Vortex identification in the wake of a model wind turbine array

Vortex identification techniques are used to analyse the wake of a 4 × 3 array of model wind turbines. The Q-criterion, Δ-criterion, and λ₂-criterion are applied to particle image velocimetry data gathered fore and aft of the last row centerline turbine. The Q-criterion and λ₂-criterion provide a clear indication of regions where vortical activity exists, while the Δ-criterion is not successful. Galilean decomposition, Reynolds decomposition, vorticity, and swirling strength are used to further understand the location and behaviour of the vortices. The techniques identify and display the high-magnitude vortices in high-shear zones resulting from the blade tips. Using Galilean and Reynolds decomposition, swirling motions are shown encapsuling vortex regions in agreement with the identification criteria. The Galilean decompositions selected are 20% and 50% of a convective velocity of 7 m/s. As the vortices convect downstream, the strength of the vortices decreases in magnitude, particularly in the far wake of the array, to approximately 25% of those present in the near wake. A high level of vortex activity is visualised as a result of the top tip of the wind turbine blade -- the location where the highest vertical entrainment is present. Analysing the full frame set, the Q-criterion, λ₂-criterion, and swirling strength prove comparable, while the Δ-criterion under-performs in regions of high turbulence activity, namely in the back of the turbine. Entraining flow into the turbine canopy interacting with the turbine generates high-magnitude vortices concentrated at the blade tips. The count of vortices decreases when moving from the top tip down to the wall, as well as their strength for each Galilean technique when a non-zero threshold is applied. Vortex sizes in the near wake are found comparable to turbine blade, hub, and mast dimensions. In the far wake, the resulting size of the vortices is approximately 30% of those in the near wake. These vortices increase in velocity as they convect downstream, following the mean velocity behaviour. The lowest magnitude vortices reside at the hub height in the near-wake region, where they convect at nearly half the speed of those at the blade tips.     

Control of a coupled map lattice model for vortex shedding in the wake of a cylinder

The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns, vortex dislocations and frequency cells. These structures have been observed in experiments and numerical simulations, and are predicted by a previously developed low-order coupled map lattice (CML). The discrete (in time and space) CML models consist of a series of diffusively coupled circle map oscillators along the cable span. Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics. Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, and the controller was designed for the resulting linearized system using eigenvalue assignment. These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow. Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory. The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span. The DNL method was found to be the most efficient controller of the low-order CML model. The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map.     

Coherence and Reynolds stresses in the turbulent wake behind a curved circular cylinder

The turbulent wake behind a curved circular cylinder is investigated based on data obtained from a direct numerical simulation. Here, emphasis is placed in the assessment of two approaches for simplified modelling: reduced-order modelling (ROM) and Reynolds-averaged Navier–Stokes equations. To this end, the instantaneous vortical structures, the proper orthogonal decomposition (POD) of the flow, and relevant Reynolds stress components have been analysed. The results show that despite the complexity of the instantaneous vortical structures, the wake dynamics are governed by the quasi-periodic shedding of primary vortices. Between 24% and 50% of the kinetic energy in the POD is captured by the two most energetic modes, and about 200 modes are needed to capture 90% of the kinetic energy. These findings suggest that, as long as the large-scale structures of the von Kármán vortex shedding are concerned, the present case can be approached by ROM; but a detailed representation of the flow dynamics without an eddy viscosity model that accounts for the unresolved turbulent fluctuations would require a large amount of degrees of freedom. Concerning the Reynolds stresses, their magnitude varies considerably depending on the depth at which they have been sampled. This dependence is related to the strength of the vortex shedding, and the intensity of the secondary flows induced by the curvature of the cylinder. As a consequence of the combination of these two effects, the correlation between streamwise and vertical velocity fluctuations is highest in the wake behind the midspan of the curved cylinder, and the correlation between cross-flow and vertical velocity fluctuations reaches large values in the lower wake.     

离心压气机叶排间涡脱落及气流脉动行为研究

对某一带叶片扩压器跨声速离心压气机内部三维非定常流场进行了数值模拟,依据计算结果描述了叶轮叶片尾缘尾迹涡脱落行为,给出了叶轮尾缘脉动压力频谱特性图和叶轮出口位置脉动速度动能分布图。研究结果表明,主叶片与分流叶片尾缘尾迹涡脱落过程交替进行;转静干涉和转子叶片尾缘的涡脱落行为是造成叶轮尾缘气流脉动行为的主要原因,随着时间的...     

Electromagnetic interactions in a cluster of cylinders

We present a rigorous multiple-scattering method to calculate the interaction energies due to electromagnetic field fluctuations in a cluster of parallel cylinders. Various kinds of cluster structure with both isotropic and anisotropic materials are considered. It is shown that Casimir interactions are sensitive to the positions of the cylinders in the cluster or the structure of the system. The sign of the interaction energy cannot only be changed by tuning the parameters of anisotropic materials, it can also be caused by changing the cylinders configuration of the system.     

平流涡度方程及其在2006年Bilis台风分析中的应用

推导得到气压坐标中的动量叉乘形式的垂直涡度方程,这个动量叉乘形式的涡度方程包含了水平风的平流旋转效应,可称为平流涡度方程.由于水平风场的平流作用可由等压面天气图直观分析得到,因此平流涡度方程可方便用于实际天气分析.对2006年的Bilis台风移动过程中由经典涡度方程和平流涡度方程计算得到的垂直涡度倾向进行对比分析发现,二者计算得到的垂直涡度倾向变化的分布形式接近,但平流涡度方程计算得到的倾向的数值明显大于经典涡度方程的数值,正负涡度倾向区也更集中.对Bilis移动过程中的垂直涡度方程和平流涡度方程中各项的计算分析表明,水平风场的平流旋转作用是Bilis发展移动过程中垂直涡度变化的一个主要因素,是造成垂直涡度增强并发展的主要原因.因此,当水平风场平流旋转效应较强时,平流作用对垂直涡度倾向变化起主导作用,可直接用平流项来近似分析Bilis台风的涡度变化.而平流涡度方程中地转涡度和散度项的变化趋势与Bilis台风的移动路径有较好的一致性,这一项对台风的移动路径预报有更好的指示意义.     

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates Ω is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of Ω = 5 rad/s (with Rossby number much smaller than unity). Typically, the Taylor-scale Reynolds number in our experiments is around Re_λ ≈ 100. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see L.J.A. van Bokhoven, H.J.H. Clercx, G.J.F. van Heijst, and R.R. Trieling, Experiments on rapidly rotating turbulent flows, Phys. Fluids 21 (2009) 096601. Based on the full set of velocity derivatives, measured in a Lagrangian way by three-dimensional (3D) particle tracking velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. For the range of rotation rates considered, the experimental results show how the turbulence evolves from almost isotropic 3D turbulence (Ω ? 0.2 rad/s) to quasi-two-dimensional turbulence (Ω ≈ 5.0 rad/s), and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect of background rotation is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.     

Mean velocity behaviour in the near wake of long slender cylinder with a sharp trailing edge at a high Reynolds number

A simple eddy viscosity model is applied to the governing equations to establish the behaviour of the mean velocity in the turbulent axisymmetric near wake. The near wake develops from a long slender cylinder which is kept parallel to the flow and is developing under zero streamwise pressure gradient. The upstream turbulent boundary layer on the body of revolution is fully developed. In the inner layer of the flow downstream of the trailing edge, the turbulent inner layer of the upstream boundary layer grows into the initial logarithmic layer, and as a consequence, the centreline velocity in the near wake is shown to increase logarithmically with streamwise distances for large streamwise distances. The analysis further leads to two regions of the near wake flow (the inner near wake and the outer near wake), similar to that of a fully developed turbulent boundary layer, for which the governing equations have been derived. The matching between these two regions leads to a logarithmic variation in the normal direction. Also shown is the variation of the square of the wake width which varies logarithmically with streamwise distance in the near wake. These features are validated by comparison with available experimental data.     

Forces and torque on a pair of uncharged conducting cylinders in an external electric field

Exact results are given for the forces per unit length acting on each of a pair of parallel conducting cylinders when polarized by an external electric field perpendicular to the cylinders. Simple analytic results are obtained at small and large separations of the cylinders. The torque on the cylinders (which acts to align them with the electric field) is proportional to the difference between the longitudinal and transverse polarizabilities. The forces acting on the cylinders (which are equal and opposite) are given by the derivatives of the polarizabilities with respect to their separation.     

Numerical simulation and flow visualization using soap film of the self-organized vortex structure in the wake of an array of cylinders

Abstract  

With the aid of computational fluid dynamics (CFD) and simple flow visualization technique using flowing soap-film, we present here the wake structures behind an array of cylinders for Reynolds numbers corresponding to both laminar and turbulent flow regimes. The image results illustrate interesting vortex interactions past these equally spaced cylinders; for low Reynolds number flow, well-organized wake pattern persists and manifests unsteadily to different symmetry states. An increase of free stream flow velocity causes the wake transition, resulting in the formation of asymmetric flow wake with chaotic mixing at the far wake. Observations from both the numerical simulations and soap-film are in good agreement at least qualitatively.     

正弦高斯涡旋光束的远场传输特性

根据角谱法和稳相法,推导了正弦高斯涡旋光束TE波和TM波在远场传输和能流密度的解析表达式,研究了正弦高斯涡旋光束在远场中的相位奇点和能流密度分布.结果表明:正弦高斯涡旋光束的远场特性与高斯光束的束腰宽度、涡旋离轴量、坐标位置以及与正弦项相关的参量有关.在一定条件下,远场中会出现相位奇点和能流密度黑核;当控制参量改变时,相位奇点和黑核的位置会发生移动,但原点处不受影响.相位奇点和能流密度的对称性主要受涡旋离轴量影响,当涡旋离轴量为0时,相位奇点和能流密度分布关于原点对称;当涡旋离轴量改变时,相位奇点和能流密度分布呈现出非对称性.     

圆管管翅散热器肋侧主流方向绝对涡通量研究

本文以圆管管翅式散热器为研究对象,采用数值模拟的方法对圆管管翅式散热器肋侧空气通道主流方向绝对涡通量的特性进行了探讨。给出了肋侧空气通道主流方向绝对涡通量无量纲化参数,二次流雷诺数;横向管间距、肋侧空气流动雷诺数对二次流雷诺数及努塞尔数的影响。     

超音速射流火焰的DNS研究:计算方法与涡结构

介绍了可压缩反应流的计算方法,然后计算了超音速射流火焰,对超音速射流火焰中的涡结构进行了分析。认为超音速射流火焰中的涡结构特征,与亚音速射流中有本质差异,且涡结构在燃料与组分的混合中起到了重要作用,进而直接影响火焰结构和燃烧效率。     

部分相干涡旋光束在大气湍流中的远场传输特性

运用广义惠更斯-菲涅耳原理,详细研究了部分相干涡旋光束在湍流介质中的远场传输规律.研究表明,部分相干涡旋光束的光谱相干度及光强分布与光束的拓扑电荷数、空间相对相干长度及湍流介质的折射率结构常数等因素有关.在湍流介质中,光谱相干度存在相位奇点,并且随着空间相对相干长度的增大,相干涡旋逐渐演化为强度涡旋,而湍流介质的强弱对部分相干涡旋光束的影响则相反,随着湍流介质的折射率常数的增大,强度涡旋逐渐演化为相干涡旋.     

Green’s function-stochastic methods framework for probing nonlinear evolution problems: Burger’s equation, the nonlinear Schrödinger’s equation, and hydrodynamic organization of near-molecular-scale vorticity

A framework which combines Green’s function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green’s function and stochastic representative solutions of linear drift–diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems – Burgers’ equation and the nonlinear Schrödinger’s equation – are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole–Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger’s vortex sheets. Here, the governing vorticity equation corresponds to the Fokker–Planck equation of an Ornstein–Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion and spread of single, multiple, and continuous sets of Burger’s vortex sheets, evolving within deterministic and random strain rate fields, under both viscous and inviscid conditions, are obtained. In order to promote application to other nonlinear problems, a tutorial development of the framework is presented. Likewise, time-incremental solution approaches and construction of approximate, though otherwise difficult-to-obtain backward-time GF’s (useful in solution of forward-time evolution problems) are discussed.     

Differential Geometry and Integrability of the Hamiltonian System of a Closed Vortex Filament

The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequence of constants of motion in involution. An algebraic framework is given with the aim of describing the differential geometry of this system and a geometrical structure related to the integrability of this system is revealed. It is not a bi-Hamiltonian structure but a similar one. As a related topic, a remark on the inspection of J. Langer and R. Perline (J. Nonlinear Sci. 1 (1991), 71) is given.     

Time and direction of arrival detection and filtering for imaging in strongly scattering random media

We study detection and imaging of small reflectors in heavy clutter, using an array of transducers that emits and receives sound waves. Heavy clutter means that multiple scattering of the waves in the heterogeneous host medium is strong and overwhelms the arrivals from the small reflectors. Building on the adaptive time-frequency filter of [Borcea et al, SIIMS 2011;4(3)], we propose a robust method for detecting the direction of arrival of the direct echoes from the small reflectors, and suppressing the unwanted clutter backscatter. This improves the resolution of imaging. We illustrate the performance of the method with realistic numerical simulations in a non-destructive testing setup.     

Comparisons of Performances of a Flat Tube Bank Fin Model Mounted Vortex Generators and the Real Heat Exchanger

Abstract

In this article, we compared the model results obtained by the naphthalene sublimation method with the results obtained by experiments with the real heat exchanger based on the model used in the naphthalene sublimation experiment. The results reveal that in the Reynolds number region studied in the present article, the experimental results obtained by naphthalene sublimation agree with the experimental data of the real heat exchanger under the working conditions within a 10% deviation. The heat/mass transfer coefficient obtained with an isothermal condition using naphthalene sublimation can be applied to the mixed thermal boundary condition. The effects of mounted and punched vortex generators on thermal-hydraulic performances are limited to the configuration studied in this article.     

A theoretical and experimental study of the behaviour of a parametric array in a random medium

The fluctuations of a parametric signal in a random medium have been investigated. A theoretical expression for the mean square amplitude and phase fluctuations has been derived, by using the small perturbation method. A simplified version of the theoretical model, which predicts the axial amplitude fluctuations of the difference frequency signal, was computerized. Laboratory experiments were carried out in a heated tank in which the fluctuations of a parametric signal and a linearly generated signal were compared. A similar experiment was also carried out in an estuary. The experimental results obtained were consistent with the theoretical estimates.