Thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

Thermocapillary migration of a planar non-deformable droplet in flow fields with two uniform temperature gradients at moderate and large Marangoni numbers is studied numerically by using the front-tracking method. It is observed that the thermocapillary motion of planar droplets in the uniform temperature gradients is steady at moderate Marangoni numbers, but unsteady at large Marangoni numbers. The instantaneous migration velocity at a fixed migration distance decreases with increasing Marangoni numbers. The simulation results of the thermocapillary droplet migration at large Marangoni numbers are found in qualitative agreement with those of experimental investigations. Moreover, the results concerned with steady and unsteady migration processes are further confirmed by comparing the variations of temperature fields inside and outside the droplet. It is evident that at large Marangoni numbers the weak transport of thermal energy from outside of the droplet into inside cannot satisfy the condition of a steady migration process, which implies that the advection around the droplet is a more significant mechanism for heat transfer across/around the droplet at large Ma numbers. Furthermore, from the condition of overall steady-state energy balance in the flow domain, the thermal flux across its surface is studied for a steady thermocapillary droplet migration in a flow field with uniform temperature gradient. By using the asymptotic expansion method, a non-conservative integral thermal flux across the surface is identified in the steady thermocapillary droplet migration at large Marangoni numbers. This non-conservative flux may well result from the invalid assumption of a quasi-steady state, which indicates that the thermocapillary droplet migration at large Marangoni numbers cannot reach a steady state and is thus an unsteady process.     

Boundary element simulation of inviscid flow around an oscillatory foil with vortex sheet

The dynamic performance of a rigid foil with harmonic vertical and rotational motions in fluid flow has been studied through velocity potential theory. A boundary element based time stepping scheme is introduced to simulate the flow around the foil and the vortex wake. The body surface condition is satisfied on the exact foil surface and the motion and deformation of the wake sheet shed at the trailing edge is tracked. Kelvin condition is satisfied and a Kutta condition for the unsteady motion is proposed to circumvent the singularity at the trailing edge. Point vortex, which is reduced from wake vortex dipole, is introduced to approximate the vorticity. The performance of foil NACA0012 with harmonic vertical and rotational motions are studied extensively; the propulsion/swimming mode, energy harvesting mode and the flying mode are analysed in detail.     

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

A complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.     

深水铰接塔平台的非线性动力特性分析

研究了铰接塔平台在波浪和海流作用下的非线性动力特性。将平台顶部工作单元简化为集中质量,塔柱和浮力仓简化为均匀直杆,建立了铰接塔平台动力分析模型。考虑海流和波浪对平台的作用,应用Morison公式计算铰接塔平台瞬时位置所受水动力,依据拉格朗日原理建立了铰接塔平台的强非线性运动方程。分别考虑波浪作用和波流联合作用,采用数值计算的方法研究了铰接塔平台超谐共振和混沌运动。研究表明,波流联合作用下平台的超谐共振运动响应增加,在大幅和较高频率波浪激励下,平台系统出现混沌运动。     

Surface vorticity modeling of flow around airfoils

A surface vorticity method based on the new Kutta condition has been developed for solving the steady flow around an airfoil and unsteady separated flow past airfoil with a spoiler. In a discussion of the Kutta condition, it is argued that the appropriate Kutta condition is required to obtain a satisfactory solution. In this paper, two new methods of satisfying the Kutta condition incorporated in the surface vorticity method are described. The first method, which is based on results from flow visualization, is to introduce an additional control point at a short distance downstream of the trailing edge. In order to account for the fact that the velocity above the trailing edge is different from that below as in the real flow, the second method is to add a finite segment of vortex sheet downstream of the trailing edge. The present Kutta conditions are incorporated into the surface vorticity method and extend to solve unsteady flow around an airfoil with a spoiler. The computational results are in reasonable agreement with other computation as well as experiments.     

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition

The use of the Helmholtz decomposition for exterior incompressible viscous flows is examined, with special emphasis on the issue of the boundary conditions for the vorticity. The problem is addressed by using the decomposition for the infinite space; that is, by using a representation for the velocity that is valid for both the fluid region and the region inside the boundary surface. The motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. It is shown that at each instant of velocity discontinuity, vorticity is generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is then diffused into the surroundings: this yields that the no-slip conditions are thus automatically satisfied (since the presence of a vortex layer on the surface is required to obtain a velocity slip at the boundary). This result is then used to show that in order for the solution to the Euler equations to be the limit of the solution to the Navier-Stokes equations, a trailing-edge condition (that the vortices be shed as soon as they are formed) must be satisfied. The use of the results for a computational scheme is also discussed. Finally, Lighthill's transpiration velocity is interpreted in terms of Helmholtz decomposition, and extended to unsteady compressible flows.     

On-line particle-image velocimeter: an integrated approach

We describe an on-line particle-image velocimeter (PIV) and its implementation for the measurement of the velocity field in steady and unsteady flows. The instrument uses up-to-date solid-state sensors, dedicated electronic boards, and digital microcomputers to combine the image-acquisition and processing steps into a single, fully integrated unit. A calibration experiment evaluates the accuracy of the velocity measurement instrument. The experiment consists of the measurement of the velocity distribution of a laminar wall jet and shows that the velocity, as well as the vorticity profiles, obtained by using the on-line PIV compare well with those obtained by means of a conventional photographic PIV and a numerical prediction.     

三维波流耦合水槽模拟模型

水中结构物通常会受到波浪和水流的联合作用,为了得到作用在结构上的波流荷载,该文基于Flow-3D软件建立了三维波流水槽的模拟模型。为了准确模拟波浪和水流的相互作用,避免将造波边界和水流边界同时叠加在入口边界处,采用质量源造波法来实现内造波。利用Flow-3D的二次开发功能在水槽两端设置海绵层消波区,并结合Sommerfeld辐射边界条件来实现水槽的通流消波。对波浪的传播、波流相互作用试验的流场以及波流和柱体结构相互作用试验的流场进行数值模拟,结果表明:所建立的三维波流水槽模型可以准确地模拟波浪和水流的相互作用以及波流对结构的联合作用,并有效地进行消波,避免了二次反射,可用于波浪和水流联合作用下水中结构物波流荷载的研究。     

Acoustically generated unsteady vorticity field in a long narrow cylinder with sidewall injection

Asymptotic and computational analyses of a well-posed initial-boundary-value problem are used to describe the time history of co-existing acoustic and rotational velocity disturbances in a long, narrow cylinder with uniform steady sidewall mass injection. Transient planar pressure disturbances prescribed on the open exit plane of the cylinder are the source of acoustic disturbances in the axisymmetric flow. Both the asymptotic and numerical solutions describe the nonlinear aspects of the flow interactions. The full computational results are compared favorably with those of the asymptotic study to show that; (1) transient vorticity is generated near the injection surface and is transported into the cylinder by the radial velocity component of the flow field, (2) at any sufficiently small value of time, a well defined front separates the fluid containing transient vorticity from a flow field in the interior of the cylinder containing a much smaller amplitude vorticity and, (3) at sufficiently large values of time, vorticity is present throughout the cylinder. In addition, the analytically derived acoustic solution obtained from the asymptotic analysis is used to show that the present numerical solution and all earlier studies of similar problems are missing travelling waves (eigenfunctions) which should be present in a complete mathematical solution of the defined initial-boundary-value problem.     

A combined BEM–FEM model for the velocity–vorticity formulation of the Navier–Stokes equations in three dimensions

This paper describes a combined boundary element and finite element model for the solution of velocity–vorticity formulation of the Navier–Stokes equations in three dimensions. In the velocity–vorticity formulation of the Navier–Stokes equations, the Poisson type velocity equations are solved using the boundary element method (BEM) and the vorticity transport equations are solved using the finite element method (FEM) and both are combined to form an iterative scheme. The vorticity boundary conditions for the solution of vorticity transport equations are exactly obtained directly from the BEM solution of the velocity Poisson equations. Here the results of medium Reynolds number of up to 1000, in a typical cubic cavity flow are presented and compared with other numerical models. The combined BEM–FEM model are generally in fairly close agreement with the results of other numerical models, even for a coarse mesh.     

A 3D hybrid BE–FE solution to the forward problem of electrical impedance tomography

This paper presents a three dimensional (3D) hybrid boundary element–finite element (BE–FE) method solution to the electrical impedance tomography (EIT) forward problem. EIT is a method to find the distribution of electrical conductivity within an object through injecting current on surface electrodes placed on the object, and measuring the distribution of potential around the object. Existing 3D models are based on the finite element (FE) method and the boundary element (BE) method. In this paper, a hybrid BE–FE method approach is demonstrated for modeling the forward problem of EIT. Such a hybrid BE–FE technique combines strengths of FE and BE methods by dividing the regions into some homogeneous BE regions and heterogeneous FE regions. To validate numerical results, a homogenous test problem is solved analytically for the electrical potential. A cylindrical model of human thorax is studied. Results obtained for this model from BE, FE, and hybrid BE–FE methods with three different meshes and two different electrode placement strategies are compared.     

BEM modeling of surface water wave motion with laminar boundary layers

This study is concerned with numerical modeling of viscous surface wave motion using boundary element method (BEM). The equations of motion for thin boundary layers at the solid surfaces are coupled with the potential flow in the bulk of the fluid, and a mixed BEM-finite difference technique is used to obtain the viscosity-related quantities such as wave damping rate, shear stress, and velocity distribution inside the boundary layer. The technique is presented for standing surface wave motion. An excellent agreement is obtained between the numerical predictions and the previous results. The extension to other free surface problems is straightforward.     

Viscous vortex core generation

Summary The unsteady flow of a viscous incompressible fluid between two porous co-axial circular cylinders is analysed when the outer cylinder is impulsively set into rotation. When there is radial inflow, vorticity is transferred from an unsteady boundary layer initially over the outer cylinder to a steady boundary layer over the inner cylinder.With 1 Figure     

Boundary integral equation for wave equation with moving boundary and applications to compressible potential aerodynamics of airplanes and helicopters

This work presents a general boundary-integral-equation methodology for the solution of the wave equation around objects moving in arbitrary motion, with applications to compressible potential aerodynamics of airplanes and helicopters. The paper includes the derivation of the boundary integral equation for the wave equation, in a frame of reference moving in arbitrary motion (in particular, in translation and in rotation). The formulation is then applied to study unsteady potential compressible aerodynamic flows around streamlined bodies, such as airplanes and helicopters. The formulation is given in terms of the velocity potential, for which an explicit treatment of the wake is required; a discussion of the formulation for the wake transport is included. The advantages of the velocity-potential formulation over the acceleration-potential formulation are discussed. The boundary-element algorithm used for the computational implementation is briefly outlined. Validation of the formulation is presented for airplane wings and helicopter rotors in hover. The test cases fall into two categories. prescribed-wake and free-wake analyses. The validation of the prescribed-wake analysis is presented for compressible flows, subsonic for helicopter rotors, transonic for airplanes. The numerical validation of the free-wake analysis of helicopter rotors is presented for incompressible flows.     

Continuous-time state-space unsteady aerodynamic modeling based on boundary element method

In this paper a continuous-time state-space aerodynamic model is developed based on the boundary element method. Boundary integral equations governing the unsteady potential flow around lifting bodies are presented and modified for thin wing configurations. Next, the BEM discretized problem of unsteady flow around flat wing equivalent to the original geometry is recast into the standard form of a continuous-time state-space model considering some auxiliary assumptions. The system inputs are time derivative of the instantaneous effective angle of attack and thickness/camber correction terms while the outputs are unsteady aerodynamic coefficients. To validate the model, its predictions for aerodynamic coefficients variations due to the various unsteady motions about different wing geometries are compared to the results of the direct BEM computations and verified numerical and theoretical solutions. This comparison indicates a good agreement. Since the resulting aerodynamic model is in the continuous-time domain, it is particularly useful for optimization and nonlinear analysis purposes. Moreover, its state-space representation is the appropriate form for an aerodynamic model in design or control applications.     

楔形体诱导的非定常超空泡计算

采用积分方程方法,研究了楔形体外部自然超空泡流问题。提出了楔形体在静止流体中做变速运动所引起的非定常超空泡的积分方程。作为特例,得到了均匀来流时非定常超空泡的积分方程。应用时间有限差分离散化方法和有限差分法对积分方程进行了求解,得到了楔形体做变速运动、楔角变化、空化数变化、小扰动空化流等各种情况下的数值解。数值结果表明:非定常超空泡具有时滞性和波动性。楔体做变速运动时,加速度越大,时间滞后越长。在匀减速运动时,空泡不封闭,可能有回注射流发生。扰动频率越高,空泡长度变化越小,时间滞后越长。扰动以波动形式沿着空泡表面传播,传播速度为来流速度。该文所得到的结果,对于非定常超空化水翼的设计和分析能够起到参考作用。     

带窄缝多箱体系统波浪荷载特性分析

针对波浪与带有窄缝多固定直角箱体结构作用产生的流体共振问题,建立了非线性波浪荷载分析二维时域模型。该模型采用域内源造波技术产生入射波浪,自由水面满足完全非线性运动学和动力学边界条件,窄缝内自由水面引入人工阻尼来等效由于涡旋运动和流动分离引起的粘性耗散,建立边界积分方程并采用高阶边界元离散求解物面上速度势等未知量,进而利用加速度势的方法来求得速度势时间导数,并基于伯努利方程积分得到作用结构上的瞬时波浪荷载。通过模拟带两窄缝的三箱体所受水平力与垂向力,并与已发表结果对比验证了模型的准确性。同时通过大量的数值计算,分析了箱体数量对各箱体所受波浪荷载大小及变化规律的影响。     

Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

A detailed and systematic analysis is performed on the local and global properties of the recently developed harmonic polynomial cell (HPC) method, a very accurate and efficient field solver for problems governed by the Laplace equation. At the local cell level, a simple rule is identified for the proper choice of harmonic polynomials in the local representation of the velocity potential in cells with symmetry properties. The local solution error, its convergence rate, its dependence on the cell topology, its distribution inside the cell, and its features across cells with different dimensions are carefully examined with relevant findings for HPC numerical implementations. At the global level, the error convergence rate is analytically estimated in terms of error contributions from the boundary conditions and from inside the liquid domain. In most cases, the error associated with boundary conditions dominates the global error. In order to minimize it, Quadtree grid strategies or high‐order local expressions of the velocity potential are proposed for cells near critical boundary portions. To model accurately the boundary conditions on rigid or deformable surfaces with generic geometries, 3 different grid strategies are proposed by adopting concepts of immersed boundary method and overlapping grids. They are comparatively studied for a circular rigid cylinder in infinite fluid and for the propagation of a free‐surface wave. Then, an immersed boundary strategy, using numerical choices suggested in this paper, is successfully compared against a fully nonlinear boundary element method for the case of a surface‐piercing circular cylinder heaving in otherwise calm water.     

突风作用下圆柱结构气动特性的试验研究

突风(平均风速随时间快速变化)作用在结构或构件上时,结构的气动力和振动状态与平稳风作用下的结果有何不同,是值得研究的问题。在风洞实验室,利用电压控制的方法,实现了具有一定风速加速度的突升和突降的风速变化过程,测试了圆柱结构在突变风速平稳风速作用下的气动力和振动状态,试验结果表明：当突升风速作用在模型上时,采用瞬时风速和气动力算得的力系数和在平稳风速下的结果一致;当突降风速作用在模型上时,采用瞬时风速和气动力算得的力系数虽然在大小上和在平稳风速下的结果一致,但是其对应的临界雷诺数范围比平稳风速对应的临界雷诺数范围,整体向小的方向上偏移了一定的量值。当不涉及到临界雷诺数时,本文的突变风速不会激发模型的大幅振动;当风速升至或降至临界雷诺数区域时,模型将发生稳定的大幅振动;当风速经过临界雷诺数时,在临界雷诺数对应的风速下发生大幅振动,随着风速的升高或降低使得对应的雷诺数离开临界区域时,振动逐渐消失     

Biofluid flow in a channel under the action of a uniform localized magnetic field

In this work the fundamental problem of the biomagnetic (blood) fluid flow in a channel under the influence of a steady localized magnetic field is studied. For the mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and blood is considered as a homogeneous Newtonian fluid. For the numerical solution of the problem, which is described by a coupled, non linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is adopted. The solution is obtained by the development of an efficient numerical technique based on finite differences. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the magnetic field influences considerably the flow field. It is also obtained that the electrical conductivity of blood should be taken into account at the area of the uniform magnetic field.