多物质流体动力学方法与结构动力学方法结合的流固耦合计算技术

建立一种基于重叠网格空间覆盖判断的流固耦合计算技术,把流场计算的Euler多物质流体动力学计算过程和Lagrange结构动力学计算过程相结合以描述流固间的相互作用.介绍该计算技术的具体实现过程,讨论提高几何判断效率、避免耦合遗漏、流固计算时间步协调等处理技术.应用建立的流固耦合计算程序模拟爆炸容器中爆炸流场对容器内部结构、容器壳体的作用过程.计算结果表明其可以反映流场发展过程、流场结构相互作用和结构的运动变形和破坏过程.     

基于格子Boltzmann方法的超声速非平衡流模拟

基于D1Q4可压缩格子Boltzmann模型,按照流通矢量分裂方法的思路,采用坐标旋转技术构造求解三维带化学反应Navier-Stokes方程对流通量求解器.结合有限体积法求解三维化学非平衡流Navier-Stokes方程,采用时间算子分裂算法解决化学反应刚性问题,数值模拟超声速化学非平衡流的三个经典算例.数值结果表明:在高马赫数下,采用D1Q4可压缩格子Boltzmann模型构造的三维对流通量求解器数值模拟中没有出现非物理解,同时在超声速化学非平衡流场中正确分辨激波、燃烧波等物理现象,精度和分辨率均较高,验证了本文构造的三维对流通量求解器的可靠性,拓宽了D1Q4可压缩格子Boltzmann模型的应用范围,为计算超声速化学非平衡流提供一种新方法.     

基于浸入边界-多松弛时间格子玻尔兹曼通量求解法的流固耦合算法研究

针对流固耦合问题,发展了基于浸入边界-多松弛时间格子玻尔兹曼通量求解法(immersed boundary method multi-relaxation-time lattice Boltzmann flux solver,IB-MRT-LBFS)的弱耦合算法.依据多尺度Chapman-Enskog展开,建立不可压宏观方程状态变量和通量与格子玻尔兹曼方程中粒子密度分布函数之间的关系;采用强制浸入边界法处理流固界面使固壁表面满足无滑移边界条件,根据修正的速度求解动量方程力源项;结构运动方程采用四阶龙格-库塔法求解.格子模型与浸入边界法的引入使流固耦合计算可以在笛卡尔网格下进行,无需生成贴体网格及运用动网格技术,简化了计算过程.数值模拟了单圆柱横向涡激振动、单圆柱及串列双圆柱双自由度涡激振动问题.结果表明,IB-MRT-LBFS能够准确预测圆柱涡激振动的锁定区间、振动响应、受力情况以及捕捉尾流场结构形态,验证了该算法在求解流固耦合问题的有效性和可行性.     

温度体动网格模型中控制参数的研究

采用调整导热系数和源项分布的方式,对温度体动网格模型所生成的网格品质进行控制.温度体动网格模型将运动边界的位移虚拟为求解域的温度边界条件,以流体能量方程或固体导热方程作为控制方程,通过选取不同的导热系数或源项分布可以得到适合不同求解问题需要的温度分布,并将求解得到的网格节点的温度作为其动态位移量.采用温度体动网格模型计算平动、三维旋转运动、柔性体运动等流固耦合计算中可能涉及的动网格算例.结果表明,在计算效率和生成网格的品质方面,与已有的动态网格生成方法相比,具有较大的优势,可以有效解决流固耦合数值模拟中存在的动态网格生成难题.     

耦合不可压流场输运方程的格子Boltzmann方法研究

基于格子Boltzmann方法,提出了求解耦合不可压缩流场输运方程的一种改进数值方法. 该方法使用格子Boltzmann方法求解流场方程,并根据流场格子模型的密度分布函数构建了输运方程的二阶离散格式. 通过二维平板通道流场输运系统验证了该方法的有效性.数值结果表明,该方法可以有效地减少计算过程中出现的非物理耗散, 并克服了传统模型所需巨大存储量的缺点.     

中子测井问题中输运方程的谱有限元方法

讨论了谱有限元方法在中子测井数值模拟中的应用,用球谐函数谱展开和有限元耦合方法求解Boltzmann中子输运方程,得到了这种耦合方法的收敛性。研制了三维有限元程序,实现了中子测井问题数值模拟的正演计算,实际算例表明此方法是有效的。     

静止水中单个上升气泡的直接数值模拟

本文发展了基于Front Tracking的直接数值模拟方法研究气液两相界面的迁移特性,该方法对气液两相采用半隐式的分步法直接求解N-S方程,耦合Front Tracking Method获得两相界面的三维变形。针对无边界以及垂直壁面附近静止水中的单个气泡上升过程进行模拟,研究气泡运动的机理以及气泡与壁面的相互作用。数值模拟准确再现了气泡的上升过程和变形,不同Re数下气泡的上升速度计算结果同经验关联式非常吻合,验证了该方法的有效性。随后分析了气泡周围流场的结构,发现壁面对气泡周围流场的抑制是壁面对气泡作用力的主要原因,将导致气泡逐渐偏离垂直壁面。     

基于气体动理学方法的高超声速支杆降热模拟

基于气体动理学方法(gas kinetic scheme, GKS)分别从单独流场和流固耦合两方面开展了针对支杆结构热防护系统的数值模拟研究。首先利用二维标准圆管模型验证算法在单独流场计算中的可靠性,然后通过比较不带支杆和带支杆情形下圆管外壁面的气动热特性及相应流场特征,分析得到支杆降热的有效性及其降热机理。接着在将GKS应用到流场/结构温度场耦合模拟并进行验证后,进一步分析流固耦合作用下的支杆降热性能,结果发现支杆的降热效果随着流固耦合时间的推进不断增强,从而有利于高超声速飞行器长时间巡航飞行。     

基于绝对节点坐标法的大变形柔性梁几种动力学模型研究

对在平面内大范围转动的大变形柔性梁动力学进行了研究, 基于绝对节点坐标法建立了一种新的大变形柔性梁的非线性动力学模型. 该动力学模型中考虑了柔性梁的轴向拉伸变形和横向弯曲变形, 利用Green-Lagrangian应变张量计算柔性梁的轴向应变及应变能, 利用曲率的精确表达式计算柔性梁的横向弯曲变形能. 运用拉格朗日恒等式给出了柔性梁横向弯曲变形能新的表达式, 该变形能表达式更加简洁, 通过新的变形能表达式得到了新的弹性力模型, 由此得到的动力学方程可以精确地描述柔性梁的几何大变形问题. 通过与高次耦合模型以及ANSYS中BEAM188非线性梁单元模型的比较, 验证了本模型在计算大变形时的正确性以及高次耦合模型在处理大变形问题时的不足. 进一步研究发现, 新的广义弹性力模型可以适当地简化, 给出了两种简化模型, 根据不同模型的计算效率以及计算精度的比较确定了不同模型的适用范围.     

大展弦比气弹机翼柔性非线性变形的气动力效应分析与风洞试验

从飞行器刚弹耦合动力学模型出发,引入柔性机翼准定常假设,建立大柔性飞行器非线性静气动弹性气动力方程,利用非线性迭代求解思路模拟了柔性飞行器的静气动弹性响应行为,开展了大展弦比飞机静气动弹性风洞试验验证,采用气动力有限基本解与机翼的耦合计算,发现了大柔性飞机大变形状态下载荷及结构变形形式随风速的变化规律.传统基于小变形假设的线性分析方法和刚体分析由于无法考虑气动面随结构变形的曲面气动力因素和结构变形后的非线性刚度特性,均与风洞试验存在一定的误差.对于大展弦比柔性飞机的非线性静气动弹性分析十分必要.      

Curvilinear Immersed Boundary Method for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies

The sharp-interface CURVIB approach of Ge and Sotiropoulos [L. Ge, F. Sotiropoulos, A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, Journal of Computational Physics 225 (2007) 1782-1809] is extended to simulate fluid structure interaction (FSI) problems involving complex 3D rigid bodies undergoing large structural displacements. The FSI solver adopts the partitioned FSI solution approach and both loose and strong coupling strategies are implemented. The interfaces between immersed bodies and the fluid are discretized with a Lagrangian grid and tracked with an explicit front-tracking approach. An efficient ray-tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies. Numerical experiments are carried out for two FSI problems: vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions. For both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements. The numerical experiments suggest that both the properties of the structure (mass, geometry) and the local flow conditions can play an important role in determining the stability of the FSI algorithm. Under certain conditions unconditionally unstable iteration schemes result even when strong coupling FSI is employed. For such cases, however, combining the strong-coupling iteration with under-relaxation in conjunction with the Aitken's acceleration technique is shown to effectively resolve the stability problems. A theoretical analysis is presented to explain the findings of the numerical experiments. It is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the FSI algorithm. The stabilizing role of under-relaxation is also clarified and an upper bound of the required for stability under-relaxation coefficient is derived.     

Modified Ghost Fluid Method as Applied to Fluid-Plate Interaction

The modified ghost fluid method (MGFM) provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction (FSI) simulations. However, this methodology for one specific class of FSI problems, where the structure is plate, remains to be developed. This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate. In order to take into account the influence of simultaneous interaction at the interface, a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states. Then, ghost fluid states and plate load can be defined by utilizing the obtained interfacial states. A type of acceleration strategy in the coupling process is presented to pursue higher efficiency. Several one-dimensional examples are used to highlight the utility of this method over loosely-coupled method and validate the acceleration techniques. Especially, this method is applied to compute the underwater explosions (UNDEX) near thin elastic plates. Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated. Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.     

A fluid–structure interaction model of insect flight with flexible wings

We present a fluid–structure interactions (FSI) model of insect flapping flight with flexible wings. This FSI-based model is established by loosely coupling a finite element method (FEM)-based computational structural dynamic (CSD) model and a computational fluid dynamic (CFD)-based insect dynamic flight simulator. The CSD model is developed specifically for insect flapping flight, which is capable to model thin shell structures of insect flexible wings by taking into account the distribution and anisotropy in both wing morphology involving veins, membranes, fibers and density, and in wing material properties of Young’s modulus and Poisson’s ratios. The insect dynamic flight simulator that is based on a multi-block, overset grid, fortified Navier–Stokes solver is capable to integrate modeling of realistic wing-body morphology, realistic flapping-wing and body kinematics, and unsteady aerodynamics in flapping-wing flights. Validation of the FSI-based aerodynamics and structural dynamics in flexible wings is achieved through a set of benchmark tests and comparisons with measurements, which contain a heaving spanwise flexible wing, a heaving chordwise-flexible wing with a rigid teardrop element, and a realistic hawkmoth wing rotating in air. A FSI analysis of hawkmoth hovering with flapping flexible wings is then carried out and discussed with a specific focus on the in-flight deformation of the hawkmoth wings and hovering aerodynamic performances with the flexible and rigid wings. Our results demonstrate the feasibility of the present FSI model in accurately modeling and quantitatively evaluating flexible-wing aerodynamics of insect flapping flight in terms of the aerodynamic forces, the power consumption and the efficiency.     

Dynamic simulation of a tilting-disc valve with clearance in pulsatile channel flow

Abstract  

In this study, a fully coupled fluid–structure interaction (FSI) software system for a pulsatile flow across a moving tilting-disc valve with clearance is developed. Unsteady pulsatile flow coupled with induced valve motion has been examined in details. State-of-the-art computational fluid dynamics (CFD) methods are adopted in the present flow solver development. To account for nonstationary valve motion, the meshes surrounding the valve are generated and updated in each time-marching step using hybrid grid method. A single-degree-of-freedom rotational valve model is integrated simultaneously with the CFD adaptive time-stepping. It is found in the present study that, on both side of the occluder, strong shedding vortices occur and persist in the valve closing phase. These closure vortices show great influence on the prediction of the regurgitate flow characteristics and the subsequent valve opening dynamics as well. Based on the present software system, the results obtained from quasi-steady simulations performed at various instants of interest with prescribed valve motion are critically evaluated to assess whether simplified flow and valve conditions may lead to erroneous conclusions.     

An improved penalty immersed boundary method for fluid–flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid–flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid–flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.     

Smoothed particle hydrodynamics(SPH) for modeling fluid-structure interactions

Fluid-structure interaction(FSI) is a class of mechanics-related problems with mutual dependence between the fluid and structure parts and it is observable nearly everywhere, in natural phenomena to many engineering systems. The primary challenges in developing numerical models with conventional grid-based methods are the inherent nonlinearity and timedependent nature of FSI, together with possible large deformations and moving interfaces. Smoothed particle hydrodynamics(SPH) method is a truly Lagrangian and meshfree particle method that conveniently treats large deformations and naturally captures rapidly moving interfaces and free surfaces. Since its invention, the SPH method has been widely applied to study different problems in engineering and sciences, including FSI problems. This article presents a review of the recent developments in SPH based modeling techniques for solving FSI-related problems. The basic concepts of SPH along with conventional and higher order particle approximation schemes are first introduced. Then, the implementation of FSI in a pure SPH framework and the hybrid approaches of SPH with other grid-based or particle-based methods are discussed. The SPH models of FSI problems with rigid, elastic and flexible structures, with granular materials, and with extremely intensive loadings are demonstrated. Some discussions on several key techniques in SPH including the balance of accuracy, stability and efficiency, the treatment of material interface, the coupling of SPH with other methods, and the particle regularization and adaptive particle resolution are provided as concluding marks.     

基于旋转场曲率的二维剪切梁单元建模

对二维剪切梁单元进行研究,利用平面旋转场理论推导了精确曲率模型.采用几何精确梁理论构建了剪切梁单元弹性力矩阵.通过绝对节点坐标方法建立了系统的非线性动力学方程,提出基于旋转场曲率的二维剪切梁单元,并分别引入经典二维剪切梁单元和基于位移场曲率的二维剪切梁单元进行比较研究.首先,静力学分析证明了所提模型的正确性;其次,特征频率分析验证了模型可与理论解符合,收敛精度高,并且能准确地预测单元固有频率对应的振型;最后,在非线性动力学问题上,通过与ANSYS结果对比分析,证明了该模型可有效处理柔性大变形问题,并且与经典二维剪切梁单元相比具有缓解剪切闭锁的优势.因此,本文提出的基于旋转场曲率的二维剪切梁单元在处理几何非线性问题中具有较大的应用潜力.     

Numerical Simulations of Unsteady Flows from Rarefied Transition to Continuum Using Gas-Kinetic Unified Algorithm

Numerical simulations of unsteady gas flows are studied on the basis of Gas-Kinetic Unified Algorithm (GKUA) from rarefied transition to continuum flow regimes. Several typical examples are adopted. An unsteady flow solver is developed by solving the Boltzmann model equations, including the Shakhov model and the Rykov model etc. The Rykov kinetic equation involving the effect of rotational energy can be transformed into two kinetic governing equations with inelastic and elastic collisions by integrating the molecular velocity distribution function with the weight factor on the energy of rotational motion. Then, the reduced velocity distribution functions are devised to further simplify the governing equation for one- and two-dimensional flows. The simultaneous equations are numerically solved by the discrete velocity ordinate (DVO) method in velocity space and the finite-difference schemes in physical space. The time-explicit operator-splitting scheme is constructed, and numerical stability conditions to ascertain the time step are discussed. As the application of the newly developed GKUA, several unsteady varying processes of one- and two-dimensional flows with different Knudsen number are simulated, and the unsteady transport phenomena and rarefied effects are revealed and analyzed. It is validated that the GKUA solver is competent for simulations of unsteady gas dynamics covering various flow regimes.     

Modelling atmospheric flows with adaptive moving meshes

An anelastic atmospheric flow solver has been developed that combines semi-implicit non-oscillatory forward-in-time numerics with a solution-adaptive mesh capability. A key feature of the solver is the unification of a mesh adaptation apparatus, based on moving mesh partial differential equations (PDEs), with the rigorous formulation of the governing anelastic PDEs in generalised time-dependent curvilinear coordinates. The solver development includes an enhancement of the flux-form multidimensional positive definite advection transport algorithm (MPDATA) — employed in the integration of the underlying anelastic PDEs — that ensures full compatibility with mass continuity under moving meshes. In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem. The benefits of the solution-adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated. The developed solver is verified for two idealised flow problems with distinct levels of complexity: passive scalar advection in a prescribed deformational flow, and the life cycle of a large-scale atmospheric baroclinic wave instability showing fine-scale phenomena of fronts and internal gravity waves.     

基于OpenFOAM的投影法磁流体求解器开发与验证

在开源计算流体力学C++工具包OpenFOAM环境下开发了低磁雷诺数条件下的磁流体求解器,并进行了验证。采用投影算法求解动量方程和压力泊松方程;采用非结构网格同位相容守恒算法求解电势泊松方程、感应电流和洛伦兹力;采用边界耦合方法求解流固耦合电势场。通过对均匀磁场下导电方管和导电圆管内的完全发展磁流体层流的数值模拟和解析解的对比,对求解器进行了验证。进一步对非均匀强磁场作用下导电方管和导电圆管内完全发展磁流体层流进行了数值模拟,并与ALEX实验结果进行了比较。数值解和实验结果吻合良好。所开发的求解器可用于复杂结构强磁场作用下磁流体的数值模拟研究。