Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition(POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.     

Velocity profile reconstruction using orthogonal decomposition

It is illustrated how a one-dimensional, time-dependent form of orthogonal decomposition can be employed to effectively smooth spatial-temporal velocity profile data to remove irregularities introduced during data acquisition, while retaining the dominant profile characteristics. This essential filtering feature of orthogonal decomposition is employed to establish smoothed velocity profile sequences for a turbulent boundary layer flow. Establishment of the dominant eigenmodes (up to the first nine eigenmodes) of the flow as well as the effect of the filtering process on time-mean statistics are illustrated.     

Experimental study of transient forced turbulent separation and reattachment on a bevelled trailing edge

The purpose of this experimental study is to analyze the transient processes of the separation and reattachment of a turbulent boundary layer at the trailing edge of a splitter plate. The separation is driven by a steady pneumatic injection, considered here as an actuator controlling the mixing layer. Particle image velocimetry and hot-film measurements are performed at various stages of the processes. The results highlight the behavior of each transient. Analysis of the time scale of the processes is realized by means of bi-orthogonal decomposition. This gives essential information (e.g., time scale, qualitative features) for future applications using duty cycle mode to excite instabilities of the mixing layer.     

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     

Reliability of bi-orthogonal decomposition applied to a rotating disk boundary layer

An application of bi-orthogonal decomposition to an experiment on the transition of the boundary layer over a rotating disk is performed and compared with linear, wavelet and Fourier analyses. We show how this bi-orthogonal decomposition can detect the results of these three methods, the critical Reynolds number (R _c = 268) and the first transition Reynolds number (R _t=445), and a new Reynolds number (R = 365) where the entropy fluctuates significantly, before nonlinear effects appear.     

Simultaneous PIV and concentration measurements in a gas-turbine combustor model

Simultaneous velocity and concentration measurements have been performed in a gas-turbine combustor model. Particle image velocimetry (PIV) was used to acquire planar velocity information and to identify coherent flow structures. The Mie scattering technique, based on a slightly modified experimental setup, was used for concentration measurements in this mixing flow. The degree of mixing was assessed by examining local concentration measurements while inhomogeneously seeding the primary and secondary stream of the mixing layer. Connections between flow field and concentration distribution were highlighted using the proper orthogonal decomposition algorithm (POD). Uncertainties and systematic errors for the PIV measurements due to the suboptimal seeding are discussed using a comparison with a second test series at optimal seeding conditions. Results are presented for several flow parameters and at various lateral planes.     

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 10⁶. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.     

POD investigation of the unsteady turbulent boundary layer developing over porous moving flexible fishing net structure

Particle image velocimetry (PIV) measurements are made to investigate the boundary layer developing over a modeled bottom trawl. The random motion of the fishing net structure as well as the flexibility and the porosity of this structure means that it is not enable to access the main characteristics of such a flow, using classical post-processing mathematical tools. An innovative post-treatment tool based on proper orthogonal decomposition (POD) is then developed to extract the mean velocity flow field from each available PIV instantaneous unsteady velocity field. In order to do so, the whole available velocity database is used to compute POD eigenfunctions and the first POD modes are identified as representing the mean flow field. It is then possible to deduce the mean boundary layer flow field for each position of the fishing net structure during PIV measurements. It is then observed that the mean flow field strongly depends on multiple parameters such as surface curvature, structure porosity, random motion of the structure. Streamwise evolution of classical thicknesses of boundary layer flow are also analyzed. The present work also provides benchmark PIV data of the unsteady flow developing on fishing net porous structures, which helps the progress in unsteady numerical codes for this investigation.     

Self-sustained global oscillations in a jet in crossflow

A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier?CStokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.     

Global two-dimensional stability measures of the flat plate boundary-layer flow

The stability of the two-dimensional flat plate boundary-layer is studied by means of global eigenmodes. These eigenmodes depend both on the streamwise and wall-normal coordinate, hence there are no assumptions on the streamwise length scales of the disturbances. Expanding the perturbation velocity field in the basis of eigenmodes yields a reduced order model from which the stability characteristics of the flow, i.e. the initial condition and forcing function leading to the largest energy growth, are extracted by means of non-modal analysis. In this paper we show that, even when performing stability analysis using global eigenmodes, it is not sufficient to consider only a few of the least damped seemingly relevant eigenmodes. Instead it is the task of the optimization procedure, inherent in the non-modal analysis, to decide which eigenmodes are relevant. We show that both the optimal initial condition and the optimal forcing structure have the form of upstream tilted structures. Time integration reveals that these structures gain energy through the so called Orr mechanism, where the instabilities extract energy from the mean shear. This provides the optimal way of initiating Tollmien–Schlichting waves in the boundary layer. The optimal initial condition results in a localized Tollmien–Schlichting wavepacket that propagates downstream, whereas the optimal forcing results in a persistent Tollmien–Schlichting wave train.     

Analysis and reconstruction of a pulsed jet in crossflow by multi-plane snapshot POD

In this work, snapshot proper orthogonal decomposition (POD) is used to study a pulsed jet in crossflow where the velocity fields are extracted from stereoscopic particle image velocimetry (SPIV) results. The studied pulsed jet is characterized by a frequency f = 1 Hz, a Reynolds number Re _j  = 500 (based on the mean jet velocity ${\overline{U}_{j}}$  = 1.67 cm/s and a mean velocity ratio of R = 1). Pulsed jet and continuous jet are compared via mean velocity field trajectory and Q criterion. POD results of instantaneous, phase-averaged and fluctuating velocity fields are presented and compared in this paper. Snapshot POD applied on one plane allows us to distinguish an organization of the first spatial eigenmodes. A distinction between “natural modes” and “pulsed modes” is achieved with the results obtained by the pulsed and unforced jet. Secondly, the correlation tensor is established with four parallel planes (multi-plane snapshot POD) for the evaluation of volume spatial modes. These resulting modes are interpolated and the volume velocity field is reconstructed with a minimal number of modes for all the times of the pulsation period. These reconstructions are compared to orthogonal measurements to the transverse jet in order to validate the obtained three-dimensional velocity fields. Finally, this POD approach for the 3D flow field reconstruction from experimental data issued from planes parallel to the flow seems capable to extract relevant information from a complex three-dimensional flow and can be an alternative to tomo-PIV for large volume of measurement.     

Investigation of aeroacoustic noise generation by simultaneous particle image velocimetry and microphone measurements

A correlation technique is tested, which enables the identification of flow structures that are involved in sound generation processes. At first, the method is applied to the problem of induced noise from flow over a cylinder. The velocity field around a circular cylinder is measured by particle image velocimetry (PIV), while the radiated sound is recorded with a microphone. Both measurements are conducted in a synchronized manner so as to enable the calculation of the cross-correlation between velocity or vorticity fluctuations and the acoustic pressure. The therewith obtained coefficient matrix provides time- and space-resolved information about the statistical dependency between flow structures and the acoustic pressure. Furthermore, a proper orthogonal decomposition (POD) is applied to the velocity field. Then the correlation between dominating modes and the acoustic pressure is computed to identify which modes are mainly involved in the sound generation. Finally, the developed method is applied to the more applied problem of the flow-field inside a leading-edge slat-cove. The results show that, in this case, the signal-to-noise ratio is too low to allow an identification of noise-relevant flow structures, as opposed to the case of the cylinder wake flow, where 5,000 PIV recordings were sufficient to identify the flow structures, which are involved in the noise-generation process. A maximum in spatial distribution of the cross-correlation coefficient is observed 1.6 diameters downstream of the cylinder; its value decreases as one moves further downstream. In this area of maximal correlation, a rapid acceleration of the released vortices takes place. The cross-correlation coefficient fluctuates over time in a sine-type oscillation with maximum values of about and show a periodic behavior with a phase shift of π/2 with respect to each other. These regular oscillations can be explained by coherent periodic structures in the flow-field. These structures generate a sound field with the same periodicity, which is perceived as tone. Hence, the correlation between the velocity fluctuations and the acoustic pressure show oscillations identical to those of the input signals. A filtering of uncorrelated noise can be observed; this being caused by the averaging process during the cross-correlation calculation. The correlation with the eigenmodes of a POD gives correlation coefficients, which are no larger than the correlation with a local near-field quantity.     

On short-crested waves: experimental and analytical investigations

Analytical and experimental investigations were conducted on short-crested wave fields generated by a sea-wall reflection of an incident plane wave. A perturbation method was used to compute analytically the solution of the basic equations up to the sixth order for capillary-gravity waves in finite depth, and up to the ninth order for gravity waves in deep water. For the experiments, we developed a new video-optical tool to measure the full three dimensional wave field η(x,y,t). A good agreement was found between theory and experiments. The spatio-temporal bi-orthogonal decomposition technique was used to exhibit the periodic and progressive properties of the short-crested wave field.     

Dynamical eigenfunction decomposition of turbulent channel flow

The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loéve(K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher-order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.     

斑马鱼直线加速游动试验研究

海洋生物低噪音、高速、髙效游动能力是任何人造水下航行器所无法比拟的. 借助时间解析粒子图像测速技术对斑马鱼直线加速游动过程进行精细流场测量, 对其运动学行为特性和动力学机理进行分析. 同时应用双正交分解对涡量场进行模态分解, 获取流场的时间演化和空间分布特征. 从流动机理的角度探究斑马鱼游动过程的流动结构特征及旋涡动态演化特性. 试验结果表明: 流动可视化展现了整体涡流尾迹的结构分布,方便探究运动特性与旋涡尾迹之间的耦合关系. 斑马鱼从运动开始时体干保持着鲹科式的运动规律, 游动时的动能主要由前几次大幅的摆尾过程提供, 后续的摆尾主要调整方向及姿态. 两次不同方向的摆尾动作会形成一对方向相反的旋涡, 并在时序下旋涡逐渐脱落. 同时尾流的涡量变化在一定程度上反映鱼体的游向的变化. 基于双正交分解分解后的时间演化结果验证本次试验在时间上涡量场具有合理的恒定幅度, 空间分布表明低阶空间模态表征斑马鱼游动的主要涡流动结构, 高阶空间模态表征涡流动的细节结构. 研究鱼类游动时的摆尾推进机制与动力学特性能够为高效率的仿鱼类推进装置设计提供一定科学参考.      

Buoyancy instability in The Natural Convection Boundary Layer around a vertical heated flat plate

A systematic research on the buoyancy instability in the natural convection boundary layer was conducted, including the basic characteristics such as its spectral components, wave length and velocity, the location of its critical layer, and amplitude distributions of the triple independent eigenmodes with the linear instability theory, the growth rates of its temperature and velocity fluctuations and the corresponding neutral curves for the buoyancy eigenmode were also obtained. Results indicated that the neutral curve of the velocity fluctuation had a nose shape consistent with that obtained in the numerical calculation, but for the temperature fluctuation, a ring-like region could be measured at a lower Grashof number before the nose-shaped main portion of the neutral curve. The project supported by the National Natural Science Foundation of China (No. 10072003)     

Flow characterization of flickering methane/air diffusion flames using particle image velocimetry

Phase-resolved measurements of the velocity field in acoustically forced, flickering laminar co-flowing methane/air diffusion flames were made. Identical flames have been studied extensively in the past in order to characterize the effects of the vortical structures responsible for the flicker on the flame structure, but the initial velocity perturbation and the velocity fields have not been reported previously. Phase-locked measurements of the instantaneous two-dimensional velocity field at ten phases within a full excitation cycle were made using particle image velocimetry. The velocity measurements were complemented by phase-resolved shadowgraphs recorded in the vicinity of the flame base. Measurements are reported for the two forcing conditions that have most often been studied for this burner. When integrated with the results of previous studies, these measurements provide a clearer picture of the interactions between the buoyancy-induced vortical structures and the flame sheets, as well as providing the initial conditions required for realistic modeling of these flames.