Energetic Large-scale Structures Research Articles

Large-scale motions in a plane wall jet

The plane wall jet (PWJ) is a wall-bounded flow in which a wall shear layer develops in the presence of extremely energetic flow structures of the outer free-shear layer. The structure of a PWJ, developing in still air, was studied with the focus on the large scales in the flow. Wall-normal hot-wire anemometry (HWA) measurements along with double-frame particle image velocimetry (PIV) measurements (wall-normal–streamwise plane) were carried out at streamwise distances up to $162b$, where $b$ is the slot width of the PWJ exit. The nominal PWJ Reynolds number based on exit parameters was $Re_{j}\approx 5940$. Comparisons with a zero-pressure-gradient boundary layer (ZPGBL) at nominally matched friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ were also carried out as appropriate, to highlight key features of the PWJ structure. Consistent with previous work, the PWJ showed a dependence of the peak turbulent stresses on the jet exit Reynolds number. The turbulent production showed a peak corresponding to the near-wall cycle similar to the peak seen in the ZPGBL. However, another turbulent production peak was observed in the outer free-shear layer that was an order of magnitude larger than the inner one. Along with the change in sign of the viscous and Reynolds shear stresses, the PWJ was shown to have a region of very low turbulent production between these two peaks. The dissipation rate increased over the PWJ layer with a peak also in the outer region. Visualizations of the flow and two-point correlations reveal that the most energetic large-scale structures within a PWJ are vortical motions in the wall-normal–streamwise plane similar to those structures seen in free-shear layers. These structures are referred to as J (for jet) type structures. In addition two-point correlations reveal the existence of large-scale structures in the wall region which have a signature similar to those structures seen in canonical boundary layers. These structures are referred to as W (for wall) type structures. Instantaneous PIV realizations and flow visualizations reveal that these W type large-scale features are consistent with the paradigm of hairpin vortex packets in the wall region. The J type structures were seen to intrude well into the wall region while the W type structures were also seen to extend into the outer shear layer. Further, these large-scale structures were shown to modulate the amplitude of the finer scales of the flow.

POD-Based Data Mining of Turbulent Flows in Front of and on Top of Smooth and Roughness-Resolved Forward-Facing Steps

A new application of proper orthogonal decomposition (POD) to uncover the relation of the instantaneous energetic large-scale turbulent structures to the dominant POD modes had been reported. Motivated on this method, the data mining from the velocity vector fields measured by the particle image velocimetry and structural analysis on the selected POD-based reconstructed turbulent flows in front of and on top of smooth and roughness-resolved forward-facing steps (FFSs) has been performed. The velocity fields containing the most energetic large-scale structures are conditionally chosen. The conditional criterion is that the chosen velocity fields whose POD temporal coefficients of the first or second mode are correspondingly larger than twice of their root mean square values. Typically, the most energetic instantaneous structures are the large-scale second-quadrant (Q2) or fourth-quadrant (Q4) events and the mostly open separation bubbles in front of these FFSs; while the large-scale structures behave as a strong shear layer, and near or in which are a few spanwise prograde or retrograde vortices; and sometimes the alternating node and saddle points appeared. Similarly, for the flow on top of the FFSs, the most energetic structures are presented as a great many large-scale Q4 or Q2 events and a few secondary vortices at the very near wall; while the large-scale structures are overall exhibited as a strong shear layer, and in which a large number of vertex structures are created. These energetic large-scale structures here are not only sensitive to the surface roughness conditions but also to the spanwise locations.

Large-eddy simulation of circular jet mixing: Lip- and inner-ribbed nozzles

Jet mixing of a circular nozzle in two different configurations is extensively investigated using large-eddy simulation (LES), i.e., the lip-ribbed one with an annular rib at the nozzle exit, and the inner-ribbed one with a rib placed 1.0D upstream of the nozzle exit; the latter one is particularly selected to generate unsteady reattachment of the separated shear layer near the nozzle exit. A jet issuing from a hydrodynamically smooth pipe with fully developed turbulent flow into a larger cylindrical domain (a ‘pipe jet’) is used as the baseline configuration for comparison. The Reynolds number based on the mean (bulk) velocity in the pipe and the pipe diameter is 6000. Validation of the LES approach is performed on the baseline pipe jet using particle image velocimetry (PIV) and laser-induced fluorescence (LIF) measurements; perfect agreement is obtained in terms of the mean streamwise velocity and concentration and their fluctuation parts. The LES results show that both ribbed jet configurations exhibit higher levels of mixing than the pipe jet; the most rapid decay of the centreline concentration and the largest entrainment are observed in the inner-ribbed jet. The inner-ribbed nozzle induced high flow fluctuations behind the rib due to frequent reattachment of flow to the pipe wall that are similar to what is known as fluid flapping motion. These flapping motions give rise to the energetic large-scale structures at the pipe exit and serve as an effective control imposed on the jet. The ‘slice’ proper orthogonal decomposition analysis performed on the flow helps to identify the jet's ‘preferred modes’ by selecting the most energetic structures with a specified azimuthal wavenumber. In the lip-ribbed jet, the separated shear layer modified the frequencies of the axisymmetric mode but made a limited contribution to the energy level of the jet preferred mode. In the inner-ribbed jet, however, the jet preferred modes were extensively altered. The single- and double-helical modes (m=1 and 2) were substantially intensified, with increasing energy levels up to 58%, giving rise to the significant enhancement of jet mixing, especially in the upstream regions.

Chaotic dynamics of large-scale structures in a turbulent wake

The dynamics of a 3D bimodal turbulent wake downstream a square-back Ahmed body are experimentally studied in a wind-tunnel through high-frequency wall pressure probes mapping the rear of the model and a horizontal 2D velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall pressure foot-print. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low frequencies dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well defined attractors. The low frequencies dynamics associated to the large-scale structures are then analyzed. The largest Lyapunov exponent is first estimated, leading to a low positive value characteristic of strange attractors and weak chaotic systems. Afterwards, analyzing the autocorrelation function of the time-series, we compute the correlation dimension, larger than two. The signal is finally transformed and analyzed as a telegraph signal showing that its dynamics correspond to a quasi-random telegraph signal. This is the first demonstration that the low frequencies dynamics of a turbulent 3D wake are not a purely stochastic process but rather a weak chaotic process exhibiting strange attractors. From the flow-control point of view, it also opens the path to more simple closed-loop flow control strategies aiming at the stabilization of the wake and the control of the dynamics of the wake barycenter.

Combining wavelet transform and POD to analyze wake flow

To reveal the possibly existed flow phenomena that buried in a two-dimensional symmetric triangle wake, one-dimensional orthogonal wavelet transform and POD are combined to decompose the fluctuating velocity field into different wavelet components and modes. The features of reconstructed flow fields are analyzed in terms of fluctuating energy, time frequency distribution, space correlation and Reynolds shear stress. It is found that the first two wavelet components and POD modes can give representations to the most energetic large-scale structures, contributing about 77 and 73 % to the total fluctuating energy, respectively. Comparing with the first two wavelet components, the first two POD modes are more appropriate to represent the Karman-like vortical structures. The time–frequency and length scale characteristics of wavelet components suggest that frequency behavior can reflect the spatial-related length scale and the wavelet transform can be used to extract turbulent structures of different scales. Similar to the energy distribution, the most significant contributions to the Reynolds shear stresses comes from the large-scale structures that composed of first two wavelet components and POD modes, accounting for 88 and 80 % of the measured maximum Reynolds shear stress, respectively. Due to different classification criterion of wavelet and POD analyses, the combining use of these two methods tends to be more effective for analyzing multi-scale turbulent structures.

Triangle Cylinder Wake Analysis Based on Wavelet and POD Techniques

The turbulent structure behind a two-dimensional symmetric triangle cylinder is measured by PIV experiment at Reynolds number of 14440. To reveal the possibly existed flow phenomena that buried in the mean flow, one dimensional orthogonal wavelet and POD analyses are employed to decompose the fluctuating velocity field into different wavelet components and modes. The features of reconstructed flow fields are analyzed in terms of fluctuating energy, time frequency distribution and length scale. It is found that the first two wavelet components and POD modes can give representations to the most energetic large scale structures, contributing about 77% and 73% to the total fluctuating energy respectively. Comparing with the first two wavelet components, the first two POD modes are more appropriate to represent the Karman like vortical structures. The time-frequency and length scale characteristics of wavelet components suggest that frequency behavior can reflect the spatial related length scale and the wavelet analysis can be used to extract turbulent structures of different scales.

A study of energetic large-scale structures in turbulent boundary layer

This study established the connection in turbulent boundary layers between the first two dominant proper orthogonal decomposition (POD) modes and the instantaneous large-scale turbulence structures. The velocity fields consistent with the signature velocity fields of the hairpin vortex packets in two-dimensional PIV (particle image velocimetry) measurement planes are observed as the major contributors to the first two POD modes. Another kind of equally important turbulence structure is the large region of Q4 vectors, which may possibly be obtained by slicing the outskirts of the three-dimensional structure of the hairpin vortex packet by PIV planes. The streamwise Reynolds normal stress, Reynolds shear stress, and the length scales of the two-point velocity correlation coefficients ρuu and ρuv are noticeably decreased without those large-scale turbulence structures contributing significantly to the first POD mode. Similarity of these results is observed at a higher Reynolds number.

Measurements of wavenumber-celerity spectrum in plane and axisymmetric jets

The wavenumber-convection velocity spectra W(k, U) in the near and far fields of plane and axisymmetric free air jets have been computed from digitized hot-wire data. This spectrum, which is the double Fouriertransformation of the space-time correlation R(S,T) was obtained in a 3.18 X140 cm plane jet and in a 2.54-cmdiam axisymmetric jet. For both jets the exit mean velocity Ue was 30 m/s. The reference (upstream) probe was located at x/d= 8 for the near-field data and at x/d=30 for the far-field data, d denoting the exit diameter or slit width. The spectra indicate that the jets are characterized by energetic large-scale structures not only in the near field (slightly downstream of the potential core) but also in the self-preserving region. The stream wise length scale of the most energetic eddies increases in proportion with that of the jet width. The stream wise length scale of these eddies is about 3 times the local jet width in the circular jet and 3.5 times the local jet width in the plane jet. The convection velocity U of the dominant eddies decreases from about O.SUe to Q.5Ue between the two regions in the plane jet and from about 0.73Ue to 0.25 f/^ between the two regions in the axisymmetric jet. With increasing eddy sizes, the dispersion in the convection velocity U increases as W(k,U) becomes progressively skewed towards (/values higher than the local time mean velocity U.