The calculation of drag on nano‐cylinders

The study of molecular flows at low Knudsen numbers (～0.1–0.5), over nano‐scaled objects of 20–100 nm size is becoming an important area of research. The simulation of fluid–structure interaction at nano‐scale is important for understanding the adsorption and drag resistance characteristics of nano‐devices in the fields of drug delivery, surface cleaning and protein movement. A novel formulation has been proposed that calculates localised values for both the kinetic and configurational parts of the Irving–Kirkwood stress tensor at given fixed positions within the computational domain. Macroscopic properties, such as streaming velocity, pressure and drag coefficients, are predicted by modelling the fluid–structure interaction using a moving least‐squares method. The gravitation‐driven molecular flow is examined over three different cross‐sectional shapes—i.e. diamond‐, circular‐ and square‐shaped cylinders—confined within parallel walls and has been simulated for rough and smooth surfaces. The molecular dynamics formulation has allowed, for the first time, the calculation of localised drag forces over nano‐cylinders. The computational simulation has shown that existing methods, including continuum‐based approaches, significantly underestimate drag coefficients over nano‐cylinders. The proposed molecular dynamics formulation has been verified on simulation based tests, as experimental and analytical results are unavailable at this scale. Copyright © 2016 John Wiley & Sons, Ltd.     

A monolithic strategy for fluid–structure interaction problems

In this work, we present a new monolithic strategy for solving fluid–structure interaction problems involving incompressible fluids, within the context of the finite element method. This strategy, similar to the continuum dynamics, conserves certain properties, and thus provides a rational basis for the design of the time‐stepping strategy; detailed proofs of the conservation of these properties are provided. The proposed algorithm works with displacement and velocity variables for the structure and fluid, respectively, and introduces no new variables to enforce velocity or traction continuity. Any existing structural dynamics algorithm can be used without change in the proposed method. Use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. An analytical solution is presented for one of the benchmark problems used in the literature, namely, the piston problem. A number of benchmark problems including problems involving free surfaces such as sloshing and the breaking dam problem are used to demonstrate the good performance of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

A 3-D,symmetric, finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium

A weak solution of the coupled, acoustic-elastic, wave propagation problem for a flexible porous material is proposed for a 3-D continuum. Symmetry in the matrix equations; with respect to both volume, i.e. ‘porous frame’–‘pore fluid’, and surface, i.e. ‘porous frame/pore fluid’–‘non-porous media’, fluid–structure interaction; is ensured with only five unknowns per node; fluid pore pressure, fluid-displacement potential and three Cartesian components of the porous frame displacement field. Taking Biot's general theory as starting point, the discretized form of the equations is derived from a weighted residual statement, using a standard Galerkin approximation and iso-parametric interpolation of the dependent variables. The coupling integrals appearing along the boundary of the porous medium are derived for a number of different surface conditions. The primary application of the proposed symmetric 3-D finite element formulation is modelling of noise transmission in typical transportation vehicles, such as aircraft, cars, etc., where porous materials are used for both temperature and noise insulation purposes. As an example of an application of the implemented finite elements, the noise transmission through a double panel with porous filling and different boundary conditions at the two panel boundaries are analysed. © 1998 John Wiley & Sons, Ltd.     

Transient wave propagation in a one-dimensional poroelastic column

Summary Biot's theory of porous media governs the wave propagation in a porous, elastic solid infiltrated with fluid. In this theory, a second compressional wave, known as the slow wave, has been identified. In this paper, Biot's theory is applied to a one-dimensional continuum. Despite the simplicity of the geometry, an exact solution of the full model, and a detailed analysis of the phenomenon, so far have not been achieved. In the present approach, an analytical solution in the Laplace transform domain is obtained showing clearly two compressional waves. For the special case of an inviscid fluid, a closed form exact solution in time domain is obtained using an analytical inverse Laplace transform. For the general case of a viscous fluid, solution in time domain is evaluated using the Convolution Quadrature Method of Lubich. Of all the inverse methods previously investigated, it seems that only the method of Lubich is efficies and stable enough to handle the highly transient cases such as impact and step loadings. Using properties of three widely different real materials, the wave propagating behavior, in terms of stress, pore pressure, displacement, and flux, are examined. Of most interest is the identification of second compressional wave and its sensitivity of material parameters.     

Extending MLPG primitive variable-based method for implementation in fluid flow and natural,forced and mixed convection heat transfer

The purpose of the current study is to empower the MLPG primitive variable-based method using the characteristic-based split (CBS) scheme to solve the laminar fluid flow and natural, forced, and mixed convection heat transfer at, respectively, higher Rayleigh, Reynolds and Peclet, and Reynolds and Grashof numbers than those that the MLPG approach has ever solved. In this work, the CBS scheme with unity test function is employed for discretization and the moving least square (MLS) method is used for interpolation. As some test cases, natural convection within a square cavity, forced convection by fluid flow over a bundle of tubes, and mixed convection within a lid-driven square cavity are solved by the proposed method. For verifications, the obtained results are compared with those of the conventional numerical methods in the literature. Being entirely meshless, strong in nature, and able to give accurate and stable results for the broadest range of laminar fluid flow involving any of the three modes of convection heat transfer, the proposed method shows to be a flexible and reliable technique which can replace many available meshfree methods in the literature.     

An iterative BEM/FVM protocol for steady-state multi-dimensional conjugate heat transfer in compressible flows

A BEM-based temperature forward/flux back (TFFB) coupling algorithm is developed to solve the conjugate heat transfer (CHT), which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid, which is convecting heat into or out of the solid structure. There are two basic approaches for solving coupled fluid-structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid–solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the Navier–Stokes equations by finite volume methods. Interface of flux and temperature is enforced at the solid/fluid interface.     

On attenuation of floating structure response to underwater shock

This paper presents an analysis on attenuation of floating structures response to underwater shock. An explicit finite element approach interfaced with the boundary element method is used for the shock-fluid–structure interaction. The bulk cavitation induced by underwater shock near the free surface is considered in this study. Two types of floating structural configurations are modeled: one is the two-layered panel and the other is the sandwich panel, both of which are extracted from the typical floating hulls—the former corresponds the single hull with coating material and the latter corresponds to the double hull with different material fillings. Their effective structural damping and stiffness are formulated and incorporated in the fluid–structure-coupled equations, which relate the structure response to fluid impulsive loading and are solved using the coupled explicit finite-element and boundary element codes. The cavitation phenomenon near free surface is captured via the present computational procedure. The attenuation effects of the floating structure response to underwater explosion are examined. From the results obtained, some insights on the improvement of floating structures to enhance their resistance to underwater shock are deduced.     

Prediction of micro-channel flows using direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) method is a particle-based numerical modeling technique. It is recently used for simulating gaseous flow in micro-electro-mechanical-systems (MEMS) where micron-scale features become important. In this paper, numerical simulations of fluid flow in micro-channels are carried out using the DSMC method. The details in determining the parameters critical for DSMC applications in micro-channels are provided. Streamwise velocity distributions in the slip-flow regime are compared with the analytical solution based on the Navier–Stokes equations with slip velocity boundary condition. Satisfactory agreements have been achieved. Effects of the entrance and exit regions on simulation results are discussed. Simulations are then extended to transition flow regime (Kn>0.1) and compared with the analytical solution. It is shown that the results are distinguished with the analytical solutions, which fail to predict the flow due to the break down of continuum assumption. It is indicated that the gradient of the pressure along the channel direction dominates the motion of the fluid flow.     

Immersed molecular electrokinetic finite element method

A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier–Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid–structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.     

Stabilizing the retarded potential method for transient fluid–structure interaction problems

The Retarded Potential (RP) method, which is a boundary element technique and non-local in both space and time, is employed to discretize the fluid domain for the analysis of transient fluid–structure interaction problems. The retarded potential analysis program RPFS is coupled to the ABAQUS non-linear finite element code to form ABAQUS/RPFS. The standard RP is inherently unstable for time steps below a critical time step that is equal to the maximum distance in the fluid divided by the wave speed. A technique referred to as the Figueiredo method is used to convert the standard RP differential-delay equations for the fluid to simply delay equations, which are more stable. The Figueiredo approach extends the stability range of the standard RP by a factor of approximately 10–20, but this time step is still not small enough to be useful for analysis. Digital signal processing methods are used to further stablize the response of the fluid by removing the oscillating high-frequency noise in the time histories of the solution without introducing phase shifting or any significant damping. Stability of the coupled system is achieved by not extrapolating the structural accelerations. ABAQUS/RPFS is applied to both a rigid and elastic sphere subjected to a plane wave, and the results using the full time histories required are completely stable and quite accurate. With this procedure, the retarded potential method may yet prove to be a valuable analysis tool for transient fluid–structure interaction problems. © 1997 John Wiley & Sons, Ltd.     

夹层输流管道弹性波频散特征分析

对无限长夹层输流管道的管壁弹性波频散特征、管内流体声波频散特征,以及弹性体与流体声固耦合的波传播频散特征进行了研究与分析.基于铁木辛柯梁模型构建弹性体管道的波数解析式.考虑声固耦合效应,对无限长夹层输流管道的管壁弹性波与管内流体声波相互耦合的波数和模态振型进行了求解.运用参数化扫描,分别计算了管内流体域为水和空气情况下...     

A method of solving nonstationary three-dimensional problems of hydroelasticity with allowance for fluid failure

A numerical–analytical method of solving a class of nonlinear problems of dynamic hydroelasticity is proposed. The essence of the method consists in the expansion of all unknowns in trigonometric Fourier series in terms of the angular coordinate with subsequent application of the finite-difference method over a two-dimensional grid. It has been generally used to solve linear problems. Good accuracy of the developed algorithm is demonstrated on the basis of numerical experiments and trial calculations, and several specific examples have been solved. A number of effects associated with different behaviours of an ideally elastic and rupturable fluid, as well as a nonlinear dependence of the wave fields on the load amplitude are observed.     

Gravity wave interaction with porous structures in two-layer fluid

Oblique wave interaction with rectangular porous structures of various configurations in two-layer fluid are analyzed in finite water depth. Wave characteristics within the porous structure are analyzed based on plane wave approximation. Oblique wave scattering by a porous structure of finite width and wave trapping by a porous structure near a wall are studied under small amplitude wave theory. The effectiveness of three types of porous structures—a semi-infinite porous structure, a finite porous structure backed by a rigid wall, and a porous structure with perforated front and rigid back walls—in reflecting and dissipating wave energy are analyzed. The reflection and transmission coefficients for waves in surface and internal modes and the hydrodynamic forces on porous structures of the aforementioned configurations are computed for various physical parameters in two-layer fluid. The eigenfunction expansion method is used to deal with waves past the porous structure in two-layer fluid assuming the associated eigenvalues are distinct. An alternate procedure based on the Green’s function technique is highlighted to deal with cases where the roots of the dispersion relation in the porous medium coalesce. Long wave equations are derived and the dispersion relation is compared with that derived based on small amplitude wave theory. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy.     

An algorithm for modelling the interaction of a flexible rod with a two‐dimensional high‐speed flow

We present an algorithm for modelling coupled dynamic interactions of a very thin flexible structure immersed in a high‐speed flow. The modelling approach is based on combining an Eulerian finite volume formulation for the fluid flow and a Lagrangian large‐deformation formulation for the dynamic response of the structure. The coupling between the fluid and the solid response is achieved via an approach based on extrapolation and velocity reconstruction inspired in the Ghost Fluid Method. The algorithm presented does not assume the existence of a region exterior to the fluid domain as it was previously proposed and, thus, enables the consideration of very thin open boundaries and structures where the flow may be relevant on both sides of the interface. We demonstrate the accuracy of the method and its ability to describe disparate flow conditions across a fixed thin rigid interface without pollution of the flow field across the solid interface by comparing with analytical solutions of compressible flows. We also demonstrate the versatility and robustness of the method in a complex fluid–structure interaction problem corresponding to the transient supersonic flow past a highly flexible structure. Copyright © 2005 John Wiley & Sons, Ltd.     

An implicit–explicit solution method for electro‐osmotic flow through three‐dimensional micro‐channels

This paper presents a comprehensive finite‐element modelling approach to electro‐osmotic flows on unstructured meshes. The non‐linear equation governing the electric potential is solved using an iterative algorithm. The employed algorithm is based on a preconditioned GMRES scheme. The linear Laplace equation governing the external electric potential is solved using a standard pre‐conditioned conjugate gradient solver. The coupled fluid dynamics equations are solved using a fractional step‐based, fully explicit, artificial compressibility scheme. This combination of an implicit approach to the electric potential equations and an explicit discretization to the Navier–Stokes equations is one of the best ways of solving the coupled equations in a memory‐efficient manner. The local time‐stepping approach used in the solution of the fluid flow equations accelerates the solution to a steady state faster than by using a global time‐stepping approach. The fully explicit form and the fractional stages of the fluid dynamics equations make the system memory efficient and free of pressure instability. In addition to these advantages, the proposed method is suitable for use on both structured and unstructured meshes with a highly non‐uniform distribution of element sizes. The accuracy of the proposed procedure is demonstrated by solving a basic micro‐channel flow problem and comparing the results against an analytical solution. The comparisons show excellent agreement between the numerical and analytical data. In addition to the benchmark solution, we have also presented results for flow through a fully three‐dimensional rectangular channel to further demonstrate the application of the presented method. Copyright © 2007 John Wiley & Sons, Ltd.     

Characterisation of the hydraulic maldistribution in a heat exchanger by local measurement of convective heat transfer coefficients using infrared thermography

A methodology was developed to characterise the heat exchangers' performance decrease due to two-phase flow maldistribution. It consists in measuring the spatial distribution of the local heat transfer coefficients with a rapid, non-invasive and fluid independent method. The method is based on the infrared (IR) thermography measurement of the temperature response to an oscillating heat flux. The amplitude of the measured temperatures is compared to the solution of an analytical model. The problem is solved iteratively to obtain the heat transfer coefficients. This method has been applied to evaluate the uneven phase distribution of an air–water mixture in a compact heat exchanger. The exchanger is composed of seven multiport flat tubes, a vertical downward header and horizontal channels. Experiments were performed for mass flux from 29 kg m⁻² s⁻¹ to 116 kg m⁻² s⁻¹ and for quality from 0.10 to 0.70.     

Analytical layer-element approach for wave propagation of transversely isotropic pavement

Asphalt pavements have been recognised as transversely isotropic multi-layered structures. In this paper, an analytical layer-element approach is utlised to solve the wave propagation of transversely isotropic multi-layered pavement structures under the falling weight deflectometer impact load. After the application of Fourier–Hankel transform, the Navier's equation for transversely isotropic layer by impulsive force are solved analytically. The global stiffness matrix equation of multilayered structures is further obtained by assembling the interrelated layer-elements, and the actual solution is achieved by numerical inversion of the Fourier–Hankel transform after the solution in the transformed domain is obtained. The layer-element of a single layer and the global stiffness matrix only contain negative exponential functions, which leads to a considerable improvement in computation ef?ciency and stability. Numerical examples are presented to demonstrate the accuracy of this method and to inversitgate the influence of the properties of transversely isotropic elastic materials on the load-displacement responses.     

Solution of FE‐BE coupled eigenvalue problems for the prediction of the vibro‐acoustic behavior of ship‐like structures

To predict the vibro‐acoustic behavior of structures, both a structural problem and an acoustic problem have to be solved. For thin structures immersed in water, a strong interaction between the structural domain and fluid domain occurs. This significantly alters the resonance frequencies. In this work, the structure is modeled by the finite element method. The exterior acoustic problem is solved by a fast boundary element method employing hierarchical matrices. An FE‐BE formulation is presented, which allows the solution of the coupled eigenvalue problem and thus the prediction of the coupled eigenfrequencies and mode shapes. It is based on a Schur complement formulation of the FE‐BE system yielding a generalized eigenvalue problem. A Krylov–Schur solver is applied for its efficient solution. Hereby, the compressibility of the fluid is neglected. The coupled eigensolution is then used for a model reduction strategy allowing fast frequency sweep calculations. The efficiency of the proposed formulations is investigated with respect to memory consumption, accuracy, and computation time. Copyright © 2011 John Wiley & Sons, Ltd.     

桩顶柔性约束下非均质饱和土中管桩扭转振动研究

基于Biot波动方程及Novak薄层法理论,采用非线性弹簧模型近似代替上部结构对管桩的柔性约束,并考虑土体剪切模量沿深度的非均质变化,在求得桩周土和桩芯土扭转动力阻抗的基础上,将管桩扭转振动方程离散成差分格式,最终获得了桩顶柔性约束下非均质饱和土中端承管桩扭转振动的频域响应。研究表明:随着柔性约束参数n、M_u的增大,桩顶实刚度在两个参数高、低区段内数值不变,中间随n、M_u逐渐增大,而T_0的影响则与之相反;动阻尼随n、M_u、T_0的变化呈现出近似的正态曲线分布模式;增大土层非均质系数a,将使桩顶实刚度逐渐增大,动阻尼迅速减小,且最终保持不变。