Numerical experiments on the transient motions of a flapping foil

The flow field generated by a foil during transient motions is investigated by means of numerical experiments. The numerical simulations have some advantages with respect to laboratory experiments. Indeed, having access to the velocity and pressure fields both in space and in time, it is possible to 'measure' quantities like vorticity, forces and torques which are quite difficult to obtain in laboratory. Moreover, data can be easily gained for different foil kinematics. The obtained results show that the time history of the propulsive force strongly depends on the details of the kinematics of the foil. Moreover, the numerical simulations have allowed to understand the main mechanisms employed by fish to propel themselves during fast starts and to identify the values of the parameters providing optimal propulsive performances.     

Forces on oscillating foils for propulsion and maneuvering

Experiments were performed on an oscillating foil to assess its performance in producing large forces for propulsion and effective maneuvering. First, experiments on a harmonically heaving and pitching foil were performed to determine its propulsive efficiency under conditions of significant thrust production, as function of the principal parameters: the heave amplitude, Strouhal number, angle of attack, and phase angle between heave and pitch. Planform area thrust coefficients of 2.4 were recorded for 35° maximum angle of attack and efficiencies of up to 71.5% were recorded for 15° maximum angle of attack. A plateau of good efficiency, in the range of 50–60%, is noted. A phase angle of 90–100° between pitch and heave is found to produce the best thrust performance. Also, the introduction of higher harmonics in the heave motion, so as to ensure a sinusoidal variation in the angle of attack produced much higher thrust coefficient at high Strouhal numbers. Second, experiments on a harmonically oscillating foil with a superposed pitch bias, as well as experiments on impulsively moving foils in still water, were conducted to assess the capability of the foil to produce large lateral forces for maneuvering. Mean side force coefficients of up to 5.5, and instantaneous lift coefficients of up to 15 were recorded, demonstrating an outstanding capability for maneuvering force production.     

自主推进俯仰震荡翼型的数值模拟研究

运用自适应多重网格法和内置边条法研究了俯仰震荡翼型的运动.通过研究翼型的原地摆动与自由游动,提出了一种确定自主推进俯仰震荡翼型推力的方法,得到了推力系数、功率系数和推进效率与Strouhal数的关系.与以往研究不同的是,我们还得到了Strouhal数随雷诺数的变化规律.此外,从自由游动翼型诱导出的涡量场中可以清楚的观察到旋涡的合并,这与实验研究非常吻合.     

A NUMERICAL AND ANALYTICAL STUDY ON A TAIL-FLAPPING MODEL FOR FISH FAST C-START＊

The force production physics and the flow control mechanism of fish fast C-start are studied numerically and theoretically by using a tail-flapping model. The problem is simplified to a 2-D foil that rotates rapidly to and fro on one side about its fixed leading edge in water medium. The study involves the simulation of the flow by solving the two-dimensional unsteady incompressible Navier-Stokes equations and employing a theoretical analytic modeling approach. Firstly, reasonable thrust magnitude and its time history are obtained and checked by fitting predicted results coming from these two approaches. Next, the flow fields and vortex structures are given, and the propulsive mechanism is interpreted. The results show that the induction of vortex distributions near the trailing edge of the tail are important in the time-averaged thrust generation, though the added inertial effect plays an important role in producing an instant large thrust especially in the first stage. Furthermore, dynamic and energetic effects of some kinematic controlling factors are discussed. For enhancing the time-averaged thrust but keeping a favorable ratio of it to time-averaged input power within the limitations of muscle ability, it is recommended to have a larger deflection amplitude in a limited time interval and with no time delay between the to-and-fro strokes. The project supported by the CAS (KJCX-SW-L04)     

Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function

Numerical simulation of Poiseuille flow of liquid Argon in a nanochannel using the non-equilibrium molecular dynamics simulation (NEMD) is performed. The nanochannel is a three-dimensional rectangular prism geometry where the concerned numbers of Argon atoms are 2,700, 2,550 and 2,400 at 102, 108 and 120 K. Poiseuille flow is simulated by embedding the fluid particles in a uniform force field. An external driving force, ranging from 1 to 11 PN (Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. To obtain a more uniform temperature distribution across the channel, local thermostating near the wall are used. Also, the effect of other mixing rules (Lorenthz–Berthelot and Waldman–Kugler rules) on the interface structure are examined by comparing the density profiles near the liquid/solid interfaces for wall temperatures 108 and 133 K for an external force of 7 PN. Using Kong and Waldman–Kugler rules, the molecules near the solid walls were more randomly distributed compared to Lorenthz–Berthelot rule. These mean that the attraction between solid–fluid atoms was weakened by using Kong rule and Waldman–Kugler rule rather than the Lorenthz–Berthelot rule. Also, results show that the mean axial velocity has symmetrical distribution near the channel centerline and an increase in external driving force can increase maximum and average velocity values of fluid. Furthermore, the slip length and slip velocity are functions of the driving forces and they show an arising trend with an increase in inlet driving force and no slip boundary condition is satisfied at very low external force (<1 PN).     

激波诱导含灰气体边界层中的粒子分布

本文研究当激波沿着一个固体表面等速地穿越含灰气体运动时所诱导的层流边界层特性。考虑了作用在气体边界层中球形粒子的 Saffman 升力,建议了一种计算近壁区中弥散相密度剖面的方法,并给出了数值计算结果。本文结果表明:在激波后方存在着一个弯曲的薄层区域,其中的粒子密度可以比其波前原始值增加许多倍。这种粒子聚集效应对于工业中粉尘爆炸等实际问题具有重要意义。     

High fidelity numerical simulation of airfoil thickness and kinematics effects on flapping airfoil propulsion

High-fidelity numerical simulations with the spectral difference (SD) method are carried out to investigate the unsteady flow over a series of oscillating NACA 4-digit airfoils. Airfoil thickness and kinematics effects on the flapping airfoil propulsion are highlighted. It is confirmed that the aerodynamic performance of airfoils with different thickness can be very different under the same kinematics. Distinct evolutionary patterns of vortical structures are analyzed to unveil the underlying flow physics behind the diverse flow phenomena associated with different airfoil thickness and kinematics and reveal the synthetic effects of airfoil thickness and kinematics on the propulsive performance. Thickness effects at various reduced frequencies and Strouhal numbers for the same chord length based Reynolds number (=1200) are then discussed in detail. It is found that at relatively small Strouhal number (=0.3), for all types of airfoils with the combined pitching and plunging motion (pitch angle 20°, the pitch axis located at one third of chord length from the leading edge, pitch leading plunge by 75°), low reduced frequency (=1) is conducive for both the thrust production and propulsive efficiency. Moreover, relatively thin airfoils (e.g. NACA0006) can generate larger thrust and maintain higher propulsive efficiency than thick airfoils (e.g. NACA0030). However, with the same kinematics but at relatively large Strouhal number (=0.45), it is found that airfoils with different thickness exhibit diverse trend on thrust production and propulsive efficiency, especially at large reduced frequency (=3.5). Results on effects of airfoil thickness based Reynolds numbers indicate that relative thin airfoils show superior propulsion performance in the tested Reynolds number range. The evolution of leading edge vortices and the interaction between the leading and trailing edge vortices play key roles in flapping airfoil propulsive performance.     

明渠层流近床面颗粒拖曳力研究

泥沙颗粒受到的拖曳力是泥沙运动的主要驱动力,而当前应用于计算流体力学-离散颗粒法(CFD-DPM)耦合模型进行水沙运动模拟的泥沙颗粒拖曳力公式均没有考虑明渠流底床边壁作用的影响。求解不可压缩Navier-Stokes方程,对明渠层流不同雷诺数条件下床面附近不同高度处颗粒所受拖曳力进行了模拟,根据模拟结果变化规律,提出了综合考虑床面和水流惯性对标准拖曳力影响的修正拖曳力计算公式。与常用的单颗粒标准拖曳力公式和考虑遮蔽效应的多颗粒拖曳力公式相比,采用本文修正公式得到的水沙作用力更接近高精度数值解,应用于CFD-DPM输沙模拟获得的输沙结果与输沙率公式结果一致,应用分析表明输沙模拟应当采用粗糙底床边界。     

N表面张力对近固壁二空化泡影响的数值研究

在忽略浮力下，用边界积分方法数值模拟了表面张力对固壁之上且靠近固壁的二轴对称空化泡生长和溃灭的影响，发现在下空泡最大等效半径为上空泡一半情形，若固壁对下空泡的Bjerknes力大于上空泡对下空泡的Bjerknes力，则表面张力的作用将使下空泡溃灭加速，使其向下的液体射流变强变宽；若固壁对下空泡的Bjerknes力小于上空泡对下空泡的Bjerknes力，则表面张力的作用将使下空泡溃灭变慢，使其向上射流变弱变细长；若这两个Bjerknes力近于相等，则表面张力将会对下空泡溃灭有重大作用，如改变下空泡射流的方向甚至形式(如由环状变向下或由向上变环状)，当上空泡等于或小于下空泡时，表面张力将不会对这两个空泡的行为产生显著影响，定性地分析了表面张力作用的机理。     

The distribution of particles in a shock-induced boundary layer of a dusty gas over a solid surface

The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied. The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account. A method for calculating the density profile of dispersed phase near the wall is proposed and some numerical results are given. It is shown that behind the shock wave, there exists a curved thin layer where the density of particles is many times higher than the original one. This dust collection effect may be of essential importance to the problem of dust explosion in industry.     

Effect of the stiffness,inertia and oscillation kinematics on the thrust generation and efficiency of an oscillating-foil propulsion system

This paper presents an experimental study that has investigated the effects of the foil stiffness, inertia and oscillation kinematics on the thrust generation and efficiency of a flexible oscillating-foil propulsion system. A semi-empirical damped-oscillator model, which included a quadratic damping element, was developed and fitted to the experimental results. The model was used to develop explanations for the observed trends in the propulsive performance. For all of the foils constructed for the study, a consistent relationship between the efficiency and frequency ratio was observed. The maximum efficiency occurred at the same frequency ratio that resulted in both a beneficial phasing of the deformation with respect to the driven motion and also the maximum overall amplitude of the motion. For foils of equivalent resonant frequency operating at the same frequency ratio, the stiffer and heavier foils were found to develop greater thrust, likely because the lower effective damping allowed for a greater amplitude of the motion. Increasing the amplitude of the driven motion was found to cause the frequency ratio providing the maximum efficiency to shift towards lower values. The use of combined pitch and heave motions was shown to increase efficiency while reducing thrust compared to the heave-only case.     

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

We perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.     

Flapping dynamics of a flexible propulsor near ground

The flapping motion of a flexible propulsor near the ground was simulated using the immersed boundary method. The hydrodynamic benefits of the propulsor near the ground were explored by varying the heaving frequency (St) of the leading edge of the flexible propulsor. Propul-sion near the ground had some advantages in generating thrust and propelling faster than propulsion away from the ground. The mode analysis and flapping amplitude along the Lagrangian coordinate were examined to analyze the kine-matics as a function of the ground proximity (d)and St. The trailing edge amplitude (atail)and the net thrust (Fx)were influenced by St of the flexible propulsor. The vortical structures in the wake were analyzed for different flapping conditions.     

叠片式气体箔片推力轴承热特性分析

叠片式气体箔片推力轴承具有制造工艺简单、散热能力强等优点,针对该新型轴承提出了相应的热特性分析模型,通过数值仿真分析得到轴承气膜及各元件的温度,并对关键影响参数进行了重点分析. 研究结果表明:由于气膜在半径较大位置处的线速度大,其剪切产热效果明显,温度越高,气膜的高温区分布在靠近周向末端和顶箔侧;气膜、顶箔和推力盘温度均会随推力盘转速和轴承载荷的增大而升高;向箔片结构中通入冷却气流可以获得良好的降温效果,轴承温度随着箔片内通入冷却气流量的增大,先迅速下降后趋于平缓.      

Propulsive performance of a flapping plate near a free surface

The propulsive performance, i.e., the time-averaged thrust coefficient or the propulsive efficiency, of a flapping flat plate advancing near an otherwise quiescent free surface (liquid–gas interface) with Re of 1000, Fr of 0.2 and 0.8, and various submergence depths is numerically investigated by employing an adaptive Cartesian cut-cell/level-set method. The flapping kinematics parameters excluding the pitch-leading-heave phase angle were fixed as those commonly seen in literature. Results show that for submergence depth larger than the heave amplitude, the propulsive performance peaks at a smaller pitch-leading-heave phase angle with a shallower submergence for Fr of 0.2 but at the same phase angle for Fr of 0.8. Proximity to the free surface enhances the peak propulsive performance for Fr of 0.2 but the influence is minor for Fr of 0.8. The propulsive performance with Fr of 0.2 increases with decreasing chord-normalized submergence depth for the pitch-leading-heave phase angle smaller than 100°. The trend is reversed for the pitch-leading-heave phase angle larger than 100°. However, the propulsive performance with Fr of 0.8 hardly depends on the chord-normalized submergence depth. For submergence depth equal to the heave amplitude, the temporal variation in the thrust coefficient exhibits characteristics inherently different from those with other submergence depths for Fr of 0.2. Also, the time-averaged thrust coefficient exhibits a unique variation with the pitch-leading-heave phase angle. However, the various characteristics of the propulsive performance are similar to those with other submergence depths for Fr of 0.8. For submergence depth smaller than the heave amplitude and Fr of 0.2, the propulsive performance gains much from exposure of the upper surface of the plate to the gas phase. The efficiency enhancement is linked to the weakening of the leading edge vortices. A second harmonic with significant amplitude is found in the upstream wave for Fr of 0.2 with a typical pitch-leading-heave phase angle.     

Design and development considerations for biologically inspired flapping-wing micro air vehicles

In this paper, the decade of numerical and experimental investigations leading to the development of the authors’ unique flapping-wing micro air vehicle is summarized. Early investigations included the study of boundary layer energization by means of a small flapping foil embedded in a flat-plate boundary layer, the reduction of the recirculatory flow region behind a backward-facing step by means of a small flapping foil, and the reduction or suppression of flow separation behind blunt or cusped airfoil trailing edges by flapping a small foil located in the wake flow region. These studies were followed by systematic investigations of the aerodynamic characteristics of single flapping airfoils and airfoil combinations. These unsteady flows were described using flow visualization, laser-Doppler velocimetry in addition to panel and Navier–Stokes computations. It is then shown how this flapping-wing database was used to conceive, design and develop a micro air vehicle which has a fixed wing for lift and two flapping wings for thrust generation. While animal flight is characterized by a coupled force generation, the present design appears to separate lift and thrust. However, in fact, the performance of one surface is closely coupled to the other surfaces.     

Hydrodynamic studies on two wiggling hydrofoils in an oblique arrangement

The propulsive performance of an oblique school of fish is numerically studied using an immersed boundary technique. The effect of the spacing and wiggling phase on the hydrodynamics of the system is investigated. The hydrodynamics of the system is deeply affected by the spacing between each fish in the school. When the horizontal separation is smaller than the length of the fish body, the downstream fish exhibits a larger thrust coefficient and greater propulsive efficiency than the isolated fish. However, the corresponding values for the upstream fish are smaller. The opposite behavior occurs when the horizontal separation increases beyond the length of fish body. The propulsive performance of the entire oblique school of fish can be substantially enhanced when the separations are optimized.     

Bifurcation and pull-in voltages of primary resonance of electrostatically actuated SWCNT cantilevers to include van der Waals effect

In this work the voltage response of primary resonance of electrostatically actuated single wall carbon nano tubes (SWCNT) cantilevers over a parallel ground plate is investigated. Three forces act on the SWCNT cantilever, namely electrostatic, van der Waals and damping. While the damping is linear, the electrostatic and van der Waals forces are nonlinear. Moreover, the electrostatic force is also parametric since it is given by AC voltage. Under these forces the dynamics of the SWCNT is nonlinear parametric. The van der Waals force is significant for values less than 50 nm of the gap between the SWCNT and the ground substrate. Reduced order model method (ROM) is used to investigate the system under soft excitation and weak nonlinearities. The voltage-amplitude response and influences of parameters are reported for primary resonance (AC near half natural frequency).