Large-scale Coherent Structures Research Articles

A draft tube to improve mixing in swirling flow-based solid–liquid mixing reactors

The Swirl Flow Reactor (SFR) is a recently proposed specially designed reactor to address challenges of solid–liquid mixing for high-temperature and high-pressure processes. Previous research has shown that the mixing homogeneity of the SFR is not yet optimal and has still potential for improvement. To enhance the homogeneity of the SFR and to optimize the utilization of the previously identified Precessing Vortex Core at the nozzle, an improvement is proposed by the inclusion of a draft tube in the reactor center. Computational Fluid Dynamics is used to study the flow structure, particle distribution, and large-scale coherent structures in the SFR. The improved SFR has been validated for its more homogenous mixing, where the homogeneity is improved from 0.945 for the original reactor to 0.991 in the new proposed design. Also, the influence of the draft tube on the fluctuating velocities and turbulence within the improved SFR has been indicated. In addition, Spectral Proper Orthogonal Decomposition (SPOD) is used to identify and reconstruct the coherent structures in the reactor. A flattened double-layer helical precessing vortex core (PVC) and its second-order harmonic at frequencies of 35.8 Hz and 71 Hz have been identified, which introduce extra large scale mixing near the nozzle of the reactor.

Lagrangian and Eulerian perspectives of turbulent transport mechanisms in a lateral cavity

The dynamics of turbulent flows past lateral cavities is relevant for multiple environmental applications. In rivers and coastal environments, these lateral recirculating regions constitute surface storage zones, where large-scale turbulent coherent structures control the transport and fate of contaminants. Mass transport in these flows is typically represented by one-dimensional first-order equations that predict the evolution of the spatially integrated concentration between the cavity and the main channel. These models, however, cannot represent the long-term evolution of the concentration or incorporate memory effects induced by turbulence. In this investigation, we carry out large-eddy simulations (LES) of the open-channel flow with a lateral square cavity of Mignot et al. (Phys. Fluids, vol. 28, issue 4, 2016, 045104). The model is coupled with an advection–diffusion equation and a Lagrangian particle model to investigate the transport mechanisms in the cavity and across the interface. From the simulations we provide quantitative comparisons of the physical processes from both perspectives, and investigate the effects of turbulent coherent structures on residence times and trajectories from finite-time Lyapunov exponents. From the Lagrangian results, we identify general spatial distributions of time scales in the cavity associated with the dynamics of coherent structures, providing new insights into the mechanisms that drive the global transport. We also show that an upscaled model informed by LES and based on a fractional derivative captures the evolution of concentration, and the exchange between the cavity and the main channel, providing accurate predictions of mass transport and reproducing the temporal dependence observed at larger scales.

Karhunen–Loéve decomposition of high Reynolds number turbulent pipe flows: a Voronoi analysis

We perform the Karhunen–Loéve decomposition of the data from direct numerical simulations pertaining to incompressible turbulent pipe flow at various Reynolds numbers, in order to identify large-scale coherent structures. A novel approach based on the Voronoi diagram is introduced to estimate the energy distribution along the radial direction as a function of the geometrical properties of the modes. In contrast to previous classifications, no user-defined criterion, threshold or ad-hoc separation of the eddies is required since the two most energetic branches are inherently present as the Reynolds number increases. Details about the Voronoi analysis are provided, together with a comprehensive validation and comparison with previous classifications at low Reynolds numbers. We discuss the results and potential of the presented approach at Reτ = 180 and 5200, commenting on the two classes of coherent structures with a varying and constant size in the radial direction appearing at Reτ = 5200.

Numerical simulation of fluid-particle flow of jet in supercritical water environment

Supercritical water gasification provides a new approach to the green transformation of coal. Nevertheless, the flow characteristics of fluids and particles injected into the reactor through the nozzle still need to be further investigated. In this paper, a three-dimensional numerical simulation of the particle jet in supercritical water environment is carried out coupling Large Eddy Simulation (LES) with Discrete Phase Model (DPM). The simulation focuses on the effects of particle size, Stokes number, mass flux ratio and initial fluid velocity on the flow characteristic of the fluid-particle flow, especially on the vortex structure evolution, particle distribution and velocity profile. The findings are that as the particle size decreases and the initial fluid velocity increases, the evolution of vortex structures become increasingly fierce, such as the destruction of large-scale coherent structures, the disappearance of vortex ribs, and the lateral expansion of vortices in the development section. Particle distribution exhibits characteristics similar to the vortex structure, as particles adhere closely to the carrier fluid at low Stokes number (St < 1). On the contrary, with increasing of Stokes number (St > 1), the particles are freer from fluid interference and keep their original motion state moving forward. The fluid velocity at the center of the transverse interface jet decrease with increased mass flow ratio. For higher initial fluid velocities, particle distribution is more uniform, and more particles are carried to areas with larger radial distances.

A Spatial Correlation Identification Model for Coherent Structure Extraction and Three-Dimensional Visualization

Multi-scale coherent structures have been observed in ocean currents, which are induced by the interaction of shear flows with different velocities. Understanding the spatial configuration and scale characteristics of coherent structures will promote the explanation of physical ocean phenomena. Considering the self-similarity, we propose a spatial correlation identification model for coherent structure extraction and three-dimensional visualization based on the wavelet transform and time-dependent intrinsic correlation method. The spatial and scale distributions of coherent structures are related to the dissipation rate variation. Most large-scale coherent structures, with the largest length scale of 13 m, are found to exist in stable fluid, such as the water column below 50 m. However, small-scale structures are found in chaotic fluids, such as the upper layer. Furthermore, we found that coherent structures of different scales coexist simultaneously in the same depth range, indicating a simultaneous multi-scale structure pattern for turbulent flow investigations.

Nuclear rings are the inner edge of a gap around the Lindblad Resonance

ABSTRACT Gaseous nuclear rings are large-scale coherent structures commonly found at the centres of barred galaxies. We propose that they are an accumulation of gas at the inner edge of an extensive gap that forms around the Inner Lindblad Resonance (ILR). The gap initially opens because the bar potential excites strong trailing waves near the ILR, which remove angular momentum from the gas disc and transport the gas inwards. The gap then widens because the bar potential continuously excites trailing waves at the inner edge of the gap, which remove further angular momentum, moving the edge further inwards until it stops at a distance of several wavelengths from the ILR. The gas accumulating at the inner edge of the gap forms the nuclear ring. The speed at which the gap edge moves and its final distance from the ILR strongly depend on the sound speed, explaining the puzzling dependence of the nuclear ring radius on the sound speed in simulations.

Intermittency of density fluctuations and zonal-flow generation in MAST edge plasmas

The properties of the edge ion-scale turbulence are studied using the beam emission spectroscopy (BES) diagnostic on MAST. Evidence of the formation of large-scale high-amplitude coherent structures, filamentary density blobs and holes, 2–4 cm inside the plasma separatrix is presented. Measurements of radial velocity and skewness of the density fluctuations indicate that density holes propagate radially inwards, with the skewness profile peaking at 7–10 cm inside the separatrix. Poloidal velocities of the density fluctuations measured using cross-correlation time delay estimation (CCTDE) are found to exhibit an intermittent behaviour. Zonal-flow analysis reveals the presence of poloidally symmetric coherent oscillations – low-frequency (LF) zonal flows and geodesic acoustic modes (GAM). Shearing rates of the observed zonal flows are found to be comparable to the turbulence decorrelation rate. The observed bursts in density-fluctuation power are followed by quiescent periods with a transient increase in the power of sheared flows. Three-wave interactions between broadband turbulence and a GAM are illustrated using the autobispectral technique. It is shown that the zonal flows and the density-fluctuation field are nonlinearly coupled and LF zonal flows mediate the energy transfer from high- to low-frequency density fluctuations.

A physics-informed data-driven algorithm for ensemble forecast of complex turbulent systems

A new ensemble forecast algorithm, named the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the probability density functions (PDFs) of complex turbulent systems with partial observations. The PIDD-CG algorithm integrates a unique multiscale statistical closure modeling strategy with a highly efficient nonlinear data assimilation scheme to create a mixture of conditional statistics. An effective data-driven modeling method is integrated with the dominant conditional statistics to serve as the forecast ensemble members that can significantly reduce the high computational cost of recovering high-dimensional PDFs. The multiscale features in the time evolution of these conditional statistics ensembles are effectively predicted by an appropriate combination of physics-informed analytic formulae and recurrent neural networks. An information metric is adopted as the loss function for the latter to more accurately capture the desirable turbulent features. The proposed algorithm displays effective forecasting performance in both the transient and statistical equilibrium non-Gaussian PDFs of strongly turbulent systems with intermittency, regime switching, and extreme events. It also facilitates the development of efficient statistical reduced-order models in recovering and predicting the large-scale coherent structures of a large group of multiscale complex systems.

Investigation of unsteady engulfment flows in a cross‑shaped mixer by particle image velocimetry

An experimental study was conducted to characterize flow fields in a cross-shaped mixer by particle image velocimetry technique (PIV). Instantaneous flow fields describe the formation and development of secondary flows at 20 ≤ Re ≤ 400, with focus on the dynamic evolution of vortices for periodic unsteady engulfment flows. Three stages are detected during one flow period, i.e., vortex merging, growing, and splitting. Vortex characteristics including populations, distributions, and strengths, are evaluated by a vortex identification and vorticity distributions. Reversal flow regions triggered by vortex breakdown are identified in merging and splitting vortices, which periodically shed downstream, thus causing an axial oscillation. The statistical properties and proper orthogonal decomposition (POD) modes of unsteady engulfment flows are analyzed. The peak of turbulent kinetic energy appears near the chamber corners where two co-rotating vortices are observed, and it decreases with Re. The second and third-order POD modes describe large-scale coherent structures in unsteady engulfment flows.

Feature identification in complex fluid flows by convolutional neural networks

Recent advancements have established machine learning’s utility in predicting nonlinear fluid dynamics, with predictive accuracy being a central motivation for employing neural networks. However, the pattern recognition central to the networks function is equally valuable for enhancing our dynamical insight into the complex fluid dynamics. In this paper, a single-layer convolutional neural network (CNN) was trained to recognize three qualitatively different subsonic buffet flows (periodic, quasi-periodic and chaotic) over a high-incidence airfoil, and a near-perfect accuracy was obtained with only a small training dataset. The convolutional kernels and corresponding feature maps, developed by the model with no temporal information provided, identified large-scale coherent structures in agreement with those known to be associated with buffet flows. Sensitivity to hyperparameters including network architecture and convolutional kernel size was also explored. The coherent structures identified by these models enhance our dynamical understanding of subsonic buffet over high-incidence airfoils over a wide range of Reynolds numbers.

Effects of inflow velocity on transverse jet injection in a supersonic cavity combustor

The flow, mixing, and combustion mechanisms in the wide range scramjet engine are complex and far from clear. In the present work, the mixing flow of a sonic transverse jet injection in a supersonic cavity combustor is numerically investigated at two typical inflow velocities. The basic flow structures, unsteady flow dynamics, average flow structures, and several significant mixing performance parameters are well captured and compared based on high-resolution large eddy simulation. The simulation results show that separation shock induced by the jet is gradually merged with the bow shock at low Mach inflow so that the curved shock flow patter is produced. In addition, smaller large-scale coherent structures at the windward side and slower large-scale vortex transport are observed at low Mach inflow. At low Mach inflow, moreover, much narrower range of jet species mass fraction distributions and more upstream large-scale vortices breakdown and dissipation can be observed. The low Mach inflow generates weaker pair of counter-rotating vortices and some trailing counter-rotating vortices, which primarily leads to the weaker jet/cavity interaction. The baroclinic term effects are considerably weaker at low Mach inflow in the near field. In view of mixing efficiency and flammability efficiency, the effect of the cavity in enhancing mixing is more evident at low Mach inflow.

Impact of density stratification and azimuthal velocity on the growth of coherent structures in a convectively unstable swirl flame

Large-scale coherent structures resulting from hydrodynamic instabilities can interact with turbulent swirl flames and lead to combustion instabilities. The present work investigates the impact of density stratification and azimuthal velocity on the growth of coherent structures in a convectively unstable swirl flame. Flame structure and flow field are measured by simultaneous hydroxyl planar laser-induced fluorescence and stereoscopic particle image velocimetry (S-PIV) at a repetition rate of 10 kHz and are analyzed by using the spectral proper orthogonal decomposition (SPOD) and spatial linear stability analysis (LSA). The SPOD reveals that the dominant symmetric and anti-symmetric modes are within the frequency range from 156 to 585 Hz, accounting for more than 25% of the turbulent kinetic energy. The spatial growths of these coherent structures are quantified by the LSA that predicts large growth rates near the nozzle exit with the corresponding frequency band matching well with the SPOD analysis. The LSA results show that both density stratification and azimuthal velocity have little effect on the instability frequencies of the most spatially unstable modes. However, the flame-induced density stratification suppresses the growth of the coherent structures by altering the pressure gradient and viscous diffusion, whereas the azimuthal velocity promotes flow instabilities through the changes in convection and production of the coherent perturbations. The results also suggest that the conventional PIV technique with two-component velocity measurement is inadequate for linear modeling of coherent structures, and the density stratification should also be taken into account in convectively unstable swirl flames.

A 3D Numerical Study of Anisotropies in Supernova Remnants

We develop a suite of 3D hydrodynamic models of supernova remnants (SNRs) expanding against the circumstellar medium (CSM). We study the Rayleigh–Taylor instability forming at the expansion interface by calculating an angular power spectrum for each of these models. The power spectra of young SNRs are seen to exhibit a dominant angular mode, which is a diagnostic of their ejecta density profile as found by previous studies. The steep scaling of power at smaller modes and the time evolution of the spectra are indicative of the absence of a turbulent cascade. Instead, as the time evolution of the spectra suggests, they may be governed by an angular mode-dependent net growth rate. We also study the impact of anisotropies in the ejecta and in the CSM on the power spectra of velocity and density. We confirm that perturbations in the density field (whether imposed on the ejecta or the CSM) do not influence the anisotropy of the remnant significantly unless they have a very large amplitude and form large-scale coherent structures. In any case, these clumps can only affect structures on large angular scales. The power spectrum on small angular scales is completely independent of the initial clumpiness and governed only by the growth and saturation of the Rayleigh–Taylor instability.

Modal analysis of EHD jets through the SVD-based POD technique

An EHD flow has complex characteristics with superimposed characteristic structures of various scales due to the coupling effect of the electric and flow fields. This paper provides a new research perspective on active control techniques of EHD flows by unraveling the large-scale dynamic structure of the dominant electroconvection from the manifold of the jet. The SVD-based POD technique in our work marks the first comprehensive investigation of modal analysis for EHD jets, aiming at extracting reduced-order modes that capture the main features and exploring the mechanisms that govern these jets through a deeper understanding of dynamic physics. The findings indicate that large-scale coherent structures that determine the EHD flows regularly emerge in the low-order modes, and fine-scale vortex structures typically appear in the high-order modes. In addition, the POD-based flow field recovery technique can effectively remove the spurious vectors from the PIV dataset by simply excluding the high-order modes from the expansion during reconstruction.

Effects of the wall heat flux on the flow characteristics of large-scale coherent structures in a pipe with enhanced heat transfer

In this study, we use stereoscopic particle image velocimetry (SPIV) to measure the internal instantaneous flow field of a typical pipe with enhanced heat transfer (a single-start spirally corrugated pipe with a pitch-to-diameter ratio S/D = 2.22) with and without a wall heat flux for Reynolds number ReD = 10000 and 25000. Proper orthogonal decomposition (POD) is used to extract the large-scale structures of the internal flow field. The POD results for the flow in the spirally corrugated pipe are employed to quantitatively analyze the turbulent kinetic energy (TKE) and Reynolds shear stress (RSS) using the corresponding results for a straight circular pipe as a benchmark. The results reveal the flow patterns of the large-scale motions in the flow field of spirally corrugated pipes are not sensitive to the wall heat flux and Reynolds number. Nevertheless, convective heat transfer can boost the energy content of large-scale coherent structures in a spiral pipe because of an increase in in-plane velocity fluctuations. Furthermore, the large-scale coherent structures of the swirling flow are reflected in multiple Q2 and Q4 events, which contribute positively to the net RSS. However, convective heat transfer reduces the contribution of these structures to the total RSS through the various parameters associated with these events.

On application of empirical mode decomposition for turbulence analysis in open-channel flows

Large-scale coherent structures are key elements of open-channel flow turbulence, quantification of which remains elusive. In this work, we use empirical mode decomposition (EMD) to break down a velocity time series into different modes, denoted as “intrinsic mode functions” (IMFs). Analysis of velocity auto- and co-spectra indicates that large-scale (LSMs) and very large-scale (VLSMs) fluid motions are sufficiently represented by particular groups of IMFs. A correlation between LSMs and VLSMs, identified by the EMD analysis, was found to generate 7% of the Reynolds shear stresses. However, the EMD analysis of surrogate velocity signals with randomized spectral phases demonstrated that the revealed correlation is actually an artefact of the EMD approach and should not be interpreted physically.

Large-scale coherent structure and canopy-level turbulence in the convective boundary layer over urban areas

Thermally unstable stratification alters the winds over urban areas and excites organized, large-scale motions (LSMs) in the atmospheric boundary layer (ABL). The current understanding of the interaction between urban turbulence and buoyancy-induced coherent structures is rather limited due to their multiscale, multiphysics nature. Nine sets of large-eddy simulation (LES) are performed to critically examine the influence of atmospheric instability on turbulent boundary layers (TBLs) interacting with idealized urban roughness elements. Varying the stratification from neutral to almost free convective conditions enables the coherent structures to transit from horizontal rolls to open cellular patterns. The aerodynamic roughness parameters tend to decrease in more unstable stratification, potentially a result of buoyancy effects that might enhance organized ejections and suppress energetic sweeps within the roughness sublayers (RSLs). Unexpectedly, roughness-induced sweeps dominate the vertical momentum fluxes within urban canopies even under the most convective condition. However, decoupling the momentum and heat transports in highly convective states results in a subtle influence of urban roughness on the vertical heat fluxes therein. The spatial distribution of canopy-level turbulent momentum fluxes is found to be strongly modulated by the overlying large-scale coherent structures. The modulation is enhanced with increasing instability. In addition, urban-like surfaces elevate the large-scale rolls and assist them in forming under a weaker stratification than in canonical settings.

Outer-layer similarity and energy transfer in a rough-wall turbulent channel flow

Direct numerical simulations (DNSs) are performed to investigate the roughness effects on the statistical properties and the large-scale coherent structures in the turbulent channel flow over three-dimensional sinusoidal rough walls. The outer-layer similarities of mean streamwise velocity and Reynolds stresses are examined by systematically varying the roughness Reynolds number $k^{+}$ and the ratio of the roughness height to the half-channel height $k / \delta$ . The energy transfer mechanism of turbulent motions in the presence of roughness elements with different sizes is explored through spectral analysis of the transport equation of the two-point velocity correlation and the scale-energy path display of the generalized Kolmogorov equation. The results show that, with increasing $k^+$ , the downward shift of the mean streamwise velocity profile in the logarithmic region increases and the peak intensities of turbulent Reynolds stresses decrease. At an intermediate Reynolds number ( $Re_{\tau }= 1080$ ), the length scale and intensity of the large-scale coherent structures increase for a small roughness ( $k^{+}=10$ ), which leads to failure of the outer-layer similarity in rough-wall turbulence, and decrease for a large roughness ( $k^{+}=60$ ), as compared with the smooth-wall case. The existence of the small roughness ( $k^{+}=10$ ) enhances the mechanism of inverse energy cascade from the inner-layer small-scale structures to the outer-layer large-scale structures. Correspondingly, the self-sustaining processes of the outer-layer large-scale coherent structures, including turbulent production, interscale transport, pressure transport and spatial turbulent transport, are all enhanced, whereas the large roughness ( $k^{+}=60$ ) weakens the energy transfer between the inner and outer regions.

Large eddy simulation study of the effect of pilot swirler blade angle on the coherent structure in a dual-swirl combustor

Large-scale coherent structures in a dual-swirl direct-mix combustor and the effect of the pilot swirler blade angle variations (35°, 40° and 45°) on them are investigated by using the large eddy simulations. The results show that no apparent coherent structure is observed downstream of the main swirler, and four typical helical vortex structures are captured downstream of the pilot swirler, representing the PVC and its three higher harmonic modes, respectively. According to the "decoupling" position from the shear layer, the spiral vortex is divided into two regions in space, the "development zone" and the "dissipation zone", respectively. In the frequency domain, as the pilot swirler blade angle increases, the characteristic frequency of the PVC and its higher harmonic structures first decrease and then increase, the energy contribution of the harmonic mode increase, and the double-helix structure replaces the single-helix structure as the dominant structure in the non-constant flow field. In the space domain, as the pilot swirler blade angle increases, the total length of PVC remains basically constant, the initial radius gradually increases, the expansion angle first increases and then decreases, and the position of "decoupling" between shear layer and spiral vortex gradually advances.

Symmetry-reduced low-dimensional representation of large-scale dynamics in the asymptotic suction boundary layer

An important feature of turbulent boundary layers are persistent large-scale coherent structures in the flow. Here, we use Dynamic Mode Decomposition (DMD), a data-driven technique designed to detect spatio-temporal coherence, to construct optimal low-dimensional representations of such large-scale dynamics in the asymptotic suction boundary layer (ASBL). In the ASBL, fluid is removed by suction through the bottom wall, resulting in a constant boundary layer thickness in streamwise direction. That is, the streamwise advection of coherent structures by the mean flow ceases to be of dynamical importance and can be interpreted as a continuous shift symmetry in streamwise direction. However, this results in technical difficulties, as DMD is known to perform poorly in presence of continuous symmetries. We address this issue using symmetry-reduced DMD (Marensi et al., 2023), and find the large-scale dynamics of the ASBL to be low-dimensional indeed and potentially self-sustained, featuring ejection and sweeping events at large scale. Interactions with near-wall structures are captured when including only a few more modes.