Multiscale Proper Orthogonal Decomposition Research Articles

On the coupling instability of a gas jet impinging on a liquid film

We investigate the dynamics of a gas jet impinging perpendicular to a thin liquid film dragged by a rising vertical substrate. This configuration is relevant to the jet-wiping process in hot-dip galvanization and it is unstable. Previous studies analysed the dynamics of the instability in the case of liquids with low Kapitza numbers (highly viscous liquids), more amenable to experimental and numerical investigations. This work extends the previous investigations by focusing on the wiping at much higher Kapitza numbers, which are more relevant to the galvanizing process. The simulations are carried out by combining volume of fluid and large-eddy simulations, and the dynamics of the gas–liquid interaction is analysed using extended multiscale proper orthogonal decomposition. The simulations allowed for analysing the jet-wiping instability in new flow conditions. Despite the largely different conditions, the results show that the interaction between the gas jet and the liquid film is qualitatively similar, featuring two-dimensional waves in the liquid correlated with oscillations and deflections of the gas jet in all cases. The wave characteristics (e.g. frequency and propagation speed) scale remarkably well using the Shkadov-like scaling based on the liquid, suggesting a dominant role of the liquid film in the coupling, and potentially enabling extrapolation of the results to a broader range of wiping conditions. Finally, we use the numerical results to discuss the limitations of liquid-film models, which constitute currently the only possible approach to study the jet-wiping process in industrial conditions.

Advanced multiscale modal and frequency analysis of swirling spray flame near to lean blowout

This study provides an in-depth characterization of Jet-A1 swirled flames' dynamics using advanced decomposition techniques on high-speed OH* chemiluminescence images. Research conducted in a 300-kW combustor with global fuel-to-air ratios Φ = 0.36, 0.24, and 0.18 reveals dominant low-frequency components under ultra-lean conditions through statistical and wavelet analyses. Integrating Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Multiscale Proper Orthogonal Decomposition (mPOD) enhances understanding by detailing the energy and frequency of flame modal structures. Observations show that as Φ decreases, flame size and intensity reduce, while fluctuations increase, indicating a transition towards unstable combustion dynamics. Furthermore, the frequency and intensity of burst phenomena increase, particularly in higher modes, indicating the system's approach to lean blowout (LBO). The application of nonlinear time series analysis, including autocorrelation (AFC) and phase space reconstruction, to mPOD eigenvalues, detects early warning signs of LBO. At lower Φ, the ACF reveals significant and frequent bursts, indicating high instability and intermittent behavior. Phase space reconstruction shows distorted orbits with a spiral-like structure, characteristic of substantial damping and irregular behavior near blowout conditions.

Multi-spatial scale and multi-frequency resolution Proper Orthogonal Decomposition for patterns of wall-streamwise pressure gradient fluctuation of impinging jets

In the coating industry, seemingly ordered millimeter-scale W or X-like patterns inevitably appear on the coating wiped by jets. Considering the dynamic control of coating thickness by the maximum wall-streamwise pressure gradient on the impinging wall, exploring its fluctuation characteristics may provide insights into W or X-like patterns formation and suppression. Large Eddy Simulation is conducted to simulate jets impinging on a dry wall. The computed pressure gradient is processed by a two-dimensional Discrete Wavelet Transform using Coif2 wavelet, helping determine the spatial scale dominated by its fluctuation energy and providing snapshots on specific spatial scales. Afterward, snapshots on selected spatial scales undergo processing using either multi-scale Proper Orthogonal Decomposition (mPOD) or spectral POD, depending on the presence of some distinguishable peaks in its spectrum. This process can extract modes with spectral purity on the corresponding spatial scale, providing an advantage in addressing problems strongly linked to spatial scales. Applying this methodology, the study unveiled the evolution of the pressure gradient modes with frequency on the energy-dominant spatial scale, ranging from 0.625 mm × 0.785 mm to 1.25 mm × 1.57 mm. This evolution may be the cause of W or X-like patterns and suggests introducing a guiding jet to mitigate them.

Energy Contribution Study of Blade Cavitation Control by Obstacles in a Waterjet Pump Based on mPOD and EEMD

Abstract It has been confirmed that the passive obstacles would substantially depress the leading-edge cavitation in a waterjet pump. Combined with the experiments and numerical simulations, this work revisits blade cavitation evolutions to demonstrate the stabilizing effects of obstacles on cavitation unsteadiness. The multiscale proper orthogonal decomposition (mPOD) and ensemble empirical mode decomposition (EEMD) are adopted to study the energy contributions regarding the cavitation-induced loading and thrust. The mPOD modes illuminate that the leading-edge loading oscillations of the obstacle blade are consequently eliminated where the cavitation is completely depressed and the obstacle cavitation wakes greatly contribute to loading excitation. The thrust statistics demonstrate that the thrust extremes and standard deviation in some revolutions can be well reduced as the large-scale leading-edge cavity depression. The adaptive spectra obtained by EEMD further illuminate that both the tonal and broadband components of blade thrust would be reasonably degraded to some degree. The pump with only one obstacle implementation, as an improvement strategy, is comparatively studied and indicates that single obstacle configuration presents positive effects on the leading-edge cavity depression owing to the pressure-raising effects and can reduce the un-necessary energy loss compared with two obstacles.

Multi-scale proper orthogonal decomposition (mPOD) analysis of vortex evolution and viscous dissipation in a circular-cylinder wake controlled by parallel symmetric jets

This paper describes a novel flow control scheme over circular-cylinder wakes using parallel symmetric jets. The effects of different jet momentum coefficients (Cm) at θ = ±30° on vortex evolution and viscous dissipation in the circular-cylinder wake are experimentally investigated using high-speed particle image velocimetry (PIV) in an open-jet wind tunnel at a Reynolds number of 1.01 × 104. Multiscale proper orthogonal decomposition (mPOD) is used to analyze the evolution of coherent structures and establish the relationship between flow structures and viscous dissipation. At Cm ≤ 0.0089, the vortex formation length is elongated and the scale and intensity of the vortex are suppressed. Small-scale jet vortices are then generated by the interaction between the jet shear layers at Cm = 0.0174, whereupon the turbulent kinetic energy attains a minimum and the Reynolds shear stress in the wake is basically eliminated. At higher values of Cm, band-like jet oscillations appear in the wake, increasing the turbulence intensity. The inhibition effect of the jets on the wake vortex decreases the viscous dissipation in the wake, with optimal viscous dissipation control obtained at Cm = 0.0089. When Cm > 0.0089, the coupling between the jets increases the viscous dissipation of small-scale, high-frequency turbulent structures, and this effect gradually becomes more obvious with increasing Cm.

Enhanced nucleate boiling of Novec 649 on thin metal foils via laser-induced periodic surface structures

The low boiling temperature of dielectric fluids makes them suitable for satisfying the cooling requirements of advanced high-energy-density devices commonly found in microelectronics. However, the high wettability/wickability of such coolants significantly affects the boiling dynamics, opening new research questions on the crucial role played by micro- and nanostructures on the boiling surface. While different studies point out the importance of microscale grooves, pillars and cavities to promote nucleation and enhance boiling heat transfer coefficient (HTC) for water, the scientific data to support such observations for dielectric fluids is sparse. In this regard, the present work provides an experimental investigation of the nucleate boiling enhancement of Novec 649 on thin metallic stainless-steel foils with tailored, laser-induced periodic surface structures (LIPSS). Femtosecond laser surface texturing was utilized to produce LIPSS with a periodicity of approx. 720 nm, while selected samples additionally included microscale grooves with a depth of 19.6 µm and a width of 25 µm, overlapped with the LIPSS features (labelled as GLIPSS). During boiling performance evaluation, high-speed IR thermography was used to measure the transient temperature fields of the boiling surface. LIPSS samples exhibited a reduction in wall superheat at the onset of boiling from 28 K to about 16 K, resulting in an HTC enhancement of about +65 %. Analysis of IR data was performed through multiscale proper orthogonal decomposition (mPOD) and revealed that the HTC enhancement in the presence of LIPSS is related to a faster heat transfer dynamics (dominant frequency: +54 %) occurring at a smaller spatial scale (dominant mean active site diameter: −12.5 %) and larger spatial density (dominant mean active site density: +39 %). Furthermore, the results for GLIPSS samples revealed a weak impact of micro features to the boiling performance of Novec 649, implying that sub-microscale surface topography is crucial to promote boiling in applications using dielectrics.

Analysis of the information overlap between the PIV and [formula omitted] chemiluminescence signals in turbulent flames using a sparse sensing framework

The purpose of this study is to quantify the information overlap between the OH* chemiluminescence signal and the three-dimensional Particle Image Velocimetry (PIV) signal for a set of bluff-body stabilized, swirling and non-swirling turbulent methane/air flames issued from the Cambridge/Sandia Stratified Swirl Burner. The time-resolved velocity data was collected using high-speed stereoscopic PIV operated at 3 kHz. This sampling rate was sufficiently high to enable accurate tracking of the large-scale spatial and temporal features of the flow. To investigate flame-flow interactions, high-speed (8 kHz) OH* chemiluminescence imaging was applied on the same set of flames. The two datasets are first independently analyzed using multi-scale Proper Orthogonal Decomposition (mPOD) for the purpose of detecting the relevant flow and heat release rate structures. The resulting modes are qualitatively compared to assess if it is possible to identify the same flow structures from the two datasets. Finally, the information overlap is quantified by predicting the velocity field from the chemiluminescence signal using a sparse sensing framework. Sparse sensing is a mathematical technique that leverages the low-dimensional representation of a physical phenomenon to predict the entire state of the system using few measurements. The results show that the velocity and chemiluminescence mPOD modes display broadly similar features, from which is possible to retrieve the same flow instabilities in the corresponding frequency range. Moreover, the prediction of the velocity field obtained using chemiluminescence as input of the sparse sensing model achieves a good level of accuracy, pointing to an important degree of information overlap between the two signals.

Frequency characteristics of axisymmetric conical boattail models with different slant angles

This study focuses on the unsteady behavior of the flow around axisymmetric conical boattail models under low-speed conditions. Particle image velocimetry was conducted on the symmetric plane for four boattail models with angles of 0°, 10°, 16°, and 22°. Different data processing techniques, including variational mode decomposition (VMD), fast Fourier transform, proper orthogonal decomposition (POD), and multiscale proper orthogonal decomposition (mPOD), were applied to understand the effects of boattail angles on the characteristic frequency of the wake flow. Our results indicated that vortex shedding, bubble pumping, and the rotation of vortex shedding are the three dominant modes for four boattail configurations. However, the energy of vortex shedding mode becomes comparable to that of bubble pumping for the model with the boattail angle of 22°. The orientation of the shear layer remarkably changes near the boattail surfaces for different angles, which is connected to the flow behavior on the surface. This study also suggests that VMD and mPOD are advantageous data-driven methods for analyzing turbulent flows.

Data-driven modal decomposition methods as feature detection techniques for flow problems: A critical assessment

Modal decomposition techniques are showing a fast growth in popularity for their wide range of applications and their various properties, especially as data-driven tools. There are many modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are the most widespread methods, especially in the field of fluid dynamics. Following their highly competent performance on various applications in several fields, numerous extensions of these techniques have been developed. In this work, we present an ambitious review comparing eight different modal decomposition techniques, including most established methods, i.e., POD, DMD, and Fast Fourier Transform; extensions of these classical methods: based either on time embedding systems, Spectral POD and Higher Order DMD, or based on scales separation, multi-scale POD (mPOD) and multi-resolution DMD (mrDMD); and also a method based on the properties of the resolvent operator, the data-driven Resolvent Analysis. The performance of all these techniques will be evaluated on four different test cases: the laminar wake around cylinder, a turbulent jet flow, the three-dimensional wake around a cylinder in transient regime, and a transient and turbulent wake around a cylinder. All these mentioned datasets are publicly available. First, we show a comparison between the performance of the eight modal decomposition techniques when the datasets are shortened. Next, all the results obtained will be explained in detail, showing both the conveniences and inconveniences of all the methods under investigation depending on the type of application and the final goal (reconstruction or identification of the flow physics). In this contribution, we aim at giving a—as fair as possible—comparison of all the techniques investigated. To the authors' knowledge, this is the first time a review paper gathering all these techniques have been produced, clarifying to the community what is the best technique to use for each application.

Experimental investigation of the flow control over an airfoil with owl-inspired trailing-edge modification: On the material, length, and spacing sensitivity

We experimentally investigate the effect of material, length, and spacing of trailing-edge extensions on controlling the flow over an airfoil based on our recent experimental work. Force measurements and flow field quantifications were carried out to investigate the aerodynamic performance and flow structures in the wake of an airfoil and, thus, to reveal differences in control effectiveness and mechanisms. Moreover, multi-scale proper orthogonal decomposition and spectral proper orthogonal decomposition are employed to extract coherent flow structures in the flow field. The results indicate that the owl feather can improve the aerodynamic performance, while artificial materials lead to decreased lift-to-drag ratio. However, nylon has optimal adaptability and robustness in controlling turbulent fluctuations, including Reynolds stress and turbulent kinetic energy at different angles of attack (AOAs). The length sensitivity is highly associated with the AOA, i.e., the optimal length increases with the increase in AOA. In addition, the spacing sensitivity correlates with the Reynolds number (Re), i.e., the optimal spacing decreases with higher Re at high AOA. These differences root in the competition effect between the increasing adverse pressure gradient and the interference on regular vortex shedding. It is concluded that nylon with mediate length (L = 0.2D) and relatively large spacing (S = 0.5B) is recommended for wake control and noise attenuation of the S833 airfoil.

Dynamics of cavity structures and wall-pressure fluctuations associated with shedding mechanism in unsteady sheet/cloud cavitating flows

The physics and mechanism of sheet/cloud cavitation in a convergent–divergent channel are investigated using synchronized dynamic surface pressure measurement and high-speed imaging in a water tunnel to probe the cavity shedding mechanism. Experiments are conducted at a fixed Reynolds number ofRe = 7.8 × 105for different values of the cavitation numberσbetween 1.20 and 0.65, ranging from intermittent inception cavitation, sheet cavitation to quasi-periodic cloud cavitation. Two distinct cloud cavitation regimes, i.e. the re-entrant jet and shockwave shedding mechanism, are observed, accompanied by complex flow phenomenon and dynamics, and are examined in detail. An increase in pressure fluctuation intensity at the numbers 3 and 4 transducer locations are captured during the transition from re-entrant jet to shockwave shedding mechanism. The spectral content analysis shows that, in cloud cavitation, several frequency peaks are identified with the dominant frequency caused by the large-scale cavity shedding process and the secondary frequency related to re-entrant jet/shockwave dynamics. Statistical analysis based on defined grey level profiles reveals that, in cloud cavitation, the double-peak behaviours of the probability density functions with negative skewness values are found to be owing to the interactions of the re-entrant jet/shockwave with cavities in the region of 0.25 ~ 0.65 mean cavity length (Lc). In addition, multi-scale proper orthogonal decomposition analysis with an emphasis on the flow structures in the region of 0.25 ~ 0.65Lcreveals that, under the shockwave shedding mechanism, both the re-entrant jet and shockwave are captured and their interactions are responsible for the dynamics and statistics of cloud shedding process.

Multi-scale proper orthogonal decomposition analysis of instabilities in swirled and stratified flames

This study examines the flow field dynamics of bluff-body stabilized swirling and non-swirling flames produced from the Cambridge/Sandia Stratified Swirl Burner. This burner has been used in previous studies as a benchmark for high-resolution scalar and velocity measurements and for validating numerical models. The burner was designed to create reacting flow conditions that are representative of turbulent flows in modern combustion systems, including sufficiently high turbulence levels, and to operate under both premixed and stratified conditions. High-speed stereoscopic particle image velocimetry was used to acquire time-resolved velocity data for a series of turbulent methane/air flames at both premixed and stratified conditions. We employ the multi-scale proper orthogonal decomposition (mPOD) to identify the main flow patterns in the velocity field and isolate coherent structures linked to various flow instabilities. The results show that the most energetic structures in the flow are consistent with the Bénard–von Kármán (BVK) instability due to the presence of the bluff-body and the Kelvin–Helmholtz (KH) instability caused by the shear layer between the inner and the outer flow. In both the swirling and non-swirling cases, the BVK is suppressed by the combustion, except for the most stratified swirling case. Moreover, the results show that combustion does not affect the KH instability because the shear layer does not coincide with the flame position.

Identification and analysis of very-large-scale turbulent motions using multiscale proper orthogonal decomposition

A multiscale proper orthogonal decomposition (mPOD) has been used to decompose the multiscale features of very long turbulent channel flow. The very-large-scale motions (VLSM) can be clearly visualized, even for flow at relatively low Reynolds number. A new energetic mode, called eVLSM, has been identified, which contains substantial energy. The large-scale structures (apart from eVLSM) are inclined to the streamwise direction and appear to be responsible for the typical meandering behavior or even for the breakup of VLSM.

Large eddy simulations and modal decomposition analysis of flow past a cylinder subject to flow-induced vibration

Large eddy simulations (LES) are carried out to investigate the flow around a vibrating cylinder in the subcritical Reynolds number regime at Re = 3900. Three reduced velocities, Ur = 3, 5, and 7, are chosen to investigate the wake structures in different branches of a vortex-induced vibration (VIV) lock-in. The instantaneous vortical structures are identified to show different coherent flow structures in the wake behind the vibrating cylinder for various branches of VIV lock-in. The combined effects of the frequency and amplitude of the oscillation on the flow pattern in the wake region, the hydrodynamic quantities of the cylinder, and the spanwise length scale of the energetic wake flow structures are discussed in detail. It is found that the typical spanwise lengths of the flow structures are 0.22D at Ur = 5 and 0.3D at Ur=[3,7] in the near-wake region and level out at 0.5D further downstream. Furthermore, multiscale proper orthogonal decomposition (mPOD) is used to analyze the dominant flow features in the wake region. With the increasing Ur, the total kinetic energy contribution of superharmonic modes increases and the contribution of subharmonic modes decreases. The dominant flow characteristics associated with the vortex shedding and their super harmonics, and the low-frequency modulation of the wake flow can be captured by the mPOD modes.

Outer-layer structure arrangements based on the large-scale zero-crossings at moderate Reynolds number

The structural arrangements in the outer layer of turbulent boundary layer flows were explored with large-field time-resolved particle image velocimetry measurements at moderate Reynolds number. The large- and small-scale structures were reconstructed by the modes of multiscale proper orthogonal decomposition. The association between hairpin packets and uniform momentum zones (UMZs) was examined by the conditional averaging results based on the large-scale positive-to-negative/negative-to-positive (PN/NP) zero-crossings. The scale arrangements provided the spatial evidence that the intense small-scale swirling motions are aligned in the confined internal shear layers along the backside of the large-scale, low-speed region, which was characterized by hairpin vortex packets. The uniform momentum zones (UMZs) conditioned on the large-scale PN/NP zero-crossings were detected from the histograms of the instantaneous streamwise velocity. The attached eddy behavior was consolidated based on the conditional events, by presenting the joint probability of UMZs thickness and wall-normal location. A close agreement of the conditional averaging raw velocity and modal velocity was examined. Moreover, the conditional averaging results of the UMZs interface probability exhibited a similar spatial distribution as the small-scale turbulent kinetic energy and swirling strength, which manifests the coincidence between the hairpin heads and the UMZs interfaces. This result was confirmed by the distribution of the wall-normal locations corresponding to the maximum value of interface probability and small-scale representations, which performs a streamwise inclination angle of 15°. The statistical spatial feature demonstrated the association between hairpin packets and uniform momentum as proposed by Adrian et al. [“Vortex organization in the outer region of the turbulent boundary layer,” J. Fluid Mech. 422, 1–54 (2000)].

On the dynamics of jet wiping: Numerical simulations and modal analysis

We analyze the flow of a planar gas jet impinging on a thin film dragged by a vertical moving wall. In the coating industry, this configuration is known as jet wiping, a process in which impinging jets control the thickness of liquid coatings on flat plates withdrawn vertically from a coating bath. We present three-dimensional (3D) two-phase flow simulations combining large eddy simulation (LES) and volume of fluid techniques. Three wiping configurations are simulated and the results are validated with experimental data from previous works. Multiscale modal analysis is used to analyze the dynamic interaction between the gas flow and the liquid film. In particular, we present a combination of multiscale Proper Orthogonal Decomposition (mPOD) and correlation analysis. The mPOD is used to identify the dominant traveling wave pattern in the liquid film flow, and the temporal structures are used to determine the most correlated flow features in the gas jet. This allows for revealing a two-dimensional mechanism for wave formation in the liquid coat. Finally, we use the numerical results to analyze the validity of some of the critical assumptions underpinning the derivation of integral film models of jet wiping.

Cross-term events of scale-decomposed skewness factor in turbulent boundary layer at moderate Reynolds number

This study reports the observation of cross term events of scale-decomposed skewness factor in turbulent boundary layer at moderate Reynolds number. The large field-of-view particle image velocimetry was utilized to measure the flow fields. By the approach of multi-scale proper orthogonal decomposition (mPOD), the large- and small-scale structures were reconstructed by the mPOD modes relevant to the predefined frequency bands. Then, the cross term of the scale-decomposed skewness was observed, which was proposed in the previous works by Schlatter and Örlü [Phys. Fluids 22, 051704 (2010)] and Mathis et al. [Phys. Fluids, 23, 121702 (2011)]. The cross term events are featured by both the large and small scales, which were consolidated by the linear fitting of correlation coefficients with different slope angles. The characteristic length of the local intense cross term events is around 0.1δ (δ is the boundary layer thickness), which is comparable with that of the swirling structures related to hairpin vortice in the form of hairpin packets. The conditional averaging results presented the arrangement that the local cross term event appears underneath the hairpin vortex in the statistical viewpoint. Based on the hairpin vortex model, it was proposed that the local intense cross term events are associated with the local low-speed fluids induced by the hairpins through the ejection process. Especially, in the wake region, the cross term events are promoted, and also well-correlated with the swirling structures. This kind of configuration was attributed to the combination of the vortex induction and the entrainment process relative to the turbulent/non-turbulent intermittency.

Tomographic particle image velocimetry flow structures downstream of a dynamic cylindrical element in a turbulent boundary layer by multi-scale proper orthogonal decomposition

This study reports the modification of large and small scales in a turbulent boundary layer (TBL) perturbed by a dynamic cylindrical element (DCE). Tomographic particle image velocimetry (Tomo-PIV) was utilized to measure the flow fields downstream of the dynamic perturbation. By the approach of multi-scale proper orthogonal decomposition (mPOD), the coherent modes relevant to the predefined frequency bands were extracted from the Tomo-PIV dataset. Then, a method was developed to construct the large- and small-scale structures and the DCE-perturbed structure based on the mPOD modes. The DCE impact on the large- and small-scale structures was elaborated by comparing with the unperturbed TBL case. The two-point correlation analysis indicated that large-scale structures appear downstream of the DCE perturbation in a short streamwise length scale. More importantly, the scale rearrangements were further examined by presenting the modulation coefficients between the large scales and small-scale energy. It revealed that even though the DCE perturbation alters the level of correlation, three different types of interaction scenario can still be observed. In the near-wall region, the large-scale structures have an amplitude modulation effect on the small-scale energy with the lower positive coefficients. The reversal scale arrangement was observed at the wall-normal height around the DCE amplitude, which could be attributed to the fluid exchange caused by the new-generated turbulent structures. In the log region, it confirmed that the inclined shear layer resides along the low-speed regions, which supported the robustness of the conceptual model of hairpin packets in the current DCE-perturbed TBL.

Spectral and modal analysis of a cavitating flow through an orifice

Cavitation phenomena, produced when a flow is accelerated through a restriction, are of fundamental importance because of the large pressure oscillation they induce on pipelines. This paper presents an experimental investigation of various cavitation regimes produced at the exit of an orifice and its downstream propagation and attenuation. A cylindrical and a conical orifice are investigated over a range of cavitation number σ=0.2-1, keeping the ratio between saturation pressure (Psat) and downstream pressure (Pdw) at two different values ξ=Psat/Pdw=0.05,0.3. The range of operating conditions allows to investigate cavitation from the inception to the cloud, the developed, and the super-cavitation regime.For each configuration, the experimental analysis includes flow rate measurements, pressure signals via fast pressure transducers, and high-speed videos. The videos are analyzed using Multiscale Proper Orthogonal Decomposition (mPOD), to extract the coherent patterns that arise during the cloud cavitation and the developed cavitation regimes.The simultaneous analysis of the high-speed video in the proximity of the orifice and the time-resolved downstream pressure signal allows highlighting the effect of the cavitation intensity on the downstream evolution of these fundamental flows.

Multiscale proper orthogonal decomposition (mPOD) of TR-PIV data—a case study on stationary and transient cylinder wake flows

Data-driven decompositions of particle image velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g. vortical structures), filtering operations (e.g. outlier removal or random noise mitigation), data reduction and compression. This work presents the application of a novel decomposition method, referred to as multiscale proper orthogonal decomposition (mPOD, Mendez et al 2019) to time-resolved PIV (TR-PIV) measurement. This method combines multiresolution analysis and standard proper orthogonal decomposition (POD) to achieve a compromise between decomposition convergence and spectral purity of the resulting modes. The selected test case is the flow past a cylinder in both stationary and transient conditions, producing a frequency-varying Karman vortex street. The results of the mPOD are compared to the standard POD, the discrete Fourier transform and the dynamic mode decomposition. The mPOD is evaluated in terms of decomposition convergence and time-frequency localization of its modes. The multiscale modal analysis allows for revealing beat phenomena in the stationary cylinder wake, due to the three-dimensional nature of the flow, and to correctly identify the transition from various stationary regimes in the transient test case.