基于浸入边界-有限元法的流固耦合碰撞数值模拟方法

针对流固耦合碰撞问题,建立了流体中固体与固体碰撞界面解析直接模拟方法,采用清晰界面浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时网格出现负体积的问题,采用基于罚函数的有限元方法对固体的运动和碰撞进行求解,以分域耦合方式实现流体域和固体域的耦合求解.通过与静止流体中球形颗粒与壁面正碰撞和斜碰撞的实验数据对比,验证了建立的数值模拟方法对流体中固体与固体碰撞数值模拟的正确性,获得了流体域流场在碰撞前后随时间的变化,同时通过该文建立的数值模拟方法也获得了固体域中固体的碰撞力和应力.未来,将把该数值模拟方法应用到流体流动环境中,如固体颗粒对管道的冲蚀、流体诱导海洋立管之间的碰撞、坠物对海底管道的撞击等.     

基于MPS-FEM耦合方法对比研究刚性与弹性挡板对液舱晃荡的抑制作用（英文）

由流体冲击载荷引起的流固耦合问题广泛存在于船舶与海洋工程领域.例如:在特定激励频率下载液货舱内流体的非线性运动引起对舱壁的砰击作用,进而可能影响液舱围护系统的安全性.由于此类流固耦合问题通常涉及多学科知识,且流体自由面的变化具有强非线性特征,对研究人员带来较大挑战.考虑到Lagrange类方法在处理结构和流体自由面大变形问题上的优势,基于MPS-FEM耦合方法开发了流固耦合求解器.其中,采用MPS方法来数值模拟流体场瞬态变化,FEM方法来分析结构场的变形问题.此外,该求解器采用了弱耦合的方式来实现流体场和结构场之间的数据传递.为了验证该方法在处理流固耦合问题上的可靠性,首先数值研究了溃坝泄洪流与弹性挡板之间的流固耦合标准算例,数值结果与实验标准结果能够较好地吻合.此后,采用该求解器数值研究了带刚性挡板和弹性挡板的液舱晃荡问题,对比分析了多种激励频率下两种挡板对液舱内流体运动及舱壁上冲击压力的抑制效果.     

基于MPS-FEM耦合方法对比研究刚性与弹性挡板对液舱晃荡的抑制作用

由流体冲击载荷引起的流固耦合问题广泛存在于船舶与海洋工程领域.例如:在特定激励频率下载液货舱内流体的非线性运动引起对舱壁的砰击作用,进而可能影响液舱围护系统的安全性.由于此类流固耦合问题通常涉及多学科知识,且流体自由面的变化具有强非线性特征,对研究人员带来较大挑战.考虑到Lagrange类方法在处理结构和流体自由面大变形问题上的优势,基于MPS-FEM耦合方法开发了流固耦合求解器.其中,采用MPS方法来数值模拟流体场瞬态变化,FEM方法来分析结构场的变形问题.此外,该求解器采用了弱耦合的方式来实现流体场和结构场之间的数据传递.为了验证该方法在处理流固耦合问题上的可靠性,首先数值研究了溃坝泄洪流与弹性挡板之间的流固耦合标准算例,数值结果与实验标准结果能够较好地吻合.此后,采用该求解器数值研究了带刚性挡板和弹性挡板的液舱晃荡问题,对比分析了多种激励频率下两种挡板对液舱内流体运动及舱壁上冲击压力的抑制效果.     

喷涂于运动边界上液体薄膜射流的流变效应

采用非Newton流体的二阶流体模型分析了相对高温的液体熔体薄膜由模口喷出并涂于运动的固体膜上. 讨论了由自由面上温度梯度驱动的非Newton液体薄膜的热毛细流动, 考虑热毛细流动的流变效应. 分析是基于润滑理论近似和摄动理论近似. 得到了液体高度方程和非Newton液体薄膜的热流体力学过程描述, 具体求解了弱流变流体效应的情况.     

计入气穴的水下爆炸作用下结构流固耦合三维数值模拟

水下爆炸在结构物面附近产生的气穴现象,严重影响水下爆炸作用下的流固耦合动响应,是舰船水下爆炸领域的难点,传统的边界元方法、有限元方法(FEM)难以解决水下爆炸气穴现象这类强非线性问题．针对此问题,计及流体中的气穴现象,考虑流体的可压缩型,忽略流体粘性,建立水下爆炸瞬态强非线性流固耦合三维数值模型,采用流体谱单元方法(SEM)和结构有限元方法求解该模型．计算结果表明:相对有限元法,谱单元法具有更高的计算精度,且谱单元解与解析解、试验值吻合良好．在此基础上,结合ABAQUS软件,分别探讨三维球壳、船体板架在水下爆炸作用下的瞬态流固耦合机理,给出气穴区域及其对水中结构物动响应的影响特征,旨在为舰船水下爆炸瞬态流固耦合问题的相关研究提供参考．     

黏性流体中运动界面上的速度分解

本文研究黏性流体与零厚度弹性材料界面上的耦合运动问题.利用沉浸边界法与时间步长法,半Lagrange离散法,对速度分解后的Stokes部分与正则部分进行求解,获得了关于耦合运动中二阶PDE求解的一般方法,推广了文献[14,15,18]的结果.     

变温度荷载作用下半无限成层饱和介质的热固结分析

对半无限成层饱和多孔介质作用随时间变化的温度荷载的热固结问题进行解析求解．其中,热-水-力耦合线性弹性控制方程考虑了热渗效应和等温热流效应的影响．先采用Laplace变换求其在变换域上的解,然后用数值方法求逆变换．对半无限体表面作用呈指数衰减热荷载的双层体系进行研究,分析了两层介质热固结系数、弹性模量等的差异性对热固结特征的影响．研究表明:位移场和应力场对温度场的耦合作用可以忽略,而热渗效应对温度和孔压有显著影响．     

基于嵌套网格的环空流体内旋转杆柱与井筒碰撞特性研究北大核心CSCD

针对浸没在流体中杆管柱间相互接触问题,基于嵌套网格技术,该文建立了环空流体内旋转杆柱与井筒间碰撞的数值求解方法.将环空流体域分为相互嵌套的子区域:背景网格和组件网格,推导了各嵌套区域流场边界传递信息的插值计算公式,采用分域方法对环空流体域与杆柱固体域耦合进行求解.通过静止流体中球形颗粒与壁面正、斜碰撞实验对比,验证该文数值方法的正确性.研究了不同流体黏度、杆柱旋转速度条件下杆柱与井筒的碰撞特性,结果表明:1)杆柱与井筒碰撞的碰撞力、速度随黏度增大而降低,即杆柱与井筒碰撞的剧烈程度与流体黏度负相关;2)随着杆柱旋转速度增大,杆柱与井筒的碰撞力、速度也增大,即杆柱与井筒碰撞的剧烈程度与转速正相关.     

求解粘性流体和热迁移联立方程的迎风局部微分求积法

微分求积方法(DQM)已成功地应用于数值求解流体力学中的许多问题．但是已有的工作大多限于正规区域的流动问题,同时缺少用迎风机制来描述流体流动的对流特性．该文对一个不规则区域中的不可压缩层流和热迁移的耦合问题给出了一种具有迎风机制的局部微分求积方法,对通过边界和坐标不平行的收缩管道中的流体,只用少数网格点得到了比较好的数值解．和有限差分方法（FDM）相比较,这一方法具有计算工作量少、存储量小和收敛性好等优点．     

多孔固体充满黏性流体时的边界条件

基于物理学基本原理和能量守恒定律的精确检查,导出充满黏性流体多孔固体边界呈连续性要求的边界条件.当孔隙流体具有黏性时,多孔弹性固体就是一个耗散的充满黏性流体的多空固体.孔隙流体的黏性造成的耗散应力准确地表达了边界条件.边界上两种固体连接的不完全,导致孔隙流体的流出,多孔骨料两边微粒运动的不平衡.导出多孔.多孔固体界面孔隙局部连接时的数学模型.在该界面上,滑移的松.紧,以及孔隙开.合,能造成一部分应变能的耗散.数值结果表明,在水和饱和油砂岩之间的界面上,修正的边界条件将影响各向同性多孔介质中折射波的能量.     

四段式有限元法分析热耦合的流体-固体相互作用问题

给出了一种流(体)-热-结构综合的分析方法,固体中的热传导耦合了粘性流体中的热对流,因而在固体中产生热应力.应用四段式有限元法和流线逆风Petrov-Galerkin法分析热粘性流动,应用Galerkin法分析固体中的热传导和热应力.应用二阶半隐式Crank-Nicolson格式对时间积分,提高了非线性方程线性化后的计算效率.为了简化所有有限元公式,采用3节点的三角形单元,对所有的变量:流体的速度分量、压力、温度和固体的位移,使用同阶次的插值函数.这样做的主要优点是,使流体-固体介面处的热传导连接成一体.数个测试问题的结果表明,这种有限元法是有效的,且能加深对流(体)-热-结构相互作用现象的理解.     

Couple stress fluid flow with variable properties: A second law analysis

The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge‐Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.     

Numerical Simulation of Heat Loads in a Cryogenic H2/O2 Rocket Combustion Chamber

A Finite Element solver for a coupled simulation of fluid and structure in an axisymmetric domain is presented. The method employs an explicit solution of the flow and structure variables. The computational domain of the fluid is discretised by unstructured triangles and rectangles while the sturcture domain is discretised by unstructured triangles only. For the purpose of code validation the solution of in total three test cases are shown. One test case deals with the structure only while the other two simulate heat transfer problems with a defined temperature distribution along a boundary wall and coupled conditions. Finally the code is used to simulate the heat load in a cryogenic H₂/O₂ rocket combustion chamber.     

Numerical simulation of thermal problems coupled with magnetohydrodynamic effects in aluminium cell

A system of partial differential equations describing the thermal behavior of aluminium cell coupled with magnetohydrodynamic effects is numerically solved. The thermal model is considered as a two-phases Stefan problem which consists of a non-linear convection–diffusion heat equation with Joule effect as a source. The magnetohydrodynamic fields are governed by Navier–Stokes and by static Maxwell equations. A pseudo-evolutionary scheme (Chernoff) is used to obtain the stationary solution giving the temperature and the frozen layer profile for the simulation of the ledges in the cell. A numerical approximation using a finite element method is formulated to obtain the fluid velocity, electrical potential, magnetic induction and temperature. An iterative algorithm and 3-D numerical results are presented.     

Inverse determination of thermal conductivity using semi-discretization method

In this work a semi-discretization method is presented for the inverse determination of spatially- and temperature-dependent thermal conductivity in a one-dimensional heat conduction domain without internal temperature measurements. The temperature distribution is approximated as a polynomial function of position using boundary data. The derivatives of temperature in the differential heat conduction equation are taken derivative of the approximated temperature function, and the derivative of thermal conductivity is obtained by finite difference technique. The heat conduction equation is then converted into a system of discretized linear equations. The unknown thermal conductivity is estimated by directly solving the linear equations. The numerical procedures do not require prior information of functional form of thermal conductivity. The close agreement between estimated results and exact solutions of the illustrated examples shows the applicability of the proposed method in estimating spatially- and temperature-dependent thermal conductivity in inverse heat conduction problem.     

磁场和热辐射对可变表面热通量作用下的竖直圆锥体自然对流的影响

就圆锥体表面受到可变表面热通量作用,计及磁场和热辐射的综合影响,数值研究了流经竖直圆锥体的自然对流及其热交换特点.认为流体是灰色的、吸收-发射的辐射介质,而非散射介质,通过近似变换,将自由对流区中流动的边界层控制方程,简化为无量纲方程.利用Crank-Nicol-son形式的隐式有限差分法(具有收敛快、精度高、无条件稳定的特点),求解了无量纲的控制方程.得到了数值结果,以及空气和水中的速度、温度、局部和平均的壁面剪应力、局部和平均的Nusselt数.将所得到的结果与先前文献报道的结果进行比较,发现两者有着很好的一致性.     

Time–accurate Modular CFD‐CSD Coupling for Aeroelastic Rotor Simulations

This paper addresses the timewise accuracy of different coupling approaches applied to instationary aeroelastic simulations of rotors in forward flight. Two different approaches which are widely discussed in literature are examined: the tight or strong coupling, and the fully integrated or monolithic coupling. Strong coupling means an exchange of fluid loads and structural deformations at each time step which is effectuated in a fully modular manner. We will address aspects of conservativity and time‐accuracy, and will present results for a helicopter forward flight scenario. However, objections concerning the correct solution of the global non‐linear three field problem – structure, grid deformation, aerodynamics – remain. These objections are normally rejected by the monolithic approach. Here, a common set of partial differential equations is derived and solved in a single code. However, a truly monolithic system of equations is only needed for stability analysis, and it can be decomposed in a three field problem respecting appropriate boundary conditions for each domain. Thus, modularity can be maintained, conceiving a quasi‐monolithic procedure, when both domains are simultaneously solved in a common non‐linear iteration loop on a per time‐step basis. First results will be shown for a 2D flutter testcase.     

Numerical study of melting in an enclosure with discrete protruding heat sources

In order to explore the capability of a solid–liquid phase change material (PCM) for cooling electronic or heat storage applications, melting of a PCM in a vertical rectangular enclosure was studied. Three protruding generating heat sources are attached on one of the vertical walls of the enclosure, and generating heat at a constant and uniform volumetric rate. The horizontal walls are adiabatic. The power generated in heat sources is dissipated in PCM (n-eicosane with the melting temperature, T_m = 36 °C) that filled the rectangular enclosure. The advantage of using PCM is that it is able to absorb high amount of heat generated by heat sources due to its relatively high energy density. To investigate the thermal behaviour and thermal performance of the proposed system, a mathematical model based on the mass, momentum and energy conservation equations was developed. The governing equations are next discretised using a control volume approach in a staggered mesh and a pressure correction equation method is employed for the pressure–velocity coupling. The PCM energy equation is solved using the enthalpy method. The solid regions (wall and heat sources) are treated as fluid regions with infinite viscosity and the thermal coupling between solid and fluid regions is taken into account using the harmonic mean of the thermal conductivity method. The dimensionless independent parameters that govern the thermal behaviour of the system were next identified. After validating the proposed mathematical model against experimental data, a numerical investigation was next conducted in order to examine the thermal behaviour of the system by analyzing the flow structure and the heat transfer during the melting process, for a given values of governing parameters.     

Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling

This present study consists of a numerical investigation of transient heat transfer in channel flow of an electrically conducting variable viscosity Boussinesq fluid in the presence of a magnetic field and thermal radiation. The temperature dependent nature of viscosity is assumed to follow an exponentially model and the system exchanges heat with the ambient following Newton’s law of cooling. The governing nonlinear equations of momentum and energy transport are solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that combined effect of thermal radiation, magnetic field, viscosity variation and convective cooling have significant impact in controlling the rate of heat transfer in the boundary layer region.     

Calculation of conjugate heat transfer problem with volumetric heat generation using the Galerkin method

A mathematical model of fluid flow across a rod bundle with volumetric heat generation has been built. The rods are heated with volumetric internal heat generation. To construct the model, a volume average technique (VAT) has been applied to momentum and energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with a semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, a whole-section drag coefficient C_d and a whole-section Nusselt number Nu have also been calculated. To validate the developed solution procedure, the results have been compared to the results of a finite volume method. The comparison shows an excellent agreement. The present results demonstrate that the selected Galerkin approach is capable of performing calculations of heat transfer in a cross-flow where thermal conductivity and internal heat generation in a solid structure has to be taken into account. Although the Galerkin method has limited applicability in complex geometries, its highly accurate solutions are an important benchmark on which other numerical results can be tested.