Vorticity evolution mechanism in near‐field of a transverse jet

Abstract

Flow structure and vorticity evolution processes in the near field of an elevated jet in a crossflow are experimentally studied in a wind tunnel. The instantaneous and time‐averaged flow field characteristics are observed and measured by using a flow visualization technique and a high‐speed Particle Image Velocimeter (PIV). Time histories of the instantaneous velocity of the vortical flows in the shear‐layer are recorded by a hot‐wire anemometer and a high‐speed data acquisition system in order to analyze the frequency characteristics of the traveling coherent structure in the shear‐layer. Experiments are performed between two different jet‐to‐crossflow momentum flux ratios R = 0.08 and 0.56, which are selected from two regimes with different kinds of flow patterns at a fixed crossflow Reynolds number 2051. The behaviors and mechanisms of the vortical flow structure and the vorticity evolution mechanisms appear to be distinct in different flow regimes. By analyzing the pictures of the smoke flow visualization and the instantaneous vorticity contour maps, two kinds of vorticity evolution mechanisms, “shear‐induced vortices” and “swing‐induced vortices”, can be identified in the shear‐layer evolving from the jet exit. The time‐averaged velocity field and vorticity properties are also discussed in this paper.     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

Characteristics of the turbulent/non-turbulent interface of a non-isothermal jet

The turbulent/non-turbulent interface of a jet is characterized by sharp jumps ('discontinuities') in the conditional flow statistics relative to the interface. Experiments were carried out to measure the conditional flow statistics for a non-isothermal jet, i.e. a cooled jet. These experiments are complementary to previous experiments on an isothermal Re=2000 jet, where, in the present experiments on a non-isothermal jet, the thermal diffusivity is intermediate to the diffusivity of momentum and the diffusivity of mass. The experimental method is a combined laser-induced fluorescence/particle image velocimetry method, where a temperature-sensitive fluorescent dye (rhodamine 6G) is used to measure the instantaneous temperature fluctuations. The results show that the cooled jet can be considered to behave like a self-similar jet without any significant buoyancy effects. The detection of the interface is based on the instantaneous temperature, and provides a reliable means to detect the interface. Conditional flow statistics reveal the superlayer jump in the conditional vorticity and in the temperature.     

Nanostructure of vortex during explosion welding

The microstructure of a bimetallic joint made by explosion welding of orthorhombic titanium aluminide (Ti-30Al-16Nb-1Zr-1Mo) with commercially pure titanium is studied. It is found that the welded joint has a multilayered structure including a severely deformed zone observed in both materials, a recrystallized zone of titanium, and a transition zone near the interface. Typical elements of the transition zone-a wavy interface, macrorotations of the lattice, vortices and tracks of fragments of the initial materials-are determined. It is shown that the observed vortices are formed most probably due to local melting of the material near the contact surface. Evidence for this assumption is deduced from the presence of dipoles, which consist of two vortices of different helicity and an ultrafine duplex structure of the vortex. Also, high mixing of the material near the vortex is only possible by the turbulent transport whose coefficient is several orders of magnitude larger than the coefficient of atomic diffusion in liquids. The role played by fragmentation in both the formation of lattice macrorotations and the passage of coarse particles of one material through the bulk of the other is determined.     

On the decomposition of turbulent flow fields for the analysis of coherent structures

Summary The decomposition of the turbulent velocity, pressure, and vorticity fields for the analysis of coherent structures is examined from a fundamental theoretical standpoint. It is shown that the commonly used double and triple decompositions yield coherent and incoherent parts of the turbulence that are not Galilean invariant and, consequently, severe doubts are raised concerning their general usefulness for the eduction of coherent structures. Alternative triple decompositions are proposed which are invariant under an arbitrary change of observer. Applications of this triple decomposition to the construction of helicity fluctuations which are more suitable for the study of coherent structures are also discussed.     

Taylor vortices between almost cylindrical boundaries

Summary We consider a modified Taylor problem, with the fluid flowing between a rotating inner circular cylinder and an outer stationary surface whose radius is a constant plus a small and slowly varying function of the axial co-ordinate z. This variation is chosen in such a way that the flow is locally more unstable near z=0 than near z=±, so that Taylor vortices appear more readily near z=0. The theory is developed to show how vortices of strength varying with z develop as the speed of rotation is increased through a critical value which is a perturbation of the classical value. Wave number changes in the axial direction are also calculated.     

Application of particle image velocimetry for measuring He II thermal counterflow jets

The particle image velocimetry (PIV) technique was successfully applied for measuring the velocity of a He II thermal counterflow jet. Neutrally buoyant hydrogen-deuterium solid particles were used as tracer particles for PIV measurement. In the application, the normal component velocity was measured. The jet velocity profile and spatial decay of the jet velocity were compared with those of turbulent round jets of ordinary viscous fluids. The velocity measured near the jet nozzle exit was compared with the theoretical prediction for the normal component flow velocity.     

Instability of the Flow in a Spherical Layer under Torsional Oscillations of the Inner Boundary

The instability of viscous incompressible fluid flows caused in a thin spherical layer by torsional oscillations of the inner sphere in a thin spherical layer with respect to the sate of rest is studied numerically. It has been established that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to structures not observed earlier. The revealed instability is observed in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.     

压力梯度作用下相干结构的演化

采用共振三波的一个周期作为湍流边界层近壁区相干结构的初值，用直接数值模拟方法对有压力梯度，包括定常压力梯度和变压力梯度作用下相干结构的演化进行了研究，得出其各种特性的变化与实验观测到的结果一致。压力梯度对相干结构初始扰动波的选择以及演化过程都起作用，相比之下对前者的作用更大。条纹结构和流向涡之间有某种内在的紧密的联系，可能是产生流向涡的起因。     

大跨屋盖表面旋涡的PIV试验研究

该文通过风洞流场显示试验,观察了大跨平屋盖和马鞍屋盖表面的分离泡和锥形涡现象,给出了不同风向、不同屋盖表面的旋涡流线和涡量场分布;分析了风向角、屋盖曲率对于旋涡形态的影响。试验结果表明,当风向垂直于平屋盖迎风前缘时,屋盖表面将形成典型的分离泡现象,且分离泡的涡核位置恰好对应了涡量场的负向峰值。在斜向风作用下,平屋盖和以高点作为迎风点的马鞍屋盖表面将出现锥形涡。观察旋涡的平均流线和涡量场分布图,发现当来流沿两种屋盖对角线时,锥形涡截面形状接近圆形;当来流偏离屋盖对角线时,在靠近来流的一侧,锥形涡截面形状接近椭圆形;流场内负向涡量分布于壁面上,峰值集中在迎风前缘附近和旋涡周围。在相同的风向角下,曲率较大的马鞍表面锥形涡涡轴与屋盖迎风前缘所成角度较大,曲率较小的马鞍表面锥形涡涡轴与迎风前缘所成角度较小。此外,旋涡的瞬时流线图表明,锥形涡是一种瞬时变化的流体现象,其形态和位置在每个瞬时都不相同。     

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition

The use of the Helmholtz decomposition for exterior incompressible viscous flows is examined, with special emphasis on the issue of the boundary conditions for the vorticity. The problem is addressed by using the decomposition for the infinite space; that is, by using a representation for the velocity that is valid for both the fluid region and the region inside the boundary surface. The motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. It is shown that at each instant of velocity discontinuity, vorticity is generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is then diffused into the surroundings: this yields that the no-slip conditions are thus automatically satisfied (since the presence of a vortex layer on the surface is required to obtain a velocity slip at the boundary). This result is then used to show that in order for the solution to the Euler equations to be the limit of the solution to the Navier-Stokes equations, a trailing-edge condition (that the vortices be shed as soon as they are formed) must be satisfied. The use of the results for a computational scheme is also discussed. Finally, Lighthill's transpiration velocity is interpreted in terms of Helmholtz decomposition, and extended to unsteady compressible flows.     

Jupiter's zonal winds: are they bands of homogenized potential vorticity organized as a monotonic staircase?

The east-west striped pattern of clouds in Jupiter's weather layer is accompanied by a zonal flow containing 12 eastward-going jet streams alternating in latitude with westward-going jet streams. Based on theory, simulation and observations of the Earth's oceans and atmosphere, it is conjectured that Jupiter's weather layer is made of bands of constant potential vorticity (PV), where the interfaces between bands are at the latitudes of the maxima of the eastward-going jet streams. It is speculated that the mixing of PV on Jupiter is analogous to the mixing of salt in the ocean by the Phillips effect, which causes the salt density to form a monotonic 'staircase'. It is hypothesized that the PV in Jupiter's weather layer is also a staircase, decreasing from north to south. PV is a function of vorticity, as well as parameters with unknown values, e.g. the vertical stratification and the zonal flow beneath the observable weather layer. Therefore, these hypotheses cannot be tested directly. Using an atmospheric model that contains these unknown parameters, we solved the inverse problem and found values of the unknown parameters (and their uncertainties) that best fit Jovian observations. The unknown parameters influence how the zonal flow interacts with large vortices, e.g. the Great Red Spot (GRS; the largest and longest-lived Jovian vortex, centred at 23° S) and the Oval BA (the second largest vortex, centred at 33° S). Although we found that the PV distribution is approximately piecewise-constant and that the peaks of the eastward-going jet streams are at the latitudes of PV interfaces, there is also a PV interface at 20° S, where there is a westward-going jet stream. We find that the zonal PV is not a monotonic staircase due to the 'backwards' interface at 20° S. We show that this backwards interface is necessary to make the GRS nearly round, and that without that interface, the Red Spot would be highly elongated in the east-west direction and probably unstable.     

On Developed Superfluid Turbulence

Superfluid turbulence is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the relative value of the friction force acting on a vortex with respect to the non-dissipative forces. The inverse parameter q^?1 plays the same role as the Reynolds number Re = U R/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence, described by a Kolmogorov cascade, occurs when Re ? 1 in classical hydrodynamics. In superfluids, the developed turbulence occurs at q ? 1. Another parameter of superfluid turbulence is the superfluid Reynolds number Re_s = U R/κ, which contains the circulation quantum κ characterizing quantized vorticity in superfluids. The two parameters q and Re_s control the crossover or transition between two classes of superfluid turbulence: (i) the classical regime, where the Kolmogorov cascade, probably modifed by the non-canonical dissipation due to mutual friction, is effective, vortices are locally polarized, and the quantization of vorticity is not important; and (ii) the Vinen quantum turbulence where the properties are determined by the quantization of vorticity. The phase diagram of these dynamical vortex states is suggested. PACS numbers: 43.37.+q, 47.32.Cc, 67.40.Vs, 67.57.Fg.     

Wind pressure features of large-span flat roof in different wind fields induced by conical vortex

The wind pressure features on a large-span flat roof in uniform flow field and turbulent field induced by conical vortex were studied, through wind tunnel tests. From the comparison of the mean and fluctuating wind pressure distributions on a flat roof in different wind fields induced by conical vortex, results indicate that the mean suction dominates in the smooth flow, whereas the fluctuating suction is more obvious in the turbulent flow. The probability density function for the pressure fluctuations under different approaching flows is analyzed. The two-peaked distribution, peculiar to turbulent flow field, is observed on the curve of probability density. The fluctuating pressures at reattachment points are larger under the turbulent flow. This indicates a more intense reattachment, which may cause overturning moment for roof-mounted items. Point vortex, RanKine vortex, and simplified Cook expression are applied to fit the pressure profiles beneath conical vortices, respectively. The results have shown that the RanKine vortex model and simplified Cook expression were applicable to forecast the wind pressure profiles beneath conical vortices, while point vortex underestimated the real wind suction. The wind pressure distributions in turbulent fields induced by different wind angles were contrasted, when the approaching flow is along the diagonal of the roof, the intensity of the vortex pairs is almost equal, with obvious reattachment. When the approaching flow deviate from the diagonal of the roof, the lateral turbulent component spins the vortex more quickly; this induces larger mean suctions beneath windward vortices. Smaller suctions are observed beneath the leeward vortex, due to less vorticity being converted to vortex motion from the freestream.     

The Rayleigh–Taylor instability for inviscid and viscous fluids

The classical Rayleigh–Taylor instability occurs when two inviscid fluids, with a sharp interface separating them, lie in two horizontal layers with the heavier fluid above the lighter one. A small sinusoidal disturbance on the interface grows rapidly in time in this unstable situation, as the heavier upper fluid begins to move downwards through the lighter lower fluid. This paper presents a novel numerical method for computing the growth of the interface. The technique is based on a spectral representation of the solution. The results are accurate right up to the time when a curvature singularity forms at the interface and the inviscid model loses its validity. A spectral method is then presented to study the same instability in a viscous Boussinesq fluid. The results are shown to agree closely with the inviscid calculations for small to moderate times. However, the high interface curvatures that develop in the inviscid model are prevented from occurring in viscous fluid by the growth of regions of high vorticity at precisely these singular points. This leads to over-turning of the interface, to form mushroom-shaped profiles. It is shown that different initial interface configurations can lead to very different geometrical outcomes, as a result of the flow instability. These can include situations when detached bubbles form in the fluid.     

PARTICLE DISPERSION BY COHERENT STRUCTURES IN FREE SHEAR FLOWS

The dispersion of particles in turbulent flows is poorly understood. Previous approaches to this problem have been found to be inadequate for nonisotropic turbulent flows. An approach involving a new physical concept is presented. This approach assumes that coherent vortex structures control the particle dispersion process in free shear flows. A simple computational model employing Stuart's vortices is used to simulate particle motion in a two-dimensional free shear layer. The results of this simulation are in reasonable agreement with previous experiments. For the first time, experimental observations indicating particle dispersion rates greater than fluid dispersion rates in free shear flows can be plausibly explained.     

Large eddy simulation of a horizontal particle-laden turbulent planar jet

Numerical simulations of the particle-vortex interactions for an unforced, incompressible, spatially developing horizontal particle-laden turbulent planar jet are reported. Effects of the initial two-phase velocity slip on the instantaneous concentration distribution of particles with and without the influence of gravity are studied. Continuous phase simulation is performed by the method of large eddy simulation (LES) while the particle phase is solved by a Lagrangian method. Extensive results on the particle-laden jet flow are obtained. Simulation of the gas-phase reproduces the essential features of the coherent structures in the planar jet. Length of the potential core and essential features of the coherent structures in the planar jet are compared with experimental and other theoretical results. The simulation shows that initial two-phase velocity slip plays an important role in enforcing particle transverse dispersion in the jet region and sharply changes the instantaneous particle distribution. Furthermore, results demonstrate the influence of gravity on particle dispersion and sedimentation. Such pronounced effect of gravity on instantaneous concentration of particles with increased Stokes number and initial slip coefficients emphasize the need for the consideration of gravity for horizontal particle-laden jet. Received 6 September 2000     

Recombination of two vortex filaments and jet noise

The recombination of two vortex filaments in a viscous incompressible fluid is analysed by the use of the vorticity equation. The analysis is confined to a local flow field, where the recombination process occurs, and is based on several assumptions, such as the conservation of the fluid impulse, spatial symmetry of the flow field etc. The flow field is expanded as polynomials of coordinates, and variations of their coefficients are obtained by the use of the vorticity equation. It is proved that the process is completed within a short time ofO (σ ²/Γ) and the viscous effect is essential;σ and Γ are the size and the circulation of the vortex filaments, respectively. This result is applied to predict the far-field noise of a circular jet by assuming that the main noise source is the recombination process in deformed vortex rings in the jet near field. The predicted noise intensity shows theU dependence and has an additional new factor (d/σ)⁶;U is the jet velocity andd is the average spacing between vortex rings.     

Role of coherent structures in turbulent shear flows

A definition for the large-scale coherent structure is presented, and the nature and role of coherent structures in turbulent shear flows are examined. The equations governing the coherent motions and the experimental considerations as well as constraints in the investigations of coherent structures in wall-bounded and free turbulent shear flows are discussed. Results from a few of our recent and ongoing studies of coherent structures in excited and unexcited free turbulent shear flows are reviewed. These results show that coherent structures are dominant in transport in the early stages of their formation, but not in the self-preserving regions of turbulent shear flows.     

PARTICLE DISPERSION BY COHERENT STRUCTURES IN FREE SHEAR FLOWS

ABSTRACT

The dispersion of particles in turbulent flows is poorly understood. Previous approaches to this problem have been found to be inadequate for nonisotropic turbulent flows. An approach involving a new physical concept is presented. This approach assumes that coherent vortex structures control the particle dispersion process in free shear flows. A simple computational model employing Stuart's vortices is used to simulate particle motion in a two-dimensional free shear layer. The results of this simulation are in reasonable agreement with previous experiments. For the first time, experimental observations indicating particle dispersion rates greater than fluid dispersion rates in free shear flows can be plausibly explained.