A study of the energetic turbulence structures during stall delay

This study revealed the three-dimensional instantaneous topologies of the large-scale turbulence structures in the separated flow on the suction surface of wind turbine’s blade during stall delay. These structures are the major contributors to the first two POD (proper orthogonal decomposition) modes. The two kinds of instantaneous flow structures as major contributors to the first POD mode are: (1) extended regions of downwash flow with an upstream upward flow beside it and a compact vortex pair closer to the blade’s leading edge; (2) a large-scale clockwise vortex with strong induced flows. The two kinds of flow structures contributing significantly to the second POD mode are: (1) large counter-rotating vortices inducing strong upward velocities and a series of small vortices; (2) strong downwash flow coming from the leading-edge shear layer with a large and strong vortex on the left side and small vortices upstream. The statistical impacts of these large-scale and energetic structures on the turbulence have also been studied. It was observed that when these turbulence structures were removed from the flow, the peak values of some statistics were significantly reduced.     

Vortex mechanism of heat transfer enhancement in a channel with spherical and oval dimples

Vortex mechanism of heat transfer enhancement in a narrow channel with dimples has been investigated numerically using LES and URANS methods. The flow separation results in a formation of vortex structures which significantly enhance heat transfer on dimpled surfaces leading to a small increase in pressure loss. The heat transfer can be significantly increased by rounding the dimple edge and use of oval dimples. To get a deep insight into flow physics LES is performed for single phase flow in a channel with a spherical dimple. The instantaneous vortex formation and separation are investigated in and around the dimple area. Considered are Reynolds numbers (based on dimple print diameter) Re_D = 20,000 and Re_D = 40,000 the depth to print diameter ratio of Δ = 0.26. Frequency analysis of LES data revealed the presence of dominating frequencies in unsteady flow oscillations. Direct analysis of the flow field revealed the presence of coherent vortex structure inclined to the mean flow. The structure changes its orientation in time causing the long period oscillations with opposite-of-phase motion. Three dimensional proper orthogonal decomposition (POD) analysis is carried out on LES pressure and velocity fields to identify spatio-temporal structures hidden in the random fluctuations. Tornado-like spatial POD structures have been determined inside dimples.     

Gappy POD方法重构湍流数据的研究

Gappy POD 是一种基于本征正交分解(proper orthogonal decomposition, POD)的数据重构方法. 本文研究了gappy POD在湍流数据重构中的应用, 主要关注了以下两个因素的影响: 第一, 数据本身的复杂程度, 即构成流场的POD模态数量; 第二, 破损区域的面积大小和几何形状. 考虑到上述因素, 本文重新严格地表述了gappy POD的重构过程, 并推导出gappy POD重构误差的公式. 论文选取旋转湍流数据为案例进行了gappy POD重构的研究, 并解释了构成gappy POD重构误差的两个部分. 第一部分来自流场POD展开的截断误差, 该截断误差会被POD基函数在已知点上的值组成的矩阵的最小特征值放大. 这部分误差主要取决于流场的复杂程度, 当流场复杂程度较低时, 相应误差随采用的POD模态数目增大而减小. 当流场复杂程度较高时, 很小的POD截断误差也会导致很大的重构误差, 此时需要采用流场所有的POD模态进行重构以消除截断误差. 重构误差的第二部分来自POD基函数在已知点上的值组成的矩阵的非列满秩性, 它主要取决于破损区域的面积大小和几何形状. 破损区域的面积越大, 或者破损面积相同时, 破损区域内信息所包含的相关性越大, 第二部分的重构误差越大.      

Turbulence-Driven Blowout Instabilities of Premixed Bluff-Body Flames

Bluff-body flame instabilities are experimentally investigated under varying turbulence conditions during lean blowout. For all turbulence conditions, the blowout process is induced through a temporal reduction of the fuel flow rate to capture the flame-flow dynamics approaching blowout. Simultaneous high-speed particle image velocimetry (PIV), stereoscopic PIV, and C₂*/CH* chemiluminescence imaging are employed, along with an independent CH* imaging system, to capture flame-flow instabilities. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques are used to identify prominent flame oscillations and evaluate recurring spatiotemporal modes during blowout. The results reveal that the dominant flame oscillations and wrinkling characteristics are directly dependent on the turbulence conditions in the combustor. Specifically, the flame-flow oscillations are strongly coupled with the integral length scales, which were able to collapse the oscillation frequencies to a unified value. The turbulence-driven flame-flow oscillations are shown to largely impact the magnitude, temporal evolution, and oscillatory behavior of the flame strain rate. As the turbulence intensity is increased, the oscillation of the flame strain rate increases in frequency, making it more likely for localized extinctions to occur. Additionally, the magnitude of the flame strain rate increases at high turbulence intensities and accelerates the lean blowout process.

     

On Modal Interaction,Stability and Nonlinear Dynamics of a Model Two D.O.F. Mechanical System Performing Snap-Through Motion

Dynamics of a simple two degrees of freedom (d.o.f.) mechanical system is considered, to illustrate the phenomena of modal interaction. The system has a natural symmetry of shape and is subjected to symmetric loading. Two stable equilibrium configurations are separated by an unstable one, so that the model system can perform cross-well oscillations. Nonlinear statics and dynamics are considered, with the emphasis on detecting conditions for instability of symmetric configurations and analysis of bi-modal non-symmetric motions. Nonlinear local dynamics is analyzed by multiple scales method. Direct numerical integration of original equations of motions is carried out to validate analysis of modulation equations. In global dynamics (analysis of cross-well oscillations) Lyapunov exponents are used to estimate qualitatively a type of motion exhibited by the mechanical system. Modal interactions are demonstrated both in the local dynamics and for snap-through oscillations, including chaotic motions. This mechanical system may be looked upon as a lumped parameters model of continuous elastic structures (spherical segments, cylindrical panels, buckled plates, etc.). Analyses performed in the paper qualitatively describe complicated phenomena in local and global dynamics of original structures.     

Control of the aerodynamic characteristics of a profile oscillating with respect to the incidence angle in subsonic viscous flow

The results of a numerical simulation of the unsteady subsonic viscous gas flow around a two-dimensional profile oscillating with respect to the incidence angle are presented and the possibility of controlling the nonstationary aerodynamic characteristics is considered. The hysteresis phenomena typical of oscillatory profile motions are investigated, the dependence of the lift force and drag is found for various laws of periodic variation of the incidence angle with time, and the effect of the frequency and amplitude of the angular profile oscillations on the shape of the hysteresis curves is studied. The calculations were based on the numerical solution of the nonstationary Navier-Stokes equations averaged in the Reynolds sense (Reynolds equations) which were closed using the k-ω turbulence model with modeling of the laminar/turbulent transition.     

On the decay process of turbulence at large Reynolds and Peclet numbers

When fluctuating temperature field is considered to be super imposed on a general field of eddy turbulence, the early period decay phenomena in regard to velocity, temperature and velocity-temperature are guided by three dynamical equations that are obtained here in a straightforward manner. The equations so obtained are simplified for the case of homogeneous turbulence and subsequently for the case of homogeneous and isotropic turbulence.     

Flow field characteristics study of a flapping airfoil using computational fluid dynamics

The flow field of a flapping airfoil in Low Reynolds Number (LRN) flow regime is associated with complex nonlinear vortex shedding and viscous phenomena. The respective fluid dynamics of such a flow is investigated here through Computational Fluid Dynamics (CFD) based on the Finite Volume Method (FVM). The governing equations are the unsteady, incompressible two-dimensional Navier-Stokes (N-S) equations. The airfoil is a thin ellipsoidal geometry performing a modified figure-of-eight-like flapping pattern. The flow field and vortical patterns around the airfoil are examined in detail, and the effects of several unsteady flow and system parameters on the flow characteristics are explored. The investigated parameters are the amplitude of pitching oscillations, phase angle between pitching and plunging motions, mean angle of attack, Reynolds number (Re), Strouhal number (St) based on the translational amplitudes of oscillations, and the pitching axis location (x/c). It is shown that these parameters change the instantaneous force coefficients quantitatively and qualitatively. It is also observed that the strength, interaction, and convection of the vortical structures surrounding the airfoil are significantly affected by the variations of these parameters.     

Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.     

Flow temporal reconstruction from non time-resolved data part II: practical implementation,methodology validation,and applications

This paper proposes a method to sort experimental snapshots of a periodic flow using information from the first three POD coefficients. Even in presence of turbulence, phase-average flow fields are reconstructed with this novel technique. The main objective is to identify and track traveling coherent structures in these pseudo periodic flows. This provides a tool for shedding light on flow dynamics and allows for dynamical contents comparison, instead of using mean statistics or traditional point-based correlation techniques. To evaluate the performance of the technique, apart from a laminar test on the relative strength of the POD modes, four additional tests have been performed. In the first of these tests, time-resolved PIV measurements of a turbulent flow with an externally forced main frequency allows to compare real phase-locked average data with reconstructed phase obtained using the technique proposed in the paper. The reconstruction technique is then applied to a set of non-forced, non time-resolved Stereo PIV measurements in an atmospheric burner, under combustion conditions. Besides checking that the reconstruction on different planes matches, there is no indication of the magnitude of the error for the proposed technique. In order to obtain some data regarding this aspect, two additional tests are performed on simulated non-externally forced laminar flows with the addition of a digital filter resembling turbulence (Klein et al. in J Comput Phys 186:652–665, 2003). With this information, the limitation of the technique applicability to periodic flows including turbulence or secondary frequency features is further discussed on the basis of the relative strength of the Proper Orthogonal Decomposition (POD) modes. The discussion offered indicates coherence between the reconstructed results and those obtained in the simulations. In addition, it allows defining a threshold parameter that indicates when the proposed technique is suitable or not. For those researchers interested on the background and possible generalizations of the technique, part I of this work (Legrand et al. in Exp Fluid (submitted in 2010) 2011) offers the mathematic fundamentals of the general space–time reconstruction technique using POD coefficients. Noteworthy, the involved computational time is relatively small: all the reconstructions have been performed in the order of minutes.     

Coupled energy patterns in zigzag molecular chains

The contribution of both longitudinal and transversal nonlinear oscillations to energy localization is investigated in a zigzag molecular chain, which include simultaneously nearest- and next-nearest neighbor interactions. Coupled amplitude equations are found in the form of discrete nonlinear Schrödinger equations, whose plane wave solutions are found to be subjected to some instabilities. They are shown to be very sensitive to transverse and longitudinal couplings, which is confirmed via direct numerical simulations. The two available modes are found to be alternatively responsible for energy localization and transport. Thermal fluctuations effects bring about highly localized modes, along with narrow structures for efficient energy transport.     

Experiments and homogeneous turbulence model of boiling flowin narrow channels

The boiling heat transfer experiments have been carried out in vertical narrow annular channels with pure water. A two-dimensional homogeneous turbulence model of boiling flow has been developed and solved numerically to yield pressure gradient, and velocity, thermal and turbulence fields, together with local heat transfer coefficient along the length of the tube. Predictions are compared with the data of experiments and agreed well with it. The model results show that the heat transfer coefficient increases as the gap size decreases in annular channels. This model can be used to predict heat transfer of boiling flow in narrow channels.     

Turbulence energy balance in reacting turbulent flows

The turbulence accompanying combustion and the propagation of detonation waves in gases has been studied theoretically and experimentally in many papers [1–8]. The attention of researchers has been concentrated on essential questions like how the turbulent flow field interacts with the kinetics of the chemical reaction and to what extent the process of chemical change is intensified, and how the turbulence itself is deformed by the heat released and the accompanying expansion of the gases. The various mechanisms proposed for these phenomena are based on various hypotheses concerning the structure of the combusion zone and the determinative stage of the interaction of the turbulence with the chemical-reaction kinetics. The mechanism of turbulence generation by combustion proposed in a number of papers [3–6] is based on the observation in turbulent flow of a weakly curved flickering laminar flame. This gives rise to a nonuniform flow field of the gas, part of the energy of which goes over into the energy of turbulent fluctuations. Other authors [7, 8] considered the turbulence field to interact with the chemical-reaction kinetics via a volume mechanism and suggested a criterion of turbulence intensification based on certain physical considerations, e.g., the condition for the intensification of thermogaskinetic oscillations proposed by Rayleigh [9]. In the present paper the problem is analyzed by introducing Kolmogorov's general equation for the turbulence energy balance in reacting turbulent flows [10]. In accordance with, this equation the turbulence energy can vary due to energy exchange between the turbulent motion and the mean gas flow as a result of the work on turbulent mass transport in the acceleration field of the mean flow, and due to the effect of pressure fluctuations on the rate of thermal expansion from the chemical reaction. Each of these effects is considered and analyzed.     

Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes

We present a comparative analysis of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) computed from experimental data of a turbulent, quasi 2-D, confined jet with co-flow (Re?=?11,500, co-flow ratio inner-to-outer flow ≈2:1). The experimental data come from high-speed 2-D particle image velocimetry. The flow is fully turbulent, and it contains geometry-dependent large-scale coherent structures; thus, it provides an interesting benchmark case for the comparison between POD and DMD. In this work, we address issues related to snapshot selections (1), convergence (2) and the physical interpretation (3) of both POD and DMD modes. We found that the convergence of POD modes follows the criteria of statistical convergence of the autocovariance matrix. For the computation of DMD modes, we suggest a methodology based on two criteria: the analysis of the residuals to optimize the sampling parameters of the snapshots, and a time-shifting procedure that allows us to identify the spurious modes and retain the modes that consistently appear in the spectrum. These modes are found to be the ones with nearly null growth rate. We then present the selected modes, and we discuss the way POD and DMD rank them. POD analysis reveals that the most energetic spatial structures are related to the large-scale oscillation of the inner jet (flapping); from the temporal analysis emerges that these modes are associated with a low-frequency peak at St?=?0.02. At this frequency, DMD identifies a similar mode, where oblique structures from the walls appear together with the flapping mode. The second most energetic group of modes identified is associated with shear-layer oscillations, and to a recirculation zone near the inner jet. Temporal analysis of these modes shows that the flapping of the inner jet might be sustained by the recirculation. In the DMD, the shear-layer modes are separated from the recirculation modes. These have large amplitudes in the DMD. In conclusion, the DMD modes with eigenvalues on the unit circle are found to be similar to the most energetic POD modes, although differences appear due to the fact that DMD isolates structures associated with one frequency only.     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

Unsteady RANS simulation of oscillating mould flows

Mould flow oscillations are of major importance for the performance of the continuous casting process. They are suspected to promote entrainment of slag and other unwanted secondary phases into the melt pool. These oscillating turbulent flows are investigated by means of numerical simulations. The numerical model is based on the equation of continuity and the unsteady Reynolds averaged Navier–Stokes equations. The system of flow equations is closed by a Reynolds stress turbulence model in combination with non‐equilibrium wall functions. The unsteady simulation resolves low‐frequency oscillations of the flow field. These frequencies and numerically resolved mean values are in agreement with results of corresponding model experiments. The proposed model should be advantageous in order to investigate the mechanisms of the oscillations and the process of slag entrainment in more detail. Copyright © 2006 John Wiley & Sons, Ltd.     

An investigation of forced structures in turbulent jet flows

In many cases, turbulence is superimposed on an unsteady organized motion of a mean flow. In the past, these turbulent flows have been studied by time or ensemble averaging methods and some decomposition techniques such as proper orthogonal decomposition (POD). In this study, a new decomposition technique called the turbulence filter will be used to decompose the forced turbulent jet flows. By using the turbulence filtering technique, the fluctuating (turbulent) part and the more organized (forced) part of the velocity field are analyzed. Within this context several experiments on organized turbulent jet flow have been carried out. In the experiments, variable frequency and amplitude oscillation are imposed on a 1D jet. An elliptical plate was used in order to obtain sinusoidal forcing. The axial distance, Reynolds number and the forcing frequency of the signal were varied. The multiple hot wires (six probes) were used to investigate the evolution of the signal along the radial distance. The obtained results of the turbulence filter are compared with those of phase-averaging and POD techniques. The eigenmodes of the data are also evaluated by using the POD method. Received: 31 July 1998/Accepted: 19 January 2000     

Ideal Turbulence

Ideal turbulence is a mathematical phenomenon which occurs in certain infinite-dimensional deterministic dynamical systems and implies that the attractor of a system lies off the phase space and among the attractor points there are fractal or even random functions. A mathematically rigorous definition of ideal turbulence is based on standard notions of dynamical systems theory and chaos theory. Ideal turbulence is observed in various idealized models of real distributed systems of electrodynamics, acoustics, radiophysics, etc. In systems without internal resistance, cascade processes are capable to birth structures of arbitrarily small scale and even to cause stochastization of the systems. Just these phenomena are inherent in ideal turbulence and they help to understand the mathematical scenarios for many features of real turbulence.     

A comparison of different analytical techniques for identifying structures in turbulence

Vortical structures play an important role in the kinematics and dynamics of turbulence, but in order to understand this role we require techniques to identify and classify them. Proper Orthogonal Decomposition (POD), conditional sampling with ensemble statistics, and conditional sampling with conditional statistics are applied to a simple test function and the results are compared to determine the strengths and weaknesses of each approach. The second method gives the closest approximation to the test signal and is the easiest to use, although it is sensitive to the choice of conditions. None of these techniques can give much insight into the dynamics of turbulence, or into the organisation of eddies with complex, fine-scale structure.New methods for investigating complex (self-similar) structures based on fractal and wavelet analyses are presented. Methods of distinguishing between locally (accumulating) and globally (fractal) self-similar structures are suggested.     

Vortex collapse and turbulence

Recent calculations related to the self-induced collapse of large-scale vortex structures into fine scale, possibly singular, structures in the Euler and Navier–Stokes equations are described. The practical importance of these intense events is their possible role in turbulence through the effects of strong intermittency and how that will direct turbulence modelling. Despite a concerted international effort to simulate these events over a decade ago, their dynamical origin remains largely unknown. A new international collaboration designed to push our understanding of the Euler singularity problem is described. These events are closely related to one of the outstanding mathematical questions of our time: whether solutions of the three-dimensional incompressible Navier–Stokes equations, lying in a bounded domain with finite energy and no external forcing, remain regular for arbitrarily long times (www.claymath.org/Millennium_Prize_Problems).