Three-dimensional flow structure in highly buoyant jet by scanning stereo PIV combined with POD analysis

The flow characteristics and the structure of highly buoyant jet of low density fluid issuing into a stagnant surrounding of high density fluid is studied by scanning stereo PIV combined with proper orthogonal decomposition (POD) analysis. The experiment is carried out at Froude number of 0.3 and Reynolds number of 200, which satisfies the inflow condition due to the unstable density gradient near the nozzle exit. An increase in the maximum mean velocity occurs and the vertical velocity fluctuation is highly amplified near the nozzle exit, which suggests the influence of inflow due to the unstable density gradient. The POD analysis indicates that the vertical velocity fluctuation is the major source of fluctuating energy contributing to the development of the highly buoyant jet. The examination of the POD modes show that the longitudinal structure of the vertical velocity fluctuation is generated along the jet axis having the opposite sign of velocity fluctuation on both sides of the jet axis. The vertical scale of the POD mode decreases with increasing the mode number and results in the frequent appearance of cross-flow across the buoyant jet. The reconstruction flow from the POD modes indicates that the vortex structure is caused by the highly sheared layer between the upward and downward velocity and the inflow is induced by the vortex structure. The magnitude of the vortex structure seems to be weakened with an increase in the distance from the nozzle and the buoyant jet approaches to an asymptotic state in the further downstream.     

Experimental study on the effect of pulsating inflow to an enclosure for improved mixing

Optimal control of inlet jet flows is of broad interest for enhanced mixing in ventilated rooms. The general approach in mechanical ventilation is forced convection by means of a constant flow rate supply. However, this type of ventilation may cause several problems such as draught and appearance of stagnation zones, which reduces the ventilation efficiency. A potential way to improve the ventilation quality is to apply a pulsating inflow, which has been hypothesised to reduce the stagnation zones due to enhanced mixing. The present study aims at testing this hypothesis, experimentally, in a small-scale two-dimensional water model using Particle Image Velocimetry with an in-house vortex detection program. We are able to show that for an increase in pulsation frequency or alternatively in the flow rate the stagnation zones are reduced in size and the distribution of vortices becomes more homogeneous over the considered domain. The number of vortices (all scales) increases by a factor of four and the swirl-strength by about 50% simply by turning on the inflow pulsation. Furthermore, the vortices are well balanced in terms of their rotational direction, which is validated by the symmetric Probability Density Functions of vortex circulation (Γ) around Γ = 0. There are two dominating vortex length scales in the flow, namely 0.6 and 0.8 inlet diameters and the spectrum of vortex diameters become broader by turning on the inflow pulsation. We conclude that the positive effect for enhanced mixing by increasing the flow rate can equally be accomplished by applying a pulsating inflow.     

Vortex intensification in convective cells

The intensification of single vortices in convective flows swirled by the Coriolis force is studied numerically. The initial disturbances, specified against the background of a steady cell, are coaxial with the cell flow and have various swirl directions, intensities, and dimensions. It is shown that the vortices are intensified no matter whether the direction of disturbing vortex rotation is co- or counter-directional with the Coriolis force. If the disturbance intensity is small as compared with that of the convective-cell flow, the growth of the azimuthal velocity circulation in the perturbing vortices depends linearly on their initial circulation. For such vortices, the energy increase is proportional to the characteristic vortex radius to the power –5/3.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 62–68. Original Russian Text Copyright © 2004 by Ivanov and Povarnitsyn.     

Iterative control of Görtler vortices via local wall deformations

Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.     

Internal waves induced by potential vortices

A linearized equation of the internal waves developing in an ideal stratified gas under the action of potential vortices concentrated in a vertical cylinder is obtained. The Cauchy problem for the internal wave equation with right side depending on the vortex intensity is solved by the integral transform method. In the case of a vortex filament the exact solution is found. Approximate formulas are obtained on the basis of the steady-phase method when the vorticity is exponentially stratified along the vertical. Expressions for the phase velocity and amplitude of the radial wave traveling away from the cylindrical vortex are found. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 118–123, January–February, 1998. The work was carried out with the support of the Russian Foundation for Fundamental Research (project No. 96-01-04599).     

Volumetric three-component velocimetry measurements of the turbulent flow around a Rushton turbine

Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a ‘swirl strength’ criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.     

Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity

High Reynolds number, low Mach number, turbulent shear flow past a rectangular, shallow cavity has been experimentally investigated with the use of dual-camera cinematographic particle image velocimetry (CPIV). The CPIV had a 3 kHz sampling rate, which was sufficient to monitor the time evolution of large-scale vortices as they formed, evolved downstream and impinged on the downstream cavity wall. The time-averaged flow properties (velocity and vorticity fields, streamwise velocity profiles and momentum and vorticity thickness) were in agreement with previous cavity flow studies under similar operating conditions. The time-resolved results show that the separated shear layer quickly rolled-up and formed eddies immediately downstream of the separation point. The vortices convect downstream at approximately half the free-stream speed. Vorticity strength intermittency as the structures approach the downstream edge suggests an increase in the three-dimensionality of the flow. Time-resolved correlations reveal that the in-plane coherence of the vortices decays within 2–3 structure diameters, and quasi-periodic flow features are present with a vortex passage frequency of ~1 kHz. The power spectra of the vertical velocity fluctuations within the shear layer revealed a peak at a non-dimensional frequency corresponding to that predicted using linear, inviscid instability theory.     

Vortex breakdown and its control on delta wings

In order to investigate the breakdown of vortices generated by the leading edge of delta wings, LDA-measurements have been performed in the flow on the suction side of a delta wing of aspect ratio A = 2. The measurements describe the growth of the vortex along the leading edge and reveal a certain radial structure upstream of the breakdown point. Moreover they shed light on the mechanism responsible for the onset of vortex breakdown on the suction side of a wing.

The occurrence of the breakdown phenomenon on a delta wing may be prevented or at least retarded by the use of spanwise blowing jets. The interaction of vortex and jets giving rise to these effects will also be discussed with the help of measured velocity profiles.     

The structure of compressible starting vortices

The structures of highly two-dimensional shock-induced compressible starting vortices were investigated. Density distributions across the vortex were measured by dual-pulsed holographic interferometry. Pressure profiles of the vortex were measured by fast-response miniature Kulite transducers. From these two independent measurements the velocity profile was calculated using the radial momentum equation. The detailed vortex structure is similar to that from the tip of a wing and consists of four well-defined regions: a core region, a logarithmic region, a transition region, and an inviscid region. The distribution of circulation of the vortices can be expressed by a set of empirical formulae. The proportionality constants of the logarithmic region were found to be 0.43±0.01 for three different two-dimensional vortices.Presently at U.S. Army Aeroflightdynamics Directorate, ATCOM, NASA-Ames Research Center, Moffett Field, CA 94035Professor     

Computation of field structure and aerodynamic characteristics of delta wings at high angles of attack

A numerical investigation of the structure of the vortical flowfield over delta wings at high angles of attack in longitudinal and with small sideslip angle is presented. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics that are dominated by the effect of the breakdown of the leading-edge vortices. The methods that analyze the flowfield structure quantitatively were given by using flowfield data from the computational results. In the region before the vortex breakdown, the vortex axes are approximated as being straight line. As the angle of attack increases, the vortex axes are closer to the root chord, and farther away from the wing surface. Along the vortex axes, as the adverse pressure gradients occur, the axial velocity decreases, that is, A is negativee, so the vortex is unstable, and it is possible to breakdown. The occurrence of the breakdown results in the instability of lateral motion for a delta wing, and the lateral moment diverges after a small perturbation occurs at high angles of attack. However, after a critical angle of attack is reached the vortices breakdown completely at the wing apex, and the instability resulting from the vortex breakdown disappears.     

Two-point correlation and integral scale of spatially advancing curved channel flow at friction-velocity-based Reynolds number 550

Two-point correlation and integral scale of curved channel turbulent flow were examined for onset and growth of large-scale vortex. Away from the two walls of the straight channel, the two-point correlation of streamwise velocity has large negative values around local minimum at y/δ = 1.6 and those of radial and spanwise components take small negative values at the same area. The large-scale motion in the straight channel is thus indicated to have conspicuous streamwise component and weak secondary motion. In the curved channel, two-point correlation of radial velocity decreased around the minimum away from the wall (y/δ = 1.6) and large negative values extended to the whole channel width. It is thus indicated that the large-scale vortex originated from the large-scale structures with conspicuous streamwise component in the outer-wall side, grew and expanded to the full channel width of the curved part. The integral scale integrating two-point correlation conditionally on the negative values greatly decreased to denote the onset and growth of the large-scale motion quantitatively. The local minima of two-point correlation for radial velocity were used as indicator of the large-scale vortex and near-wall small-scale vortex. The magnitude of it at the channel center area was as low as one thirds of those of near-wall area in the straight channel, and however increased and surpassed those of near-wall area in the curved channel. Therefore, large-scale vortices were weaker than the small-scale motion in the straight part of the channel, and they grew and surpassed the small-scale motion in strength in the curved part of the channel.     

Vortex shedding induced by a solitary wave propagating over a submerged vertical plate

Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet.     

Numerical investigation of a spatially developing turbulent natural convection boundary layer along a vertical heated plate

Large-eddy simulation (LES) on a spatially developing natural convection boundary layer along a vertical heated plate was conducted. The heat transfer rate, friction velocity, mean velocity and temperature, and second-order turbulent properties both in the wall-normal and the stream-wise direction showed reasonable agreement with the findings of past experiments. The spectrum of velocity and temperature fluctuation showed a -2/3-power decay slope and -2-power decay slope respectively. Quadrant analysis revealed the inclination on Q1 and Q3 in the Reynolds stress and turbulent heat flux, changing their contribution along the distance from the plate surface. Following the convention, we defined the threshold region where the stream-wise mean velocity takes local maximum, the inner layer which is closer to the plate than the threshold region, the outer layer which is farther to the plate than the threshold region. The space correlation of stream-wise velocity tilted the head toward the wall in the propagating direction in the outer layer; on the other hand, the correlated motion had little inclination in the threshold region. The time history of the second invariant of gradient tensor Q revealed that the vortex strength oscillates both in the inner and the outer layers in between the laminar and the transition region. In the turbulent region, the vortex was often dominant in the outer layer. Instantaneous three-dimensional visualization of Q revealed the existence of high-speed fluid parcels associated with arch-shape vortices. These results were considered as an intrinsic structure in the outer layer, which is symmetrical to the structure of canonical smooth/rough wall bounded layer flow in forced convection.     

Uncovering large-scale coherent structures in natural and forced turbulent wakes by combining PIV,POD, and FTLE

Planar velocity data of the unsteady separated flow in the turbulent wake of a circular cylinder obtained by particle image velocimetry (PIV) are analyzed in order to visualize the large-scale coherent structures associated with alternating vortex shedding at a Reynolds number of 2,150. Two different cases are examined: unforced vortex shedding in the natural wake and vortex lock-on incited by forced perturbations superimposed in the inflow velocity. Proper orthogonal decomposition (POD) is employed to reconstruct the low-order wake dynamics from randomly sampled snapshots of the velocity field. The reconstructed flow is subsequently used to determine the evolution of the finite-time Lyapunov exponent (FTLE) fields which identify the Lagrangian coherent structures. The results demonstrate that the combination of methods employed offers a powerful visualization tool to uncover large-scale coherent structures and to exemplify vortex dynamics in natural and forced bluff-body wakes.     

Self-sustained global oscillations in a jet in crossflow

A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier?CStokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.     

轴对称射流场涡结构的离散涡段方法研究

本文用三维离散涡方法,模拟了轴对称圆射流涡结构的发展。     

On one mechanism of formation of tornado‐like vortices in a rotating fluid

It is shown that during excitation of forced, resonant, inertial oscillations of large amplitude in a rigidly rotating fluid, the mechanism of formation of tornadolike vortices is primarily of a kinematic nature($advection of circulation of the azimuthal component velocity and stretching of vortex lines by the poloidal components of the velocity field that arise from excitation of inertial oscillations). The main parameters of the vortices are obtained by solutions of model problems. To excite such oscillations, it is necessary to deliver energy far exceeding the initial energy of the rotating fluid. Therefore, inertial oscillations by themselves cannot lead to the occurrence of intense atmospheric vortices. Nevertheless, such oscillations can apparently play the role of a trigger mechanism that activates more complex processes of vortex formation related to instability of the atmosphere.     

超声速尾涡的稳定性分析

从Ｎ－Ｓ方程出发,通过正则模方法,研究了超声速尾涡的绝对／对流不稳定性性质．计算了流动的稳定性特征随马赫数Ｍ,周向波数ｎ．,轴向自由流速度Ｗ０和旋转度ｑ等流动参数的变化规律,找到了绝对／对流不稳定区域的边界．通过比较发现,马赫数的增加使流动由绝对不稳定向对流不稳定乃至稳定转化．在所计算的参数范围,周向波数的增加加速了这一转化过程,而且,轴向速度的增加,同样使流动向着稳定的方向转化．同时还分析了不同旋拧程度的流动受可压缩影响的不同．这些结果对于了解旋拧流动稳定性的物理机理以及进行流动控制都有着重要意义．     

Exact solutions of equations of rotationally symmetric motion of an ideal incompressible liquid

A partially invariant solution of the Euler equations is considered, where the vertical component of velocity is a function of the vertical coordinate and time, whereas the remaining components of velocity and pressure are independent of the polar angle in a cylindrical coordinate system. Using the classification of equations obtained by analysis of an overdetermined system, we consider two hyperbolic systems: the first one describes the motion of a cylindrical layer of an ideal incompressible liquid under a punch, and the second system allows obtaining solutions in a halfcylinder with singularities at the axis of symmetry. A class of new exact solutions is obtained, which describe vortex motion of an ideal incompressible liquid, including the motion with singularities (sources of vortices) located along the axis of symmetry.