Improving power-extraction efficiency of a flapping plate: From passive deformation to active control

A flapping plate flow energy harvester in a viscous uniform flow is simulated using a two-dimensional numerical approach. Our focus is to study the effects of flexibility and active control on the power-extraction capability of the flapping plate, and consequently to find a strategy to increase its power-extraction efficiency. Four typical cases with optimal kinematics predicted by previous studies are presented and discussed: a rigid plate, a flexible plate, a plate with a flexible leading segment and a rigid trailing segment, and a rigid plate with a simple active control on the leading segment. Our simulations show that with the kinematic parameters considered, the plate flexibility cannot significantly improve the power-extraction capability of the plate while the active control on the leading segment of the rigid plate increases the power coefficient by 11.3%. The analysis of flow fields shows that the changes in the power coefficient and drag force are related to the vortex structures and pressure distributions near the plate, as well as the projection area of the plate in the direction of the translational movement.     

功能梯度板弯曲和自由振动分析的简单精化板理论

论文提出了一种可用于分析功能梯度板弯曲和自由振动行为的简单精化板理论.该理论分析功能梯度板的弯曲时只需三个未知量，而分析功能梯度板的自由振动时只需一个未知量.与包含三个未知量的经典板理论相比，论文提出的简单精化板理论考虑了横向剪切效应，提高了计算准确度.与一阶剪切变形板理论不同，该简单精化板理论引入了多项式型剪切应变函数，满足板上下表面剪切应力为零的边界条件，因此不需要剪切修正.通过与已有文献的比较，验证了该简单精化板理论的准确性和便捷性，并基于该简单精化板理论研究了功能梯度板的弯曲和自由振动力学行为.     

Flutter of a rectangular plate

We address theoretically the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.     

Interior formulation of axisymmetric Levinson plate theory

In this study, we show that the axisymmetric Levinson plate theory is exclusively an interior theory and we provide a consistent variational formulation for it. First, we discuss an annular Levinson plate according to a vectorial formulation. The boundary layer of the plate is not modeled and, thus, the interior stresses acting as surface tractions do work on the lateral edges of the plate. This feature is confirmed energetically by the Clapeyron's theorem. The variational formulation is carried out for the annular Levinson plate by employing the principle of virtual displacements. As a novel contribution, the formulation includes the external virtual work done by the tractions based on the interior stresses on the inner and outer lateral edges of the Levinson plate. The obtained plate equations are consistent with the vectorially derived Levinson equations. Finally, we develop an exact plate finite element both by a force-based method and from the total potential energy of the Levinson plate.     

Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate

The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates.     

Plate punching by a deformable indenter in the presence of discharge current

The problem of interaction of a deformable indenter with a plate and the problem of plate punching as a result of interaction between the deformable indenter and the plate in the presence of a discharge current are considered. The stresses arising in the plate and in the indenter are obtained.     

Laminar mixed convection on a horizontal plate of finite length in a channel of finite width

The steady two-dimensional laminar mixed-convection flow past a horizontal plate of finite length is analysed for large Péclet numbers, small Prandtl numbers and weak buoyancy effects. The plate is placed in a channel of finite width, with the plane walls of the channel being parallel to the plate. The temperature of the plate is assumed to be constant. The hydrostatic pressure difference across the wake behind the plate is compensated by a perturbation of the inviscid channel flow. This outer flow perturbation affects the temperature distribution in the thermal boundary layer at the plate and the heat transfer rate, respectively. Solutions in closed form are given. The forces acting on the plate due to the potential flow perturbation are also determined.     

Oscillations of a plate cascade in a transonic gas flow

The transonic unsteady flow of a gas through a cascade of thin, slightly curved plates is quite complex and has received little study. The main difficulties are associated with the nonlinear dependence of the aerodynamic characteristics on the plate thickness. In [1] it is shown that, for a single thin plate performing high-frequency oscillations in a transonic gas stream, the variation of the unsteady aerodynamic characteristics with plate thickness may be neglected. For a plate cascade, the flow pattern is complicated by the aerodynamic interference between the plates, which may depend significantly on their shape. A solution of the problem of transonic flow past a cascade without account for the plate thickness has been obtained by Hamamoto [2].The objective of the present study is the clarification of the dependence of the aerodynamic characteristics of a plate cascade on plate thickness in transonic unsteady flow regimes. The nonlinear equation for the velocity potential is linearized under the assumption that the motionless plate causes significantly greater disturbances in the stream than those due to the oscillations. A similar linearization was carried out for a single plate in [3]. The aerodynamic interference between the plates is determined by the method presented in [4]. As an example, the aerodynamic forces acting on a plate oscillating in a duct and in a free jet are calculated.     

基于平面弹性—板弯曲模拟关系的薄板有限元列式——从膜单元到薄板单元

本文全面讨论了基于平面弹性－－板弯曲模拟关系的薄板有限单元的理论和方法,由于直接对弯矩函数进行插值,c1连续性的要求得以自然避免,薄板单元可以直接在c0连续的层面上加以构造,无需借用Reissner-Mindlin的中厚板理论,由之引发的闭锁问题也得以避免,本文系统地阐明了平面弹性膜单元与薄板弯曲单元的对应关系,及由平面弹性膜单元的向薄板弯曲单元转换的一整套方法。为薄板单元的构造提供了一条新的有余的途径,文中给出了对应于平面弹性膜单元CST,LST,Q4,Q8的薄板单元,我们称之为MPS板单元,MPS板元以挠度和转角为自由度,便于实际应用,和其它板单元相比具有非常高的精度。     

Comparison of Reissner,Mindlin and Reddy plate models with exact three dimensional solution for simply supported isotropic and transverse inextensible rectangular plate

In the article, the exact solution of a sinusoidal loaded simply supported rectangular plate is given for the case of an isotropic plate and for the case of a transversally inextensible plate. Asymptotic and numerical comportment with Reissner, Mindlin and Reddy plate models is present.     

Streamwise vibrations of a plate in a viscous fluid flow in a channel,induced by forced transverse vibrations of the plate

Aeroelastic vibrations of a plate aligned at a zero angle of attack in a viscous incompressible fluid flow in a channel with parallel walls are considered within the framework of a plane model. Forced vibrations of the plate in the transverse direction give rise an unsteady component of the flow friction force, induced by the perturbation of the fluid flow velocity by the vibrating plate. Under the assumption of the laminar character of the fluid flow, it is demonstrated that this force can excite streamwise vibrations of the plate if the channel width is small as compared with the plate length; these streamwise vibrations have the same order as the transverse vibrations of the plate excited by external forces.     

Numerical investigation of the interaction of a vortex dipole with a deformable plate

Energy harvesting from coherent fluid structures is a current research topic due to its application in the design of small self-powered sensors for underwater applications. The impact of a vortex dipole with a deformable cantilevered plate at the plate tip is herein studied numerically using a strongly coupled staggered fluid–structure interaction algorithm. Three dipole Reynolds numbers, Re=500, 1500, and 3000, are investigated for constant plate properties. As the dipole approaches the plate, positive vorticity is produced on the impact face, while negative vorticity is generated at the tip of the plate. Upon impact, the dipole splits into two, and two secondary dipoles are formed. The circulation and, therefore, the trajectories of these dipoles depend on both the Reynolds number and the elasticity of the plate, and these secondary dipoles may return for subsequent impacts. While the maximum deflection of the plate does not depend significantly on Reynolds number, the plate response due to subsequent impacts of secondary dipoles does vary with Reynolds number. These results elucidate the strong interdependency between plate deformation and vortex dynamics, as well as the effect of Reynolds number on both.     

Unsteady radiative-convective heat transfer in a high-temperature gas-particle flow past a semi-transparent plate

Numerical simulations of unsteady radiative-convective heat transfer in a turbulent flow of a mixture of gases and solid particles past a semi-transparent plate are performed. An ablation process is demonstrated to occur on the plate surface in the case of intense radiative heating of the plate by an external source with emission in a limited spectral range. Temperature fields and distributions of heat fluxes in the boundary layer and in the plate are calculated. Calculation results are presented, which allow determining the effect of ablation and reflecting properties of the plate surface on the thermal state of the medium in the system containing the boundary layer and the plate under conditions of plate heating by a high-temperature source of radiation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 140–146, May–June, 2009.     

炸药爆炸驱动下铜板的层裂现

在进行炸药驱动铜板实验中,用激光速度干涉仪(VISAR)记录铜板自由面速度,观察到了铜板层裂现象,并用非线性有限元方法对爆炸载荷下铜板层裂过程进行数值模拟分析,得到了与实验结果吻合的计算结果。     

各向异性对平板裂纹扩展路径的影响研究

近场动力学理论克服了经典连续介质力学在模拟裂纹扩展方面的不足。本文基于微梁键构建了一般各向异性近场动力学平面模型,并探讨了各向异性对于裂纹扩展路径的影响。首先,建立一般各向异性的微梁键,并基于插值法建立了一般各向异性近场动力学平面模型的应变能密度表达式;然后,利用应变能密度互等原理求解出近场动力学平面本构模型的一般各向异性参数;最后,通过带初始切口的平板断裂实验研究了不同各向异性参数对于平板裂纹扩展路径的影响。     

Analysis of the aerodynamic interaction between two plunging plates in tandem at low Reynolds number for maximum propulsive efficiency

The thrust generated by two heaving plates in tandem is analyzed computationally by solving the Navier–Stokes equations for an incompressible and two-dimensional flow at low Reynolds numbers. We consider with detail two particular sets of configurations of interest in forward flight in a wide range of heaving amplitudes and frequencies: a plunging leading plate with the trailing plate at rest, and the two plates heaving with the same frequency and amplitude, but varying the phase difference. In almost all cases the thrust efficiency of the leading plate is augmented in relation to a single plate heaving with the same frequency and amplitude. In the first configuration with a trailing plate at rest, we characterize the range of nondimensional heaving frequencies and amplitudes of the leading plate for which the stationary trailing plate contributes positively to the global thrust. The maximum global thrust efficiency of this configuration, reached for an advance ratio slightly less than unity and a reduced frequency close to 5, is about the same as the maximum efficiency for an isolated plate, reached for slightly smaller frequencies. But for low frequencies the tandem configuration with the trailing plate at rest is more thrust efficient than the isolated plate. We also characterize the nondimensional frequency and amplitude regions for which the flow becomes chaotic. In the second configuration, the maximum of the total thrust efficiency is reached for a phase lag of 180° (counterstroking), particularly for an advance ratio unity and a reduced frequency 4.4. It is almost the same as the maximum thrust efficiency in the other configuration with the trailing plate at rest and that of a single plate. We discuss the flow structures and the aerodynamic interaction between plates responsible for the optimal thrust configuration in both cases.     

Scattering of water waves by a submerged thin vertical elastic plate

The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli–Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green’s function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green’s integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small.     

一种考虑横向剪切变形的三角形板弯曲单元

本文从部分协调的三角形薄板弯曲单元出发,并假设横向剪切应变在单元内线性变化,提出了一种考虑横向剪切变形的具有15个自由度的三角平板弯曲单元。该单元应用于薄板和中等厚度板分析均有较高的精度,计算效率高,可用于工程中具有复杂形状的薄板和中等厚度板结构的分析。     

Winkler地基上变厚度圆板的轴对称弯曲

本文提出了Winkler地基上变厚度圆板轴对称弯曲的传递矩阵算法。首先，根据贝塞尔函数理论获得了等厚度圆板和环板单元在任意荷载作用下轴对称弯曲的解析解，这些解均由通解和特解两部分组成。基于这些解析解，导出了等厚度圆板和环板单元的传递矩阵。然后沿径向将变厚度圆板划分成一个等厚度圆板单元和一系列等厚度环板单元，应用传递矩阵算法原理获得了变厚度圆板的整体传递矩阵。引入圆板的边界条件，给出了该板每条节线上的挠度、径向转角、径向弯矩和径向剪力。最后，讨论了受均布荷载作用的简支线性变厚度圆板的弯曲，将本文数值解与解析解进行比较，证实了本文方法的有效性，并简要地讨论了地基参数对板挠度和径向弯矩的影响。     

磁驱动单侧飞片实验的数值模拟

磁驱动单侧飞片实验的数值模拟通常可不考虑厚的阴极的运动状态和厚度方向上烧蚀宽度的影响，采用单侧计算模型进行模拟。为了理解磁驱动单侧飞片实验可采用单侧计算模型的原因，为磁驱动单侧飞片实验的单侧计算建模提供理论依据，建立了磁驱动单侧飞片实验的双侧计算模型，并对PTS-061、PTS-064磁驱动单侧飞片实验进行了模拟分析。在PTS-061、PTS-064实验中，飞片的电流加载面的位移随着时间的增加持续增大；厚的阴极的电流加载面的位移不随时间的增加持续增大，在磁驱动实验中后期基本保持不变。PTS-061实验结束时，飞片的电流加载面的位移为4.9 mm，阴极电流加载面的位移仅为1.7 mm。PTS-064实验结束时，飞片的电流加载面的位移为4.1 mm，阴极电流加载面的位移仅为0.9 mm。磁驱动单侧飞片实验能采用单侧计算模型模拟的原因，不是阴极板面保持位置不动，而是阴极电流加载面的位移不随时间持续增加；在磁驱动实验后期，飞片电流加载面位移对边界磁场的影响远大于阴极电流加载面的位移对边界磁场的影响。