不可压粘性流体浸入边界直接力法及软件实现

浸入边界法通过在N-S方程中施加体积力模拟不可滑移固壁边界及动边界,避免生成复杂贴体网格及动网格,极大地节省了网格建模时间及动网格计算消耗。本文提出一种新型附加体积力简化计算方法,将简化附加体积力以源项形式嵌入动量方程迭代中,通过用户自定义函数对CFD软件FLUENT二次开发,实现了浸入边界法和通用流体力学求解器的耦合计算。通过静止圆柱和动圆柱绕流数值模拟进行了验证,并探讨了插值函数对计算精度的影响。研究表明,通过引入浸入边界模型,能够提高计算效率,并实现结构网格背景下复杂边界和动边界的高效建模。     

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.     

基于反馈力浸入边界法模拟复杂动边界流动

浸入边界法是模拟流固耦合的重要数值方法之一。本文采用反馈力浸入边界方法,对旋转圆柱和水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟。其中,固体边界采用一系列离散的点近似代替,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。固体对流场的作用通过构造适宜的反馈力函数实现。本文首先通过旋转圆柱绕流的计算结果同实验结果进行对比,吻合较好,验证了该计算方法的可靠性。然后针对水电站水力过渡过程中水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟,得到导叶动态绕流后的流场分布特性和涡结构的演化特性。     

近床面水平圆柱局部冲刷二维数值模拟

为研究近床面水平圆柱的局部冲刷问题,基于N-S方程和有限体积法,在FLUENT中通过二次开发建立了局部冲刷二维数值模型。模型采用标准κ-ε紊流模型来计算水平圆柱周围的流场,同时借助FLUENT软件中的自定义函数功能提取床面剪应力参数来计算该时刻的推移质输沙率及床面节点位移变化值,然后运用动网格技术来模拟床面地形的变化,通过物理模型试验来进行模型验证。结果表明,计算结果与试验结果基本一致,从而证实了冲刷模型的准确性。     

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。     

自主泳动弹性绳的轨迹模拟

研究柔性结构与流体间耦合作用,可以促进软体机器人的发展.通过速度快、精度高的数值模拟方法模拟水下机器人的实时运动轨迹,可以为真实实验提供测试方向与理论牵引,增大实验成功的可能性.本文研究有自主运动趋势的弹性绳在二维流场中的运动轨迹.首先,对弹性绳离散化建模并同时考虑拉压与扭转弹性力,从能量角度建立动力学方程,此模型可以较为真实地反映弹性绳内力对其运动产生的作用.然后基于半拉格朗日法建立流体求解器. 最后,提出简化的基于动量方程的浸入边界法作为耦合算法,通过直接修正网格速度代替浸入边界力法中力源项的作用.使用这种算法求解耦合作用兼具简便性与快速性.对弹性绳模型、流体模型与简化耦合模型依次解算,模拟了正弦形式波动弹性绳在水中的运动轨迹.结果显示,弹性绳在弹性内力与流固相互作用力共同影响下,该种新的浸入边界法可以实现对水下弹性绳运动轨迹的模拟.数值实验显示弹性绳的自主运动参考模型的初相位改变时,其前进方向会发生改变.该仿真模拟算法与平台可以为细长形软体水生机器人的研发提供参考.      

自主泳动弹性绳的轨迹模拟

研究柔性结构与流体间耦合作用,可以促进软体机器人的发展.通过速度快、精度高的数值模拟方法模拟水下机器人的实时运动轨迹,可以为真实实验提供测试方向与理论牵引,增大实验成功的可能性.本文研究有自主运动趋势的弹性绳在二维流场中的运动轨迹.首先,对弹性绳离散化建模并同时考虑拉压与扭转弹性力,从能量角度建立动力学方程,此模型可以较为真实地反映弹性绳内力对其运动产生的作用.然后基于半拉格朗日法建立流体求解器.最后,提出简化的基于动量方程的浸入边界法作为耦合算法,通过直接修正网格速度代替浸入边界力法中力源项的作用.使用这种算法求解耦合作用兼具简便性与快速性.对弹性绳模型、流体模型与简化耦合模型依次解算,模拟了正弦形式波动弹性绳在水中的运动轨迹.结果显示,弹性绳在弹性内力与流固相互作用力共同影响下,该种新的浸入边界法可以实现对水下弹性绳运动轨迹的模拟.数值实验显示弹性绳的自主运动参考模型的初相位改变时,其前进方向会发生改变.该仿真模拟算法与平台可以为细长形软体水生机器人的研发提供参考.     

非结构动网格在三维可动边界问题中的应用

研究用于非结构动网格的弹簧近似方法，采用顶点弹簧描述，导出并讨论了弹簧倔强系数的取值。通过引入边界修正和扭转效应修正，对标准弹簧近似方法进行了改进，转动翼型算例的结果表明，改进后的方法大大提高了网格变形能力和网格质量，应用该动网格方法耦合求解基于（Arbitrary Lagrangian-Eulerian,ALE）描述的三维Euler方程，模拟了作俯抑振动的矩形机翼绕流，计算结果与实验数据及文献计算结果十分一致，作为多个自由刚与流体耦合运动问题的简单例证，耦合刚体动力学方程，模拟了激波与双立方体的相互作用，得到了非定常流场结构，研究表明，基于弹簧近似的非结构动网格与有限体积流式流场解算器相结合，是模拟包含运动边界的非定常流动问题的有效方法。     

幂律流体圆柱绕流的格子波尔兹曼模拟

基于插值补充格子波尔兹曼方法和幂律流体的本构方程,建立了贴体坐标系下适用于幂律流体的格子波尔兹曼模型,模拟了幂律流体的圆柱绕流问题,采用非平衡外推格式处理圆柱表面的速度无滑移边界,利用应力积分法确定曳力系数和升力系数,并与基于标准的格子波尔兹曼方法和有限容积法获得的数值数据进行对比,吻合良好. 进行了网格无关性验证之后,分析了稳态流动时,不同雷诺数下幂律指数对于尾迹长度、分离角、圆柱表面黏度分布、表面压力系数及曳力系数的影响,以及非定常流动中,幂律指数对于流场、曳力系数、升力系数和斯特劳哈尔数的影响. 获得的变化规律与基于其他数值模拟方法得到的结果相一致,充分验证了模型的有效性和正确性. 结果表明:插值补充格子波尔兹曼方法可以用来模拟幂律流体在具有复杂边界流场内的流动问题,通过引入不同的非牛顿流体本构方程,该方法还可以进一步应用于其他类型的非牛顿流体研究中.      

幂律流体圆柱绕流的格子波尔兹曼模拟简

基于插值补充格子波尔兹曼方法和幂律流体的本构方程,建立了贴体坐标系下适用于幂律流体的格子波尔兹曼模型,模拟了幂律流体的圆柱绕流问题,采用非平衡外推格式处理圆柱表面的速度无滑移边界,利用应力积分法确定曳力系数和升力系数,并与基于标准的格子波尔兹曼方法和有限容积法获得的数值数据进行对比,吻合良好. 进行了网格无关性验证之后,分析了稳态流动时,不同雷诺数下幂律指数对于尾迹长度、分离角、圆柱表面黏度分布、表面压力系数及曳力系数的影响,以及非定常流动中,幂律指数对于流场、曳力系数、升力系数和斯特劳哈尔数的影响. 获得的变化规律与基于其他数值模拟方法得到的结果相一致,充分验证了模型的有效性和正确性. 结果表明：插值补充格子波尔兹曼方法可以用来模拟幂律流体在具有复杂边界流场内的流动问题,通过引入不同的非牛顿流体本构方程,该方法还可以进一步应用于其他类型的非牛顿流体研究中.     

Moving immersed boundary method

A novel implicit immersed boundary method of high accuracy and efficiency is presented for the simulation of incompressible viscous flow over complex stationary or moving solid boundaries. A boundary force is often introduced in many immersed boundary methods to mimic the presence of solid boundary, such that the overall simulation can be performed on a simple Cartesian grid. The current method inherits this idea and considers the boundary force as a Lagrange multiplier to enforce the no‐slip constraint at the solid boundary, instead of applying constitutional relations for rigid bodies. Hence excessive constraint on the time step is circumvented, and the time step only depends on the discretization of fluid Navier‐Stokes equations, like the CFL condition in present work. To determine the boundary force, an additional moving force equation is derived. The dimension of this derived system is proportional to the number of Lagrangian points describing the solid boundaries, which makes the method very suitable for moving boundary problems since the time for matrix update and system solving is not significant. The force coefficient matrix is made symmetric and positive definite so that the conjugate gradient method can solve the system quickly. The proposed immersed boundary method is incorporated into the fluid solver with a second‐order accurate projection method as a plug‐in. The overall scheme is handled under an efficient fractional step framework, namely, prediction, forcing, and projection. Various simulations are performed to validate current method, and the results compare well with previous experimental and numerical studies.     

基于2D网格的轴对称浸没边界法

浸没边界法是处理颗粒两相流中运动边界问题的一种常用数值模拟方法. 当研究的物理问题的无量纲参数满足一定要求时, 该流场结构呈现轴对称状态. 为此本文提出了一种基于2D笛卡尔网格和柱坐标系的轴对称浸没边界法. 该算法采用有限体积法(FVM)对动量方程进行空间离散, 并通过阶梯状锐利界面替代真实的固体浸没边界来封闭控制方程. 为了提高计算效率, 本文采用自适应网格加密技术提高浸没边界附近网格分辨率. 由于柱坐标系的使用, 使得动量方程中的黏性项产生多余的源项, 我们对其作隐式处理. 此外, 在对小球匀速近壁运动进行直接数值模拟时, 由于球壁间隙很小, 间隙内的压力变化比较剧烈. 因此想要精确地解析流场需要很高的网格分辨率. 此时, 需要在一个时间步内多次实施投影步来保证计算的稳定性. 而在小球自由碰壁运动中, 我们通过引入一个润滑力模型使得低网格分辨率下也能模拟小球近壁处的运动. 最后通过小球和圆盘绕流、Stokes流小球近壁运动以及小球自由下落碰壁弹跳算例验证本算法对于轴对称流的静边界和动边界问题均是适用和准确的.      

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.     

HYDRODYNAMIC RESISTANCE EFFECT OF FLUID LAYER BETWEEN TWO IMMERSED APPROACHING PARTICLES

1. Introduction The mechanisms of impact and rebound of solid parti- cles in particulate flow systems are of interest over a wide range of application areas such as fluidized beds, pneu- matic transport, filtration processes, erosion and pollution control of suspended particles. In many cases, the colli- sions of particles against themselves and against walls may affect the properties of the mixture. Efforts have been made to describe the fundamental mechanics of particle collisions. The conta…     

Simulation of dynamic fluid–solid interactions with an improved direct-forcing immersed boundary method

Dynamic fluid–solid interactions are widely found in chemical engineering, such as in particle-laden flows, which usually contain complex moving boundaries. The immersed boundary method (IBM) is a convenient approach to handle fluid–solid interactions with complex geometries. In this work, Uhlmann's direct-forcing IBM is improved and implemented on a supercomputer with CPU–GPU hybrid architecture. The direct-forcing IBM is modified as follows: the Poisson's equation for pressure is solved before evaluation of the body force, and the force is only distributed to the Cartesian grids inside the immersed boundary. A multidirect forcing scheme is used to evaluate the body force. These modifications result in a divergence-free flow field in the fluid domain and the no-slip boundary condition at the immersed boundary simultaneously. This method is implemented in an explicit finite-difference fractional-step scheme, and validated by 2D simulations of lid-driven cavity flow, Couette flow between two concentric cylinders and flow over a circular cylinder. Finally, the method is used to simulate the sedimentation of two circular particles in a channel. The results agree very well with previous experimental and numerical data, and are more accurate than the conventional direct-forcing method, especially in the vicinity of a moving boundary.     

Wall-modeling for large-eddy simulation of flows around an axisymmetric body using the diffuse-interface immersed boundary method

A novel method is proposed to combine the wall-modeled large-eddy simulation(LES) with the diffuse-interface direct-forcing immersed boundary(IB) method.The new developments in this method include:(i) the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall shear stress predicted by the wall model;(ii) a set of Lagrangian points near the wall are introduced to compute the normal component of the effective body force for the IB method by reconstructing the normal component of the velocity. This novel method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near the wall. The method is used to simulate the flows around the DARPA SUBOFF model. The results obtained are well comparable to the measured experimental data and wall-resolved LES results.     

一种模拟动边界绕流的锐利界面浸入边界法

When the structural wall moves over a fixed grid, the structure coverage will change, resulting in many dead and emerging elements. To avoid the influence of malformation and reconstruction of body-fitted grids on the calculation efficiency and accuracy of the fluid-structure interaction problems with coupled boundary movement on the fixed grid, an improved numerical method for describing the interaction between an immersed rigid body and fluid based on a sharp-interface is proposed. In this method, both the fluid and solid are regarded as pure fluid domains in the whole computational domain, and the solid boundary is divided into several Lagrangian grid points. The flow parameter or velocity is reconstructed by interpolation at the interface element, which is then directly used as the boundary condition of the flow field, thus reflecting the influence of the wall boundary conditions. The method constructs the calculation structure of “virtual point, force point and vertical foot point”, and the velocity of the virtual point is obtained by bilinear interpolation. Then, the velocity of the force point is calculated by forcing the solid boundary to meet the no-slip condition, and the equations of the coupling system based on the immersion boundary method are finally solved to realize the numerical simulation of the flow with a complex moving boundary. The numerical program for this immersed boundary method is established using C++, then the accuracy and reliability of the proposed method are validated by comparison with the literature and experimental results of the basic numerical example of flow around a cylinder. Furthermore, the effects of the structural shape and the angle of attack on the trailing vortex structure, the vortex shedding frequency, and the lift/ coefficient characteristics of the flow around the elliptical cylinder have been analyzed. The anti-symmetric S-type, “P+S” Ⅰ-type and “P+S” Ⅱ-type trailing vortex shedding modes, as well as the variation laws of the vortex structure size, vortex shedding frequency and lift-drag coefficients ratio with axis ratio and angle of attack, are captured. The critical angle of attack (25°) corresponding to the maximum lift-drag ratio is determined as 25°.     

A new modification of the immersed‐boundary method for simulating flows with complex moving boundaries

In this paper, a new immersed‐boundary method for simulating flows over complex immersed, moving boundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. The present method is based on a finite‐difference approach on a staggered mesh together with a fractional‐step method. It must be noted that the immersed boundary is generally not coincident with the position of the solution variables on the grid, therefore, an appropriate strategy is needed to construct a relationship between the curved boundary and the grid points nearby. Furthermore, a momentum forcing is added on the body boundaries and also inside the body to satisfy the no‐slip boundary condition. The immersed boundary is represented by a series of interfacial markers, and the markers are also used as Lagrangian forcing points. A linear interpolation is then used to scale the Lagrangian forcing from the interfacial markers to the corresponding grid points nearby. This treatment of the immersed‐boundary is used to simulate several problems, which have been validated with previous experimental results in the open literature, verifying the accuracy of the present method. Copyright © 2006 John Wiley & Sons, Ltd.     

Extension of the local domain-free discretization method to large eddy simulation of turbulent flows

In this work, an immersed boundary method, called the local domain-free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near-wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES-DFD method. The predicted results agree well with the published experimental or numerical data.     

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。