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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Wavelet filtering for topological decomposition of flow fields

The experimental technique of high-image-density particle image velocimetry makes it possible to resolve quantitatively instantaneous, two-dimensional sections of complex fluid flows. Detailed distributions of velocity in the plane of the section and instantaneous out-of-plane vorticity field can be calculated. The key features of complex flows, such as the onset of vortex breakdown, correspond to distinct topological structures of the vorticity field. It is often desirable to determine the location, size, and orientation of these topological structures in large sets of vorticity data. A mother wavelet function that imitates the topology of the vorticity field in the vicinity of breakdown has been constructed. The wavelet transform based on this mother wavelet is applied to the vorticity data. When the scale and orientation of the wavelet closely match those of the breakdown zone in the data sets, local signal maxima at the location of the breakdown can be observed in the corresponding transform planes. When the scale or orientation do not match, the peaks are not observed. With this approach, information on the location, size and orientation of the breakdown zone can be derived using the wavelet transform. The wavelet transform therefore serves as an effective means of pattern recognition, and has potential application to a broad range of problems in fluid mechanics. © 1996 John Wiley & Sons, Inc.     

Structure and dynamics of low Reynolds number turbulent pipe flow

Using large-scale numerical calculations, we explore the proper orthogonal decomposition of low Reynolds number turbulent pipe flow, using both the translational invariant (Fourier) method and the method of snapshots. Each method has benefits and drawbacks, making the 'best' choice dependent on the purpose of the analysis. Owing to its construction, the Fourier method includes all the flow fields that are translational invariants of the simulated flow fields. Thus, the Fourier method converges to an estimate of the dimension of the chaotic attractor in less total simulation time than the method of snapshots. The converse is that for a given simulation, the method of snapshots yields a basis set that is more optimal because it does not include all of the translational invariants that were not a part of the simulation. Using the Fourier method yields smooth structures with definable subclasses based upon Fourier wavenumber pairs, and results in a new dynamical systems insight into turbulent pipe flow. These subclasses include a set of modes that propagate with a nearly constant phase speed, act together as a wave packet and transfer energy from streamwise rolls. It is these interactions that are responsible for bursting events and Reynolds stress generation. These structures and dynamics are similar to those found in turbulent channel flow. A comparison of structures and dynamics in turbulent pipe and channel flows is reported to emphasize the similarities and differences.     

Melt Flow Instability and Turbulence in Electro-Magnetically Levitated Droplets

This article addresses fluid flow instabilities and flow transition to turbulent chaotic motions through numerical analysis and turbulence in electro-magnetically levitated droplets through direct numerical simulations. Numerical implementation and computed results are presented for flow instability and turbulence flows in magnetically levitated droplets under terrestrial and microgravity conditions. The linear melt flow stability is based on the solution of the Orr-Sommerfeld linearized equations with the base flows obtained numerically using high order numerical schemes. The resulting eigenvalue problems are solved using the linear transformation or Arnold's method. Melt flow instability in a free droplet is different from that bounded by solid walls and flow transits to an unstable motion at a smaller Reynolds number and at a higher wave number in a free droplet. Also, flow instability depends strongly on the base flow structure. Numerical experiments suggest that the transition to the unstable region becomes easier or occurs at a smaller Reynolds number when the flow structures change from two loops to four loops, both of which are found in typical levitation systems used for micro-gravity applications. Direct numerical simulations (DNS) are carried out for an electro-magnetically levitated droplet in a low to mild turbulence regime. The DNS results indicate that both turbulent kinetic energy and dissipations attain finite values along the free surface, which can be used to derive necessary boundary conditions for calculations employing engineering k--ε models.     

大气边界层大涡模拟入口湍流生成方法研究

生成满足大气边界层风场特性的入口湍流是开展结构风效应大涡模拟的关键问题之一。该文的主要目的是验证并探讨两类主要的大气边界层大涡模拟入口湍流生成方法的合理性与可行性。采用CDRFG(Consistent Discretizing Random Flow Generation)方法和被动模拟法生成大气边界层风场,从统计特性、流场结构和计算效率等方面进行对比分析,比较不同网格系统下的数值模拟结果,提出结构风效应大涡模拟的网格划分策略。结果表明:相比于CDRFG方法,被动模拟法生成的流场结构更加合理,但无法预先考虑脉动风场的空间相关性,且需要较高的计算成本和先验的流场信息。计算域的网格分辨率对于统计特性和流场结构的模拟精度具有重要影响,而目标区域的网格分辨率应依据控制工程结构风致响应的主要频带范围确定。     

Fundamentals of the double – decomposition concept for turbulent transport in permeable media

Environmental impact analyses as well as engineering equipment design can both benefit from reliable modeling of turbulent flow in porous media. A number of natural and engineering systems can be characterized by a permeable structure through which a working fluid permeates. Turbulence models proposed for such flows depend on the order of application of time and volume average operators. Two methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. This paper reviews recently published methodologies to mathematically characterize turbulent transport in porous media. A new concept, called double‐decomposition, is here discussed and models for turbulent transport in porous media are classified in terms of the order of application of the time and volume averaging operators, among other peculiarities. Within this paper Instantaneous Local Transport Equations are reviewed for clear flow before Time and Volume Averaging Procedures are applied to them. The Double‐Decomposition Concept is presented and thoroughly discussed prior the derivation of macroscopic governing equations. Equations for Turbulent Transport follow, showing detailed derivation for the mean and turbulent field quantities.     

Denoising quadrature Doppler signals from bi-directional flow using the wavelet frame

A novel approach was proposed to denoise quadrature Doppler signals from bi-directional blood flow using the wavelet frame and a soft-thresholding algorithm. A direction separation step was carried out first to avoid the phase distortion of quadrature Doppler signals, which is induced from the nonlinear, soft-thresholding processing. Then real parts of separated complex signals from the unidirectional flow were denoised independently. The quadrature Doppler signals from the bi-directional flow were reconstructed from the denoised separated signals. The approach has been applied to the simulated Doppler signals from a femoral artery. It is concluded from the experimental results that this method is practical for denoising quadrature Doppler signals.     

Systematic errors in optical-flow velocimetry for turbulent flows and flames

Optical-flow (OF) velocimetry is based on extracting velocity information from two-dimensional scalar images and represents an unseeded alternative to particle-image velocimetry in turbulent flows. The performance of the technique is examined by direct comparison with simultaneous particle-image velocimetry in both an isothermal turbulent flow and a turbulent flame by use of acetone-OH laser-induced fluorescence. Two representative region-based correlation OF algorithms are applied to assess the general accuracy of the technique. Systematic discrepancies between particle-imaging velocimetry and OF velocimetry are identified with increasing distance from the center line, indicating potential limitations of the current OF techniques. Directional errors are present at all radial positions, with differences in excess of 10 degrees being typical. An experimental measurement setup is described that allows the simultaneous measurement of Mie scattering from seed particles and laser-induced fluorescence on the same CCD camera at two distinct times for validation studies.     

Numerical experiments on feedback EMHD control of large scale coherent structures in channel turbulence

Summary The current work focusses on the spatio-temporal evolution of large scale coherent structures in the turbulent boundary layer of a plane channel both with and without microtile-based EMHD control. The heuristic concept behind the microtile designs that we have simulated apparently does not yield a successful drag reduction strategy (for the open-loop case [1]). In this work we investigate the flow response when the Lorentz force is applied with feedback conditioned on the advection of large-scale flow structures (e.g. hairpin vortices). We performed a long-time simulation conditioned on the passage of strong ejection events but obtained no reduction in skin friction. Based on short-time simulations we found that the near-wall flow structures undergo merely a spatial phase-shift when advecting above a single Lorentz force actuator: the structures are simply decelerated or accelerated with little change in their appearance, based on flow visualization. During this interaction of the applied Lorentz force with the flow, the Reynolds stress is unchanged.     

Premixed combustion study: Turbulence in the nozzle behind grids and spheres

The experimental investigation of turbulence in the nozzle behind grids and spheres as the instrumentation for turbulent combustion of premixed flows by means of PIV and thermoanemometry was carried out. These methods were compared and applied in turbulent flows behind grids and spheres. Flows with relatively low turbulence intensities of the mean flow velocity (~1%), corresponding to the laminar flow in the case of absence of obstacles at low flow rates were investigated. Numerical simulation of the flow in a channel with changing geometry was carried out. A good agreement between laboratory experiments and numerical simulations was obtained. The developed experimental device is recommended for use in turbulent combustion of premixed flows.     

Efficient representation of turbulent flows using data-enriched finite elements

Efficient modal decomposition of high-dimensional turbulent flow data is an important first step for data reduction, analysis, and low-dimensional predictive modeling. The conventional modal decomposition techniques, such as proper orthogonal and dynamic mode decompositions, aim to represent the system response using spatially global basis vectors that span a broad spatial domain. A significant challenge facing approaches based on global domain decomposition is the rapid increase in both the amount of training data and the number of modes that must be retained for an accurate representation of convection dominated turbulent flows. An alternative generalized finite element (GFEM) based approach is explored for efficient representation of high-dimensional fluid flow data. Here, the standard finite element interpolation method is enriched with numerical functions that are learned from a small amount of high-fidelity training data over spatially localized subdomains. The GFEM approach is demonstrated on a 3D flow past a cylinder at Reynolds number of 100 000 and flows inside a 2D lid-driven cavity over a range of Reynolds numbers. Compared with a global proper orthogonal decomposition, the GFEM-based approach increases efficiency in reconstructing the datasets while also substantially reducing the amounts of training data.     

基于拉格朗日方法的非定常空化流动研究

采用基于拉格朗日体系的有限时间李雅普诺夫指数、拉格朗日拟序结构和粒子追踪方法对绕水翼典型非定常云状空化流场进行研究。采用计算流体动力学方法获得空化流场数据数值,湍流模型采用经典大涡模拟方法,空化相变过程采用基于相间质量传输的Zwart模型进行处理。根据有限时间李雅普诺夫指数分布在空化核心区域定义了前缘拟序结构和尾缘拟序结构。在不同的空化发展阶段,两种拟序结构相互作用并呈现不同的分布规律,揭示不同空化发展阶段的典型流场结构。