Energetic Modes Research Articles

Dynamic mode decomposition and reconstruction of the transient propeller wake under a light loading condition

This research aims to extend our understanding of propeller wake dynamics under a light loading condition, thereby laying a foundation for design optimization and flow control of the propeller. Dynamic mode decomposition (DMD) and reconstruction are used to analyze the transient vortical wake structures obtained by large eddy simulation. The propeller wake includes stable tip and hub vortices without interacting evolution at the light loading condition, and elliptical instabilities are observed downstream of the tip vortices. DMD describes the most energetic modes and the corresponding dominant frequencies are the blade passing frequency and its multiples. The coherent structures identified via DMD are primarily associated with the ordered convection of the tip vortices and have little correlation with the hub vortices. Additionally, the propeller wake flow is reconstructed using the first four DMD modes, and the primary wake features are well restored with a maximum reconstructed error of 7.98%. This demonstrates that the flow-field reconstruction based on the DMD reduced-order model is promising for predicting the propeller wake and controlling the propeller operation.

Proper orthogonal decomposition modal analysis in a baffled stirred tank: a base tool for the study of structures

Proper orthogonal decomposition (POD) is applied to three-dimensional (3-D) velocity fields collected from large-eddy simulations (LES) of a baffled stirred tank. In the LES, the tank operates with a Rushton-type impeller under turbulent conditions (at least in the near-impeller region) and the working fluid exhibits either Newtonian or shear-thinning rheology. The most energetic POD modes are analysed, and a POD reconstruction based on the higher modes is proposed to approximate the fluctuating component of the velocity field. Subsequently, the POD reconstruction is used to identify vortical structures and characterise them in terms of their shape. The structures are identified by considering a frame-invariant formulation of a popular, Eulerian, local-region-type method: the $Q$ -criterion. Statistics of shape-related parameters are then investigated to address the morphology of the structures. It is found that: (i) regardless of the working fluid rheology, it seems feasible to decompose the 3-D field into its mean, most energetic periodic and fluctuating components using POD, allowing, for instance, reduced-order modelling of the energetic periodic motions for mixing enhancement purposes, and (ii) vortical structures related to turbulence are mostly tubular. Finding (ii) implies that, as starting point, phenomenological models for the interaction between fluid particles (drops and bubbles) and vortices should consider the latter as cylindrical structures rather than of spherical shape, as classically assumed in these models.

Analysis of the ECH effect on EPM/AE stability in Heliotron J plasma using a Landau closure model

The aim of the present study is to analyze the effect of the electron cyclotron heating (ECH) on the linear stability of Alfvén eigenmodes (AEs) and energetic particle modes (EPMs) triggered by energetic ions in Heliotron J plasma. The analysis is performed using the FAR3d code that solves a reduced MHD model to describe the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The simulations reproduce the AE/EPM stability trends observed in the experiments as the electron temperature (T e ) increases, modifying the thermal plasma β, EP β and EP slowing-down time. Particularly, the EPM and Global AE are stabilized in the low-bumpiness (LB) configuration due to an enhancement of the continuum, finite Larmor radius and e-i Landau damping effects as the thermal β increases. On the other hand, a larger ECH injection power cannot stabilize the AE/EPM in medium-bumpiness and high-bumpiness (HB) configurations because the damping effects are weaker compared to the LB case, unable to balance the further destabilization induced by an enhanced EP resonance as the EP slowing-down time and EP β increases with T e .

How incoming turbulence affects wake recovery of an NREL-5MW wind turbine

The present work aims at investigating the effect of inflow turbulence on the wake recovery of the NREL-5MW reference wind turbine. The wake produced by a utility-scale wind turbine invested by both a laminar uniform inflow and a turbulent flow, is analyzed by means of proper-orthogonal decomposition (POD). The considered turbine is the NREL-5MW at tip-speed ratio λ = 7 and a diameter-based Reynolds number of the order 108. The flow is simulated through Large Eddy Simulation, where the forces exerted by the blades are modeled using the Actuator Line Method, whereas tower and nacelle are modeled employing the immersed boundary method. The main flow structures identified by modal decomposition in both of the considered cases are compared, and some differences emerge, which can be of great importance for the formulation of a reduced-order model. Among the most energetic modes, a high-frequency mode directly related to the tip vortices is found only in the flow case with laminar inflow. In the presence of inflow turbulence, the most energetic modes are all composed by large-scale low-frequency structures filling the whole domain. We evaluate the contribution of each POD mode to wake recovery reconstructing the total flux of mean kinetic energy due to turbulent fluctuations on a closed surface enclosing the wake of the wind turbine. In the laminar-inflow case, we have found that the POD modes related to the tip and root vortices do not contribute positively to the wake recovery, but they rather sustains the velocity gradient, as already established by Lignarolo et al. (2015) for a wind-turbine model. Whereas, in the turbulent-inflow case, all the most energetic modes contribute positively to wake recovery. These results clearly indicate that inflow turbulence should be taken into account for accurately estimate the entrainment process in the wake of wind turbines.NREL 5MW wind turbine, POD, laminar or turbulent inflow, wake recovery, turbulent kinetic energy entrainment.

Gyrokinetic modelling of the Alfvén mode and EGAM activity in ASDEX Upgrade

Energetic particles present in tokamak machines can drive through resonant wave-particle interaction different plasma instabilities, e.g Alfvén modes and energetic particle-driven geodesic acoustic modes (EGAMs). While the former are potentially detrimental as they can enhance the energetic particle transport and damage the machine wall, the latter are axisymmetric, possibly benign modes that can act to regulate turbulence. A unique scenario, the so-called NLED-AUG case, has been developed in ASDEX Upgrade by tuning the plasma parameters so that the energetic particle kinetic energy is 100 times higher than that of the background plasma, like in ITER. An intense energetic particle-driven activity is observed, most prominently various Alfvén mode bursts triggering chirping EGAMs. The present work reports studies on the Alfvén mode and EGAM dynamics showing, for the first time, many toroidal mode gyrokinetic simulations with ORB5 where the NLED-AUG case scenario is considered. We study the mode dynamics modelling the energetic particles with different equilibrium distribution functions, such as: isotropic slowing-down, double-bump-on-tail and equivalent Maxwellian. We retain, at the beginning, the nonlinearities only in the energetic particle dynamics. Later, also the background plasma species nonlinearities are taken into account.

Wall pressure fluctuations in supersonic boundary layers over compression ramps with different turning angles

In the present study, we investigate influences of shock intensity on wall pressure fluctuations by performing direct numerical simulations of supersonic turbulence boundary layers over compression ramps with different turning angles. We found that as the turning angle increases, low-frequency motions of the separation shock are enhanced, accompanied by enlarged energetic pressure structures with lower convection velocities. By inspecting wavenumber-frequency spectra under the assumption of streamwise homogeneity, we further identified two energetic modes convected at different velocities. The one with the lower convection velocity, namely, the “slow mode,” inherited from the upstream pressure fluctuations of the turbulent boundary layer, is decelerated when passing through the oblique shock, during which the “rapid mode” with pressure fluctuations convected at higher speeds are generated. The increasing turning angle decelerates the slow mode and intensifies the fast mode. The reconstruction of the flow field suggests that the rapid mode is associated with the shear layer generated adjacent to the interaction zone, while the slow mode is associated with the Görtler vortices on the ramp.

On the benefits and limitations of Echo State Networks for turbulent flow prediction

The prediction of turbulent flow by the application of machine learning (ML) algorithms to big data is a concept currently in its infancy which requires further development. It is of special importance if the aim is a prediction that is good in a statistical sense or if the vector fields should be predicted as good as possible. For this purpose, the statistical and deterministic prediction of the unsteady but periodic flow of the von Kármán Vortex Street (KVS) was examined using an Echo State Network (ESN) which is well suited for learning from time series due to its recurrent connections. The experimental data of the velocity field of the KVS were collected by Particle Image Velocimetry (PIV). Then, the data were reduced by Proper Orthogonal Decomposition (POD) and the flow was reconstructed by the first hundred most energetic modes. An ESN with 3000 neurons was optimized with respect to its three main hyperparameters to predict the time coefficients of the POD modes. For the deterministic prediction, the aim was to maximize the correct direction of the vertical velocities. The results indicate that the ESN can mimic the periodicity and the unsteadiness of the flow. It is also able to predict the sequence of the upward and downward directed velocities for longer time spans. For the statistical prediction, the similarity of the probability density functions of the vertical velocity fields between the predicted and actual flow was achieved. The leaking rate of the ESN played a key role in the transition from deterministic to statistical predictions.

Energetic particle-induced geodesic acoustic modes on DIII-D

Various properties of the energetic particle-induced geodesic acoustic mode (EGAM) are explored in this large database analysis of DIII-D experimental data. EGAMs are n = 0 modes with m = 0 electrostatic potential fluctuations (where n/m = toroidal/poloidal mode number), m = 1 density fluctuations, and m = 2 magnetic fluctuations. The fundamental frequency (∼20–40 kHz) of the mode is typically below that of the traditional geodesic acoustic mode frequency. EGAMs are most easily destabilized by beams in the counter plasma current (counter-I p) direction as compared to co-I p and off-axis beams. During counter beam injection, the mode frequency is found to have the strongest linear dependence (correlation coefficient r = −0.71) with the safety factor (q). The stability of the mode in the space of q and poloidal beta (β p) shows a clear boundary for the mode stability. The stability of the mode depends more strongly on damping rate than on fast-ion drive for a given injection geometry.

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.

Study of trailing vortices and impeller jet instabilities of a flat blade impeller in small‐scale reactors

AbstractThe design of economically feasible and profitable production processes has driven companies toward integrated continuous manufacturing by reducing working volumes and increasing operating frequencies. Thus, the development of robust small‐scale devices capable of multivariate process optimization is essential. The aim of this work is to characterize the flow developed in a ml‐scale stirred tank operating at intermediate 𝑅𝑒 ~3732, and assess trailing vortex stability with respect to baffle presence and size. Velocity characteristics are computed via computational fluid dynamics (CFD) and validated experimentally for an unbaffled (UB) and two baffled configurations. Proper orthogonal decomposition (POD) is used to extract dominant spatial–temporal flow features affecting the underlying flow patterns. Results show very good agreement between simulations and experiments, while POD analysis revealed the existence of highly energetic and periodic modes, linked to interactions between impeller jet and reactor walls. These modes are responsible for an impeller jet instability, which is amplified by the presence and size of baffles.

Sparse sensor-based flow estimation with spectral proper orthogonal decomposition

The application of Artificial Neural Networks (ANNs) in developing sensor-based estimators for unsteady flows has become an active area of research over the last decade. One of the challenges in this area is the selection of a low-dimensional subspace that enables the ANN to reconstruct relevant spatiotemporal dynamics in the flow, as both sparsity and interpretability are simultaneously desired. The present study demonstrates the use of a flow-estimation framework based on Long Short-Term Memory (LSTM) neural networks and the time-domain Spectral Proper Orthogonal Decomposition (SPOD) [Sieber et al., “Spectral proper orthogonal decomposition,” J. Fluid Mech. 792, 798–828 (2016)], which was proposed as an extension to the traditional POD. The two-cylinder flow selected for analysis in this study is referred to as the “flip-flop” regime for exhibiting intermittent changes in the phase alignment of the vortices shed by the two cylinders. This flow has dynamics occurring over a wide range of frequencies, and it was selected to demonstrate the usefulness of SPOD in characterizing the wake dynamics of periodic wake flows and to determine if it can provide a better subspace for training and estimation when compared to POD. It was found that a particular SPOD basis obtained with an empirically determined filter length completely separated the frequency centered phenomena present in the spectrum of the most energetic POD modes into different modes. These new SPOD modes were observed to have a direct relationship with the vortex dynamics in the flow, providing direct access to the antiphase and in-phase flow states. The LSTM neural networks estimation capacities were very similar across all the modal spaces investigated, performing well regardless of whether the frequency content of the modal space used for training and estimation was found superimposed in the spectrum of the most energetic modes (POD) or separated into different modes (SPOD). Further investigation is required to determine if this result holds for turbulent flows.

Wave-packet modulation in shock-containing jets

We propose a new reduced-order approach to predict the modulation of wavepackets in shock-containing jets, based on the Floquet ansatz. Good agreement is observed between the wavepackets predicted by the method and the most energetic modes extracted from a numerical simulation, suggesting that the method is able to capture the underlying physical mechanism associated with wavepacket modulation: the extraction of energy from the mean flow by the Kelvin-Helmholtz mode and a redistribution of energy to modulation wavenumbers due to the interaction of this mode with the shock-cell structure.

Experimental study of cavitating flow around a NACA 0012 hydrofoil in a slit channel

An experimental study of a cavitating NACA0012 hydrofoil with aspect ratio 0.02 in a slit channel was carried out using a high-speed visualization at sampling rate more than 100 kHz. The features of the formation and development of cavities in a quasi-two-dimensional turbulent flow were studied. The most energetic modes of unsteady cavitation flow around the hydrofoil were obtained using dynamic mode decomposition. The presence of the second and third modes in the cavitation flow is shown here for the first time. It was shown that each of these modes corresponds to a certain period of development of the unsteady cavity. Experimental data on the reverse motion of the vapor–gas mixture into the inner region of supercavitation are presented.

Very-large-scale motions in the turbulent cylinder wake

This work studied the very-large-scale motions (VLSMs), which were first observed in wall-bounded flows, in a turbulent cylinder near wake using two experimental datasets from Chen et al. [“Three-dimensional vorticity, momentum and heat transport in a turbulent cylinder wake,” J. Fluid Mech. 809, 135–167 (2016)] and Tang et al. [“Secondary vortex street in the intermediate wake of a circular cylinder,” Exp. Fluids 59, 119 (2018)]. It is found that the premultiplied spectra of both the streamwise velocity and temperature fluctuations measured with hot and cold wires by Chen et al. [“Three-dimensional vorticity, momentum and heat transport in a turbulent cylinder wake,” J. Fluid Mech. 809, 135–167 (2016)] display a peak at a low wavenumber corresponding to a frequency of about 1/4 of that of the Kármán vortices in the flow. A proper orthogonal decomposition method was utilized to decompose the velocity field measured with particle image velocimetry by Tang et al. [“Secondary vortex street in the intermediate wake of a circular cylinder,” Exp. Fluids 59, 119 (2018)] into modes with different frequencies. A prolonged coherent structure with a wavelength of about four times the Kármán vortices is observed in the visualization of the energetic velocity modes with the same frequency of the spectral peak, which is consistent with the spectral data and confirms the existence of VLSMs in the wake.

Experimental evidence of nonlinear avalanche dynamics of energetic particle modes

Recent observations in HL-2A tokamak give new experimental evidences of energetic particle mode (EPM) avalanche. In a strong EPM burst, the mode structure propagates radially outward within two hundred Alfvén time, while the frequency of the dominant mode changes self-consistently to maximize wave-particle power exchange and mode growth. This suggests that significant energetic particle transport occurs in this avalanche phase, in agreement with theoretical framework of EPM convective amplification. A simplified relay runner model yields satisfactory interpretations of the measurements. The results can help understanding the nonlinear dynamics of energetic particle driven modes in future burning plasmas, such as ITER.

Effects of Expansion Ratio and Nozzle Asymmetry on Flowfield of Diamond Jets

A joint experimental and computational study is performed to quantify the effects of various expansion ratios on the flowfields and acoustic properties of a jet, issuing from a diamond-shaped nozzle. Three expansion ratios are studied corresponding to perfectly expanded, overexpanded, and underexpanded regimes, which progressively increase the far-field acoustic impact. Nozzle asymmetry leads to distinct mean flow properties across the two principal (major/minor) axes of the jets, with the potential core and shock-expansion cells exhibiting a faster collapse on the major axis plane. Asymmetry is also observed in the computed near-field pressure spectra, which exhibits higher amplitudes in the minor axis plane, consistent with the higher far-field sound levels experimentally measured on this plane for all three jets. Near-field spectra also identify three specific bands, corresponding to broadband shock-associated noise (BBSAN), mixing noise, and that associated with nonradiating subsonic convecting eddies. Further analysis of noise mechanisms through the turbulent kinetic energy (TKE) budget shows enhanced levels of TKE on the minor axis plane, resulting from correlations between fluctuations in streamwise and cross-stream velocities, and gradients across the shear layers. Fourier analysis of near-field coherent structures in pressure identified axisymmetric features in the most energetic modes, followed by the first helical mode, which was enhanced in the presence of shock-expansion cells in the imperfectly expanded jets. The most energetic modes in the overexpanded shock-expansion cells have a strong harmonic nature to it, corresponding to the peak frequencies of its near-field BBSAN component.

Modal Analysis of Separation Bubble Unsteadiness in Conical Shock Wave/Turbulent Boundary Layer Interaction

The frequency properties and the typical flow features within the interaction zone in conical shock-wave/turbulent boundary-layer interactions (CSBLIs) are analyzed by performing proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) on a time-resolved direct numerical simulation database. The streamwise velocity and pressure fluctuations are processed according to their energy and frequency, respectively. As is the case of planar shock-wave/boundary-layer interactions, fluctuations in some bands of frequencies are more energetic downstream of the flow separation zone. The energetic low-frequency modes of the streamwise velocity fluctuations are reminiscent of Görtler-like vortices, whereas those of pressure fluctuations are connected with the “breathing” motion of the separation bubble. Higher-frequency modes, on the other hand, are related to wrinkling of the impinging conical shock. Although they bear resemblance with those in planar shock/turbulent boundary-layer interactions, it was found that the flow structures herein are less coherent owing to spanwise inhomogeneity of the impinging shock strength. The POD and DMD results of CSBLI support the notion that Görtler-like vortices might be an intrinsic mechanism of the interaction zone, which is probably responsible for the low-frequency unsteadiness of CSBLI. The present results may serve as a basic guidance for the design of fluidic control strategies of shock-induced flow separation.

TR-PIV measurements of turbulent confined impinging twin-jets in crossflow

In this work, time-resolved particle image velocimetry (TR-PIV) measurements have been carried out to study the flow structure and flow dynamics of submerged transverse impinging twin-jet flows discharged into a confined laminar crossflow. A parametric study has been carried out for fixed spacing ratio between the jets of s=L/D=3, fixed jet-to-target spacing ratio of H/D=6.73, fixed crossflow Reynolds number of Re=3500, and two jet Reynolds numbers based on the outlet velocities and jet diameter D of Rej=8670 and 9933 that correspond to jet-to-cross-flow velocity ratios of r=vj/u0=10 and 11.46, respectively. Flow measurements in several different planes of the test section are acquired to assess the confinement effect of the bounded jets. Flow visualization images of the mean velocity, vorticity, strain rate distributions, turbulence kinetic energy, and Reynolds stresses have been obtained. The results reveal the dependence of Rej on the trajectory, penetration, crossflow entrainment and lateral spreading of the twin jets. Spectral analysis of the fluctuating velocity components shows the characteristic frequencies related to vortex pairing and vortex breakup, and the shedding frequencies of the upstream and downstream wall jets have also been obtained. The swirling strength criteria has been applied to identify coherent structures, and their development confirms that these structures undergo two or three stages of vortex pairing prior to the vortex breakdown activity. The experimental data has been analyzed using proper orthogonal decomposition (POD), and the most energetic modes, the relative and cumulative energy contributions, dominant POD modes, and temporal POD coefficients have been obtained. The results show that the for Rej=8670, the first two POD modes account for 16.50% of the total kinetic energy, and the cumulative energy of the first 20 POD modes is 55.10%. For Rej=9933, the first two POD modes account for 17.98% of the total energy, and the sum of energies of the first 20 POD modes is 57.13%.

The model of particles modes. I. A paradigm for phase synchronization in tokamak turbulence

Superthermal energetic particles may alter the kinetic and resonant nature of zonal flows by leading to new types of instabilities. Here, we study the effects induced by superthermal energetic ions on trapped-ion modes (TIM) by using a reduced Hamiltonian gyrokinetic model, where both fast scales (cyclotron and bounce or transit motions) are gyro-averaged. In particular, we analyze the enhancement of resonant processes induced by energetic ions associated with nonlinear phase synchronization, in an extended version of the TIM model including circulating ions. Once an energetic particle mode is driven unstable, a rich nonlinear dynamics is observed, which encompasses a frequency chirping associated with a synchronization process driven by TIM and a transition scenario. An equivalence with the classic Kuramoto model—the paradigm describing the synchronization of a system of coupled oscillators—explains much of this phenomenology.

The model of particles modes. II. Transition to a fishbone-like state triggered by global synchronization and energetic particles

The interplay between kinetic aspects induced by energetic particles on turbulence is analyzed with a simplified model of ion-temperature-gradient-driven turbulence in magnetically confined plasmas. These topics are presented within an unified Hamiltonian framework in light of a new approach based on global phase synchronization between trapped particle modes and energetic particle modes. Numerical experiments have been carried out to elucidate concepts and physical processes of transition to a fishbone-like state triggered by energetic particles.