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.     

Laser-sheet flow visualization of the confined wake behind a ring

The flow over a ring model situated axisymmetrically in a circular pipe has been studied by the laser-sheet flow visualization technique. Over 25 rings of different sizes are investigated. The flow characteristics are observed and summarized into six regimes, in terms of the two geometrical parameters G/W and . Here, W is the width of the ring, is the mean diameter of the ring, and G is the gap width between the pipe wall and the outer edge of the ring. It is interesting to point out that vortex-shedding structures produced by a ring model can persist over a considerable distance downstream in three of the six regimes which correspond to different physical processes of shedding.     

The interaction of a bluff body with a vortex wake

A theoretical, experimental and numerical study is presented of the interaction of a vortex–wake created by an upstream blade with a downstream prismatic block. The aim of the study is to investigate the fundamentals of force and noise generation for this type of flow and explain how inter-object spacing affects the far-field noise level. A theoretical model, based on a compact form of Curle's formulation, is developed and shows that acoustically constructive or destructive interference is determined by the amplitude and phase of the forces on each object. Experimental and two-dimensional, unsteady numerical results of the vortex–wake interaction case are presented for several blade–block separation distances. Using a combination of experimental and numerical data, the theoretical model is able to explain observed variations in far-field noise level with blade–block separation distance. The numerical model accurately predicts the phase relationship between the unsteady forces on each object.     

Process of formation of a vortex street in the wake behind a flat plate

The process of the formation of a vortex street in the wake behind a flat plate set parallel to a uniform flow was investigated in a low speed wind tunnel. The vorticity distributions in the wake were calculated from the measured velocities using Taylor's hypothesis.

Just behind the plate, the equi-vorticity lines were nearly parallel to the free stream. At locations somewhat downstream, sinusoidal contour lines appeared near the wake center. Further downstream, some closed contour lines appeared in the figures mapped. The arrangement of the closed lines suggests the existence of a vortex street. The maximum value for vorticity in a wave length of the fundamental velocity fluctuation decreased in the downstream direction; the concentration of vorticity, however, increased in a region the further downstream it was. Meanwhile, the value for circulation obtained by the surface integral of vorticity within the closed contours of a vortex increased until the vortex street was established.     

Plunging wake analysis of an airfoil equipped with a Gurney flap

Experimental Techniques - Experimental measurements were conducted on a plunging Eppler 361 Gurney flapped airfoil to study wake structure and dynamic stall phenomenon in the wake. The heights of...     

Aerodynamic loading on a cylinder behind an airfoil

The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Re_d=2,100–20,000, and the airfoil chord-length-based Reynolds numbers of Re_c=14,700–140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as T increases. For Re_c<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Re_c>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding.     

Translationally nonequilibrium free jet boundary layer in the wake behind a wedge

Macroscopic equations obtained as a thin-layer version of the 13-moment Grad equations derived from kinetic considerations are used for describing the translationally nonequilibrium monatomic gas flow in a hypersonic free jet boundary layer formed in the wake behind a wedge. This model makes it possible to investigate flows with strong violations of equilibrium with respect to the translational degrees of freedom. A method of constructing the solution of this kinetically justified problem based on the solution of an analogous problem in the Navier-Stokes interpretation is proposed. It is established that for the kinetic variant of the problem considered the gas flow velocity distribution along the separating streamline in a plane orthogonal to the wedge generator coincides with the distribution obtained in solving the Navier-Stokes variant. It is found that taking into account the nonequilibrium nature of the flow with respect to the translational degrees of freedom of the gas particles has no effect on the base pressure and the wake angle.     

The nonlinear interaction of vortex rings with a free surface

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like ‘cavity’ is formed on the free surface and the vortex is trapped in the ‘cavity’ for quite a long time, resulting in a large amount of fluid above the mean fluid surface. The project supported by the National Education Commission of China and NASA under cooperative grant agreement # NCC5-34     

一种风力机气动计算的全自由涡尾迹模型

采用全自由方式建立风力机尾流场的涡尾迹模型,引入“虚拟周期”的概念,并发展一种自适应松弛因子方法,从而改善了自由尾迹迭代的稳定性,提高了迭代收敛速度。利用建立的自由涡尾迹模型,计算了风力机叶片的尾流场结构、气动性能及叶片载荷,并与实验结果进行了对比分析。结果表明,尖速比越大,自适应松弛因子方法对缩小模型计算时间越有效;全自由涡尾迹模型能准确给出风力机尾流场的结构,包括尾迹的扩张以及叶尖涡和叶根涡的产生、发展和耗散的过程,风轮扭矩与实验数据吻合;叶片载荷分布的计算结果在低风速下与实验值基本一致,但是在大风速下差别较大,说明需要一个准确的失速模型。     

Experimental study of boundary-layer transition on an airfoil induced by periodically passing wake

 Hot-wire measurements are performed in boundary-layer flows developing on a NACA 0012 airfoil over which wakes pass periodically. The periodic wakes are generated by rotating circular cylinders clockwise or counterclockwise around the airfoil. The time- and phase-averaged mean streamwise velocities and turbulence fluctuations are measured to investigate the phenomena of wake-induced transition. Especially, the phase-averaged wall shear stresses are evaluated using a computational Preston tube method. The passing wakes significantly change the pressure distribution on the airfoil, which has influence on the transition process of the boundary layer. The orientation of the passing wake alters the pressure distribution in a different manner. Due to the passing wake, the turbulent patches are generated inside the laminar boundary layer on the airfoil, and the boundary layer becomes temporarily transitional. The patches propagate downstream at a speed smaller than the free-stream velocity and merge together further downstream. Relatively high values of phase-averaged turbulence fluctuations in the outer part of the boundary layer indicate the possibility that breakdown occurs in the outer layer away from the wall. It is confirmed that the phase-averaged mean velocity profile has two dips in the outer region of the transitional boundary layer for each passing cycle. Received: 12 February 2001 / Accepted: 6 July 2001 Published online: 23 November 2001     

A study of the dimensions of the wake behind a cone travelling at hypersonic speed

In a series of papers (see, for example, [1–5]) numerous results have appeared detailing experimentally determined dimensions of wakes behind spheres or spherically blunted cylinders travelling with hypersonic speed in air. During this same period substantially less attention has been paid to the study of the parameters of the wake behind a cone, in particular, a cone at an angle of attack. In the present paper we present the results of measuring the mean width of the wake, and the mean-square deviation of the wake boundary, for a spherically blunted cone of 10 half-angle with nose radius 6% of the base diameter, travelling in air at Mach number M=12 and Reynolds number Re=0.3·10⁶, and with an angle of attack varying from 12 to 24.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–163, November–December, 1976.The author expresses his thanks to N. N. Baulin for his help In the experimental work.     

Formation of a vortex street behind an oscillating cylinder

The paper presents the results of an experimental study of the vortex street behind a circular cylinder oscillating across a water stream at Reynolds numbers less than the critical value at which a vortex street is formed behind a stationary cylinder. The asymptotic dependence of the nondimensional vortex separation frequency (the Strouhal number) on the main relevant parameters is obtained. The value of a constant coefficient appearing in this relationship has been found experimentally.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 51–56, January–February, 1995.     

Nonlinear interaction of a vortex pair with clean and surfactant-covered free surfaces

Two-dimensional unsteady viscous-flow problem associated with the normal incidence of a counter-rotating vortex pair on a free surface is analyzed. Effects of surface tension and insoluble surfactants on the generation of free-surface vorticity and surface waves are investigated. A recently developed finite-difference method based on boundary-fitted coordinates is used to solve the fully-nonlinear problem. Results show that in the absence of surfactants and at low Froude number (based on circulation strength and initial separation distance of the vortex pair), waves of short lengths are generated. However, secondary vorticity generated in this case is not strong enough to affect the outward translation of the primary vortices. At intermediate Froude number, a transient wave developing outboard of the primary vortex becomes steep, and eventually breaks because of local instability. Consequently, free-surface vorticity inhibits the outward translation of the primary vortices. Surface tension in a clean free surface dampens the steep short waves, hence also the generation of free-surface vorticity. However, variation in surface tension induced by surfactants intensifies the generation of surface vorticity, thereby causing the primary vortices to rebound. The increase in the rotational part of wave motion results in the dampening of overall free-surface deformations. However, it is found that the shear stress associated with a large gradient of surfactant concentration could cause local steepening of the short wave generated outboard of the primary vortex.     

Experimental study on the wake behind tapered circular cylinders

The flow around tapered cylinders can act as basic models for numerous bluff body flows with a spanwise variation of either the body shape or the inflow conditions. The well-known vortex street is influenced by strong three-dimensional effects from the spanwise variation of the shedding frequency, namely oblique vortex shedding and vortex dislocations. Stereo-PIV was chosen to study these phenomena, since it allows analyzing planes with the full three-component, instantaneous velocity fields and local, time-dependent variations in the same setting. Hence, detailed aspects of the vortex dislocation phenomenon are presented. Single vortex dislocation events are presented through the local variation of the three measured velocity components u, v and w. Longer time-series reveal both period and location of these dislocation events, as well as quantity and sizes of the cells of constant shedding velocity in between them. The influence of the Reynolds number and the cylinder aspect ratio on the vortex cells could be shown. The analysis of the vortex shedding behavior shows good agreement with previously published results. At the same time, the applied PIV technique provides more spatial information than point-based measurements and offers insight into a Reynolds number range that is currently out of reach of Direct Numerical Simulations.     

An experimental study on a wake behind a torus using the UVP monitor

 The flow around a torus has a complicated three-dimensional structure. Measuring the spatiotemporal field of velocity by means of conventional methods such as hot-wire anemometers and other one-point measuring instruments is thus difficult. Research is made on the spatiotemporal structure of the wake behind the torus by using a flow-visualizing technique and an ultrasonic velocity profile (UVP) monitor, in which two kinds of tori with different diameter ratios or solidity are set in a uniform flow with zero inclination and oblique postures. For the torus with zero inclination, there are two modes of flow structure according to the diameter ratio; at lower ratio, a disk mode is dominant, and at higher ratio, a ring wake mode appears. For the torus set with an oblique posture, the structure of the wake changes with respect to the oblique angle in a complicated fashion. The power spectra of the fluctuating velocities reveal an aspect of the character of this structural change. The Strouhal numbers estimated from the power spectra suggest that the flow patterns can be classified into four categories with respect to the oblique angle. Received: 15 May 1997/Accepted: 10 September 1998     

Design of airfoil with flap simulated by a point vortex

The method of quasisolutions of inverse boundary-value problems (see [4]) is used to solve the problem of designing an airfoil with a flap, replaced by a fixed vortex, from given velocity distribution along the contour of the wing main part. Profiles are constructed and the effect of the flap (vortex) on the shape and aerodynamic properties of the mechanized wing is examined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1992.     

Coherent structure in the turbulent wake behind a circular cylinder 2. numerical simulation using the vortex filament model

In the previous paper the authors reported observing the formation of a spoon-shaped vortex chain in a wake behind a circular cylinder as a coherent structure in turbulence. In this report numerical simulation is carried out based on the assumption that the structure is formed by deformation of the Kánnán vortices. The basic equation is the localized induction equation for a single vortex filament with an influence of the background mean flow. The vortex filament is given an initial deformation within a plane at an angle θ to the x−z plane (x is the mean flow direct and z the spanwise direction) with the width Z_w, and the further deformation process of the filament is numerically traced. The first calculation is made with fixed Z_w and various values of θ. The result shows that the vortex filament finally reaches a structure lying on a plane with a constant angle of 30° ~ 45° to the x-z plane irrespective of the initial values of θ. The second calculation is made with fixed θ and various values of Z_w. In this case the final spanwise scale of the deformed region of the filament has almost constant values of about 4d−6d (d is diameter of the cylinder). These results indicate that the final structure of the vortex filament is stable and definite irrespective of the initial disturbances.