3D Proper Orthogonal Decomposition Research Articles

Tomographic particle image velocimetry measurement on three-dimensional swirling flow in dual-stage counter-rotating swirler

Three-Dimensional (3D) swirling flow structures, generated by a counter-rotating dual-stage swirler in a confined chamber with a confinement ratio of 1.53, were experimentally investigated at Re = 2.3 × 105 using Tomographic Particle Image Velocimetry (Tomo-PIV) and planar Particle Image Velocimetry (PIV). Based on the analysis of the 3D time-averaged swirling flow structures and 3D Proper Orthogonal Decomposition (POD) of the Tomo-PIV data, typical coherent flow structures, including the Corner Recirculation Zone (CRZ), Central Recirculation Zone (CTRZ), and Lip Recirculation Zone (LRZ), were extracted. The counter-rotating dual-stage swirler with a Venturi flare generates the independence process of vortex breakdown from the main stage and pilot stage, leading to the formation of an LRZ and a smaller CTRZ near the nozzle outlet. The confinement squeezes the CRZ to the corner and causes a reverse rotation flow to limit the shape of the CTRZ. A large-scale flow structure caused by the main stage features an explosive breakup, flapping, and Precessing Vortex Core (PVC). The explosive breakup mode dominates the swirling flow structures owing to the expansion and construction of the main jet, whereas the flapping mode is related to the wake perturbation. Confinement limits the expansion of PVC and causes it to contract after the impacting area.

On the role of low frequency modes in the thermal and momentum mixing in parallel plane jets

Parallel plane jet mixing has been the subject of extensive study and its physics are characterized well in literature. However, the physics of parallel plane jet mixing in relatively small confined regions is not well known. In this study we investigate the effects of re-circulatory flow on thermal and momentum mixing in confined parallel plane jets. Studying confined jet interaction is important for a variety of engineering applications. One of these applications is sodium cooled fast reactors (SFR). It is common in SFRs to have coolant stream mixing in a confined domain, often the upper plenum. The Reactor Cavity Cooling System (RCCS) facility at the University of Michigan models this problem in a simplified enclosure with isothermal parallel plane jets as the incoming coolant streams. A Large Eddy Simulation (LES) of this simplified plenum was developed using optimal boundary conditions, proven mesh convergence, and consistent resolution. This model was then validated against experimental results from the RCCS facility. After model validation, flow structures in the jet interaction were discerned by means of Proper Orthogonal Decomposition (POD). Comparison of 3D POD to a clipped 2D POD region reveals that re-circulatory flow can lead to dominant oscillations within the jet mixing region. Subsequently, Power Spectrum Density (PSD) and Continuous Wavelet Transforms (CWT) were used to ascertain frequency-based phenomena that might occur in this mixing region. Frequency analysis uncovered a dominant low-frequency oscillation in both velocity and temperature PSDs. These frequencies fall within the known ranges of thermal striping in sodium. The data generated in this study can be used for the benchmarking of less computationally intensive approaches. This data will be made available upon request to ebm5351@psu.edu.

INVESTIGATION OF FLOW OVER NACA0021 AIRFOIL WITH LEADING-EDGE TUBERCLES USING TRANSITION-BASED HYBRID RANS/LES MODEL

The present paper numerically investigates flow control over NACA0021 (National Advisory Committee for Aeronautics) airfoil by applying a leading-edge tubercle as a passive flow control device at transitional Reynolds number (Re) regime. The study includes simulations over the unmodified airfoil and modified airfoil operating at Re=120000 using kT-kL-{\omega} based Delayed Detached Eddy Simulation (DDES) model. The calculations include both the pre-stall and post-stall regions, while the performance of the mean flow aerodynamic properties like pressure, lift, skin-friction, and drag coefficients are also investigated in the presence of tubercles. The spanwise flow over the modified airfoil interacts with the primary flow. The turbulent separation gets delayed compared to the unmodified airfoil, thereby significantly improving the stall behavior and flow behavior in the post-stall region. The modified airfoil provides the gradual stall behavior against the steep stall behavior for the unmodified airfoil. To optimize tubercle configuration, the study considers two modified airfoils with different combinations of amplitude and wavelength. The unsteady analysis, including the reduced-order modeling, i.e. 3D Proper orthogonal decomposition (POD), characterizes the dominant vortical structure of the flow to evaluate the improvement in the aerodynamic performance of the modified airfoil. The model decomposition for flow over airfoil helps to provide a deeper understanding of the flow control phenomenon.

3D proper orthogonal decomposition analysis of engine in-cylinder velocity fields

Cycle-to-cycle variation of flow fields inside an internal combustion engine has a significant influence on the combustion efficiency and emission. Meanwhile, the velocity field inside the engine is very complex because of its turbulent and transient nature. Particle imaging velocimetry (PIV) has been widely used to investigate the instantaneous flow field within optical engines and various numerical tools were used to analyze the velocity fields. This method is limited since PIV is usually 2D or 3D for a small volume, which cannot reflect the overall flow field characteristics within the cylinder. This work utilized 3D computational fluid dynamics (CFD) simulations validated by sensor measurements and PIV measurements using an optical engine. Then, 3D proper orthogonal decomposition (POD) analysis was performed to analyze large scale and small-scale velocity characteristics, as well as vortex structures. This study then introduces an improved 2D POD scheme with multi-plane measurement and its performance is then compared against volumetric POD results. Finally, optimal plane parameters are found for practical experiments considerations and the multi-plane scheme was discussed for practical experimental investigations.

Large-eddy simulation and 3D proper orthogonal decomposition of the hydrodynamics in a stirred tank

The present study attempts to characterize the time-dependent three-dimensional hydrodynamics in a stirred tank reactor using computational fluid dynamics (CFD). The rotating propellers produce a complex, unsteady, three-dimensional turbulent flow field. This results in efficient mixing and is therefore widely used in various process engineering applications. The time-dependent turbulent single-phase flow is computed using large eddy simulation, relying on the sliding mesh approach. The unresolved subgrid scales are treated using the Smagorinsky-Lilly model. The dominant coherent flow structures are characterized in the entire three-dimensional computational domain using the 3D proper orthogonal decomposition (POD) technique. The design of the propeller is evaluated in a separate POD analysis in a rotating frame which encloses the propeller. The most energetic POD modes characterize the organized large scale structures, the so-called coherent flow structures, while the higher modes correspond to the small-scale disorganized turbulence. It was found that the dynamics of the main flow structures can be reconstructed using only 3 modes corresponding to 98% of the overall energy in the entire 3D inner rotating domain and 21 modes are necessary for the same amount of energy in the outer stationary region.Furthermore, the macro instability (MI) was characterized by monitoring the velocity in more than 1 million computational cells, as well as using FFT analyses of the three-dimensional POD temporal coefficients. In the outer stationary domain, both approaches showed characteristic frequencies around one-eighth and one-fifth of the blade passage frequency.

The near wake of sinusoidal wavy cylinders: Three-dimensional POD analyses

Three-dimensional (3D) proper orthogonal decomposition (POD) analyses are conducted to investigate the near wake of sinusoidal wavy cylinders. For a wave amplitude a/Dm = 0.152, three typical spanwise wavelengths (λz) of the wavy cylinder are taken into account, i.e., λz/Dm = 1.89, 3.79 and 6.06, where Dm is the mean diameter of the wavy cylinder, among which λz/Dm = 1.89 and 6.06 are the optimum wavelengths corresponding to the largest reduction/suppression of fluid forces acting on the wavy cylinder. Time- and space-resolved three-component velocities of the near wake flow, obtained from large eddy simulation (LES) at a subcritical Reynolds number Re = 3 × 103, are used in the 3D POD analyses. Comparison is made among the wavy cylinders of the three λz/Dm values as well as between them and a smooth cylinder, in terms of POD modes, mode energy, mode coefficients, as well as reconstructed flow structures by lower modes. For the optimum λz/Dm = 1.89 and 6.06, energy associated with the first two POD modes is significantly reduced compared with that for λz/Dm = 3.79 and the smooth cylinder. Distinct characteristics are observed on the lower POD modes for the wavy cylinders. It is found that the first two POD modes for λz/Dm = 1.89 and 6.06 are linked to large-scale streamwise vortices that are additionally introduced into the near wake due to the wavy geometry. Meanwhile, POD mode 3 suggests that the wavy cylinder with the larger optimum λz/Dm (= 6.06) generates dominant hairpin-like and spanwise coherent structures (CSs) shedding from the saddle at a different frequency from those shedding from the node. Evolutionary development of these CSs is discussed based on reconstructed flows.

On the unsteady wake dynamics behind a circular disk using fully 3D proper orthogonal decomposition

In the present work, the wakes behind a circular disk at various transitional regimes are numerically explored using fully 3D proper orthogonal decomposition (POD). The Reynolds numbers considered in this study (Re = 152, 170, 300 and 3000) cover four transitional states, i.e. the reflectional-symmetry-breaking (RSB) mode, the standing wave (SW) mode, a weakly chaotic state, and a higher-Reynolds-number state. Through analysis of the spatial POD modes at different wake states, it is found that a planar-symmetric vortex shedding mode characterized by the first mode pair is persistent in all the states. When the wake develops into a weakly chaotic state, a new vortex shedding mode characterized by the second mode pair begins to appear and completely forms at the higher-Reynolds-number state of Re = 3000, i.e. planar-symmetry-breaking vortex shedding mode. On the other hand, the coherent structure at Re = 3000 extracted from the first two POD modes shows a good resemblance to the wake configuration in the SW mode, while the coherent structure reconstructed from the first four POD modes shows a good resemblance to the wake configuration in the RSB mode. The present results indicate that the dynamics or flow instabilities observed at transitional RSB and SW modes are still preserved in a higher-Reynolds-number regime.

Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part I: Unforced Jets

The effects of jet flow-rate modulation were investigated in the case of a 35 deg inclined jet in cross-flow over a flat plate using Mie scattering visualizations, time-resolved flow rate records, and large eddy simulations (LES). An unforced jet study was conducted over a wide range of blowing ratios to provide a baseline for comparison to the pulsed results. The two distinct and well known steady jet regimes (attached jet with high film cooling performance for BR < 0.4 and detached jet with poor film cooling performance for BR > 1.0) were related to the dynamics of characteristic vortical structures, significant in the transition from one regime to the other. Similarity of the inclined jet results with a past vertical jet study are also put in perspective when comparing wall adiabatic effectiveness results. 3D proper orthogonal decomposition (3D-POD) was performed on LES results of an unforced case at BR = 0.15 to provide an analysis of dominant modes in the velocity and temperature fields. Error calculations on the reconstructed fields provided an estimation of the number of modes necessary to obtain satisfactory reconstruction while revealing some of the shortcomings associated with POD.

Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part II: Forced Jets

The effects of jet flow-rate modulation were investigated in the case of a 35 deg inclined jet in cross-flow over a flat plate using Mie scattering visualizations, time-resolved flow rate records, and large eddy simulations (LES). In forced experiments, average blowing ratios of 0.3 and 0.4 were investigated with a duty cycle of 50% and pulsing frequencies of St = 0.016 and 0.159. Time-resolved flow rate measurements during the experiments provided precise knowledge of the instantaneous jet blowing ratio and adequate inlet boundary conditions for large eddy simulations. The dynamics of the vortical structures generated during the transient parts of the forcing cycle as well as their impact on film cooling performance were investigated with respect of the forcing parameters. At the considered blowing ratios, a starting ring vortex was consistently generated at the transition from low to high blowing ratio. Ingestion of cross-flow fluid at the transition from high to low blowing ratio was also observed and had a negative impact on film cooling performance. All studied cases exhibited an overall decrease in coverage regardless of pulsing parameters over their corresponding steady jet cases at fixed mass flow rate. Comparisons between pulsed and steady jets at constant pressure supply (same high blowing ratio) did exhibit some film-cooling improvement with pulsing. 3D Proper orthogonal decomposition was performed on LES results at distinct forcing frequencies to provide an analysis of dominant modes in the velocity and temperature fields. Significantly different results were obtained depending on the forcing frequency.

LES of turbulent jet in cross flow: Part 2 – POD analysis and identification of coherent structures

The paper presents results of a Proper Orthogonal Decomposition (POD) investigation of the LES based numerical simulation of the jet-in-crossflow (JICF) flowfield with Reynolds number based on the cross flow velocity and jet diameter Re=2400 and the velocity ratio of R=3.3. LES results are validated against pointwise time averaged Laser Doppler Anemometry (LDA) measurements in PART1 of this study. In PART2 of the presented study – a planar (2D) LES based snapshot POD analysis is first conducted on two mutually perpendicular planes located in the jet-to-crossflow entrance zone. The obtained results are directly compared and found to be in close agreement with results of a Particle Image Velocimetry (PIV) based planar (2D) snapshot POD analysis by Meyer et al. (JFM 583, p. 199–227, 2007), indicating that LES is able to predict the same large scale flow dynamics as that captured by PIV. Some differences are also observed, but appear to be directly connected to the differences in levels of the resolved turbulent kinetic energy (TKE) between LES and PIV datasets. Those differences proved to be linked to the process of filtering out the small-scale fluctuations implicit to the PIV measurement technique. Comparisons of TKE captured by the first POD modes showed that they are not affected by this implicit filtering.The LES based POD analysis was also conducted in 3D. The 3D POD analysis results based on the first two POD modes show a full ability to directly visualize details of the relationship between the counter-rotating vortex pair (CVP), the hanging vortex and the wake vortices. POD reconstruction shows that the CVP originates from the hanging vortex formed at the lateral sides of the jet. It also shows that the shedding process involving oscillation of the jet core is responsible for the creation of wake vortices and that the wake vortex originates from the hanging vortex, but grows quickly by “sucking up” the wall boundary layer fluid and vorticity.