Large-scale Coherent Structures Research Articles

Characteristics of Large-Scale Coherent Structures on Irregularly Arranged Rough-Bed Open-Channel Flows

Large-scale coherent structures (LSCSs) in rough-bed open-channel flow (OCF) are significant in turbulence research. A recent breakthrough is the bimodal feature of LSCSs on regular rough-bed OCF (i.e., LSCSs exhibit two typical motions: large-scale motions (LSMs) and very-large-scale motions (VLSMs)). However, the presence and characteristics of LSMs and VLSMs in irregularly arranged rough-bed OCF remain unclear. Thus, in this study, high-precision indoor flume experiments were performed under typical irregularly arranged rough-bed conditions, and time-resolved particle image velocimetry was used for velocity measurements. Statistical quantities of velocity fluctuations revealed that the friction Reynolds number and roughness exerted a certain modulation on the velocity fluctuating properties. The spectra of velocity fluctuations provided direct and statistical evidence for the presence of LSMs and VLSMs in irregularly arranged rough-bed OCF. VLSMs contributed more than 60% of the streamwise turbulent kinetic energy and 40% of the Reynolds shear stress in the outer region of the irregularly arranged rough-bed OCF, which was slightly higher than that in the smooth-bed or regular rough-bed OCF scenarios. No apparent dependence of the wavelength of VLSMs on the flow submergence (H/d50) was observed in the present irregularly arranged rough-bed OCF, which is in contrast to that reported for regular rough-bed OCF. Furthermore, the relationship between the peak wavelength of VLSMs and the aspect ratio did not strictly follow a linear increase, in contrast to that documented in the literature.

Wavelet analysis of mixing layers with emphasis on intermittency and cavitation events

Many previous studies show that shear cavitation dominates the cavitation characteristics of inducers under the design point. However, understanding this cavitation type is quite difficult due to some complex coupled factors in inducers, such as the rotation and wall effects between the rotator and stator. Therefore, as a first step, a fundamental investigation concerning two-dimensional cavitating mixing layers is carried out in this work. The present study uses a large eddy simulation coupled with a homogeneous cavitation model to clarify the linkage between turbulence and cavitation in fully developed cavitating mixing layers. Special emphasis is put on the analysis of cavitation events at a single point in cavitating mixing layers. With the help of potent wavelet analysis, nonstationary turbulent cavitating flow signals are analyzed in the time-frequency domain. The results indicate that cavitation in mixing layers is more closely associated with the small-scale intermittency features that correspond to the violent fluctuation of the energy distribution in small-scale structures rather than with the large-scale coherent structures, providing a new perspective from which to understand the cavitation process in mixing layers. The close relationship between cavitation events and turbulent intermittency may also explain the discrepancies in the energy spectrum between cavitating and conventional mono-phase flows in the inertial subrange. Ensemble averaging of the velocity signal allows for the reconstruction of the time signatures of small-scale intermittency, whose results indicate that the three cavitating cases do not reveal any evident coherent structures.

Network-Based Characterization of Blood Large-Scale Coherent Motion in the Healthy Human Aorta With 4D Flow MRI.

The need for distilling the hemodynamic complexity of aortic flows into clinically relevant quantities resulted in a loss of the information hidden in 4D aortic fluid structures. To reduce information loss, this study proposes a network-based approach to identify and characterize in vivo the large-scale coherent motion of blood in the healthy human aorta. The quantitative paradigm of the aortic flow as a "social network" was applied on 4D flow MRI acquisitions performed on forty-one healthy volunteers. Correlations between the aortic blood flow rate waveform at the proximal ascending aorta (AAo), assumed as one of the drivers of aortic hemodynamics, and the waveforms of the axial velocity in the whole aorta were used to build "one-to-all" networks. The impact of the driving flow rate waveform and of aortic geometric attributes on the transport of large-scale coherent fluid structures was investigated. The anatomical length of persistence of large-scale coherent motion was the 29.6% of the healthy thoracic aorta length (median value, IQR 23.1%-33.9%). Such length is significantly influenced by the average and peak-to-peak AAo blood flow rate values, suggesting a remarkable inertial effect of the AAo flow rate on the transport of large-scale fluid structures in the distal aorta. Aortic geometric attributes such as curvature, torsion and arch shape did not influence the anatomical length of persistence. The proposed in vivo approach allowed to quantitatively characterize the transport of large-scale fluid structures in the healthy aorta, strengthening the definition of coherent hemodynamic structures and identifying flow inertia rather than geometry as one of its main determinants. The findings on healthy aortas may be used as reference values to investigate the impact of aortic disease or implanted devices in disrupting/restoring the physiological spatiotemporal coherence of large-scale aortic flow.

Experimental investigations on central vortex core in swirl spray flames using high-speed laser diagnostics

Centrally staged swirl combustion can effectively reduce NOx emission. However, the complex combustion field is susceptible to producing large-scale coherent structures, such as precessing vortex core and central vortex core (CVC). This study mainly investigates the effect of CVC on the flow and flame in a centrally staged swirl spray combustor at elevated temperature and pressure using 10 kHz high-speed CH* chemiluminescence (CL), 20 kHz particle image velocimetry, and CH2O planar laser-induced fluorescence (PLIF). For the pilot flame, both CH* CL and CH2O PLIF flame are fork-shaped with three long parts, and the middle parts of flame dynamics indicate CVC structure. For the stratified flame, the CVC structure exists in an extended strip area of strong vorticity near the centerline of the combustor. The analysis of proper orthogonal decomposition modes shows that the motion of CVC is mainly swing, followed by precessing. Simultaneous diagnostics indicates that the entrainment of CVC leads to CH2O transport from the shear layer to the central region of the combustor. In general, the CH2O signal is mainly distributed in two positive velocity regions, the pilot/main jet and around CVC. Taking advantage of the CVC effect on radical transportation is a potential method to improve the mixing of the combustor, such as temperature distribution.

Relationship between coherent Reynolds shear stress and large-scale vortical structures

An equation that relates the principal derivative of the Reynolds shear stress and large-scale vorticity fluxes is developed and validated using experimental data in a cylinder near wake. When large-scale vortices prevail, the Reynolds shear stress associated with the coherent motion is a good approximation to the conventional Reynolds shear stress. The latter is essentially determined by the imbalance between the dynamic pressure arising from the streamwise non-homogeneity caused by large-scale vortical structures and the lateral coherent vorticity flux.

Dynamic Mode Decomposition for Large-Scale Coherent Structure Extraction in Shear Flows.

Large-scale structures have been observed in many shear flows which are the fluid generated between two surfaces moving with different velocity. A better understanding of the physics of the structures (especially large-scale structures) in shear flows will help explain a diverse range of physical phenomena and improve our capability of modeling more complex turbulence flows. Many efforts have been made in order to capture such structures; however, conventional methods have their limitations, such as arbitrariness in parameter choice or specificity to certain setups. To address this challenge, we propose to use Multi-Resolution Dynamic Mode Decomposition (mrDMD), for large-scale structure extraction in shear flows. In particular, we show that the slow motion DMD modes are able to reveal large-scale structures in shear flows that also have slow dynamics. In most cases, we find that the slowest DMD mode and its reconstructed flow can sufficiently capture the large-scale dynamics in the shear flows, which leads to a parameter-free strategy for large-scale structure extraction. Effective visualization of the large-scale structures can then be produced with the aid of the slowest DMD mode. To speed up the computation of mrDMD, we provide a fast GPU-based implementation. We also apply our method to some non-shear flows that need not behave quasi-linearly to demonstrate the limitation of our strategy of using the slowest DMD mode. For non-shear flows, we show that multiple modes from different levels of mrDMD may be needed to sufficiently characterize the flow behavior.

Application of proper orthogonal decomposition in particle image velocimetry in ocean engineering

Particle image velocimetry (PIV) plays a vital role in flow measurement. Eliminating the effects of overexposure and shadow in particle images is an urgent problem to be solved in the detailed flow measurement of ocean engineering. Seek a robust denoising method for bad test environments, and apply it to the PIV experiments to achieve dual denoising at the image preprocessing and data postprocessing. This study verified the superiority of the Proper Orthogonal Decomposition (POD) filter in pre- and postprocessing compared with traditional mathematical filters. Subsequently, the POD filter is applied to a practical project: the wake field measurement of bulk carrier. Regarding preprocessing, the POD filter is a valuable tool for objectively filtering typical high-frequency spatial noise from the energy perspective based on preserving the original information of particles to the greatest extent, effectively alleviating the impact of overexposure and shadow areas. Regarding postprocessing, the POD filter can fill the data gap by considering the surrounding flow characteristics. At the same time, the flow's spatial distribution and time evolution characteristics can be obtained by POD. The flow reconstructed by selecting the appropriate order model can clearly show the evolution characteristics of large-scale coherent structures, which may provide a deep understanding of complex flow field mechanisms.

Effect of Rigid Vegetation Arrangement on the Mixed Layer of Curved Channel Flow

Curved channels and aquatic vegetation are commonly present in the riverine environment. In this study, the effects of vegetation density and distribution on the hydrodynamic characteristics of a mixed layer developed over a 180-degree curved channel were investigated through flume experiments. Wooden sticks were used to simulate rigid vegetation distributed along the half side of the channel, and a 200 Hz acoustic Doppler velocimeter (ADV) was employed to measure the three-dimensional instantaneous velocity at five selected cross sections along the curved channel. Experimental results show that the vegetation covering the half of the channel significantly affects the hydrodynamic structure of the curved channel flow, and the unequal vegetation resistance induces the K-H instability at the vegetation and non-vegetation interface, resulting in a standard hyperbolic tangent function of streamwise velocity distribution along the lateral direction. The influence of curve position on turbulence kinetic energy is far greater than that of vegetation density and vegetation distribution. The peak value of turbulent kinetic energy is comprehensively affected by vegetation density and distribution, and the peak position of turbulent kinetic energy at the interface is changed by different vegetation distribution. The combined effect of the curve and the partly covered vegetation increases the mixing between the water bodies, enhancing turbulent kinetic energy, and vegetation along the concave bank plays a more significant role. For turbulent bursting, the inward and outward interactions are mainly bursting events in the vegetation area, while ejections and sweeps are dominant in the non-vegetation area. However, the critical vegetation condition to initiate large-scale coherent structure (LSS) in the mixed layer and the influence of flexible vegetation need to be further studied in the future.

Experimental investigation of the effects of the turbulence on the impact force of flash flood

Flash floods cause damage to engineering structures and buildings mainly due to their huge impact force. Scientific investigation of the impact process of flash floods has significant theoretical and engineering implications in ensuring the safety of flood-resistant structures and human life. In this experimental study, the impact pressure and flow velocity in the flow field were measured synchronously using the impact detection system and a particle image velocimetry system in a water channel and the effects of the turbulence structure on the impact process of flash flood were investigated. As shown by the experimental measurements, the large-scale coherent structure in the flow field reached six times the boundary layer thickness. The turbulence and impact force energy spectra were very similar in the low-frequency, large-scale wave band, indicating that the large-scale turbulence structure dominated the impact process. Both the mean and maximum impact pressures increased with the turbulence kinetic energy. An equation for impact force characterization that considers the effects of turbulence and thus was more accurate was given, providing a theoretical basis for the protection of engineering structures from the damage by flash floods.

A unified theory for the envelope radiation of ring-mode coherent structures in the very-near-nozzle and developed regions of a circular jet

Large-scale coherent structures (CS) are present on a turbulent circular jet and are known to constitute an important source of jet noise. These structures may be treated as wavepackets of instability modes supported by the time-averaged mean flow. The nonlinear evolution and acoustic radiation of such CS in the fully developed region of a jet have been described in our recent work [Zhang and Wu, “Nonlinear evolution and low-frequency acoustic radiation of ring-mode coherent structures on subsonic turbulent circular jets,” J. Fluid Mech. 940(A39), 1–56 (2022)], where the mechanism of envelope radiation, or low-frequency radiation, was identified. The present paper focuses on the distinguished very-near-nozzle region, where the nozzle diameter is comparable with the length scale of the envelope of the CS. The CS resides in the thin shear layer developing from the lip line, and its nonlinear dynamics resembles that on a planar shear layer, only slightly affected by circular geometry, or circularity. However, circularity causes a leading-order effect on the acoustic radiation. One of significant new features is the presence of an inner acoustic field in the potential core. The outer and inner acoustic fields interact with each other, and the equivalent sources of sound have to be determined along with the sound fields. The waves in the inner acoustic field propagate mainly upstream. It is shown for the first time that nonlinear interactions of CS in the thin shear layer excite via receptivity the so-called discrete “trapped acoustic modes” as well as low-frequency Kelvin–Helmholtz modes, which may evolve into preferred modes in the developed region. The envelope radiation provides a key mechanism coupling the dynamics in the thin shear layer with the dynamics in the jet column regions. As the jet develops downstream, the inner acoustic field narrows gradually and disappears eventually. It is demonstrated that the theory developed here for nonlinear dynamics and acoustic radiation is valid from the very-near-nozzle to the developed regions, and thus stands as a unified theory.

An experimental study on the effects of wall heating on coherent structures in a turbulent boundary layer

An experimental investigation was conducted for a better understanding of the turbulence behavior and the coherent structure in a turbulent boundary layer over a heated plate, which is horizontal facing upwards. To explore the effects of wall temperature on the turbulent boundary layer behavior, the boundary layer flow was observed at four different temperatures between the plate and inlet flow (δT=0, 15, 30, and 50 K), with the momentum Reynolds number of the inlet flow set to Reθ=1196. We show that based on the comparison of turbulent kinetic energy (TKE) distribution between unheated- and heated-wall cases, the wall-heated turbulent boundary layer can be divided into three regions, namely, the near-wall region, the intermediate region, and the outer region. The relationship between the TKE distribution and the coherent structures in each region is explored by comparing the detailed flow-field measurement results for the unheated- and heated-wall cases. In the near-wall region, the decrease in fluid viscosity caused by wall heating has stabilization effects on the turbulent fluctuation. With the increase in wall temperature, the streaky structures display a continuous decrease in their spanwise meandering and an increase in their streamwise coherency. The intermediate region ranges from the logarithmic region to the thermal boundary layer edge. The buoyant force caused by wall heating has a significant effect on the turbulence behavior in this region. Under the influence of buoyant force, the large-scale coherent structures for the wall-heating case were found to contain more kinetic energy and incline away from the wall with a larger angle, which leads to the increased TKE in the intermediate region for the wall-heating case. In the outer region, the occurrence of separated turbulent structures is measurably more common for the wall-heating case. Owing to the shedding of the turbulent structures from the turbulent production source (i.e., large-scale coherent structures originating from the near-wall region), the TKE in the outer region for the wall-heating case is less than that of the unheated case.

Large eddy simulation of highly compressible film cooling in transonic crossflow

Large eddy simulation is performed to study the thermal energy transport and mixing process of compressible film cooling in the fully-turbulent high-Mach-number crossflow. Three Mach numbers, 0.8, 1.2, and 1.4, based on the bulk crossflow velocity, are adopted. And the influence of both the compressibility and shock waves on the transverse jet from cylindrical orifices is discussed in detail. The results reveal that the effects of compressibility should be distinguished from shocks in supersonic flows. The compressibility effect strengthens the jet penetration and lateral spreading by increasing the energy contained in the large-scale coherent structures. The mixing of the jet is enhanced by the strong compressibility in the near field whether shocks exist or not. When the crossflow transits from the subsonic to the supersonic state, the effect of shock waves becomes more significant than that of the compressibility. Various interactions between shocks, coherent structures, and thermal energy transport are analyzed in this study. The results show that the appearance of the separation shock and bow shock reduces the jet penetration and strengthens its interaction with the bottom wall. The generation of this type of shock system suppresses the flow separation on the leeward side of the jet, which results in a higher cooling effectiveness in the jet near field. The incident oblique shock wave also induces lifting of the jet trajectory in the far-field region as a result of the intensified separation trend. In the highly compressible film cooling process with great temperature difference, the advection transport associated with turbulent motion, rather than the one associated with mean motion, turns out to dominate the thermal energy transfer in general. Moreover, the counter gradient behavior of this thermal energy transport in compressible turbulence is also shown.

Large-Scale Coherent Turbulence Structures in the Atmospheric Boundary Layer over Flat Terrain

Abstract We investigate characteristics of large-scale coherent motions in the atmospheric boundary layer using field measurements made with two long-range scanning wind lidars. The joint scans provide quasi-instantaneous wind fields over a domain of ∼50 km2, at two heights above flat but partially forested terrain. Along with the two-dimensional wind fields, two-point statistics and spectra are used to identify and characterize the scales, shape, and anisotropy of coherent structures—as well as their influence on wind field homogeneity. For moderate to high wind speeds in near-neutral conditions, most of the observed structures correspond to narrow streaks of low streamwise momentum near the surface, extending several hundred meters in the streamwise direction; these are associated with positive vertical velocity ejections. For unstable conditions and moderate winds, these structures become large-scale rolls, with longitudinal extent exceeding the measuring domain (>∼5 km); they dominate the conventional surface-layer structures in terms of both physical scale and relative size of velocity-component variances, appearing as quasi-two-dimensional structures throughout the entire boundary layer. The observations shown here are consistent with numerical simulations of atmospheric flows, field observations, and laboratory experiments under similar conditions. Significance Statement Coherent structures have attracted the interest of researchers for decades, being viewed as the closest to “order” that we can find within the chaos of turbulence. In the turbulent atmospheric boundary layer, micro- and mesoscale coherent structures come in many shapes and sizes, such as convective cells, rolls, or streaks. In this study we used dual lidars (remote sensing measurements), developing analysis of their tandem usage to characterize in detail some of the large-scale coherent structures generated over flat terrain. This allowed us to better understand the mechanisms that generate such structures and describe their influence on the morphology of the turbulent atmospheric boundary layer across a good deal of its depth.

Turbulent Transition of a Flow from Small to O(1) Rossby Numbers

Abstract Oceanic flows are energetically dominated by low vertical modes. However, disturbances in the form of atmospheric storms, eddy interactions with various forms of boundaries, or spontaneous emission by coherent structures can generate weak high-baroclinic modes. The feedback of the low-energy high-baroclinic modes on large-scale energetically dominant low modes may be weak or strong depending on the flow Rossby number. In this paper we study this interaction using an idealized setup by constraining the flow dynamics to a high-energy barotropic mode and a single low-energy high-baroclinic mode. Our investigation points out that at low Rossby numbers the barotropic flow organizes into large-scale coherent vortices via an inverse energy flux while the baroclinic flow accumulates predominantly in anticyclonic barotropic vortices. In contrast, with increasing Rossby number, the baroclinic flow catalyzes a forward flux of barotropic energy. The barotropic coherent vortices decrease in size and number, with a strong preference for cyclonic coherent vortices at higher Rossby numbers. On partitioning the flow domain into strain-dominant and vorticity-dominant regions based on the barotropic flow, we find that at higher Rossby numbers baroclinic flow accumulates in strain-dominant regions, away from vortex cores. Additionally, a major fraction of the forward energy flux of the flow takes place in strain-dominant regions. Overall, one of the key outcomes of this study is the finding that even a low-energy high-baroclinic flow can deplete and dissipate large-scale coherent structures at O(1) Rossby numbers.

A spectral inspection for turbulence amplification in oblique shock wave/turbulent boundary layer interaction

Turbulence amplification and the large-scale coherent structures in shock wave/turbulent boundary layer interaction flows have been studied at length in previous research, while the direct association between these two flow features is still lacking. In the present study, the transport equation of turbulent kinetic energy spectra is derived and utilized to analyse the scale-by-scale energy budget across the interaction zone, enabling us to reveal the association between the genesis of the large-scale motions and the turbulence amplification. For the presently considered flow with incipient shock-induced separation, we identified in turbulent kinetic energy spectra distribution that the most energetic motions are converted from the near-wall small-scale motions to large-scale motions consisting of velocity streaks and cross-stream circulations as they go through the interaction zone. The amplification of streamwise velocity fluctuation is triggered first, resulting in the emergence of large-scale velocity streaks, which is attributed to the adverse pressure gradient, as indicated by the spectra of the production term. The energy carried by large-scale velocity streaks is transferred to other velocity components by the pressure-strain term, producing large-scale cross-stream circulations. When large-scale motions are convected downstream, their energy is transferred via turbulent cascade to smaller scales and dissipated by viscosity. The spanwise uniform fluctuations, reminiscent of the unsteadiness of the separation bubble, are contributed primarily by the inter-scale energy transfer from the finite spanwise scale motions.

Large-scale circulations in a shear-free convective turbulence: Mean-field simulations

It has been previously shown [Elperin et al., “Formation of large-scale semi-organized structures in turbulent convection,” Phys. Rev. E 66, 066305 (2002)] that a non-rotating turbulent convection with nonuniform large-scale flows contributes to the turbulent heat flux. As a result, the turbulent heat flux depends explicitly not only on the gradients of the large-scale temperature, but also on the gradients of the large-scale velocity. This is because the nonuniform large-scale flows produce anisotropic velocity fluctuations, which modify the turbulent heat flux. This effect causes an excitation of a convective-wind instability and formation of large-scale semi-organized coherent structures (large-scale convective cells). In the present study, we perform mean-field numerical simulations of shear-free convection, which take into account the modification of the turbulent heat flux by nonuniform large-scale flows. We use periodic boundary conditions in horizontal direction as well as stress-free or no-slip boundary conditions in vertical direction. We show that the redistribution of the turbulent heat flux by the nonuniform large-scale motions in turbulent convection plays a crucial role in the formation of the large-scale semi-organized coherent structures. In particular, this effect results in a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale convective cells. We demonstrate that the convective-wind instability is excited when the scale separation ratio between the height of the convective layer and the integral turbulence scale is large. The level of the mean kinetic energy at saturation increases with the scale separation ratio. We also show that inside the large-scale convective cells, there are local regions with the positive vertical gradient of the potential temperature, which implies that these regions are stably stratified.

Hydrodynamic mechanism of Misgurnus anguillicaudatus during turning maneuvers

Aquatic organisms in their natural environment have soft bodies and flexible mobility. Clarifying the generation, evolution, and dissipation of vortices and jets during turning maneuvers is crucial for understanding the propulsion principle of aquatic species, which, in turn, provides guiding value for fish-like propulsion device design. In this study, time-resolved particle image velocimetry is used to explore the kinematic and dynamic characteristics of Misgurnus anguillicaudatus while turning. The results showed that M. anguillicaudatus maintained the wavy movement of its trunk by bending different body parts. Pressure gradients that are weaker and stronger than the surrounding environment were formed at the peaks and troughs, respectively, resulting in a thrust mechanism dominated by suction. The body fluctuation and relative fluid motion served to form a vortex. The connection of the separation line of the saddle point to the focus in this process creates an unstable flow structure that accelerates vortex dissipation. Jets are formed between the reverse vortices; the thrust jets provide forward power for turning maneuvers, and the side jets provide turning torque. As the jets and tail are situated at angles to one another, only part of the jet-generated kinetic energy provides power for the fish to swim. Additionally, proper orthogonal decomposition is utilized for objectively filtering high-frequency spatial noise in complex fish wake data. The flow field reconstructed via the mode selection of an appropriate order can be used to clearly show the evolution characteristics of large-scale coherent structures.

Interaction between a stationary sphere and turbulent flow in a boundary layer

We investigate the interaction of a stationary sphere with turbulent flows in a spatially developing boundary layer over a flat plate by means of fully resolved direct numerical simulations. The diameter of the sphere D is much larger than the Kolmogorov length scale. The sphere Reynolds number ReD is changed by varying the sphere diameter, while the gap ratio is held constant with G/D=0.1, where G is the distance between the bottom of the sphere and the flat plate. The simulation results indicate that there exist complex interactions between the small-scale vortex in the wake of the sphere and the large-scale coherent structures inside the turbulent boundary layer. The jet-like flow through the gap is deflected away from the wall, and the level of deflection increases with ReD. As a result, asymmetrical flow structures are observed in the recirculation zone. In addition, the mean recirculation length is found to decrease with the increase in ReD. Concerning the turbulence modulation, statistics show that the skin-friction drag and boundary layer thickness are decreased in the recirculation region with respect to the undisturbed flow, whereas the displacement thickness is increased due to the presence of reverse flow. These effects become more pronounced as ReD increases. The budget of the turbulent kinetic energy in the sphere wake is also examined. It is revealed that the turbulent production and viscous dissipation rate are significantly enhanced under the effect of the sphere with size of the same order of magnitude as the local boundary layer thickness.

Lagrangian Identification of Coherent Structures and Mass Transport in a Buoyant Jet Diffusion Flame

ABSTRACT Using Lagrangian coherent structures (LCSs), the mass transport process of large-scale coherent structures in a buoyant jet diffusion flame is studied numerically to gain a key understanding of combustion instability. First, the reacting flow fields of the jet diffusion flame are numerically simulated for two cases, a stable case without considering the buoyancy effect and an unstable case that includes the buoyancy effect corresponding to combustion instability. In particular, large-scale Kelvin-Helmholtz instability (KHI) vortex structures outside the flame surface are captured in the unstable case. Then, the ridges in finite-time Lyapunov exponent (FTLE) fields that sketch the distinct regions in the reacting flow field are extracted as LCSs. The mass transport process is studied by comparing the distribution of LCSs with reaction fields. The flame surface is found to coincide with the attracting LCSs, which separate the fuel and air on opposite sides of the flame surface. In contrast, the reaction products, including species and reaction heat, are confined in the boundaries consisting of repelling LCSs on the inner and outer sides of the flame surface. Finally, the evolution of LCSs is tracked to analyze the generation of KHI vortices and species transport in the jet diffusion flame. With the aid of LCSs, it is found that there exist some saddle-type flow features separating the distinct flow structures into several regions, and the jet fuel and airflow enter into the separated regions from different open boundaries. Importantly, the attracting LCSs in the separated regions then bulge outwards, forming KHI vortices as the attracting LCSs further stretch and fold. Furthermore, the vortices continue moving upwards while species flow from repelling LCSs to attracting LCSs, leading to mixing. These results show that attracting and repelling LCSs can act as the flame surface and the mass and energy transport boundary of the reaction products, respectively. In summary, the work presented can provide a new method in combustion controlling to estimate the location of the flame surface and the transport boundaries of species from the velocity field, by using LCSs.

Proper Orthogonal Decomposition Method for the Prediction of Fan Broadband Interaction Noise

The turbulent wake generated by a rotor interacting with outlet guide vanes (OGVs) is one of the dominant broadband noise sources in a turbofan engine. An accurate representation of the rotor wake turbulence is therefore important for the reliable prediction of the rotor–OGV interaction noise. This paper presents a turbulence synthesis method based on a spectral proper orthogonal decomposition (POD) representation of the turbulent wake that aims to reproduce the desired velocity cross-spectrum along the OGV leading edges where noise is emitted due to turbulence–OGV interaction. The method is first developed in the frequency domain based on a superposition of vortical modes with the appropriate amplitudes. Fourier modes and POD modes are proposed to represent the two-point velocity spectrum. The POD modes will be shown to be highly efficient in reconstructing the flowfield near the tip region where a large-scale coherent structure is present. An extension of the POD synthetic turbulence method to the time domain is also presented by means of a white noise filtering technique to allow the generation of time-varying velocity signals with the desired cross-spectral characteristics. The results show that both the one- and two-point statistics can be closely reproduced. The proposed frequency-domain POD synthetic turbulence method for fan broadband noise prediction for a realistic fan–OGV configuration is illustrated by the use of a frequency-domain linearized Navier–Stokes solver to predict the sound power radiation due to each vortical mode. Overall sound power levels at a number of discrete frequencies are predicted and compared against measured noise data. Agreement is found to be within the uncertainty of the noise sound power measurement.