Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures

The effect of the shallowness on meandering jets in a shallow rectangular reservoir is investigated. Four meandering flows were investigated in an experimental shallow rectangular reservoir. Their boundary conditions were chosen to cover a large range of friction numbers (defined with the sudden expansion width). Due to the unsteady characteristics of the flows, a proper orthogonal decomposition (POD) of the fluctuating part of the surface velocity fields measured using Large-Scale Particle Image Velocity was used for discriminating the flow structures responsible for the meandering of the jet. Less than 1 % of the calculated POD modes significantly contribute to the meandering of the jet, and two types of instability are in competition in such a flow configuration. The sinuous mode is the dominant mode in the flow, and it induces the meandering of the flow, while the varicose mode is a source of local mixing and weakly participates to the flow. The fluctuating velocity fields were then reconstructed using the POD modes corresponding to 80 % of the total mean fluctuating kinetic energy, and the coherent structures were identified using the residual vorticity, their centres being localised using a topology algorithm. The trajectories of the structures centres emphasise that at high friction number the coherent structures are small and laterally paired in the near, middle and far fields of the jet, while with decreasing friction number, the structures merge into large horizontal vortices in the far field of the jet, their trajectories showing more variability in space and time. The analysis of the stability regime finally reveals that the sinuous mode is convectively unstable and may become absolutely unstable at the end of the reservoir when the friction number is small.     

POD analysis of a finite-length cylinder near wake

The near wake of a wall-mounted finite-length square cylinder with an aspect ratio of 7 is investigated based on the proper orthogonal decomposition (POD) of the PIV data measured in three spanwise planes, i.e., z/d = 6, 3.5 and 1.0, near the cylinder free end, mid-span and fixed end (wall), respectively. The Reynolds number based on free-stream velocity (U _∞) and cylinder width (d) is 9,300. A two-dimensional (2D) square cylinder wake is also measured and analyzed at the same Reynolds number for the purpose of comparison. The structures of various POD modes show marked differences between the two flows. While the coefficients, a ₁ and a ₂, of the POD modes 1 and 2 occur within an annular area centered at a ₁ = a ₂ = 0 in the 2D wake, their counterparts are scattered all over the entire circular plane at z/d = 1.0 and 3.5 of the finite-length cylinder wake. Flow at z/d = 6 is dominated by POD mode 1, which corresponds to symmetrical vortex shedding and accounts for 54.0 % of the total turbulent kinetic energy (TKE). On the other hand, the POD modes 1 and 2, corresponding to anti-symmetrical vortex shedding, are predominant, accounting for about 45.0 % of the total TKE, at z/d = 3.5 and 1. It has been found that the flow structure may be qualitatively and quantitatively characterized by the POD coefficients. For example, at z/d = 6, a larger a ₁ corresponds to a smaller length of flow reversal zone and a stronger downwash flow. At z/d = 3.5 and 1, two typical flow modes can be identified from a ₁ and a ₂. While large a ₁ and/or a ₂ correspond to anti-symmetrical vortex shedding, as in a 2D cylinder wake, small a ₁ and a ₂ lead to symmetrical vortex shedding. Any values between the large and small a ₁ and/or a ₂ correspond to the flow structure between these two typical flow modes. As such, the probability of occurrence of a flow structure may be determined from the distribution of the POD coefficients.     

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.     

Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet

A pulsed jet with a period of no flow between pulses (i.e., a fully pulsed jet) produces a multiplicity of vortex rings whose characteristics are determined by the jet pulsing parameters. The present study analyzes the case of impulsively initiated and terminated jet pulses in the limit of equal pulse duration and period to determine the minimum possible vortex ring separation obtainable from a fully pulsed jet. The downstream character of the flow is modeled as an infinite train of thin, coaxial vortex rings. Assuming inviscid flow and matching the circulation, impulse, kinetic energy, and frequency of the jet and vortex ring train allow the properties of the vortex ring train to be determined in terms of the ratio of jet slug length-to-diameter ratio (L/D) used for each pulse. The results show the minimum ring separation may be made arbitrarily small as L/D is decreased and the corresponding total ring velocity remains close to half the jet velocity for L/D < 4, but the thin-ring assumption is violated for L/D > 1.5. The results are discussed in the context of models of pulsed-jet propulsion.     

Flow analysis of two-dimensional pulsed jets by particle image velocimetry

A purely alternating jet without mean mass flux and a mixed pulsed jet containing an additional blowing component were investigated by particle image velocimetry (PIV). The jets issued from a two-dimensional slit connected to a converging nozzle, opening normally from a flat wall. The pulsation was driven by a loudspeaker. The mean velocity fields were characterized by the combination of downstream directional blowing and omni-directional suction. The velocity fluctuations were dominated by contra-rotating eddy pairs synchronized with the pulsation and formed at the jet edges during blowing. Phase-synchronized measurements permit the investigation of the averaged patterns and the cycle-to-cycle fluctuations of these vortices. The mean trajectories of vortex centers during a whole injection cycle show how large lateral jet expansions are achieved. For a purely alternating jet, the expansion takes place close to the slit. For a mixed pulsed jet, the vortices develop farther from the orifice. In addition, proper orthogonal mode decomposition demonstrates that only a few modes are required to represent the main events of the flow dynamics. Received: 10 August 1999 / Accepted: 10 January 2001     

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.     

Extended Proper Orthogonal Decomposition: Application to Jet/Vortex Interaction

The Proper Orthogonal Decomposition (POD) is used in the present work to study the interactions between different regions of a flow. The standard analysis would select structures that are best correlated with the entire fluctuating velocity field. It is therefore not helpful if one flow region S of interest contains only a small percentage of the total kinetic energy. Using POD modes computed in the sub-domain S only, extended modes are introduced using the method of snapshots. We demonstrate that they provide a decomposition of the velocity field in the whole domain and that the extended mode number p provides the only local contribution to the velocity field correlated with the projection of the velocity field on POD mode p in S. This method is general and can be applied to either experimental or numerical velocity fields. As an example, it is applied to the analysis of an internal turbulent flow in a model engine cylinder with tumble. Data are obtained at a given phase with Particle Image Velocimetry. We focus our analysis on the middle of the intake stroke when the energy containing intake jet rolls up to feed a large vortex structure. Preferred directions of the jet/vortex interaction are clearly identified. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Particle image velocimetry measurements of a backward-facing step flow

Particle image velocimetry (PIV) measurements were carried out on a backward-facing step flow at a Reynolds number of Re_h=U_Xh/9=4,660 (based on step height and freestream velocity). In-plane velocity, out-of-plane vorticity, Reynolds stress and turbulent kinetic energy production measurements in the x-y and x-z planes of the flow are presented. Proper orthogonal decomposition was performed on both the fluctuating velocity and vorticity fields of the x-y plane PIV data using the method of snapshots. Low-order representations of the instantaneous velocity fields were reconstructed using the velocity modes. These reconstructions provided insight into the contribution that the various length scales make to the spatial distribution of mean and turbulent flow quantities such as Reynolds stress and turbulent kinetic energy production. Large scales are found to contribute to the Reynolds stresses and turbulent kinetic energy production downstream of reattachment, while small scales contribute to the intense Reynolds stresses in the vicinity of reattachment.     

Effect of novel synthetic jet on wake vortex shedding modes of a circular cylinder

A novel actuator signal achieved by changing the ratio of the suction duty cycle to the blowing duty cycle is adopted to enhance the control effect of the synthetic jet for the flow around a circular cylinder. The suction duty cycle factor k defined as the ratio between the time duration of the suction cycle and the blowing cycle and the equivalent momentum coefficient C_μ are introduced as the determining parameters. The synthetic jet is positioned at the rear stagnation point in order to introduce symmetric perturbations upon the flow field. The proper orthogonal decomposition (POD) technique is applied for the analysis of the spanwise vorticity field. Increasing the suction duty cycle factor, the momentum coefficient is enhanced, and thus a stronger and larger scale synthetic jet vortex pair with a higher convection velocity is generated. The synthetic jet vortex pair interacts with the spanwise vorticity shear layers behind both sides of the cylinder, resulting in the variations of the wake vortex shedding modes at Re=950: for k=0.25, C_μ=0.148, vortex synchronization at the subharmonic excitation frequency with antisymmetric shedding mode; for 0.50≤k≤1.00, 0.213≤C_μ≤0.378, vortex synchronization at the excitation frequency with the symmetric or antisymmetric shedding modes; for 2.00≤k≤4.00, 0.850≤C_μ≤2.362, vortex synchronization at the excitation frequency with symmetric shedding mode. Hence, the control effect of the synthetic jet upon the wake vortex of a circular cylinder can be enhanced by increasing the suction duty cycle factor so as to increase the momentum coefficient. This is also validated at a higher Reynolds number Re=1600.     

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     

PIV measurements of an air jet impinging on an open rotor-stator system

The current work experimentally investigates the flow characteristics of an air jet impinging on an open rotor-stator system with a low non-dimensional spacing, G?=?0.02, and with a very low aspect ratio, e/D?=?0.25. The rotational Reynolds numbers varied from $0.33\times10^5$ to $5.32\times10^5$ , while the jet Reynolds numbers ranged from 17.2?×?10³ to 43?×?10³. Particle image velocimetry (PIV) measurements were taken along the entire disk diameter in three axial planes. From the obtained PIV velocity fields, the flow statistics were computed. A recirculation flow region, which was centered at the impingement point and possessed high turbulence intensities, was observed. Local peaks in root-mean-square fluctuating velocity distributions appeared in the recirculation region and near the periphery, respectively. Proper orthogonal decomposition analysis was applied to the cases of the jet impinging on the rotor with and without rotation to reveal the coherent structures in the jet region.     

Large-eddy Simulation of Motored Flow in a Two-valve Piston Engine: POD Analysis and Cycle-to-cycle Variations

Large-eddy simulation (LES) has been performed for a single-cylinder, two-valve, four-stroke-cycle piston engine through 70 consecutive motored cycles. Initial comparisons of ensemble-averaged velocity fields have been made between LES and experiment, and proper orthogonal decomposition (POD) has been used to analyze the complex in-cylinder turbulent flows. Convergence of POD modes has been quantified, several POD variants have been explored, and sensitivity of results to analyzing different subsets of engine cycles has been studied. In general, it has been found that conclusions that were drawn earlier from POD analysis of a simplified non-compressing piston-cylinder assembly with a fixed valve carry over to the much more complex flow in this motored four-stroke-cycle engine. For the cases that have been examined, the first POD mode essentially corresponds to the ensemble-averaged mean velocity. The number of engine cycles required to extract converged POD modes increases with mode number, and varies with phase (piston position). There is little change in the lower-order phase-invariant POD modes when as few as 24 phases per cycle (30° between samples) are used, and complex 3-D time-dependent in-cylinder velocity fields through full engine cycles can be reconstructed using a relatively small number of POD modes. Quantification of cycle-to-cycle variations and insight into in-cylinder flow dynamics can be extracted through analysis of phase-invariant POD modes and coefficients.     

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.     

Visualization of coherent structure in scalar fields of unsteady jet flows with interferometric tomography and proper orthogonal decomposition

Proper orthogonal decomposition (POD) is a method of examining spatial coherence in unsteady flow fields from an ensemble of multidimensional measurements. When applied to experimental data, the proper orthogonal decomposition is generally restricted to data sets with low spatial resolution. This is because of the inherent difficulties in generating an ensemble of measurements that contain a large number of data points. In this paper, a system for obtaining a large ensemble of three-dimensional scalar measurements using interferometric tomography is presented. The proper orthogonal decomposition is applied in three spatial dimensions to experimental data of two jet-like flows. The coherent structure present in the near field of a neutrally buoyant, helium–argon jet and the far field of a buoyant helium jet into air is visualized. The POD results of the helium–argon jet clearly reveal the breakdown region of a sequence of vortex rings and a large-scale flapping motion in the jet far field. The POD of the buoyant helium jet shows a number of competing modes with varying degrees of helicity. Received: 14 January 2000/Accepted: 26 September 2000     

Turbulence Filter and POD Analysis for Velocity Fields in Lifted CH4-Air Diffusion Flames

The turbulence filter and the proper orthogonal decomposition (POD)methods are applied to PIV measurements of lifted CH₄-air diffusionflames at three different Reynolds numbers. Properties such as vorticityand strain rate distributions of the decomposed fields are analyzed inorder to assess the physical behavior. The turbulence filter can userelatively less data than the POD method while still providingsignificant insight about the flow field. The energy activation ratesshow the first modes (mean flow) account for 85% of the total energy.Reconstruction of the POD modes reveals that the combination of modesyields a complex fluctuating behavior. The averaged Reynolds stress ofthe mean flow removed parts shows interesting correlation with the meanflow vorticity and strain rate distributions. Selected turbulentproperties are calculated and discussed.     

Turbulent transport in an inclined jet in crossflow

The present study experimentally investigates a turbulent jet in crossflow relevant to film cooling applications. The jet is inclined at 30°, and its mean velocity is the same as the crossflow. Magnetic resonance imaging is used to obtain the full three-dimensional velocity and concentration fields, whereas Reynolds stresses are obtained along selected planes by Particle Image Velocimetry. The critical role of the counter-rotating vortex pair in the mixing process is apparent from both velocity and concentration fields. The jet entrainment is not significantly higher than in an axisymmetric jet without crossflow, because the proximity of the wall inhibits the turbulent transport. Reynolds shear stresses correlate with velocity and concentration gradients, consistent with the fundamental assumptions of simple turbulence models. However the eddy viscosity is strongly anisotropic and non-homogeneous, being especially low along the leeward side of the jet close to injection. Turbulent diffusion acts to decouple mean velocity and concentration fields, as demonstrated by the drop in concentration flux within the streamtube issued from the hole. Volume-averaged turbulent diffusivity is calculated using a mass–flux balance across the streamtube emanating from the jet hole, and it is found to vary slowly in the streamwise direction. The data are compared with Reynolds-Averaged Navier–Stokes simulations with standard k − ε closure and an optimal turbulent Schmidt number. The computations underestimate the strength of the counter-rotating vortex pair, due to an overestimated eddy viscosity. On the other hand the entrainment is increasingly underpredicted downstream of injection. To capture the correct macroscopic trends, eddy viscosity and eddy diffusivity should vary spatially in different ways. Therefore a constant turbulent Schmidt number formulation is inadequate for this flow.     

Three-dimensional flow structure in highly buoyant jet by scanning stereo PIV combined with POD analysis

The flow characteristics and the structure of highly buoyant jet of low density fluid issuing into a stagnant surrounding of high density fluid is studied by scanning stereo PIV combined with proper orthogonal decomposition (POD) analysis. The experiment is carried out at Froude number of 0.3 and Reynolds number of 200, which satisfies the inflow condition due to the unstable density gradient near the nozzle exit. An increase in the maximum mean velocity occurs and the vertical velocity fluctuation is highly amplified near the nozzle exit, which suggests the influence of inflow due to the unstable density gradient. The POD analysis indicates that the vertical velocity fluctuation is the major source of fluctuating energy contributing to the development of the highly buoyant jet. The examination of the POD modes show that the longitudinal structure of the vertical velocity fluctuation is generated along the jet axis having the opposite sign of velocity fluctuation on both sides of the jet axis. The vertical scale of the POD mode decreases with increasing the mode number and results in the frequent appearance of cross-flow across the buoyant jet. The reconstruction flow from the POD modes indicates that the vortex structure is caused by the highly sheared layer between the upward and downward velocity and the inflow is induced by the vortex structure. The magnitude of the vortex structure seems to be weakened with an increase in the distance from the nozzle and the buoyant jet approaches to an asymptotic state in the further downstream.     

Interaction of plane turbulent jets in a confined space: mean flow characteristics

The present study deals with the experimental investigations of static pressure and mean velocity fields obtained as a result of the interaction of two plane turbulent jets at impingement angles of α equal to 30° and 45°, with an additional central jet in a confined space. The investigation is carried out for the velocity ratios of U _c/U _o=1.0, 2.0 and 3.0, where U _c and U _o are the velocities in the central plane at the exit of the central jet and the outer jets, respectively. The introduction of the central jet alters the various recirculation zones present in the flow field for all the cases considered above. Also, the change in the velocity ratio U _c/U _o has a significant effect on the pressure and mean velocity flow fields. Flow visualisation results are presented which give a better physical insight into the flow field considered. Received: 26 July 1999/Accepted: 14 February 2000     

A spatiotemporal decomposition of a fully inhomogeneous turbulent flow field

The three-dimensional orthogonal spatial modes and their temporal counterparts have been extracted from a large-eddy simulation of turbulent flow over a surface-mounted cube, using a space-time symmetric version of proper orthogonal decomposition (POD), proposed by Aubry et al. (1991). A relatively small domain of interest, located immediately above the top face of the flow obstacle, has been selected for the application of POD. Within that volume of interest, time records of the velocity field have been sampled at 6000 locations simultaneously. The space-time duality of POD can be demonstrated by deriving two alternative eigenvalue problems for either the orthogonal spatial modes or the orthogonal temporal modes. For a particular case, the choice between the two alternatives can be done on the basis of computational convenience and of data-storage requirements. The results show that the first spatiotemporal mode can be identified with the mean flow. The second spatiotemporal mode is dominated by the alternating vortex shedding from the side edges of the flow obstacle. A Fourier analysis of the second temporal mode leads to a Strouhal number of S=0.125 which corresponds to the measured Strouhal number for the vortex shedding (Martinuzzi, 1992). The third and the fourth spatiotemporal modes are connected with the rolls created at the horizontal leading edge of the cube. For the flow field investigated, the dual space-time point of view of POD is rather realistic in the sense that the first four spatiotemporal modes can actually be observed in the flow.This work is currently supported by the German Research Society (DFG), Priority Research Program, Project No. We 705/3 (Wengle /Römer). We also gratefully acknowledge the support by the Universität der Bundeswehr München (UniBwM) and by the Leibniz Computing Center of the Bavarian Academy of Sciences (LRZ).