Identification of vortex motions in turbulent mixing of choked jets

A specially adapted schlieren system is used to generate fluctuating signals which respond strongly to large scale coherent components of a turbulent mixing jet flow and which have a relatively reduced response to random disturbances. The schlieren signals also provide a direct indication of the presence of vortex-like structures in the turbulent mixing layers by virtue of the phase relationship of the schlieren signals to the pressure field. This system gives a clear resolution of the fluctuating periodic effects associated with vortex structures in the flow from a choked convergent nozzle. It has thus been possible to determine that vortex-like eddies are associated with the feedback screech mechanism, and also generate periodic disturbances due to their passage through the diamond shaped wave structure in the flow. The regular disturbances in the flow move at 0.77 of the fully expanded flow velocity. Phase spectral observations demonstrate clearly the vortex like structure of coherent disturbances in the flow by virtue of the quadrature phase relation between the schlieren and microphone signals. Movement of the sensing microphone in the pressure field external to the flow shows disturbance propagation at the acoustic velocity, and also shows that disturbances at Strouhal numbers above 0.7 emanating from the inner mixing zone can be identified by an additional time delay to reach the microphone and only influence the microphone when it is located downstream of the flow sensing schlieren system due to confinement of pressure disturbances within Mach cones of the flow.     

Fine structure of a stratified flow near a flat-plate surface

The pattern of disturbances arising during the motion of a strip along a horizontal surface in a continuously stratified fluid with identified upstream and attached internal waves, boundary layers, and edge singularities is calculated in the liner approximation. The flow pattern behind a flat plate moving with a constant velocity in a continuously stratified fluid is studied with the use of the optical schlieren technique; transformation of waves and finely structured elements of the flow with increasing plate velocity is analyzed. The calculated and experimentally observed patterns of internal waves at low velocities are demonstrated to be in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 77–91, November–December, 2007.     

Vortex dynamics and scalar transport in the wake of a flat-plate controlled by a vibrating trailing-edge flap

We investigate the onset and development of vortical flow disturbances introduced into the wake of a horizontally fixed flat-plate by means of the controlled motion of a trailing edge flap. The vibrating mechanics of the flap allows for the introduction of both impulsive and harmonic weak amplitude velocity disturbances which are propagated downstream into the wake flow of the flat-plate. Quantitative experimental and numerical predictions of both steady and unsteady wake flow velocity resulting from different flapping frequencies are made at low Reynolds numbers (Re < 10⁴). Frequency response tests of the wake confirmed the existence of two dominant frequencies where the wake flow organises with a particular arrangement of downstream moving vortex structures. Numerical predictions of steady (unforced) and forced wake velocity profiles and kinetic energy profiles are in good agreement with the experimental results. In order to understand practical implications of the dominant vortex structures in scalar transport, we have extended the numerical part of the study solving for the concentration equation of a passive scalar being injected in particular regions of the physical domain. A spatial correlation between the trajectory of vortex structures and the scalar concentration downstream the wake is observed. Moreover, the onset of tip vortex structures produced during the forcing cycle seems to be responsible of a local increase of scalar concentration near the span wise flap ends.     

Internal wave generation by a fountain in a stratified fluid

The purpose of the study is the direct numerical and theoretical modeling of fountain dynamics in a fluid with density stratification in the form of a pycnocline. The fountain is formed as a vertical jet penetrates through the pycnocline. In numerical simulation the jet flow is initiated by means of preassigning a boundary condition in the form of an upward-directed laminar flow of a neutral-buoyancy fluid with an axisymmetric Gaussian velocity profile. The calculations show that at a Froude number Fr greater than a certain critical value the flow becomes unstable and the fountain executes self-oscillations accompanied by internal wave generation in the pycnocline. Depending on Fr, two self-oscillation modes can be distinguished. At fairly low Fr the fountain executes circular motion in the horizontal plane, in the vicinity of the center of jet, its shape remaining almost invariant. In this case, internal waves in the form of unwinding spirals are radiated. At fairly high Fr another mode predominates, when the fountain top chaotically “strays” in the vicinity of the center of the jet and, periodically breaking down, generates wave packets propagating toward the periphery of the computation domain. In both cases, the main peak in the frequency spectrum of the internal waves coincides with the fountain top oscillation frequency which monotonically decreases with increase in Fr. In numerical simulation the Fr-dependence of the fountain top oscillation amplitude is in good agreement with that predicted by the theoretical model of the concurrence of the interacting modes in the soft self-excitation regime.     

Implementation and validation of a slender vortex filament code: Its application to the study of a four‐vortex wake model

A computational code EZ‐vortex is developed for the motion of slender vortex filaments of closed or open shape. The integro‐differential equations governing the motion of the vortex centre lines are either the Callegari and Ting equations, which are the leading order solution of a matched asymptotic analysis, or equivalent forms of these equations. They include large axial velocity and nonsimilar profiles in the vortical cores. The fluid may be viscous or inviscid. This code is validated both against known solutions of these equations and results from linear stability analyses. The linear and non‐linear stages of a perturbed two‐vortex wake and of a four‐vortex wake model are then computed. Copyright © 2004 John Wiley & Sons, Ltd.     

The effect of air-water interface on the vortex shedding from a vertical circular cylinder

The flow past an interface piercing circular cylinder at the Reynolds number Re=2.7×10⁴ and the Froude numbers Fr=0.2 and 0.8 is investigated using large-eddy simulation. A Lagrangian dynamic subgrid-scale model and a level set based sharp interface method are used for the spatially filtered turbulence closure and the air-water interface treatment, respectively. The mean interface elevation and the rms of interface fluctuations from the simulation are in excellent agreement with the available experimental data. The organized periodic vortex shedding observed in the deep flow is attenuated and replaced by small-scale vortices at the interface. The streamwise vorticity and the outward transverse velocity generated near the edge of the separated region, which enforces the separated shear layers to deviate from each other and restrains their interaction, are primarily responsible for the devitalization of the periodic vortex shedding at the interface. The lateral gradient of the difference between the vertical and transverse Reynolds normal stresses, increasing with the Froude number, is the main source of the streamwise vorticity and the outward transverse velocity at the interface.     

Transformation of hanging discontinuities into vortex systems in a stratified flow behind a cylinder

The mechanisms of formation of hanging discontinuities, vortex dipoles, and vortex arrays in the wave wake behind a cylinder moving at a constant velocity in a stratified fluid are investigated using various schlieren methods. The existence of discontinuities is attributable to the distortion of the internal-wave phase pattern in the shear flow and to the varying stratification and subsequent interaction of the waves with the appearing nonuniformities. Hanging discontinuities and vortex systems are low-velocity analogs of shock waves. An analysis of the internal-wave pattern indicates that the values of the normal velocity component differ on the upper and lower edges of the discontinuities. A regime diagram for flows of this kind is given.     

The temporal evolution of a pair of streamwise vortices

A detailed investigation of the velocity and vorticity fields of a pair of vortices growing over a 75°-sweep delta wing is carried out through LDV measurements of three components of velocity and vorticity. Data are obtained along one of the vortices. The wing is undergoing a ramp-like pitch-up motion. The evolution of the flow field in four planes normal to the free-stream velocity is captured at 100 time instants through the wing motion. The delta wing is pitched through angles of attack ranging from 28° to 68°. From the velocity data at each incidence, the corresponding vorticity field is calculated. Hysteresis effects on vortex development and breakdown are studied through axial velocity and vorticity contours. The topologies of streamlines and vortex lines are compared with the corresponding topologies of the steady case. It is found that vortex breakdown can be detected first by a drastic reduction of the axial velocity. This phenomenon is developing in a non-axisymmetric fashion, beginning at the inboard side of the vortex. This is followed by a reduction of the axial vorticity component and finally by a reversal of the azimuthal vorticity component.This work was supported by the Air Force Office of Scientific Research, Project No. AFOSR-91-0310 and was monitored by Major Daniel Fant.     

Instability of a vertical columnar vortex in a stratified fluid

In this article, we study experimentally the evolution of a vertical columnar vortex in a stratified fluid. Three different measurement techniques are used. Particle image velocimetry allows us to monitor the time evolution of the characteristics of the vortex (Froude and Reynolds numbers). Dye visualizations reveal the existence of an instability for Froude numbers smaller than one, which creates an undulation of the vortex centerline. Synthetic schlieren visualization shows that the density structure of the unstable mode is very similar to the structure found recently numerically for the radiative instability of a Lamb–Oseen vortex (Riedinger et al. in J Fluid Mech, 2010). The experimental stability diagram and unstable wavelengths are compared with these numerical results. A secondary instability associated with the presence of critical layers is also observed for Froude numbers larger than one.     

Localized convective flows in a nonuniformly heated liquid layer

Within the class of exact solutions of the thermal-convection equations in the Oberbeck-Boussinesq approximation, which assumes a linear dependence of the temperature and the vertical velocity component on the height, a non-self-similar behavior of localized disturbances of a special type in a nonuniformly heated liquid layer is studied. It is shown that in an unstably stratified medium these disturbances can evolve to isothermal vortex structures of Burgers type. In the conditions of stable stratification or uniform heating of the layer, the disturbances considered tend to the state of rest in an oscillating or monotonic manner. New solutions describing self-similar convective vortices are found.     

Analytic investigation of a nonlinear problem of the effect of buoyancy on the evolution of an annular vortex

The evolution of a heavy axisymmetric vortex whose density differs from that of the surrounding irrotational ideal fluid is investigated analytically. If the vortex had no buoyancy (i.e., if the densities were identical), it would preserve its shape and velocity. An approximate analytic solution of the problem is obtained. This solution describes two types of evolution of the vortex shape corresponding to different values of the initial velocity and small buoyancy. The spectrum of a nonlinear wave developing on the vortex boundary is estimated.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 56–66, January–February, 1996.     

Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

脉冲激光与正激波相互作用过程和减阻机理的实验研究

纳秒脉冲激光具有峰值功率密度高、易于击穿空气形成等离子体这一突出优势,在降低超声速波阻方面具有重要应用价值.以深刻揭示减阻机理为目的,针对激光与正激波相互作用这一基本物理现象开展实验研究.发展高精度纹影技术以测量复杂激波结构,时间分辨率达到 30ns,空间分辨率达到 1mm;搭建快速~PIV 实验系统以定量测量流场速度和涡量,时间分辨率达到 500ns.探明了激光等离子体引致的球面激波和高温低密度区域特性,揭示了激光等离子体在正激波冲击下的流动特性与演化规律,并结合数值模拟结果阐明了脉冲激光等离子体降低超声速波阻的根本原因.研究表明:激光等离子体引致激波的初始马赫数随着激光能量而增大,形状由水滴形逐渐发展为球面形,传播速度随着时间降低,在50$\mu$s 后接近于声速;高温低密度区域初始近似于球形,而后从激光入射方向的下游开始失稳,形成尖刺结构;在正激波冲击下,高温低密度区域演化为上下对称的双涡环结构,尺寸随着激光能量而增大.涡的卷吸和逆流可改变飞行器头部激波结构,是流场重构的重要形式,引起飞行器表面压力的大幅降低,是引起超声速飞行器波阻降低的重要机理.      

Dipole-wall collision in a shallow fluid

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the importance of vertical secondary flows on top of the primary horizontal motion. The present contribution focuses on the interaction of such a dipolar vortex with a sidewall. Accurate measurements of the three velocity components in a single horizontal plane have been performed using the Stereoscopic Particle Image Velocimetry (SPIV) technique. The experimental results, supported by numerical simulations, indicate that the complex vertical structure of a shallow-layer dipole becomes even more complex during the collision process. The observed growth of the kinetic energy associated with enhanced vertical motion pinpoints the strong discrepancies between vortex-wall interactions in shallow fluid layers and in purely two-dimensional wall-bounded turbulence.     

前体涡发生器对轴对称高超声速进气道激波振荡流动的影响实验

激波振荡是高超声速进气道不起动过程中常见的流动现象,会显著降低进气道气流捕获与压缩效率、产生剧烈的非定常气动力载荷而危害飞行器安全. 从激波振荡的控制出发,实验研究了前体转捩带位置的涡发生器对轴对称高超声速进气道激波振荡流动的影响. 分别在起动和激波振荡两种进气道流态下,选择无、0.5 mm与1 mm高度涡发生器工况进行对比研究. 并采用高速纹影与壁面动态测压同步记录非定常流动特征. 结果表明,1 mm高度内的涡发生器对起动状态的进气道主流流场结构、壁面压强分布影响不显著. 但对于激波振荡流动,涡发生器会明显缩小外压缩面分离区运动范围,缩短振荡周期,提升振荡周期内壁面压强的时均值. 涡发生器的影响程度随其高度的增大而增强,其中振荡周期从无涡发生器的4 ms缩短到1 mm高度涡发生器的3.13 ms. 此外,0.5 mm高度涡发生器会使得进气道内部测点的压强振荡幅值整体下降,相比无涡发生器工况的下降幅度可达23%. 流场结构与壁面压强信号的分析表明,涡流发生器主要通过其产生的流向涡影响激波振荡流动,包含流向涡对下游边界层的扰动以及流向涡与分离区的相互干扰.      

Reynolds number effects on leading edge vortex development on a waving wing

The waving wing experiment is a fully three-dimensional simplification of the flapping wing motion observed in nature. The spanwise velocity gradient and wing starting and stopping acceleration that exist on an insect-like flapping wing are generated by rotational motion of a finite span wing. The flow development around a waving wing at Reynolds number between 10,000 and 60,000 has been studied using flow visualization and high-speed PIV to capture the unsteady velocity field. Lift and drag forces have been measured over a range of angles of attack, and the lift curve shape was similar in all cases. A transient high-lift peak approximately 1.5 times the quasi-steady value occurred in the first chord length of travel, caused by the formation of a strong attached leading edge vortex. This vortex appears to develop and shed more quickly at lower Reynolds numbers. The circulation of the leading edge vortex has been measured and agrees well with force data.     

Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

The flow past a flat plate with a blunted leading edge by a flow of a viscous incompressible fluid with a small spanwise-periodic, steady nonuniformity of the velocity profile is considered. Such a flow simulates the interaction of one type of vortex disturbances of a turbulent external flow with the boundary layer. The solution obtained predicts generation of strong disturbances in the boundary layer, which are similar to the streaky structure observed in the case of high free-stream turbulence. It is shown that the boundary-layer flow on blunted bodies is more sensitive to vortex disturbances than on a plate with a sharp leading edge. Central Aerohydrodynamic Institute, Zhukovskii, 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 93–100, July–August, 2000.     

Behavior of a small single bubble rising in a rotating flow field

A small single bubble was generated with a single-hole nozzle facing upward in a water bath contained in a rotating cylindrical vessel. The bubble size falls in the surface tension force dominant regime. The vertical, radial, and tangential migration velocities of the bubble were measured with two CCD cameras and a high-speed video camera. The tangential velocity component of water flow was measured with particle image velocimetry. A helical motion of the bubble was observed under every experimental condition. The direction of the helical motion was the same as that of the tangential velocity component. This helical motion is associated with the large initial shape deformation of the bubble near the nozzle exit and the subsequent regular shedding of vortices behind it. The period and amplitude of the helical motion were obtained by analyzing the trajectory of the bubble. These quantities were non-dimensionalized by the volume equivalent bubble diameter and the terminal bubble velocity in the vertical direction and correlated as functions of the Eotvos number. Empirical equations were proposed for the period and amplitude. Originally published in the Journal of JSEM, Vol. 4, No. 2, pp. 38–45 (2004).     

Hamiltonian structure for a neutrally buoyant rigid body interacting with N vortex rings of arbitrary shape: the case of arbitrary smooth body shape

We present a (noncanonical) Hamiltonian model for the interaction of a neutrally buoyant, arbitrarily shaped smooth rigid body with N thin closed vortex filaments of arbitrary shape in an infinite ideal fluid in Euclidean three-space. The rings are modeled without cores and, as geometrical objects, viewed as N smooth closed curves in space. The velocity field associated with each ring in the absence of the body is given by the Biot–Savart law with the infinite self-induced velocity assumed to be regularized in some appropriate way. In the presence of the moving rigid body, the velocity field of each ring is modified by the addition of potential fields associated with the image vorticity and with the irrotational flow induced by the motion of the body. The equations of motion for this dynamically coupled body-rings model are obtained using conservation of linear and angular momenta. These equations are shown to possess a Hamiltonian structure when written on an appropriately defined Poisson product manifold equipped with a Poisson bracket which is the sum of the Lie–Poisson bracket from rigid body mechanics and the canonical bracket on the phase space of the vortex filaments. The Hamiltonian function is the total kinetic energy of the system with the self-induced kinetic energy regularized. The Hamiltonian structure is independent of the shape of the body, (and hence) the explicit form of the image field, and the method of regularization, provided the self-induced velocity and kinetic energy are regularized in way that satisfies certain reasonable consistency conditions.