New studies in vortex dynamics: Incompressible and compressible vortex reconnection,core dynamics,and coupling between large and small scales

Coherent structure dynamics in turbulent flows are explored by direct numerical simulations of the Navier-Stokes equations for idealized vortex configurations. For this purpose, two dynamically significant coherent structure interactions are examined: (i) incompressible and compressible vortex reconnection and (ii) core dynamics (with and without superimposed small-scale turbulence). Reconnection is studied for two antiparallel vortex tubes at a Reynolds number (Re) of 10³. Incompressible reconnection consists of three distinct phases: inviscid advection, bridging and threading. The key mechanism, bridging, involves the ‘cutting’ of vortex lines by viscous cross diffusion and their subsequent reconnection in front of the advancing vortex dipole. We conjecture that reconnection occurs in successive bursts and is a physical mechanism of cascade to smaller scales. Compressible reconnection is seen to be significantly affected by the choice of pressure and density initial conditions. We propose a polytropic initial condition which is consistent with experimental results and low-Mach number asymptotic theories. We also explain how compressibility initiates an early reconnection due to shocklet formation, but slows down the circulation transfer at late times. Thus, the reconnection timescale increases with increasing Mach number. Motivated by the important role of helical vortex lines in the reconnected vortices (bridges), we focus our attention on the dynamics of an axisymmetric vortex column with axial variation of core size. The resulting core dynamics is first explained via coupling between swirl and meridional flows. We then show that core dynamics can be better understood by applying a powerful analytical tool —helical wave decomposition — which extracts vorticity wave packets, thereby providing a simple explanation of the dynamics. The increase in core size variation with increasing Re in such a vortex demonstrates the limitation of the prevalent vortex filament models which assume constant core size. By studying the columnar vortex with superimposed small-scale, homogeneous, isotropic turbulence, we address the mutual interactions between large and small scales in turbulent flows. At its boundary the columnar vortex organizes the small scales, which, if Re is sufficiently high, induce bending waves on the vortex which further organize the small scales. Such backscatter from small scales cannot be modelled by an eddy viscosity. Based on the observation of such close coupling between large and small scales, we question the local isotropy assumption and conjecture a fractal vortex model for high Re turbulent flows.     

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.     

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.     

Spatial correlation properties and correlation vortices of partially coherent vortex beams diffracted by an aperture

Taking the Gaussian–Schell model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices of partially coherent vortex beams diffracted by an aperture are studied. It is shown that the off-axis displacement and spatial coherence affects the spectral degree of coherence. The number and position of correlation vortices depend on the off-axis displacement, spatial coherence, aperture truncation and propagation distance, where the effect of aperture diffraction on the correlation vortices is stressed. The number of correlation vortices decrease as the truncation parameter increases. The correlation vortices in the diffracted field result from the vortex embedded in partially coherent beams at the source plane rather than from the aperture diffraction. The correlation vortices in the diffracted field appear even when the vortex core is stopped by the aperture.     

Wavelet diagnostics for detection of coherent structures in instantaneous turbulent flow imagery: A review

A review of work over the last decade shows that 2D wavelet techniques applied on flow imagery can provide powerful insights into the nature and lifecycle of coherent structures (the latter through wavelet movies) in turbulent shear flows. The advantage of wavelet techniques in often being able to infer the nature of coherent motion from a single image is emphasized. The techniques are first calibrated by using them on well-known results in the turbulent mixing layer. They are then applied to jets and plumes, and it is shown how off-source heating in such flows can disrupt the coherent structures in the unheated flow. A suitably reduced version of the present method, using discrete wavelet transforms on signals from a finite array of sensors, could be a useful diagnostic tool in near-real-time detection of coherent structures or patterns for the purpose of selecting appropriate control signals to the actuators in a flow-control system.     

Numerical micromagnetics of small particles

The results of applying the authors' micromagnetic code to a homogeneous spherical particle that is large enough to support inhomogeneous magnetization are given. For smaller particles, magnetization reversal is by coherent rotation. Larger particles initially exhibit curling as the applied magnetic field is reduced from a saturating value. Then one of two new behaviors is observed. For weak crystalline anisotropy, the axis of the curling state rotates and bends, and the magnetization reversal process is reversible, or nearly so. For strong crystalline anisotropy, a sudden discontinuous transition occurs to a vortex state with axis perpendicular to the anisotropy axis, and the vortex moves across the particle as reversal of the applied magnetic field continues. The formation and disappearance of the vortex are irreversible, but all other aspects of the process are reversible     

Evolution properties of a partially coherent Lorentz-Gauss vortex beam in a uniaxial crystal

The propagation properties of a partially coherent Lorentz-Gauss vortex beam propagating in a uniaxial crystal orthogonal to the optical axis were studied. The analytical expressions of the partially coherent Lorentz-Gauss vortex beam propagating in a uniaxial crystal were derived. Based on the derived formulae, the average intensity properties and evolution properties of the coherent vortex of the partially coherent Lorentz-Gauss vortex beam propagating in a uniaxial crystal were illustrated using numerical examples. The influences of the uniaxial crystal and the parameters of the beam at the source plane of z?=?0 on the average intensity and evolution properties of the coherent vortex for the partially coherent Lorentz-Gauss vortex beam are analyzed in detail.     

光纤式质量流量计的研究

研究出一种光纤传感器与电磁涡流传感器相结合的新型质量流量计,并给出理论模型和实际系统结构。该流量计对旋涡发生体进行了独特设计,即将光纤嵌入到旋涡发生体内部构成光纤式升力检测器。利用光纤的微弯损耗特性,检测出流体流经旋涡发生体时产生的变动升力大小,结合信号电极测量出的涡流频率,由单片机计算出流体质量流量。与其它质量流量计相比,光纤式质量流量计结构简单,抗干扰能力强。以水为被测对象的实验证明,其测量结果的相对误差在1%以内。     

Disappearing bodies and ghost vortices

In many dispersed multiphase flows bubbles, droplets, and particles move and disappear due to a phase change. Practical examples include vapour bubbles condensing in subcooled liquids, fuel droplets evaporating in a hot gas and ice crystals melting in water. After these 'bodies' have disappeared, they leave behind a remnant 'ghost' vortex as an expression of momentum conservation. A general framework is developed to analyse why and how a ghost vortex is generated. A study of these processes is incomplete without a detailed discussion of the concept of momentum for unbounded flows. We show how momentum can be defined unambiguously for unbounded flows and show its connection with other expressions, particularly that of Lighthill. We apply our analysis to interpret new observations of condensing vapour bubbles and discuss droplet evaporation. We show that the use of integral invariants, widely applied in turbulence, introduces a new perspective to dispersed multiphase flows.     

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.     

Determination of the Coherence Length and the Cooper-Pair Size in Unconventional Superconductors by Tunneling Spectroscopy

The main purpose of the paper is to discuss a possibility of the determination of the values of the coherence length and the Cooper-pair size in unconventional superconductors by using tunneling spectroscopy. In the mixed state of type-II superconductors, an applied magnetic field penetrates the superconductor in the form of vortices which form a regular lattice. In unconventional superconductors, the inner structure of a vortex core has a complex structure which is determined by the order parameter of the superconducting state and by the pairing wavefunction of the Cooper pairs. In clean superconductors, the spatial variations of the order parameter and the pairing wavefunction occur over the distances of the order of the coherence length and the Cooper-pair size, respectively. Therefore, by performing tunneling spectroscopy along a line passing through a vortex core, one is able, in principle, to estimate the values of the coherent length and the Cooper-pair size. To our knowledge, the theoretical consideration of the density of states inside vortex cores for unconventional superconductors is presented for the first time.     

On automated analysis of flow patterns in cerebral aneurysms based on vortex identification

It is hypothesized that the risk of rupture of cerebral aneurysms is related to geometrical and mechanical properties of the arterial wall as well as to local hemodynamics. In order to gain better understanding of the hemodynamical factors involved in intra-aneurysmal flows, a thorough analysis of the 3D velocity field within an idealized geometry is needed. This includes the identification and quantification of features like vortices and stagnation regions. The aim of our research is to develop experimentally validated computational methods to analyse intra-aneurysmal vortex patterns and, eventually, define candidate hemodynamical parameters (e.g. vortex strength) that could be predictive for rupture risk. A computational model based on a standard Galerkin finite-element approximation and an Euler implicit time integration has been applied to compute the velocity field in an idealized aneurysm geometry and the results have been compared to Particle Image Velocimetry (PIV) measurements in an in vitro model. In order to analyze the vortices observed in the aneurysmal sac, the vortex identification scheme as proposed by Jeong and Hussain (JFM 285:69–94, 1995) is applied. The 3D intra-aneurysmal velocity fields reveal complex vortical structures. This study indicates that the computational method predicts well the vortex structure that is found in the in vitro model and that a 3D analysis method like the vortex identification as proposed is needed to fully understand and quantify the vortex dynamics of intra-aneurysmal flow. Furthermore, such an automated analysis method would allow the definition of parameters predictive for rupture in clinical practice.     

Convectional controlled crystal–melt interface using two-phase radio-frequency electromagnetic heating

The radio frequency floating-zone growth of massive intermetallic single crystals is very often unsuccessful due to an unfavourable solid–liquid interface geometry enclosing concave fringes. This interface depends on the flow in the molten zone. A tailored magnetic two-phase stirrer system has been developed which enables the controlled influence on the melt flow ranging from intense inwards to outwards flows. Depending on the phase shift between the two induction coils, a transition from a double vortex structure to a single vortex structure is created at a preferable phase shift of 90°. This change in the flow field has a significant influence on the shape of the solid–liquid interface. Due to their attractive properties for high temperature applications such as high melting temperature, low density, high modulus and good oxidation resistance, the magnetic system was applied to the crystal growth of TiAl alloys.     

Organised structures in wall turbulence as deduced from stability theory-based methods

In earlier work, we have explored the relevance of hydrodynamic stability theory to fully developed turbulent wall flows. Using an extended Orr-Sommerfeld Equation, based on an anisotropic eddy-viscosity model, it was shown that there exists a wide range of unstable wave numbers (wall modes), which mimic some of the key features of turbulent wall flows. Here we present experimental confirmation for the same. There is good qualitative and quantitative agreement between theory and experiment. Once the dominant coherent structure is obtained from stability theory, control of turbulence would be the next logical step. As shown, the use of a compliant wall shows considerable promise. We also present some theoretical work for bypass transition (Klebanoff/K-modes), wherein the receptivity of a laminar boundary layer to a vortex sheet in the freestream has been studied. Further, it is shown that triadic interaction between K-modes, 2D TS waves and 3D TS waves can lead to rapid algebraic growth. A similar mechanism seems to carry over to inner wall structures in wall turbulence and perhaps this is the “root cause” for sustenance of turbulence.     

Three-dimensional vortex wake structure of flapping wings in hovering flight

Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.     

Propagation properties of a partially coherent anomalous hollow vortex beam in uniaxial crystal orthogonal to the optical axis

The concept of a partially coherent anomalous hollow vortex beam generated by a Schell-model source was introduced in this paper. Next, the analytical expressions of a partially coherent anomalous hollow vortex beam propagating in a uniaxial crystal orthogonal to the optical axis were derived, and the evolution properties of a partially coherent anomalous hollow vortex beam propagating in a uniaxial crystal were illustrated using numerical examples. Finally, the influences of the uniaxial crystal and the beam parameters on the spreading properties of partially coherent anomalous hollow vortex beam were analysed in detail.     

Numerical experiments on turbulent flow using the random vortex method

Chorin's random vortex method is used to predict the growth of a large-scale coherent vortex structure in the early stages of the development of turbulence in a two-dimensional co-flowing shear layer. The numerical algorithm has been simplified to such an extent that the numerical analysis can be performed on a microcomputer. The numerical solution exhibits the same early turbulent instabilities and vorticity pairings as found in recent flow-visualization experiments. In addition the results are in reasonable agreement with experimental measurements of mean velocity, root mean square fluctuations and Reynolds stresses. One could thus test the shear layer sensitivity to initial conditions and the upsteam boundary conditions.     

A physical model of the turbulent boundary layer consonant with mean momentum balance structure

Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean momentum balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.     

绕回转体初生空化流场特性的实验及数值研究

该文采用实验与数值模型相结合的方法对绕回转体的初生空化流场进行了分析,研究了头型对初生空化流场特性的影响,数值模型中,为了精确捕捉由于分离流动而产生的漩涡结构,湍流模型采用了一种基于空间尺度修正的滤波器模型(FBM),实验中,采用高速录像技术观察了初生空化形态,并应用粒子测速系统(PIV)测量了相应工况下,初生空化流场的速度及涡量分布,研究结果表明:头型对绕回转体的初生空化流场具有显著的影响,不同回转体的初生空化数随着肩部曲率突变增大而逐渐增大,在初生空化工况下,平头和锥头回转体肩部的高剪切流动区出现了不规则的漩涡分离结构,初生空化首先在该分离区域内产生,而不是发生在回转体的物面上或在物体邻近处,此时,初生空化流场体现出明显的漩涡脉动特性,流场中的低速高脉动区域对应于空化核心区,涡量主要亦集中在该漩涡分离区域内,对于圆头回转体,其初生空化流场比较稳定,“指状”的片状空泡附着在回转体表面上。