基于浸入边界法的鱼体自主游动的数值模拟

对游动或飞行生物自主运动特性的深入研究,可促进仿生学的进一步发展。本文以"C"型游动鱼作为研究对象,建立了自主游动的柔性鱼模型。此模型较为真实地反映了鱼自主游动时鱼体内力(由鱼体肌肉收缩提供)、鱼体运动和外界流体之间的耦合作用。基于传统的反馈力方法和混合有限元浸入边界法对鱼的自主游动进行了数值模拟。分析了鱼自主游动启动阶段和巡游阶段流场特性及鱼体运动特征。模拟结果表明,受到鱼体自身组织结构和外界流场作用,鱼游动时通过呈"C"型和类"S"型的不断转换,以获取能量,实现鱼体自主游动。     

浸入边界法及其应用

浸入边界法主要用于模拟存在复杂外形结构的流场的运动情况和处理各种动边界问题,目前已广泛应用于计算流体力学领域.浸入边界法既是数学建模方法又是数值离散方法,它将物体边界与流体的相互作用通过在流体运动方程中加体积力项来体现,并在数值计算中采用简单的笛卡尔网格,避免了按照物体边界形状生成贴体网格时所遇到的各种问题.浸入边界法分为连续力法和离散力法:连续力法主要用于处理弹性边界问题,它的力源项满足特定的力学关系式;离散力法主要用于处理固体界面问题,它的力源项由边界条件推导得到.着重阐述了浸入边界法的基本原理和数学构造,对目前已有的几种不同的浸入边界法做了简单地介绍,并给出了一些应用实例,最后提出了浸入边界法未来的发展方向.     

基于浸入边界法的扑翼飞行数值模拟

本文提出了基于浸入边界法的扑翼鸟建模与仿真,首先检验了数值方法的精确性,而后对NACA 0012翼型的升沉运动与俯仰运动进行了研究,最后对三维扑翼的翅膀拍动时间非对称性进行了研究。结果表明：浸入边界法对拍动翼型的模拟能够很好地和文献结果吻合。升沉运动的推进能力由翼型前缘涡的大小和位置决定,升沉运动推进效率的峰值主要集中在0.3≤St≤0.4时。升沉运动耦合俯仰运动时,在俯仰角25°及相位差85°时,推进效率达到峰值。在三维模拟中,适当增加翅膀下拍速度,能提供更大的升力,同时耗能也更高。研究结果可以为微型扑翼飞行器的扑动参数设置提供参考。

     

一种投影浸入边界法的快速直接求解方法

根据投影浸入边界法分步投影求解的特点,同时针对压力泊松方程离散后的大型稀疏线性方程组是非奇异非对称的特点,结合开源函数库UMFPACK,在传递线性方程组的系数矩阵和右端向量时,采用函数库Eigen将系数矩阵的数据结构改写优化,大大降低了存储空间,实现对高维大型稀疏线性方程组的快速求解,同时求解保持良好的稳定性。本文首先利用一具有解析解的数值算例验证了求解泊松方程数值方法的准确性和网格依赖性,进而利用VC++编写投影浸入边界法的数值计算程序,以单圆柱绕流为基准数值算例,通过与其他文献和实验结果的对比,验证了投影浸入边界法数值计算结果的可靠性,并进一步分析了不同雷诺数下圆柱绕流的流场结构特征和尾涡结构的动态演化过程。     

浸入式边界方法的研究及应用进展

本文总结了浸入式边界方法 (immersed bundary method, IB method)中的力源建模研究进展,并且对该方法在诸如生物体绕流及流固耦合等典型的复杂边界以及运动边界问题中的应用进行了介绍.边界精度低是IB方法主要特征之一,但该方法目前在计算气动声学等高精度计算中同样有所应用.最后本文对IB方法在处理高雷诺数流动问题上所面临的挑战以及目前研究进展和未来发展方向进行了介绍.     

一种强耦合预估-校正浸入边界法

为克服传统浸入边界法的质量不守恒缺陷,提出了一种用于可压缩流固耦合问题的强耦合预估-校正浸入边界法。通过阐述一般流固耦合系统的矩阵表示,推导了流固耦合系统的强耦合Gauss-Seidel迭代格式,进一步导出预估-校正格式,提出了预估-校正浸入边界法。该方法使用无耦合边界模型对流体进行预估,将流固耦合边界视为自由面,固体原本占据的空间初始化为零质量的单元,允许流体自由穿过耦合边界。对于流体的计算,使用带有minmod限制器的二阶MUSCL有限体积格式和基于Zha-Bilgen分裂的AUSM+-up方法,配合三阶Runge-Kutta格式推进时间步。在校正步骤中,通过一组质量守恒的输运规则来实现输运过程。输运算法可概括为将边界内侧的流体进行标记,根据标记顺序以均匀方式分割和移动流体,产生一个指向边界外侧的流动,最后在边界附近施加速度校正保证无滑移条件。标记和输运算法避免了繁琐的对截断单元的几何处理,确保了算法易于实现。对于固体的计算,分别采用一阶差分格式和隐式动力学有限元格式求解刚体和线弹性体,并利用高斯积分获得固体表面的耦合力。使用预估-校正浸入边界法计算了一维问题和二维问题。在一维活塞问题中,获得了压力分布、相对质量历史和误差曲线,并与其他方法进行了对比。在二维的激波冲击平板问题中,获得了数值模拟纹影和平板结构的挠度历史,并与实验结果进行了对比。研究表明,该方法区别于传统的虚拟网格方法和截断单元方法,能够精确地维持流场的质量守恒并易于实现,且具有一阶收敛精度,能够较准确地预测激波绕射后的流场以及平板在激波作用下的挠度,为开发流固耦合算法提供了一种新的思路。     

适用于浸入边界法的大涡模拟紊流壁面模型

基于近壁定常剪切应力假设,提出了一种新的适用于浸入边界法的大涡模拟紊流壁面模型。通过引入壁面滑移速度,修正了线性速度剖面计算得到的壁面剪切应力,使之满足Werner-Wengle模型。将其应用于平板紊流和高Re数圆管紊流的数值模拟,对比采用和不采用壁面模型的结果得知,采用此模型的速度剖面与实验值吻合良好,验证了此模型的有效性。研究了不同欧拉/拉格朗日网格相对位置对结果的影响,证明了此模型具有较好的鲁棒性,以及可根据局部流动状态和网格精度自动开闭的特点。     

一种模拟动边界绕流的锐利界面浸入边界法

为避免复杂贴体网格的更新和畸形对动边界流场计算效率、精度的影响,以充分掌握结构场的受力特性,采用一种改进的锐利界面（sharp-interface）浸入边界法模拟具有动边界绕流的流动问题。该方法将计算域中的固体视为流体,固体边界离散为若干个拉格朗日网格点,通过在界面单元处插值重构流动参数（速度）,将其直接作为流动求解器的边界条件,由此来反映固体边界的影响。即通过构造“虚拟点—受力点—垂足点”的计算结构,借助双线性插值得到虚拟点的速度,再通过强制满足固体边界的无滑移条件计算出受力点的速度,以此为边界条件,最终求解基于浸入边界法的耦合系统方程,实现复杂动边界的流动数值模拟。采用C++编写该浸入边界法的数值程序,以单圆柱绕流为验证算例,通过与文献和实验结果的对比,验证了该方法的准确性和可靠性。在此基础上,对主动运动椭圆柱绕流问题进行了精细计算,探讨了不同轴长比(A_R)、不同攻角($ \theta $)下的椭圆柱对尾涡结构分布特征和水力不稳定现象的影响。捕捉到了反对称S型、“P+S” Ⅰ型、“P+S” Ⅱ型尾涡脱落模态,漩涡强度、涡脱频率和升阻比随A_R和$ \theta $的变化规律,以及确定了升阻比临界攻角(25°)。

     

风力机气动特性的浸入边界法模拟1)

风力发电机的空气动力学性能是决定风力机安全与效率的最重要因素之一。但由于影响风力机气动性能的参数众多,更加高效精确地模拟风力机气动特性一直是风力机的重要发展方向。本文提出了基于浸入边界法的风力机建模,网格离散,以及数值模拟的统一性框架。利用同伦变形来生成光滑的叶片模型,并且使用仿射变换来处理叶片的渐缩与扭转问题。首先,针对二维翼型的升阻力,检验了算法的数值精度。表明此方法对于阻力的模拟具有非常严格的一阶精度,进而提出采用理查森外推法来精确高效修正升阻力模拟结果。同时,模拟研究了拱曲度以及厚度对二维翼型升阻力的影响。随后,模拟研究了单风力机(包含塔架)在不同尖速比下的功率系数,并对塔架与叶片间的相互气动作用进行了初步分析。最后,模拟研究了双风力机在风场中不同前后间隔距离下的气动干涉问题。本文主要意义在于验证建模,离散,与数值模拟的一体化框架的有效可行性,进而为后续研究(给定约束下风力机自动优化选型)提供坚实基础。     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

Adaptive mesh refinement for simulating fluid-structure interaction using a sharp interface immersed boundary method

In this article, adaptive mesh refinement (AMR) is performed to simulate flow around both stationary and moving boundaries. The finite-difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from a coarse to a fine grid level, while a weighted-average formula is used to transfer variables inversely. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier-Stokes equations are numerically solved through the second-order central difference scheme in space and the third-order Runge-Kutta time integration. Flow around a circular cylinder rotating in a square domain is firstly simulated to examine the accuracy and convergence rate. Then three cases are investigated to test the validity of the present method: flow past a stationary circular cylinder at low Reynolds numbers, flow past a forced oscillating circular cylinder in the transverse direction at various frequencies, and a free circular cylinder subjected to vortex-induced vibration in two degrees of freedom. Computational results agree well with these in the literature and the flow fields are smooth around the interface of different refinement levels. The effect of refinement level has also been evaluated. In addition, a study for the computational efficiency shows that the AMR approach is helpful to reduce the total node number and speed up the time integration, which could prompt the application of the IB method when a great near-wall spatial resolution is required.     

An immersed boundary method for simulation of inviscid compressible flows

In this paper, an immersed boundary method for simulating inviscid compressible flows governed by Euler equations is presented. All the mesh points are classified as interior computed points, immersed boundary points (interior points closest to the solid boundary), and exterior points that are blanked out of computation. The flow variables at an immersed boundary point are determined via the approximate form of solution in the direction normal to the wall boundary. The normal velocity is evaluated by applying the no‐penetration boundary condition, and therefore, the influence of solid wall in the inviscid flow is taken into account. The pressure is computed with the local simplified momentum equation, and the density and the tangential velocity are evaluated by using the constant‐entropy relation and the constant‐total‐enthalpy relation, respectively. With a local coordinate system, the present method has been extended easily to the three‐dimensional case. The present work is the first endeavor to extend the idea of hybrid Cartesian/immersed boundary approach to compressible inviscid flows. The tedious task of handling multi‐valued points can be eliminated, and the overshoot resulting from the extrapolation for the evaluation of flow variables at exterior points can also be avoided. In order to validate the present method, inviscid compressible flows over fixed and moving bodies have been simulated. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Jump-reduced immersed boundary method for compressible flow

The main challenge of the immersed boundary approach is the proper enforcement of boundary conditions on the body interface without any spurious oscillations, which are induced by the nongrid-conforming boundary configuration. In this study, a new sharp interface ghost-cell immersed boundary method (IBM) is proposed for obtaining solutions near the immersed boundary with a high order of accuracy. The main idea is “jump-reduction” instead of jump-correction across the boundary interface by combining the ghost-cell method with the flow reconstruction method. In the proposed IBM, the unknown values at the three points, that is, boundary points, ghost cell, and flow field reconstruction point are solved simultaneously using equations formulated by the moving least-squares interpolation method. It is a hybrid of ghost-cell and flow reconstruction methods, correlated with interface values, which result in a reduced jump-discontinuity. In addition, a discontinuity-distinguishing algorithm is introduced so that the low-order method is applied only to the discontinuous or non smooth region, while the current high-order method is applied elsewhere. Reduced jump-discontinuity of the proposed IBM has been verified in both subsonic and supersonic flow using fundamental benchmark problems. We observed that the reduced jump-discontinuity does not hamper the mass conservation and shows even better conservation property than conventional methods due to the nonoscillatory performance in smooth regions. The numerical results further confirm the ability of the proposed IBM to solve complex flow physics with high-order accuracy and improved stability.     

Towards simulation of flapping wings using immersed boundary method

In this work the immersed boundary method is applied to simulate incompressible turbulent flows around stationary and moving objects. The goal is to demonstrate that the immersed boundary technique along with a large eddy simulation approach is capable of simulating the effect of the so‐called leading edge vortex (LEV), which can be found in flapping wing aerodynamics. A Lagrangian method is used to approximate the solutions in the freshly cleared cells that lay within solid objects at one time step and emerge into fluid domain at the next time step. Flow around a stationary cylinder at Re_D = 20, 40, and 3900 (based on cylinder diameter D) is first studied to validate the immersed boundary solver based on the finite volume scheme using a staggered grid. Then, a harmonically oscillating cylinder at Re_D = 10 000 is considered to test the solver after the Lagrangian method is implemented to interpolate the solution in the freshly cleared cells. Finally, this approach is used to study flows around a stationary flat‐plate at several angles of attack and fast pitching flat‐plate. The rapidly pitching plate creates a dynamic LEV that can be used to improve the efficiency of flapping wings of micro air vehicle and to determine the optimum flapping frequency. Copyright © 2012 John Wiley & Sons, Ltd.     

Mesh adaptation for simulation of unsteady flow with moving immersed boundaries

In this work, an approach for performing mesh adaptation in the numerical simulation of two‐dimensional unsteady flow with moving immersed boundaries is presented. In each adaptation period, the mesh is refined in the regions where the solution evolves or the moving bodies pass and is unrefined in the regions where the phenomena or the bodies deviate. The flow field and the fluid–solid interface are recomputed on the adapted mesh. The adaptation indicator is defined according to the magnitude of the vorticity in the flow field. There is no lag between the adapted mesh and the computed solution, and the adaptation frequency can be controlled to reduce the errors due to the solution transferring between the old mesh and the new one. The preservation of conservation property is mandatory in long‐time scale simulations, so a P1‐conservative interpolation is used in the solution transferring. A nonboundary‐conforming method is employed to solve the flow equations. Therefore, the moving‐boundary flows can be simulated on a fixed mesh, and there is no need to update the mesh at each time step to follow the motion or the deformation of the solid boundary. To validate the present mesh adaptation method, we have simulated several unsteady flows over a circular cylinder stationary or with forced oscillation, a single self‐propelled swimming fish, and two fish swimming in the same or different directions. Copyright © 2012 John Wiley & Sons, Ltd.     

Constrained moving least‐squares immersed boundary method for fluid‐structure interaction analysis

A numerical method is presented for the analysis of interactions of inviscid and compressible flows with arbitrarily shaped stationary or moving rigid solids. The fluid equations are solved on a fixed rectangular Cartesian grid by using a higher‐order finite difference method based on the fifth‐order WENO scheme. A constrained moving least‐squares sharp interface method is proposed to enforce the Neumann‐type boundary conditions on the fluid‐solid interface by using a penalty term, while the Dirichlet boundary conditions are directly enforced. The solution of the fluid flow and the solid motion equations is advanced in time by staggerly using, respectively, the third‐order Runge‐Kutta and the implicit Newmark integration schemes. The stability and the robustness of the proposed method have been demonstrated by analyzing 5 challenging problems. For these problems, the numerical results have been found to agree well with their analytical and numerical solutions available in the literature. Effects of the support domain size and values assigned to the penalty parameter on the stability and the accuracy of the present method are also discussed.     

Simulation of two‐phase flow with moving immersed boundaries

A two‐dimensional multi‐phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier–Stokes equation coupled with a phase‐field model based on van der Waals' free energy density and the Cahn–Hilliard equation. A new phase‐field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas–Washburn theory and Stefan's problem. The proposed model may be used for multi‐phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium. Copyright © 2010 John Wiley & Sons, Ltd.