Underlying principle of efficient propulsion in flexible plunging foils

Passive flexibility was found to enhance propulsive efficiency in swimming animals.In this study,we numerically investigate the roles of structural resonance and hydrodynamic wake resonance in optimizing efficiency of a flexible plunging foil.The results indicates that（1）optimal efficiency is not necessarily achieved when the driving frequency matches the structural eigenfrequency;（2）optimal efficiency always occurs when the driving frequency matches the wake resonant frequency of the time averaged velocity profile.Thus,the underlying principle of efficient propulsion in flexible plunging foil is the hydrodynamic wake resonance,rather than the structural resonance.In addition,we also found that whether the efficiency can be optimized at the structural resonant point depends on the strength of the leading edge vortex relative to that of the trailing edge vortex.The result of this work provides new insights into the role of passive flexibility in flapping-based propulsion.     

A numerical study of the wake behind a blunt‐trailing‐edged body. Part 2: the topology of the flow

This project focuses on the wake behind a two‐dimensional blunt‐trailing‐edged body. The body has an elliptical nose followed by a straight section that ends in a blunt base. For this geometry, the boundary layer separation points are defined and fixed. This permits a better assessment of the vital influence of the boundary layers upon the wake. It is hoped that the study of this special geometry will contribute to a better understanding of the wake flow. The main aim of this article is to study the topology of the wake by means of direct numerical simulation (DNS). The idea is to mimic some experimental work techniques. In an experiment, by means of proper synchronization, one is able to arrive at the mean‐in‐the‐phase fields. In the present work, similar data are obtained through the use of numerical tools. The topology of the wake flow in terms of the movement of the coherent structures, fields of Reynolds stresses, position of saddles and centers, is obtained for certain values of the body's aspect ratio. A comparison with the circular cylinder experimental data is also provided. An important result is the finding of some specific stress distributions around the main structures. The stress level lines are a hint of where the energy transfer of the mean flow to the turbulence is more intense. Copyright © 2011 John Wiley & Sons, Ltd.     

Pressure waves in a tube filled with a bubbly mixture with a nonuniform cross-sectional bubble distribution

The evolution of pressure waves in a tube filled with a gas-liquid medium with a stepped cross-sectional bubble distribution is investigated. The calculations are compared with experimental data. It is shown that in the case of a nonuniform bubble distribution, due to the appearance of transverse flows, the pressure pulse is damped faster than for a uniform distribution. The interaction of pressure waves with a bubble cluster in a tube filled with liquid is also analyzed.     

Dynamic fluid flow behaviour of a tank draining through a vertical tube

This paper describes the unsteady draining of a sealed tank partially filled with water. The water discharges via a vertical tube into an open tank at atmospheric conditions. The air inflow, compensating for the volume of the discharged liquid, enters the system in an oscillatory manner, much like the “gulping” seen in an upended beer bottle. A mathematical model, based closly on that derived by Dougall & Kathiresan [Chem. Engng Commun. 8, 289–304 (1981)], has been applied to predict the pressure fluctuations in the closed tank. The rate of water discharge from the tank has been predicted and gives a much closer agreement with experimental results than a prediction based on a steady counter-current flooding limitation approach. A drift flux model has been used to describe the two-phase flow effect in the tube and the Wallis flooding criterion has been modified for use in the slug flow regime to describe the boundary conditions at the bottom of the tube. The pressure fluctuations in the sealed tank have been measured and compared with results obtained from the mathematical prediction for a variety of tube diameters.     

Hydrodynamics of natural oscillations of neutrally buoyant bodies in a layer of continuously stratified fluid

The flow patterns induced by floats of different shapes (sphere, short and long cylinders) freely sinking to the neutral-buoyancy horizon in a continuously stratified fluid are investigated using optical methods. General flow elements, both large-scale (waves, vortices, hydrodynamic wake) and fine-scale (boundary layers, extended autocumulative jets), are distinguished. For large times, the float oscillation frequencies are of the order of or greater than the buoyancy frequency of the medium. This indicates the significant effect of the induced flows on the motion of the float.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Wall pressure fluctuations of a turbulent separated and reattaching flow affected by an unsteady wake

The spatio-temporal characteristics of the wall-pressure fluctuations in separated and reattaching flows over a backward-facing step were investigated through pressure-velocity joint measurements carried out using multiple-arrayed microphones and split-film probes. A spoke-wheel-type wake generator was installed upstream of the backward-facing step. The flow structure at the effective forcing frequency (St _f=0.2) was found to be well organized in terms of wall pressure spectrum, cross-correlation, wavenumber-frequency spectrum, and wavelet auto-correlation. Introduction of the unsteady wake (St _f=0.2) reduced the reattachment length by 10%. In addition, the unsteady wake enhanced the turbulence intensity near the separation edge and, as a consequence, enhanced the quadrupole sound sources; however, the turbulence intensity near the reattachment region was weakened and the overall flow noise was attenuated. The greater organization of the flow structure induced by the unsteady wake led to a weakening of the dipole sound sources, which are the dominant sound sources in this system. The dipole sound sources generated by wall pressure fluctuations were calculated using Curles integral formula.Abbreviations AR Aspect ratio - SBF Spatial box filtering Roman symbols C _p Wall pressure fluctuation coefficient, p/0.5U ² - H Step height of backward-facing step (mm) - H _s Shape factor (H _s = ^*/) - R _s Distance from acoustic source point to observation point (m) - Re _H Reynolds number, U H/ - St The reduced frequency, fH/U - St _f Normalized forcing frequency by unsteady wake, f _p H/U - T Vortex shedding period (s) - U Free-stream velocity (m/s) - a Speed of sound (m/s) - f Frequency (Hz) - f _p Wake passing frequency (Hz) - k Turbulent kinetic energy (m²/s²) - k _x Streamwise wave number (1/m) - k _z Spanwise wave number (1/m) - l _j Cosine of angle - p Instantaneous wall pressure (Pa) - p _rms Root-mean-square of wall pressure (Pa) - p _SBF Spatial box filtered wall pressure (Pa) - p _d Dipole sound source (Pa) - p _w Conditionally-averaged wall pressure (Pa) - q Dynamic pressure, 0.5U ² (Pa) - r Distance from origin to observation point (mm) - u _c Convection velocity (m/s) - u_max Root-mean-square of streamwise velocity (m/s) - x _R Time-mean reattachment length (mm) Greek symbols _p Forward-flow time fraction - Auto-correlation of pressure at x ₀ - Two-dimensional cross-correlation of pressure with streamwise separation interval , spanwise separation interval , and time delay , at (x ₀, z ₀) - Boundary layer thickness (mm, _99%) - ^* Displacement thickness (mm, ) - _ij Kroneckers delta function - Phase angle (°) - Wavelength (mm) - Momentum thickness (mm, ) - Angle between vertical axis and observation point (°) - Density (kg/m³) - Time delay (s) - Streamwise separation interval (m) - Spanwise separation interval (m) - _p (f; x ₀) Autospectrum of pressure measured at x ₀ (Pa² s) - _pp (, ; x ₀) Streamwise cross spectrum of pressure at x ₀ (Pa² s) - _pp (, , ; x ₀, z ₀) Streamwise and spanwise cross spectrum of pressure at (x ₀, z ₀) (Pa² s) - _pp (kx, ; x ₀) Streamwise wavenumber-frequency spectrum of pressure at x ₀ (Pa² s) - _pp (kx, kz, ; x ₀, z ₀) Two-dimensional wavenumber-frequency spectrum of pressure at (x ₀, z ₀) (Pa² s)     

高超声速层流尾迹的数值模拟

本文利用无波动、无自由参数、耗散的差分格式(NND格式),通过求解NS方程,数值模拟了高超声速层流尾迹的流动,清晰地给出了主激波、拐角膨胀波、迹激波及自由剪切层,所得流场物理量的分布与实验结果甚为一致。计算发现了底部迴流区由起始向定常的发展中,在瞬时流线图上经历了极限环形成、胀大、缩小、再胀大最后消失的演变过程。     

The Motion of Long Bubbles in a Network of Tubes

The motion and interaction of discrete bubbles in porous materials is studied numerically using a network model. The goal is to extend analytical results for the motion of bubbles through a single straight tube to a more realistic geometry for porous materials, modeled here as a planar network of straight tubes of different radii. The problem is characterized by two dimensionless parameters, the capillary number (Ca) and the volume fraction of bubbles (); results are characterized by determining the effective permeability of the network and the mean residence time of bubbles in the material. The simulations indicate that at low volume fraction most of the bubbles follow a limited number of high-flow pathways through the network. In this case the predictions of our simulations can be approximated by a simple analytical model. Bubbles interact with each other because their presence changes the local resistance to flow in individual tubes. As increases, interactions between individual bubbles become important resulting in a wider range of residence times in the porous material.     

Adaptive Feedback Linearizing Control of Proper Orthogonal Decomposition Nonlinear Flow Models

This paper treats the question of feedback linearizing control oftwo-dimensional incompressible, unsteady wake flow. For definiteness,flow past a circular cylinder is considered, but the design approachpresented here is applicable to other flow control problems. Twofinite-dimensional lower-order models based on Proper OrthogonalDecomposition (POD) of dimension N with N actuators are considered.Models I and II are obtained using control function and penalty functionmethods, respectively. Control action can be achieved by a combinationof suction, injection, and synthetic jets. For the design ofcontrollers, it is assumed that the system matrices of the POD modelsare unknown. Nonlinear adaptive control systems for the two models arederived. For model I, nontrivial zero-error dynamics exists, which playa key role in the stability of the closed-loop system. But for model II,global adaptive trajectory control is achieved. In the closed-loopsystem, the mode amplitudes asymptotically follow the referencetrajectories. Simulation results for a 4-mode POD model obtained usingthe penalty function method are presented. These results show that inthe closed-loop system, unsteadiness in the mode amplitudes can besuppressed in spite of large uncertainties in the flow model.