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.     

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.     

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.     

Dynamical systems and the transition to turbulence in linearly stable shear flows

Plane Couette flow and pressure-driven pipe flow are two examples of flows where turbulence sets in while the laminar profile is still linearly stable. Experiments and numerical studies have shown that the transition has features compatible with the formation of a strange saddle rather than an attractor. In particular, the transition depends sensitively on initial conditions and the turbulent state is not persistent but has an exponential distribution of lifetimes. Embedded within the turbulent dynamics are coherent structures, which transiently show up in the temporal evolution of the turbulent flow. Here we summarize the evidence for this transition scenario in these two flows, with an emphasis on lifetime studies in the case of plane Couette flow and on the coherent structures in pipe flow.     

Prospects for useful research on coherent structure in turbulent shear flow

Six different flows involving coherent structures are discussed with varying amounts of detail. These are the puff in a pipe, the turbulent spot, the spiral turbulence, the vortex ring, the vortex street, and the mixing layer. One central theme is that non-steady similarity arguments and topology are of the essence of coherent structure. Another is that the Reynolds equations, which are sterile when applied to a structureless mean flow, may be quite productive when applied to a single structure. A third theme is the prospect for at least partial control of technically important flows by exploiting the concept of coherent structure.     

Fundamentally excited flow past a surface-mounted rib. Part I: Turbulent structure characterisation

Different data analysis techniques for characterisation of the turbulent flow past a surface-mounted rib are reviewed. Deficiencies of the existing techniques are explained and modified techniques for determination of coherent structure magnitude and phase jitter are suggested. The effect of fundamental excitation on the flow is studied by using these turbulent signal analysis techniques. The appropriate length scale for characterizing the large-scale structures present in the reattaching shear layer of the surface-mounted rib is found to be the momentum thickness at the downstream edge of the rib, and the corresponding Strouhal number is 0.013. This is in contrast to a rib in the free stream, where the rib height is the correct scaling parameter. The post reattachment region is observed to be dominated by large-scale structures contrary to the traditional belief that large eddies break into small scales at the reattachment location. Low magnitude of phase jitter in the near field region is observed, indicating coherence of the flow structures. Phase decorrelation begins to occur beyond three rib heights from the downstream edge of the rib. From the quadrant analysis results, the outer edge of the shear layer is observed to be dominated by large-scale ejection motions.     

Chaotic stirring in quasi-turbulent flows

Transport in laminar flows is governed by chaotic stirring and striation in long thin filaments. In turbulent flows, isotropic mixing dominates and tracers behave like stochastic variables. In this paper, we investigate the quasi-turbulent, intermediate regime where both chaotic stirring and turbulent mixing coexist. In these flows, the most common in nature, aperiodic Lagrangian coherent structures (LCSs) delineate particle transport and chaotic stirring. We review the recent developments in LCS theory and apply these techniques to measured surface currents in Monterey Bay, California. In the bay, LCSs can be used to optimize the release of drifting buoys or to minimize the impact of a coastal pollution source.     

The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet

The role of coherent vortices near the turbulent/non-turbulent (T/NT) interface in a turbulent plane jet is analysed by a direct numerical simulation (DNS). The coherent vortices near the jet edge consist of large-scale vortical structures (LSVSs) maintained by the mean shear and intense vorticity structures (IVSs) created by the background fluctuating turbulence field. The radius of the LSVS is equal to the Taylor micro-scale R(lsvs)≈λ, while the radius of the IVS is of the order of the Kolmogorov micro-scale R(ivs)~η. The LSVSs are responsible for the observed vorticity jump at the T/NT interface, being of the order of the Taylor micro-scale. The coherent vortices in the proximity of the T/NT interface are preferentially aligned with the tangent to the T/NT interface and are responsible for the viscous dissipation of kinetic energy near the T/NT interface and to the characteristic shape of the enstrophy viscous diffusion observed at that location.     

Improved version of the synthetic eddy method for setting nonstationary inflow boundary conditions in calculating turbulent flows

One method for generating synthetic turbulence, i.e., the synthetic eddy method, is tested by means of the example of canonical turbulent shear flows (plane-channel and boundary-layer flows). A modification of the method, differing from the original version by the determination of the linear scale of synthetic eddy structures, is proposed. The synthetic field of turbulent fluctuations evolves more quickly to the physically realistic one when the modified method is used instead of the original one. The friction coefficient and profiles of the average velocity and Reynolds stresses also deviate less and recover faster if the modified method is used.     

A particle–particle Reynolds stress transportation model of swirling particle-laden-mixtures turbulent flows

On the basis of the gas–particle Euler–Euler two-fluid approach, a new particle–particle Reynolds stress transportation model is proposed for closing the constitution equations of particle-laden-mixtures turbulent flows. In this model, binary particle-particle interaction originating from large-scale particle turbulent diffusions are fully considered in view of an extension closure idea of second-order-moment disperse gas–particle turbulent flows. The binary-particles turbulent flows with different density and same diameter are numerically simulated. The number density, the time-averaged velocity, the fluctuation velocity, the multiphase fluctuation velocity correlations, the normal and the shear Reynolds stress are obtained. Simulated results are in good agreement with experimental data. Binary mixture system has a unique transportation behavior with a stronger anisotropy due to particle inertia and multiphase turbulence diffusions. Fluctuation velocity correlation of axial–axial gas–particle is about twice larger than those of axial–axial particle–particle interaction. Moreover, both normal and shear Reynolds stress are redistributed.     

逆压梯度下近壁湍流的喷射和扫掠

采用Fourier谱展开和紧致有限差分格式，选用两组共振三波为相干结构的初值，计算了其在零压和逆压梯度作用下的演化。对演化后期流场的2，4象限的运动进行了详细的分析。结果发现，在逆压梯度下，扫掠对雷诺应力的贡献要强于喷射。无论是在零压梯度还是逆压梯度下，uv和u2在法向的输运主要是靠Q2和Q4这两种运动来完成的。零压梯度下喷射部分对输运的贡献大于扫掠的部分。而在逆压梯度下喷射部分对输运的贡献明显减少，扫掠的作用要强于喷射。     

Large- and very-large-scale motions in channel and boundary-layer flows

Large-scale motions (LSMs; having wavelengths up to 2-3 pipe radii) and very-LSMs (having wavelengths more than 3 pipe radii) have been shown to carry more than half of the kinetic energy and Reynolds shear stress in a fully developed pipe flow. Studies using essentially the same methods of measurement and analysis have been extended to channel and zero-pressure-gradient boundary-layer flows to determine whether large structures appear in these canonical wall flows and how their properties compare with that of the pipe flow. The very large scales, especially those of the boundary layer, are shorter than the corresponding scales in the pipe flow, but otherwise share a common behaviour, suggesting that they arise from similar mechanism(s) aside from the modifying influences of the outer geometries. Spectra of the net force due to the Reynolds shear stress in the channel and boundary layer flows are similar to those in the pipe flow. They show that the very-large-scale and main turbulent motions act to decelerate the flow in the region above the maximum of the Reynolds shear stress.     

Hydrodynamic structures — elements of the self-sustained oscillation system in the flow

The character of hydrodynamic disturbances in the near-wall shear flow inducing self-oscillations in the channel has been investigated. Experiments have been performed in a small and a large wind tunnel at a flow velocity of 10–40 m / sec. It has been found that excitation of self-oscillations becomes possible as a result of narrow-band acoustic radiation generation by not only vortex formations but also large-scale coherent structures in the region of the laminar-turbulent transition and in the turbulent boundary layer.     

Evolution properties of the complex degree of coherence of a partially coherent Laguerre–Gaussian beam in turbulent atmosphere

Evolution properties of the complex degree of coherence of a partially coherent Laguerre–Gaussian beam (LGB) on propagation in free space and turbulent atmosphere are studied comparatively with the help of the general propagation formula for such beam. It is found that the behavior of the complex degree of coherence of a partially coherent LGB on propagation in turbulent atmosphere is much different from that in free space and is closely related to the initial beam parameters and the structure constant of the turbulent atmosphere. The distribution of the modulus of the complex degree of coherence of the partially coherent LGB finally becomes of Gaussian distribution at long propagation distance in turbulent atmosphere, and it becomes of Gaussian distribution more slowly with the increase of the mode orders, beam width and wavelength. Our results will be useful in long-distance free-space optical communications.     

Propagation of partially coherent Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere

Based on the generalized Huygens–Fresnel integral, propagation of partially coherent Lorentz and Lorentz–Gauss beams through a paraxial ABCD optical system in a turbulent atmosphere was investigated. Analytical propagation formulae were derived for the cross-spectral densities of partially coherent Lorentz and Lorentz–Gauss beams. As an application example, the focusing properties of partially coherent Gaussian, Lorentz and Lorentz–Gauss beams in a turbulent atmosphere and in free space were studied numerically and comparatively. It is found that the focusing properties of such beams are closely related to the initial coherence length and the structure constant of turbulence. By choosing a suitable initial coherence length, a partially coherent Lorentz beam can be focused more tightly than a Gaussian or Lorentz–Gauss beam in free space or in a turbulent atmosphere with small structure constant at the geometrical focal plane.     

Direct numerical simulation of stably and unstably stratified turbulent open channel flows

Summary Direct numerical simulation of stably and unstably stratified turbulent open channel flow is performed. The three-dimensional Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method based on high-order accurate spatial schemes. The objective of this study is to reveal the effects of thermally stable and unstable stratification on the characteristics of turbulent flow and heat transfer and on turbulence structures near the free surface of open channel flow. Here, fully developed weakly stratified turbulent open channel flows are calculated for the Richardson number ranging from 20 (stably stratified flow) to 0 (unstratified flow) and to −10 (unstably stratified flow), the Reynolds number 180 based on the wall friction velocity and the channel depth, and the Prandtl number 1. To elucidate the turbulent flow and heat transfer behaviors, typical quantities including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of velocity and temperature fluctuations are analyzed.     

Investigation of plane mixing layer using large eddy simulation

Spatially evolving turbulent mixing layers are investigated in this paper using large eddy simulation. The evolutions of large vortex structures are obtained, in which the processes of vortex roll up, growth, pairing and breaking up are shown in details. The simulated flow patterns agree well with experimental visualization results. Predicted results of mean properties of streamwise velocity, fluctuating velocity and Reynolds stress at different sections show good self-similarity and agree well with experimental measurements. Linear growth of the momentum thickness along the streamwise direction is then obtained, indicating that pairing and amalgamating of large vortex structures in plane mixing layers occur randomly in space and time. The effects of convection velocity and the rate of shear on the evolution of vortex structures, self-similarity as well as momentum thickness are also investigated. The rate of shear has a significant effect on the evolution of coherent structure and the slope of momentum thickness growth, while the convection velocity only affects the space interval of the adjoining vortices. The rate of shear and convection velocity have no significant effect on the non-dimensional distributions of turbulence statistics. Self-similarities are therefore obtained for different rates of shear and convection velocities.This work was partially supported by the National Natural Science Foundation of China (Grant No.10002009) and The Research Committee of The Hong Kong Polytechnic University (Project Account Codes G-T609 and G-T429).     

Clusterization of particles in turbulent and vortex two-phase flows

Experimental investigations and theoretical calculations devoted to studying different aspects of the formation of clusters in two-phase flows are reviewed. The physical mechanisms of the formation of the regions of increased concentrations of particles in turbulent flows and under flowing bodies by two-phase streams, as well as in free concentrated vortices, are considered.     

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.     

Numerical calculation of fully developed turbulent flow in curved channels: An extended algebraic Reynolds-stress model

The primary objective of the paper is to extend an algebraic Reynolds-stress model including a new expression for the turbulent shear stress, in order to describe the negative production of turbulent kinetic energy appearing in curved channel flows in a region between the points of maximum velocity and vanishing shear stress. This so-called energy reversal cannot be captured by the majority of turbulence models with conventional eddy-viscosity formulation. Computations are made for fully developed flows in channels of rectangular cross section and large aspect ratio with mild and strong curvature. The results are compared with different model predictions and experimental data reported in the literature. In the cases considered, the accuracy of present model predictions is comparable to that of a Reynolds-stress model. The latter, however, requires much more computing time and is thus more costly than the model here proposed.