Efficient least squares finite elements for two-dimensional laminar boundary layer analysis

This paper presents the formulations of essentially one-dimensional least squares and Galerkin-least squares finite elements for the numerical solution of two-dimensional laminar boundary layer equations. An iterative technique to cope with the non-linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.     

Efficient global optimization applied to wind tunnel evaluation-based optimization for improvement of flow control by plasma actuators

A kriging-based genetic algorithm called efficient global optimization (EGO) was employed to optimize the parameters for the operating conditions of plasma actuators. The aerodynamic performance was evaluated by wind tunnel testing to overcome the disadvantages of time-consuming numerical simulations. The proposed system was used on two design problems to design the power supply for a plasma actuator. The first case was the drag minimization problem around a semicircular cylinder. In this case, the inhibitory effect of flow separation was also observed. The second case was the lift maximization problem around a circular cylinder. This case was similar to the aerofoil design, because the circular cylinder has potential to work as an aerofoil owing to the control of the flow circulation by the plasma actuators with four design parameters. In this case, applicability to the multi-variant design problem was also investigated. Based on these results, optimum designs and global design information were obtained while drastically reducing the number of experiments required compared to a full factorial experiment.     

不同粗糙表面的圆柱风压分布试验研究

通过风洞试验研究了不同表面粗糙度、不同雷诺数条件下二维圆柱的压力分布和阻力特性。结果表明:通过合理地增大表面粗糙度,在相对较低的风速下有效地模拟了圆柱的超临界绕流特性,满足了工程应用对超临界雷诺数的要求。     

The application of the boundary integral equations method to subsonic flow with circulation past thin airfoils in a wind tunnel

Summary In this paper we apply the direct boundary integral equations method to subsonic flow with circulation past a thin airfoil in a wind tunnel. A set of Green's functions for the equations of the velocity perturbation is deduced. These functions together with the non-linear limit condition imposed just on the surface profile lead to a Fredholm integral equation of the second kind over the profile only. The integral formulation has the advantage not to truncate the flow domain and to save computing effort when numerical solving is performed, due to the lack of the tunnel walls discretisation. In the case of the incompressible fluid we use the exact equations of motion, which implies a valid solution for any shape of the profile, being not necessarily thin. In the case of the compressible fluid we use the linearized motion equations, which implies a valid solution only for thin airfoils. The integral equation obtained on the surface, together with the circulation integral formula are solved via a collocation method. The numerical tests made for the circular obstacle show a very good agreement with the theory. The numerical experiments on the NACA-4412 profile were made in order to determine the tunnel and the compressibility effects being compared to the unbounded flow.     

Free-surface flow of a fluid body with an inner circular cylinder in impulsive motion

An analytical theory and numerical computations are developed for the two-dimensional free-surface flow of an initially circular layer of inviscid fluid surrounding a rigid circular cylinder. The two cylinders are initially concentric. The fluid packet is released from rest and the flow suddenly starts forced by gravity and by the simultaneous impulsive motion of the inner body. A small-time expansion of the fully nonlinear free-surface problem is developed and a closed-form solution is found up to third order for an arbitrary radius of the rigid cylinder. For the gravitational flow around the body at rest, the solution is extended up to fourth order. Free-surface profiles and hydrodynamic forces on the cylinder are calculated and discussed against numerical solutions of the exact unsteady nonlinear problem. Some basic features, such as the formation of an almost uniform layer surrounding the upstream side of the body, are captured by the theory quite well and only later on in time significant quantitative differences appear. Similarly, the behaviour of hydrodynamic loads is rather well predicted during initial stages preceding larger fluctuations observed on a longer time-scale.     

高雷诺数下错列双圆柱气动干扰的机理研究

为了进一步澄清小间距错列双圆柱的气动干扰机理,该文采用大涡模拟方法,在高雷诺数下（Re=1.4×105）,研究了间距为2倍圆柱直径的错列双圆柱的气动性能和流场特性随风攻角的变化规律,分析了两个圆柱气动力系数相关性,探讨了下游圆柱气动力与流场结构的内在联系,对下游圆柱平均升力的流场机理提出了新的解释。研究表明,大涡模拟得到的结果与风洞试验值吻合良好;下游圆柱的气动性能、流场结构和两个圆柱气动力相关性均会随风攻角发生剧烈变化;风攻角在0°~10°时,下游圆柱受平均负阻力作用,其原因分别为两圆柱间的回流区和间隙流;风攻角在10°附近时,下游圆柱受很大平均升力作用,风压停滞点偏移、两圆柱间高速间隙流、下游圆柱间隙侧剪切层的提前分离和再附是平均升力出现的三个因素。     

A fully nonlinear implicit model for wave interactions with submerged structures in forced or free motion

The purpose of this work is to develop advanced numerical tools for modeling two-way fully nonlinear interactions of ocean surface waves (irregular waves in the general situation) with submerged structures undergoing large amplitude motion, that could represent Wave Energy Converters (WECs). In our modeling approach, an existing two-dimensional Numerical Wave Tank (NWT), based on potential flow theory, is extended to include a submerged horizontal cylinder of arbitrary cross-section. The mathematical problem and related numerical solution are first introduced. Then, conservation of volume and conservation of energy are checked, respectively, in the case of a circular cylinder in a prescribed large amplitude motion and in the case of a circular cylinder in a free motion. Interactions between waves and a submerged circular cylinder computed by the model are then compared to mathematical solutions for two situations: a cylinder in prescribed motion and a freely moving cylinder.     

直径30cm圆柱的气动力参数和绕流特性研究

为研究光滑圆柱的气动力系数和绕流特性,在均匀流中进行不同风速下的测压风洞试验,试验获得了阻力系数、升力系数、表面风压分布、风压相关性系数、斯托罗哈数等随雷诺数的变化特征,并将试验结果与以往结果进行比较。研究表明:升力系数的脉动值大于阻力系数的脉动值,说明涡脱造成的横风向激励比顺风向紊流激励剧烈;雷诺数位于临界区域时,圆柱表面风压分布呈现出对称-不对称-对称的变化过程,反映了由层流分离转化为湍流分离的全过程;在雷诺数为352000时呈现一侧为层流分离、另一侧为湍流分离的临界流态,风压呈现出左右不对称的单边泡形式;获得层流分离和湍流分离时的表面风压相关性分布特征,层流分离时圆柱同一侧的风压测点均呈较强的正相关,而湍流分离时在分离点前的区域相关性较强,分离点之后的区域相关性较弱;层流分离的升力系数谱有显著的峰值,表明尾流是规则的漩涡脱落,而湍流分离的升力系数谱没有明显峰值,表明尾流是随机的漩涡脱落。     

Free convection from a vertical cooling fibre

We study the free-convective boundary-layer flow that is induced when a slender circular cylinder emerges from an orifice and moves vertically downwards. We demonstrate, by numerical solution of the equations, that the boundary-layer solution develops a singularity at a finite point, where the limiting form of solution is as predicted by Kuiken [3] for an analogous two-dimensional flow.     

Identification of the vortex mechanism of front stabilization in modeling of asymmetric flow of an incompressible fluid along a cylinder with a protruding disk

Based on numerical solution of the Navier—Stokes equations by the finite-difference method and physical modeling in a wind tunnel of laminar flow along a cylinder with a protruding disk the vortex mechanism of front stabilization and reduction in the drag of blunt bodies is investigated.     

A fully explicit characteristic based split (CBS) scheme for viscoelastic flow calculations

In this paper, an explicit characteristic based split (CBS) scheme is proposed for the numerical solution of incompressible viscoelastic flow equations. The scheme proposed is free from simultaneous solution to the matrices arising from the finite element discretization of the governing equations. The experience gained from the solution of Newtonian fluid dynamics problems has been applied to the solution of viscoelastic flows. The Oldroyd‐B model has been employed to solve two benchmark problems of viscoelastic flow. They are viscoelastic flow past a circular cylinder and viscoelastic flow through planar contraction geometry. The results show that the solutions obtained are stable for the Weissenberg or Deborah number range studied in this paper. The solutions obtained at lower Weissenberg or Deborah numbers are accurate and agree excellently with the majority of available numerical data. However at higher Weissenberg or Deborah numbers, results show some sign of negative influence of the artificial dissipation added to the discrete constitutive equations. Copyright © 2004 John Wiley Sons, Ltd.     

锚杆支护圆形隧洞弹塑性解

该文推导了锚杆支护前后圆形隧洞的应力、位移和塑性区半径表达式。首先考虑静水压力状态下,岩石表现为弹脆塑性材料模型,采用Mohr-Coulomb线性屈服准则以及非关联流动法则,推导了无支护状态下圆形隧洞的弹塑性解析新解。在此基础上,通过均匀化方法,从宏观尺度将锚杆高密度支护模式下的岩石和锚杆复合体考虑成均匀连续、强度参数增强的等效材料,定义能够反映隧洞支护参数的锚杆密度因子,推导出等效弹性模量,等效粘聚力和等效内摩擦角的表达式,然后通过该文得到的隧洞在无支护状态下的解析解可以得到锚杆支护圆形隧洞解析解。最后将该文结果与前人研究结果及数值结果进行了比较分析,对比了锚杆支护前后圆形隧洞的塑性区半径、塑性区位移和塑性区应力,结果表明锚杆支护对隧洞的加固效果明显,该文结果可为地下工程中圆形隧洞的稳定性分析提供参考。     

Theoretical modeling of a thickness-shear mode circular cylinder piezoelectric transformer

We propose a piezoelectric transformer operating with thickness-shear modes of a circular cylinder and perform a theoretical analysis on the transformer. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The output voltage, input admittance, and efficiency of the transformer are determined. The basic behaviors of the transformer are shown by numerical results.     

Numerical Methods for Accurate Computation of Design Sensitivities for Two-Dimensional Navier-Stokes Problems

Gradient computations can be a limiting factor in algorithm efficiency and accuracy for optimization based design. In this paper, we present three parameterized flow problems and consider the evaluation of state sensitivities both theoretically and numerically. Existence and uniqueness results are given for the sensitivities of a specific group of two-dimensional Navier-Stokes problems. We then turn our attention to obtaining numerical approximations to state sensitivities. We show convergence of our numerical sensitivities using a problem having an exact solution. Next, two problems, flow around a cylinder and flow over a bump, are used to evaluate several computational schemes. In particular, a local projection scheme for improved state derivative approximations and the use of an adaptive finite element scheme are shown to be important techniques for obtaining accurate sensitivity approximations. Lastly, we evaluate the impact of these computational techniques on cost function and gradient calculation.     

缆索承重桥并列索平均气动性能的雷诺数效应

近距离并列吊索和并列斜拉索在大跨度缆索承重桥中有广泛的应用,但目前在计算并列索静力风荷载时只考虑顺风向阻力的影响,没有考虑因尾流干扰所产生的横风向升力的作用。通过风洞试验,在雷诺数Re= 0.9×105~4.6×105（涉及亚临界雷诺数区和临界雷诺数区）研究了多种不同相对位置的并列双圆柱的平均阻力、平均升力和斯特罗哈数随雷诺数的变化规律。研究结果表明:并列圆柱的平均气动性能有强烈的雷诺数效应,临界雷诺数下的气动力系数与亚临界区有很大的差异;在临界雷诺数区域,下游圆柱的平均升力系数会随雷诺数的增大发生不连续突变,这种气动力的突变很可能与双圆柱绕流场的流态结构的演变有关;受上游圆柱的尾流干扰,在临界雷诺数区域内下游圆柱的平均升力系数可达到1.25以上,远大于下游圆柱的平均阻力系数,因而在计算并列索静力风荷载时有必要考虑横风向平均升力的作用。     

Local linearization of the finite element method and its applications to compressible flows

In applications of the finite element method to complicated nonlinear problems, it is proposed to simplify the operator in each element, typically by a linerization process. Local approximations can then be more easily constructed in the usual manner, and a proper assembly can be made. Such an approach would lead to an approximate global variational statement; or if the variational principle exists but is hard to handle, it should suggest an iterative scheme with a built-in physical basis, hence a better chance to converge. The case of high subsonic flow over a circular cylinder is studied in detail by this method. With linear triangular elements, numerical results are obtained for 100 nodal unknowns in each quadrant. The convergence is extremely rapid up to a free stream Mach number of 0.42, slightly above critical. The accuracy is excellent as compared against Imai's analytical results.     

A numerical simulation of the flow development behind a circular cylinder started from rest and a criterion for investigating unsteady separating flows

Summary The numerical solution of the Navier-Stokes equations for an unsteady compressible flow is employed to follow the development of periodic vortex shedding behind a circular cylinder starded from rest. The periodic vortex shedding is found to be a direct consequence of the interaction between the upper and lower primary vortices behind the cylinder, while the topological instability of the full saddle-point joining the vortices and the outer flow can be seen to play a predominant role in the process. A criterion based upon the rate of distortion of fluid elements and derived from the previous Lagrangian analysis of boundary-layer separation has been applied to the present study of unsteady separating flow and is found to be instrumental in revealing critical regions and surfaces in the flow where the fluid elements are extremely deformed.With 12 FiguresAt DFVLR-Institute for Theoretical Fluid Mechanics on Alexander-von-Humboldt Senior-Scientist Award.At DFVLR-Institute for Theoretical Fluid Mechanics on leave from Beijing Institute of Aeronautics and Astronautics.     

Boundary elements for three-dimensional elastic crack analysis

In this paper 8-node traction singular boundary elements are employed to represent displacement and traction variations in the vicinity of the crack front in three-dimensional geometries. The numerical procedure suggested for evaluating the singular integrals extending over these special elements is described. The efficiency and accuracy of the special elements and integration procedure are demonstrated by the results obtained in a simple test problem whose analytical solution is known. The interaction of two circular coplanar cracks embedded in an infinite medium under uniform tension loading is also analysed. Finally, the stress intensity factor variation computed for a semi-circular inner surface crack in a pressurized cylinder is presented.     

自适应有限元线法在二维无穷域问题中的应用

无穷域问题广泛存在于实际工程中,半解析、半离散的数值计算方法—有限元线法（Finite ElementMethod of Lines,简称FEMOL）对其具有较好的适应性。在已有的映射型FEMOL无穷单元理论的基础上,基于单元能量投影（Element Energy Projection,简称EEP）法的自适应FEMOL被应用于二维无穷域问题的求解。用户只需输入稀疏的初始网格和误差限,算法即自动生成优化的FEMOL网格,该网格上常规单元和无穷单元的FEMOL解均按最大模度量满足给定误差限。文中首先介绍二维FEMOL的原理策略、无穷单元的构建,然后概述基于EEP法的自适应FEMOL算法,并讨论其对无穷域问题的适用性,之后对圆柱绕流的Poisson方程问题、带孔无穷大板单向拉伸的弹性力学平面问题、受圆形均布荷载半空间体的三维轴对称问题进行了自适应分析,最终不仅给出了满足误差限的函数（位移）解,也给出了具有优良性态的导数（应力）解,从而为无穷域问题的求解提供了一种高效可靠的新途径。     

Sand accumulation on a wall in flows around a near-wall circular cylinder

Summary The sand accumulation on a flat plate in flows around a near-wall circular cylinder has been mainly investigated by the method of numerical simulation at the sub-critical Reynolds number1200 (based on the diameter of the circular cylinder) and the gap ratio G/D (ratio of the gap between the circular cylinder and the plane wall to the diameter of the circular cylinder) 1.0, 0.5 and 0.25. The standard k− ε turbulent model and the vorticity-stream function formulation are adopted to analyze the wake characteristics. The lift and drag coefficients of the circular cylinder and the pressure pulsation on the wall are solved. The simulation of streak-lines for the flow visualization and PIV experiments are detailed carried out to analyze the sand accumulation phenomenon on the plane wall, and a possible mechanism has been proposed. Results of the numerical simulation indicate that the effect of the cylinder results in flow separation from the plane wall. Separations occur about 1 to 2 cylinder diameters behind the cylinder, where the particles in the flow near the plane wall accumulate gradually.