Uncovering large-scale coherent structures in natural and forced turbulent wakes by combining PIV,POD, and FTLE

Planar velocity data of the unsteady separated flow in the turbulent wake of a circular cylinder obtained by particle image velocimetry (PIV) are analyzed in order to visualize the large-scale coherent structures associated with alternating vortex shedding at a Reynolds number of 2,150. Two different cases are examined: unforced vortex shedding in the natural wake and vortex lock-on incited by forced perturbations superimposed in the inflow velocity. Proper orthogonal decomposition (POD) is employed to reconstruct the low-order wake dynamics from randomly sampled snapshots of the velocity field. The reconstructed flow is subsequently used to determine the evolution of the finite-time Lyapunov exponent (FTLE) fields which identify the Lagrangian coherent structures. The results demonstrate that the combination of methods employed offers a powerful visualization tool to uncover large-scale coherent structures and to exemplify vortex dynamics in natural and forced bluff-body wakes.     

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.     

The ultrasonic velocity profile measurement of flow structure in the near field of a square free jet

 Coherent structures in the near field of a three-dimensional jet have been investigated. Experiments were carried out for a free jet issuing from a square nozzle using a water channel. Instantaneous velocity profiles were obtained in the axial and radial directions by using an ultrasonic velocity profile (UVP) monitor. Axial variations of dominant time-scales of vortex structures were examined from one-dimensional wavelet spectra. Wavenumber-frequency spectra were calculated by two-dimensional Fourier transform along the axial direction in a mixing layer, and it was found that a convective velocity of flow structures was nearly constant independently of their scales in space and time. Coherent structures in the axial direction were investigated in terms of proper orthogonal decomposition (POD). Eigenfunctions are similar to a sinusoidal wave, and reconstructed velocity fields by the lower-order and higher-order POD modes demonstrate large-scale and smaller-scale coherent structures, respectively. Received: 8 May 2000/Accepted: 23 January 2001 Published online: 29 November 2001     

Numerical study of unsteady flow and heat transfer of circular tangential direction jets flowing over the inner cylinder surface in the annular chamber

In order to understand the dynamics of vortices on heat transfer, the unsteady flow field of tangential direction jets flowing in the annular chamber is numerically investigated by scale-adaptive simulation (SAS). The jet Reynolds number is 332,000 based on the jet’s diameter and inflow velocity for a specific geometric model. The analogy theory is used to obtain the convective heat transfer coefficient distribution on the hub surface. Spectral analysis via fast Fourier transform (FFT) is used to analyze frequency information that flows inside the chamber. The proper orthogonal decomposition (POD) method is performed on the velocity field in the chamber and the convective heat transfer coefficient on the hub surface using a snapshot method. The fast Fourier transform helps find the dominant frequency of the unsteady flow in the chamber. The time sequence of velocity fields on the radial plane shows the presence of cyclic flapping of the jet. The proper orthogonal decomposition analysis indicates that the unsteady periodic flow phenomenon in the chamber and unsteady heat transfer on the hub surface are mainly related to the dynamics of the counter-rotating vortices caused by the jet.     

Application of ultrasonic velocity profile meter to vortex shedding and empirical eigenfunctional analysis

 The vortex shedding behind a cylinder in a fully developed pipe flow is investigated by applying new measurement and data-analysis techniques. An ultrasound anemometry technique, providing the multipoint information of the flow, is employed. The measured instantaneous velocity fluctuations are decomposed by the empirical eigenfunctional analysis known as the proper orthogonal decomposition. The predominant modes of fluid motions are well identified by this technique, and their time–frequency features are discussed. Received: 11 April 2000/Accepted: 20 March 2001     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

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     

Runup and green water velocities due to breaking wave impinging and overtopping

The present study investigates, through measurements in a 2D wave tank, the velocity fields of a plunging breaking wave impinging on a structure. As the wave breaks and overtops the structure, so-called green water is generated. The flow becomes multi-phased and chaotic as a large aerated region is formed in the flow in the vicinity of the structure while water runs up onto the structure. In this study, particle image velocimetry (PIV) and its derivative, bubble image velocimetry (BIV), were employed to measure the velocity field in front and on top of the structure. Mean and turbulence properties were obtained through ensemble averaging repeated tests. The dominant and maximum velocity of the breaking wave and associated green water are discussed for the three distinct phases of the impingement–runup–overtopping sequence. Initially the flow is mainly horizontal right before the breaking wave impinges on the structure. The flow then becomes primarily vertical and rushes upward along the front wall of the structure right after the impingement. Subsequently, the flow becomes mainly horizontal on top of the structure as the remaining momentum in the wave crest carries the green water through. The distribution of the green water velocity along the top of the structure has a nonlinear profile and the maximum velocity occurs near the front of the fast moving water. Using the measured data and applying dimensional analysis, a similarity profile for the green water flow on top of the structure was obtained, and a prediction equation was formulated. The prediction equation may be used to predict the green water velocity caused by extreme waves in a hurricane.     

Structure of the temperature field in a flow over heated waves

Liquid crystal thermometry (LCT) was used to quantify temperature fields in a flow over resistively heated waves and assess the effect of the large-scale longitudinal structures that were previously obtained in the velocity field for an isothermal flow (A. Günther and P. Rudolf von Rohr, submitted article, 2002). The wavelength 6 was 10 times larger than the amplitude, and the considered Reynolds numbers were 725 and 3300, defined with the bulk velocity and the half-channel height. A constant heat flux was imposed at the wavy bottom wall. For the first time, LCT was used to determine the fluid temperature in a wall-bounded flow with heat transfer. The dominant spanwise scale obtained from a proper orthogonal decomposition (POD) of the fluid temperature field above an uphill location of the wavy wall was 1.56. It agrees well with the one previously obtained for a decomposition of the streamwise velocity.     

Turbulent pipe flow downstream a 90° pipe bend with and without superimposed swirl

In the present work, the turbulent flow downstream a 90° pipe bend is investigated by means of stereoscopic particle image velocimetry. In particular, the three dimensional flow field at the exit of the curved pipe is documented for non-swirling and swirling flow conditions, with the latter being generated through a unique axially rotating pipe flow facility. The non-swirling flow was examined through snapshot proper orthogonal decomposition (POD) with the aim to reveal the unsteady behaviour of the Dean vortices under turbulent flow conditions, the so-called “swirl-switching” phenomenon. In respect to the swirling turbulent pipe flow, covering a wide range of swirl strengths, POD has been employed to study the effect of varying strength of swirl on the Dean vortices as well as the interplay of swirling motion and Dean cells. Furthermore, the visualised large scale structures in turbulent swirling flows through the bend are found to incline and tear up with increasing swirl intensity. The present time-resolved, three component, experimental velocity field data will provide a unique and useful database for future studies; in particular for the CFD community.     

Three-dimensional vortex wake structure of a flapping-wing micro aerial vehicle in forward flight configuration

The unsteady flow field past a backward-facing step in a rectangular duct is investigated by adopting time-resolved particle image velocimetry (PIV) in the Reynolds number range of 2,640–9,880 based on step height and the inlet average velocity. The PIV realizations are subjected to post-processing techniques, namely, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). At low Reynolds numbers, the second spatial POD modes indicate the presence of the shear layer mode, whereas this feature shifts to higher modes at higher Reynolds numbers. The corresponding temporal modes are Fourier-transformed to obtain the dominant frequency, whose Strouhal number corroborates the above observation. Short-time windows in the transverse velocity component along the shear layer are selected to investigate the temporal stability of the flow field by DMD to quantify the growth rate of the shear layer mode. The higher harmonics of this mode are also observed to grow, albeit at lesser rate. By relating to POD analysis, the most energetic structures were found to correspond to the unstable modes. The correlation between these unstable DMD modes and the Fourier-filtered flow fields for the same frequencies indicate better match for the lower operating Reynolds number case as compared to higher ones. The spatial stability analysis demonstrates the growth of the shear layer vortices, which is combined with the temporal stability analysis to evaluate the phase velocity of the identified shear layer structures. The calculated phase velocity magnitude of the shear layer is found to be reasonably below the local velocity as expected.     

Flow Structures Associated with Turbulent Mixing Noise and Screech Tones in Axisymmetric Jets

A jet from an axisymmetric convergent nozzle is studied at ideal and underexpanded conditions using velocity and acoustic data. Two particle imaging velocimetry setups, a 10 kHz system and a multi-camera configuration, were used to capture near-field velocities while simultaneously sampled with far-field microphones. Proper orthogonal decomposition is performed on the velocity data to extract modes representative of physical processes in the flow. The decomposed velocity fields are then correlated with acoustic data to identify modes related to specific noise spectra. Specifically, four modes are associated with noise production in the sonic plume. Selective flow-field reconstruction is carried out, revealing interesting dynamics associated with loud flow states. In the supersonic case, screech-containing and turbulent mixing modes are isolated. The spatial modes of each data set are then compared for similarities in structures.     

Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence

The vortex formation and shedding process in the near wake region of a 2D square-section cylinder at incidence has been investigated by means of particle image velocimetry (PIV). Proper orthogonal decomposition (POD) is used to characterize the coherent large-scale flow unsteadiness that is associated with the wake vortex shedding process. A particular application of the POD analysis is to extract the vortex-shedding phase of individual velocity fields, which were acquired at asynchronous low rate with respect to the vortex shedding cycle. The phase of an individual flow field is determined from its projection on the first pair of POD modes, allowing phase averaging of the measurement data to be performed. In addition, a low-order representation of the flow, constructed from the mean and the first pair of POD modes, is found to be practically equivalent to the phase-averaged results. It is shown that this low-order representation corresponds to the basic Fourier component of the flow field ensemble with respect to the reconstructed phase. The phase-averaged flow representations reveal the dominant flow features of the vortex-shedding process and the effect of the angle of incidence upon it.     

Review of Coherent Structures in Turbulent Free Shear Flows and Their Possible Influence on Computational Methods

A review of selected experiments on coherent structures in turbulent shear flows is performed. Different experimental approaches (conditional averages, filtering techniques, wavelets, linear stochastic estimation and proper orthogonal decomposition, etc.) are illustrated and their links with computations (LES, DNS, SDM, etc.) is emphasized. It is particularly shown that some kind of universal behavior of the background turbulence can be retrieved from these various experimental methods. This revised version was published online in August 2006 with corrections to the Cover Date.     

Proper orthogonal decomposition analysis for cycle-to-cycle variations of engine flow. Effect of a control device in an inlet pipe

This paper aims to investigate cycle-to-cycle variations of non-reacting flow inside a motored single-cylinder transparent engine in order to judge the insertion amplitude of a control device able to displace linearly inside the inlet pipe. Three positions corresponding to three insertion amplitudes are implemented to modify the main aerodynamic properties from one cycle to the next. Numerous particle image velocimetry (PIV) two-dimensional velocity fields following cycle database are post-treated to discriminate specific contributions of the fluctuating flow. We performed a multiple snapshot proper orthogonal decomposition (POD) in the tumble plane of a pent roof SI engine. The analytical process consists of a triple decomposition for each instantaneous velocity field into three distinctive parts named mean part, coherent part and turbulent part. The 3rd- and 4th-centered statistical moments of the proper orthogonal decomposition (POD)-filtered velocity field as well as the probability density function of the PIV realizations proved that the POD extracts different behaviors of the flow. Especially, the cyclic variability is assumed to be contained essentially in the coherent part. Thus, the cycle-to-cycle variations of the engine flows might be provided from the corresponding POD temporal coefficients. It has been shown that the in-cylinder aerodynamic dispersions can be adapted and monitored by controlling the insertion depth of the control instrument inside the inlet pipe.     

The onset of dynamic stall revisited

Dynamic stall on a helicopter rotor blade comprises a series of complex aerodynamic phenomena in response to the unsteady change of the blade’s angle of attack. It is accompanied by a lift overshoot and delayed massive flow separation with respect to static stall. The classical hallmark of the dynamic stall phenomenon is the dynamic stall vortex. The flow over an oscillating OA209 airfoil under dynamic stall conditions was investigated by means of unsteady surface pressure measurements and time-resolved particle image velocimetry. The characteristic features of the unsteady flow field were identified and analysed utilising different coherent structure identification methods. An Eulerian and a Lagrangian procedure were adopted to locate the axes of vortices and the edges of Lagrangian coherent structures, respectively; a proper orthogonal decomposition of the velocity field revealed the energetically dominant coherent flow patterns and their temporal evolution. Based on the complementary information obtained by these methods the dynamics and interaction of vortical structures were analysed within a single dynamic stall life cycle leading to a classification of the unsteady flow development into five successive stages: the attached flow stage; the stall development stage; stall onset; the stalled stage; and flow reattachment. The onset of dynamic stall was specified here based on a characteristic mode of the proper orthogonal decomposition of the velocity field. Variations in the flow field topology that accompany the stall onset were verified by the Lagrangian coherent structure analysis. The instantaneous effective unsteadiness was defined as a single representative parameter to describe the influence of the motion parameters. Dynamic stall onset was found to be promoted by increasing unsteadiness. The mechanism that results in the detachment of the dynamic stall vortex from the airfoil was identified as vortex-induced separation caused by strong viscous interactions. Finally, a revised criterion to discern between light and deep dynamic stall was formulated.     

Experimental study of heat flux in mixed convective flow over solid waves

In this experimental study, we address transport processes in a mixed convective flow over a heated wavy surface. Therefore, we combine digital particle image velocimetry (DPIV) and two-color planar laser induced fluorescence (PLIF) to simultaneously measure the velocity and temperature field. For this, we propose to use the dye combination Rhodamine B and Rhodamine 110, both excited with the Nd:YAG laser also used for the PIV measurements. We investigate the influence of mixed convection over a wavy surface on the velocity field, turbulence statistics, the temperature field and the heat flux. By computing these quantities we find a correlation between the maximum in the Reynolds stress profiles and the components of the heat flux vector, thus regions of maximum momentum and scalar transport coincide. In addition, we apply a proper orthogonal decomposition (POD) to extract the most dominant flow structures in a measurement plane above the wavy surface. This first POD mode is identified as streamwise-oriented, counter-rotating vortices whose spanwise scaling is also correlated with the maximum of heat flux.