Schmid’s resolved shear stresses changed signs because of the inhomogeneity of the material. These results indicated that one explanation for the inelastic behavior during unloading was that the basal slip systems were primarily activated owing to their low strengths compared to that of the prismatic slip systems. Numerical tests using the sheets with random orientations and with the more pronounced texture were conducted to further examine the mechanism.     

Hybrid mesh generation with embedded surfaces using a multiple marching direction approach

This paper proposes a method for the creation of hybrid meshes with embedded surfaces for viscous flow simulations as an extension of the multiple marching direction approach (AIAA J. 2007; 45 (1):162–167). The multiple marching direction approach enables to place semi‐structured elements around singular points, where valid semi‐structured elements cannot be placed using conventional hybrid mesh generation methods. This feature is discussed first with a couple of examples. Elements sometimes need to be clustered inside a computational domain to obtain more accurate results. For example, solution features, such as shocks, vortex cores and wake regions, can be extracted during the process of adaptive mesh generation. These features can be represented as surface meshes embedded in a computational domain. Semi‐structured elements can be placed around the embedded surface meshes using the multiple marching direction approach with a pretreatment method. Tetrahedral elements can be placed easily instead. A couple of results are presented to demonstrate the capability of the mesh generation method. Copyright © 2008 John Wiley & Sons, Ltd.     

Lengthscale-dependent,elastically anisotropic,physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys

A crystal plasticity model for hcp materials is presented which is based on dislocation glide and pinning. Slip is assumed to occur on basal and prismatic systems, and dislocation pinning through the generation of geometrically necessary dislocations (GNDs). Elastic anisotropy and, through the coupling of GNDs with slip rate, physically-based lengthscale effects are included.     

Effect of Internal Heat Generation on the Onset of Marangoni Convection in a Fluid Layer Overlying a Layer of an Anisotropic Porous Medium

Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers–Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.     

薄元分解与Laplacian光顺相结合的四面体有限元网格优化方法

提出一种有效的三维实体四面体有限元网格质量优化方法以满足有限元分析对网格质量的要求。对薄元分解法进行改进,改进的薄元分解法更全面地考虑了各种劣质单元类型,能够对三维实体网格剖分中产生的各种类别的孤立劣质单元进行有效的分解;将改进的薄元分解法与Laplacian光顺优化方法相结合以解决某些网格剖分算法如推进波前法和Delaunay三角化方法产生的非孤立劣质单元问题。经过实例检验,本文提出的四面体单元网格优化算法健壮有效、易于实现,能够显著提高最差单元的质量。     

一种基于双前沿推进的边界层网格生成算法

高雷诺数粘性流动模拟对边界层内的网格正交性有特殊要求.对于复杂外形,这类问题的网格自动化生成十分困难.面向该问题,提出一种双前沿推进思想,并形成一种面向复杂几何外形的边界层网格全自动生成算法.结合多种网格技术处理局部几何特征以保证边界层网格的质量.双前沿推进思想同时适用于多块结构网格和混合网格的边界层网格生成.多个模型...     

Simulation of coating flows with slip effects

This work is concerned with the numerical prediction of wire coating flows. Both annular tube‐tooling and pressure‐tooling type extrusion–drag flows are investigated for viscous fluids. The effects of slip at die walls are analysed and free surfaces are computed. Flow conditions around the die exit are considered, contrasting imposition of no‐slip and various instances of slip models for die wall conditions. Numerical solutions are computed by means of a time marching Taylor–Galerkin/pressure–correction finite element scheme, that demonstrates how slip conditions on die walls mitigate stress singularities at the die exit. For pressure‐tooling and with appropriate handling of slip, reduction in shear rate at the die exit may be achieved. Maximum shear rates for tube‐tooling are about one quarter of those encountered in pressure‐tooling. Equivalently, extension rates peak at land entry, and tube‐tooling values are one third of those observed for pressure‐tooling. With slip and tube‐tooling, peak shear values at die exit may be almost completely eliminated. Nevertheless, in contrast to the pressure‐tooling scenario, this produces larger peak shear rates upstream within the land region than would otherwise be the case for no‐slip. Copyright © 2000 John Wiley & Sons, Ltd.     

A general theory for two- and three-dimensional wall-mode instabilities in boundary layers over isotropic and anisotropic compliant walls

An asymptotic theory is developed for two- and three-dimensional disturbances growing in a two-dimensional boundary layer over a compliant wall. The theory exploits the multideck structure of the boundary layer to derive asymptotic approximations at a high Reynolds number for the perturbation wall pressure and viscous stresses. These quantities can be regarded as driving the wall and, accordingly, the equation(s) of motion for the wall is (are) used as the characteristic equation(s) for finding the eigenvalue(s). The main assumptions are that the amplitude of the disturbance is sufficiently small for linear theory to hold, the Reynolds number is large, the disturbance wavelength is long compared with the boundary-layer thickness, and the critical and viscous wall layers are well separated. The theory was developed to study the travelling-wave flutter instability discussed by Carpenter and Garrad, i.e., the Class B instability of Benjamin and Landahl. Under certain limiting processes both the upper-branch and conventional triple-deck scalings for the Tollmien-Schlichting instability can be obtained with the present approach. Accordingly, the theory also gives a reliable qualitative guide to the effect of anisotropic wall compliance on the Tollmien-Schlichting instability.The theory is applied to various cases including two- and three-dimensional disturbances, developing in boundary layers over isotropic and anisotropic compliant walls. The disturbances can be treated as either temporally or spatially growing. Eigenvalues are very accurately predicted by means of the theory, especially near points of neutral stability. The computational requirements are trivial compared with those required for full numerical solution of the Orr-Sommerfeld equation. For isotropic compliant walls the theory confirms the earlier result of Miles and Benjamin that the phase shift in the disturbance velocity across the critical layer plays a dominant role in destabilization of the Class B travelling-wave flutter through making irreversible energy transfer possible due to the work done by the fluctuating pressure at the wall. The theory elucidates the secondary role played by the phase shift occurring across the wall layer. Viscous effects are much more important for anisotropic compliant walls which admit substantial horizontal, as well as vertical, displacement. For these walls an important mechanism for irreversible energy transfer is the work done by fluctuating shear stress. This almost invariably has a stabilizing effect on the travelling-wave flutter. In addition there is a weaker effect arising from the effect of anisotropic wall compliance on the phase shift across the wall layer. This may be stabilizing or destabilizing.This work was carried out with the support of the Ministry of Defence (Procurement Executive) and the Office of Naval Research and was completed while P.W.C. and J.S.B.G. were on study leave at the Department of Aerospace Engineering, The Pennsylvania State University, and the Department of Mathematics, Iowa State University, Ames, respectively. They would like to express their gratitude to those institutions and the Office of Naval Research for financial support during their study leaves.     

Crystal plasticity modeling of slip activity in Ti–6Al–4V under high cycle fatigue loading

Deformation micromechanisms of a Ti–6Al–4V alloy under fatigue loading at room temperature are studied using a three-dimensional crystal plasticity constitutive model. The model employs a minimum set of fitting parameters based on experimental data for Ti–6Al–4V. Single slip is strongly favored through a softening law that affects mainly the driving force for slip on the first activated slip system. Cyclic deformation behavior at the macroscopic scale and at the local scale of grains is analyzed through the simulation of 20 cycles of fatigue on a polycrystalline structure of 900 randomly oriented grains. The progressive activation of slip (basal, prismatic, and pyramidal) is analyzed and compared to experimental observations.     

Analytical solution of the contact problem of a rigid indenter and an anisotropic linear elastic layer

We use the Stroh formalism to study analytically generalized plane strain deformations of a linear elastic anisotropic layer bonded to a rigid substrate, and indented by a rigid cylindrical indenter. The mixed boundary-value problem is challenging since the a priori unknown deformed indented surface of the layer contacting the rigid cylinder is to be determined as a part of the solution of the problem. For a rigid parabolic prismatic indenter contacting either an isotropic layer or an orthotropic layer and a flat rigid punch indenting a half space, the computed solutions are found to agree well with those available in the literature. Parametric studies have been conducted to delimit the length and the thickness of the layer for which the derived relation between the axial load and the indentation depth caused by the rigid cylinder is valid. The indentation of a face centered cubic crystal with the plane of indentation oriented differently from the principal planes of symmetry has also been studied to illustrate the applicability of the technique to general layers made of anisotropic materials. Results presented herein can serve as benchmarks with which to compare solutions obtained by other methods.     

Modelling the effects of emergent vegetation on an open‐channel flow using a lattice model

A two‐dimensional lattice model has been developed to describe the influence of vegetation on the turbulent flow structure in an open channel. The model includes the influence of vegetation density on the frictional effect of the channel bed and walls. For the walls, a semi‐slip boundary condition has been considered as an alternative to overcome the no‐slip boundary condition limitations in turbulent flows. The drag stress exerted by the flow on the vegetation as well as the gravity effect has also been taken into account. The proposed lattice model has been used to simulate the experimental results reported from the study of the influence of alternate vegetated zones on the open‐channel flow. The results show that the lattice model approach is a valid tool for describing these kinds of flows. Copyright © 2007 John Wiley & Sons, Ltd.