Mechanisms of wake deflection angle change behind a heaving airfoil

An immersed-boundary numerical method is applied to simulate the wake downstream of a two-dimensional heaving airfoil. A switch of vortex pattern is found to be the major reason that a deflected asymmetric wake reverses its deflection angle. Parameters of the heaving airfoil and flow that influence the onset and location of the vortex switching are discussed. While the previous literature deliberately discussed the wake deflection in the near wake region, this study shows that the deflection angle can change from the near wake to far wake regions. A cross-flow effective phase velocity is introduced to analyze the already-formed asymmetric wake behind the airfoil. A vortex dipole model and the related vortex dynamics analysis are developed to show that the change of the distance between the vortices is the primary factor that leads to the vortex pattern switching in the far wake.     

Meander of a fin trailing vortex and the origin of its turbulence

The low-frequency meander of a trailing vortex shed from a tapered fin installed on a wind tunnel wall has been studied using stereoscopic particle image velocimetry in the near-wake at Mach 0.8. Distributions of the instantaneous vortex position reveal that the meander amplitude increases with downstream distance and decreases with vortex strength, indicating meander is induced external to the vortex. Trends with downstream distance suggest meander begins on the fin surface, prior to vortex shedding. Mean vortex properties are unaltered when considered in the meandering reference frame, apparently because turbulent fluctuations in the vortex shape and strength dominate positional variations. Conversely, a large peak of artificial turbulent kinetic energy is found centered in the vortex core, which almost entirely disappears when corrected for meander, though some turbulence remains near the core radius. Turbulence originating at the wind tunnel wall was shown to contribute to vortex meander by energizing the incoming boundary layer using low-profile vortex generators and observing a substantial increase in the meander amplitude, while greater turbulent kinetic energy penetrates the vortex core. An explanatory mechanism has been hypothesized, in which the vortex initially forms at the apex of the swept leading edge of the fin where it is exposed to turbulent fluctuations within the wind tunnel wall boundary layer, introducing an instability into the incipient vortex core.     

Wake structures behind an oscillating bubble rising close to a vertical wall

In the present study, the wake structures behind an oscillating (zigzagging in a plane) air bubble, rising in a close vicinity of a vertical wall are experimentally investigated using a high-speed two-phase particle image velocimetry. While varying the distance between the rising bubble and the wall, the spatial and temporal variations in the spanwise and streamwise vorticity components contained in the wake vortices, in addition to the bubble trajectory, are measured in a tank filled with water. In particular, the Lagrangian streamwise vorticity fields in the bubble wake have been reconstructed and investigated in detail with different conditions. Without the wall, it is confirmed that there exist counter-rotating streamwise vortex tubes in the bubble wake, agreeing with the case of a two-dimensional zigzagging bubble, as reported in the literatures. It is also found that the hairpin vortex chain structures, initially attached to the bubble rear, evolve to detached vortex ring structures as the bubble rises in an oscillating path. While the detailed vortex structures show up quite differently from the reference case depending on the distance to the wall (e.g., actual bubble-wall collision), in general the wake behind the bubble as it moves toward and away from the wall can be summarized as: (i) transition to the detached vortex ring structures is accelerated; (ii) streamwise length of vortex tubes is shortened (evolution is interfered); (iii) counter-rotating vortex tubes approaching the wall tend to slightly bounce off and slide away (being dissipated fast) from each other on the wall; and (iv) boundary-layer like secondary flow structures are induced on the wall due to additional viscous effects. These wall-induced wake modification indicates that more fluid energy is wasted due to the wall interference, rather than being used to force the lateral movement of the bubble, which agrees with the reduced amplitude and wavelength of the oscillating bubble path on the wall. Finally, this explanation has been further confirmed by estimating the vortex-induced lateral forces acting on the bubble for each case.     

LARGE-SCALE VORTICAL STRUCTURES PRODUCED BY AN IMPINGING DENSITY JET IN SHALLOW CROSSFLOW

The large-scale vortical structures produced by an impinging density jet in shallow crossflow were numerically investigated in detail using RNG turbulence model. The scales, formation mechanism and evolution feature of the upstream wall vortex in relation to stagnation point and the Scarf vortex in near field were analyzed. The computed characteristic scales of the upstream vortex show distinguished three-dimensionality and vary with the velocity ratio and the water depth. The Scarf vortex in the near field plays an important role in the lateral concentration distributions of the impinging jet in crossflow. When the velocity ratio is relatively small, there exists a distinct lateral high concentration aggregation zone at the lateral edge between the bottom layer wall jet and the ambient crossflow, which is dominated by the Scarf vortex in the near field.     

Two-dimensional unsteady flow around a waving plate in wall effects

A new method of nonlinear formulation is presented to analyze the two-dimensional incompressible flow around a flexible plate waving near a rigid wall. A system of differential and integral equations is solved for the velocity field and the wake vortex. A nonlinear unsteady Kutta condition is imposed at the trailing edge in order to treat the case of large amplitude and fast oscillation accurately. The shed vortex sheet is discretized and approximated by a large number of vortex filaments, and their movements are visualized by numerical computation. The lift, thrust, power input and hydrodynamic efficiency are computed for various values of the distance of the waving plate from the wall.     

Numerical simulation of tangentially injected turbulent swirling flow in a divergent tube

This paper studies the properties of turbulent swirling decaying flow induced by tangential inlets in a divergent pipe using the realizable k–ε turbulence model and discusses the effects of the injector pressure and injection position. The results of transient solutions show that both the recirculation zone near the wall in upstream of the injectors and the vortex breakdown in downstream of the injectors increase in size during the whole period. A nearly axisymmetric conical breakdown is formed and its internal structure consists of two asymmetric spiral‐like vortices rotating in opposite directions. The stagnation point shifts slowly toward the pipe outlet over time. The maxima of the three velocity components, which are located near the wall, decrease gradually with streamwise direction. It can also be inferred that Mach number approaches 1.0 near the injector outlets. The velocities increase with the increasing injector pressure. However, its increasing trend is not significant. With the increase of the injection position, vortex breakdown moves in downstream direction and the pitch along the streamwise direction increases. Copyright © 2008 John Wiley & Sons, Ltd.     

Dispersive bending waves in uniform bars

The traveling bending waves in a long beam of rectangular cross section were measured and calculated. The bending waves were induced by impacting with a steel sphere and measured with strain gages at several distances from the point of impact. The impact force was calculated as a function of time by integrating the dynamic equations of the sphere and the beam. The force spectrum was then found using a fast-Fourier-transform (FFT) calculation and multiplied by the moment-frequency response of the beam to determine the moment spectrum. The moment-time function was calculated by an inverse FFT. The traveling wave is dispersive; its spectrum was found from that at the point of impact by phase shifting each component by an angle proportional to the distance and to the square root of the frequency. Again the time curve was determined by an inverse FFT. The indentation stiffness of the beam was found to be very much less than that of the elastic half space because of transverse bending. After the impact force was recalculated with this correction, the calculated moment-time traces agreed very well with the measured ones.     

Numerical simulation of the accumulation of heavy particles in a circular bounded vortex flow

In present work, an Eulerian–Lagrangian CFD model based on the discrete element method (DEM) and immersed boundary method (IBM) has been developed, validated and used to investigate the accumulation of heavy particles in a circular bounded viscous vortex flow. The inter-particle and particle-wall collisions are resolved by a hard-sphere model. Effects of one-way and two-way coupling, Reynolds number, and particle diameter are systematically explored. Results show that, in case of one-way coupling, the majority of particles will spiral into an accumulation point located near the stagnation point of the flow field. The accumulation point represents a stable equilibrium point as the drag created by the flow field balances the destabilizing centrifugal force on the particle. However, in case of two-way coupling, there does not exist a stable accumulation point due to the strong interaction between the particles and fluid dynamics. Instead most particles are expelled from the circular domain and accumulate on the confining wall. The percentage of accumulated particles on the wall increases with increasing Reynolds number and particle diameter. Moreover, influence of three well-known drag models is also studied and they give consistent results on the particle accumulation behavior, although small quantitative differences can still be discerned.     

Acoustic waves emitted by a vortex ring passing near a wedge-like plate

Acoustic waves emitted by a vortex ring moving near a thin wedge-like plate of finite width have been studied. The experiments are performed for three configurations: the plate (A) is held edgeways to the direction of the vortex motion, (B) is held sideways to the direction, and (C) is held edgeways at an angle of 45° against the vortex motion. The observed sound wave is of dipole radiation type, and the magnitude of the pressure is large in the direction of the normal to the plate plane and small in parallel. The observed pressure is proportional to the third power of the vortex speed. The instantaneous force exerted on the plate by the vortex motion has also been examined. The force vector is mainly normal to the plate plane. The observed profiles agree within a reasonable degree of accuracy with the theoretical ones calculated for the vortex ring interacting with the flat plate of thickness zero.     

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

等离子体激励器控制圆柱绕流的实验研究

为了发展新型移动附面层控制技术,提升流动控制效率,采用粒子图像测速技术,开展了基于对称布局等离子体气动激励的圆柱绕流控制研究,获得了静止空气下,对称布局激励器诱导流场的演化过程,评估了来流条件下等离子体控制效果,通过等离子体诱导涡实现了虚拟移动附面层控制,分析了诱导涡随时间演化的过程,揭示了圆柱绕流等离子体控制机理.结果表明:(1)在静止空气下,对称布局激励器在刚启动瞬间,会在暴露电极两侧诱导产生一对旋转方向相反的启动涡;随着时间的推移,启动涡逐渐向远离壁面的方向运动;随后,激励器在暴露电极两侧产生了两股速度近似相等,方向相反的诱导射流,诱导射流在柯恩达效应的影响下,朝壁面方向发展.(2)当激励电压峰峰值为19.6 kV,激励频率3kHz时,施加等离子体气动激励后,圆柱脱落涡得到了较好抑制,圆柱阻力系数减小了21.8％;(3)在来流作用下,对称布局激励器在靠近来流一侧,诱导产生了较为稳定的涡结构.诱导涡通过旋转、运动,促进了壁面附近低能气流与主流之间的掺混,抑制了圆柱绕流流场分离,实现了"虚拟移动附面层控制"效果.与传统移动附面层控制技术相比,基于等离子体气动激励的新型移动附面层控制技术不需要复杂、笨重的机构,不会带来额外的阻力,具有潜在的应用前景.      

On the interplay between inertial and viscoelastic effects for the flow in weakly modulated channels

The flow inside a spatially modulated channel is examined for viscoelastic fluids of the Oldroyd‐B type. The lower wall is flat and the upper wall is sinusoidally modulated. The modulation amplitude is assumed to be small. Thus, a regular perturbation expansion of the flow field coupled to a variable‐step finite‐difference scheme is used to solve the problem. Convergence and accuracy assessment against earlier experimental results indicate that there is a significant range of validity of the perturbation approach. The influences of wall geometry, inertia and viscoelasticity on the flow kinematics and stresses are investigated systematically. In particular, the interplay between the flow and fluid parameters effects on the conditions for the onset of backflow, number of vortices, their size and location is revealed. The distance between the flow separation and reattachment locations identifies the vortex size. Non‐monotonic dependence of the vortex size on elasticity is reported. The critical conditions for the onset of negative elasticity effects on vortex size are identified. The critical Reynolds number for the onset of backflow initially decreases then levels off or even increases as elasticity increases. For highly elastic fluid and large enough Reynolds number, more than one vortex appear near the lower wall. Copyright © 2005 John Wiley & Sons, Ltd.     

Wind-Up of a Spanwise Vortex in Deepening Transition and Stall

A fundamental flow problem of unsteady wind-up of a spanwise vortex is studied in this theoretical work on deepening dynamic stall and transition in a boundary layer, internal layer or related unsteady motion. It examines the nonlinear evolution of the spanwise vortex produced when the local wall pressure develops a maximum or minimum, subsequent to the finite-time break-up of an interacting layer and the impact of normal pressure gradients. The evolution is controlled by an inner–outer interaction between the effects of the normal pressure gradient and the momentum jumps across and outside the vortex, which is situated near the strong inflexion point induced in the mean flow. Although the work concentrates on a particular internal-flow context, many of the flow properties found are generic and in particular apply for a more general case including external flows. Analysis and associated computations point to two main distinct trends in the vortex response, depending to a large extent on a parameter gauging the relative strengths of the above effects. The response is either an explosive one, provoking enhanced wind-up, growth and pressure in the vortex, or it is implosive, causing the vortex to shrink and virtually empty itself through unwinding, leaving little local pressure variation. A further discussion includes the after-effects of this vortex response and some of the connections with experiments and direct computations on deepening stall and transition. Received 22 February 1999 and accepted 28 March 2000     

一种模拟动边界绕流的锐利界面浸入边界法

When the structural wall moves over a fixed grid, the structure coverage will change, resulting in many dead and emerging elements. To avoid the influence of malformation and reconstruction of body-fitted grids on the calculation efficiency and accuracy of the fluid-structure interaction problems with coupled boundary movement on the fixed grid, an improved numerical method for describing the interaction between an immersed rigid body and fluid based on a sharp-interface is proposed. In this method, both the fluid and solid are regarded as pure fluid domains in the whole computational domain, and the solid boundary is divided into several Lagrangian grid points. The flow parameter or velocity is reconstructed by interpolation at the interface element, which is then directly used as the boundary condition of the flow field, thus reflecting the influence of the wall boundary conditions. The method constructs the calculation structure of “virtual point, force point and vertical foot point”, and the velocity of the virtual point is obtained by bilinear interpolation. Then, the velocity of the force point is calculated by forcing the solid boundary to meet the no-slip condition, and the equations of the coupling system based on the immersion boundary method are finally solved to realize the numerical simulation of the flow with a complex moving boundary. The numerical program for this immersed boundary method is established using C++, then the accuracy and reliability of the proposed method are validated by comparison with the literature and experimental results of the basic numerical example of flow around a cylinder. Furthermore, the effects of the structural shape and the angle of attack on the trailing vortex structure, the vortex shedding frequency, and the lift/ coefficient characteristics of the flow around the elliptical cylinder have been analyzed. The anti-symmetric S-type, “P+S” Ⅰ-type and “P+S” Ⅱ-type trailing vortex shedding modes, as well as the variation laws of the vortex structure size, vortex shedding frequency and lift-drag coefficients ratio with axis ratio and angle of attack, are captured. The critical angle of attack (25°) corresponding to the maximum lift-drag ratio is determined as 25°.     

On a method of comparison for plate elements in finite element engineering software programs

The purpose of this paper is to propose a method for the evaluation of plate elements in the finite element engineering software comparatively to the Kirchhoff and Reissner plate theories. The method is based on the study of transverse deflection near a crack tip. A numerical work has been conducted for the shell elements in Abaqus software with different crack lengths and various thicknesses. The deflection can be written as a function of the exponent of the distance between the crack tip and one point along the crack. This exponent is accepted to describe the behaviour of finite elements.     

Microscope activation near the wall during explosive boiling

The inception process of nucleation in explosive boiling systems is theoretically investigated. With the effect of pulse heating or sudden cooling, the temperature distribution near the surface during explosive boiling is calculated. The liquid near the wall can maintain a stable layer induced by strong attractive force, and there exists maximum supersaturation beyond this stable layer. As the surface temperature and temperature gradient are high enough, the critical distance of maximum supersaturation can be larger than the radius of critical bubble, and the homogeneous nucleation will dominate the inception boiling process. For explosive boiling induced by pulse heating, homogeneous nucleation forms after a short time; while homogeneous nucleation can dominate the initial explosive boiling induced by sudden cooling.     

Effect of surface roughness on a turbulent wall-attaching offset jet

The flow characteristics of a two-dimensional offset jet discharged parallel to a rough wall is experimentally investigated by using a split film probe. The distributions of the mean velocity and turbulent stresses in the flow field are obtained and compared with those of the wall attaching offset jet on a smooth wall. It is found that the wall-attaching region on the rough wall is longer than on the smooth wall for the same offset height and the jet speed. The normal distance of the maximum velocity point is farther away from the wall than that for the smooth wall case because of the thick wall boundary layer established by the surface roughness. It is also found that the roughness of the wall accelerates the relaxation process towards redeveloped plane wall jet and that it exhibits a quite different turbulent diffusion behavior especially near the wall from that in the wall jet over a smooth surface.     

Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet

The wall shear stress and the vortex dynamics in a circular impinging jet are investigated experimentally for Re = 1,260 and 2,450. The wall shear stress is obtained at different radial locations from the stagnation point using the polarographic method. The velocity field is given from the time resolved particle image velocimetry (TR‐PIV) technique in both the free jet region and near the wall in the impinging region. The distribution of the momentum thickness is also inspected from the jet exit toward the impinged wall. It is found that the wall shear stress is correlated with the large-scale vortex passing. Both the primary vortices and the secondary structures strongly affect the variation of the wall shear stress. The maximum mean wall shear stress is obtained just upstream from the secondary vortex generation where the primary structures impinge the wall. Spectral analysis and cross-correlations between the wall shear stress fluctuations show that the vortex passing influences the wall shear stress at different locations simultaneously. Analysis of cross-correlations between temporal fluctuations of the wall shear stress and the transverse vorticity brings out the role of different vortical structures on the wall shear stress distribution for the two Reynolds numbers.     

Vortex shedding from a square cylinder in presence of a moving wall

A numerical study on the flow past a square cylinder placed parallel to a wall, which is moving at the speed of the far field has been made. Flow has been investigated in the laminar Reynolds number (based on the cylinder length) range. We have studied the flow field for different values of the cylinder to wall separation length. The governing unsteady Navier–Stokes equations are discretized through the finite volume method on a staggered grid system. A SIMPLE type of algorithm has been used to compute the discretized equations iteratively. A shear layer of negative vortex generates along the surface of the wall, which influences the vortex shedding behind the cylinder. The flow‐field is distinct from the flow in presence of a stationary wall. An alternate vortex shedding occurs for all values of gap height in the unsteady regime of the flow. The strong positive vortex pushes the negative vortex upwards in the wake. The gap flow in the undersurface of the cylinder is strong and the velocity profile overshoots. The cylinder experiences a downward force for certain values of the Reynolds number and gap height. The drag and lift are higher at lower values of the Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd.     

Three-dimensional instability analysis of boundary layers perturbed by streamwise vortices

A parametric study is presented for the incompressible, zero-pressure-gradient flat-plate boundary layer perturbed by streamwise vortices. The vortices are placed near the leading edge and model the vortices induced by miniature vortex generators (MVGs), which consist in a spanwise-periodic array of small winglet pairs. The introduction of MVGs has been experimentally proved to be a successful passive flow control strategy for delaying laminar-turbulent transition caused by Tollmien–Schlichting (TS) waves. The counter-rotating vortex pairs induce non-modal, transient growth that leads to a streaky boundary layer flow. The initial intensity of the vortices and their wall-normal distances to the plate wall are varied with the aim of finding the most effective location for streak generation and the effect on the instability characteristics of the perturbed flow. The study includes the solution of the three-dimensional, stationary, streaky boundary layer flows by using the boundary region equations, and the three-dimensional instability analysis of the resulting basic flows by using the plane-marching parabolized stability equations. Depending on the initial circulation and positioning of the vortices, planar TS waves are stabilized by the presence of the streaks, resulting in a reduction in the region of instability and shrink of the neutral stability curve. For a fixed maximum streak amplitude below the threshold for secondary instability (SI), the most effective wall-normal distance for the formation of the streaks is found to also offer the most stabilization of TS waves. By setting a maximum streak amplitude above the threshold for SI, sinuous shear layer modes become unstable, as well as another instability mode that is amplified in a narrow region near the vortex inlet position.