Coherent Vortical Structures Research Articles

Modelling entrainment volume due to surface-parallel vortex interactions with an air–water interface

We consider the entrainment volume that results from the quasi-two-dimensional interactions of rising surface-parallel vorticity with an air–water interface. Based on systematic (three-dimensional) direct numerical simulations (DNS) of the canonical problem of a rectilinear vortex pair impinging on and entraining air at the free surface, we develop a phenomenological model to predict the resulting entrainment volume in terms of four key parameters. We identify a new parameter, a circulation flux Froude number $Fr^2_\Xi =|\varGamma |W/a^2\,g$, that predicts the dimensionless volume $\forall$ of entrained air initiated by a coherent vortical structure of circulation $\varGamma$, effective radius $a$, vertical rise velocity $W$ with gravity $g$. For $Fr^2_\Xi$ below some critical value $Fr^2_{\Xi cr}$, no air is entrained. For $Fr^2_\Xi >Fr^2_{\Xi cr}$, the average initial entrainment $\overline {\forall }_o$ scales linearly with ($Fr^2_\Xi -Fr^2_{\Xi cr}$). We also find that $\overline {\forall }_o$ is linearly dependent on circulation Weber number $We_{\varGamma }$ for a range of vortex Bond number $5 \lesssim Bo_{\varGamma } \lesssim 50$, and parabolically dependent on circulation Reynolds $Re_{\varGamma }$ for $Re_{\varGamma }\lesssim 2580$. Outside of these ranges, surface tension and viscosity have little effect on the initial entrainment volume. For the canonical rectilinear vortex problem, the simple model predicts $\overline {\forall }_o$ extremely well for individual coherent structures over broad ranges of $Fr^2_\Xi$, $We_{\varGamma }$, $Bo_{\varGamma }$ and $Re_{\varGamma }$. We evaluate the performance of this parameterisation and phenomenological entrainment model for air entrainment due to the complex periodic vortex shedding and quasi-steady wave breaking behind a fully submerged horizontal circular cylinder. For the range of parameters we consider, the phenomenological model predicts the event-by-event dimensionless entrainment volume measured in the DNS satisfactorily for this complex application.

Effect of the asymmetric bio-inspired trailing-edge serrations on sound suppression in a coupled owl-based airfoil

Trailing-edge noise plays a dominant part in blades coping with low inflow turbulence at the low Mach number. An important reason for the dramatic noise reduction of owls is on account of the distinct wing morphology of the trailing edge. In particular, its excellent hunting advantages are closely related to the angle of attack. Based on that, the bio-inspired trailing-edge design with oblique-arc profile were retrofitted to the coupled airfoil with 40% cross section of the owl wing in this study, which is contributed to break the limitation of the sound suppression of the conventional serration. High-resolution large eddy simulations combined with the acoustic analogy method are employed to perform the simulation under the specific attack angles with 0° and 15° . The results show that the potential of high-efficiency and low-noise bionic airfoil is exceedingly realized at the attack angle with 0° . The overall sound power level of the coupled airfoil is reduced by 5.47 dB compared with the smooth airfoil. An additional 3.68 dB noise reduction advantage over conventional serrations. Affected by the trailing-edge serrations, the coherent vortex structures with tube-shaped vortices in spanwise direction are dissipated into the horseshoe-type vortices, which implies that more acoustic energy of the coupled bionic airfoil is dissipated. In contrast, the wake gap flow with attack angle of 15° is conducive to intensify the turbulent wake flow that is prone to generate the V-shaped pressure fluctuations. Extra stronger broadband noise is emitted by the coupled airfoil in the longitudinal direction when the regular large-scale wake vortices of the smooth airfoil are broken into the more widespread out-of-order vortices. Consequently, the design of the innovative trailing-edge serrations is contributed to utilize the fluid physics behind it to implement a broader sound suppression strategy.

Very Large Eddy Simulation of Aero-Thermal Performance in Squealer Tip Gap

Abstract To improve the resolution accuracy and get deep insight into the flow structures in squealer tip gap, the very large Eddy simulation (VLES) method was implemented into the commercial computational fluid dynamics (CFD) solver with the user-defined function (UDF). Based on the published experimental data, the numerical accuracy of VLES method was validated. With the VLES method, the unsteady heat transfer coefficient distributions on the squealer tip and total pressure loss in the blade passage were computed. The influences of coherent vortex structures on aero-thermal performance in the squealer tip gap were analyzed. The results show that the Brown-Roshko vortices are the main driver for the formation of cavity vortex system. The direct impingement of pass-over leakage into the cavity is the main cause of high heat transfer area on the cavity floor near leading edge. The unsteady fluctuations of leakage rate through the tip gap reach about ±8% of the time-averaged value. The development of leakage vortex accounts for the major contribution of total pressure loss in the squealer tipped blade. Due to flow unsteadiness, the fluctuation of pitch-averaged total pressure loss coefficient induced by leakage vortex system reaches about ±30% of the time-averaged value. The unsteady fluctuation of pitch-averaged heat transfer coefficient on the cavity floor reaches about ±35% of the time-averaged value, while on the shroud surface it is only fluctuated by about ±10%.

Characterization of atmospheric coherent structures and their impact on a utility-scale wind turbine

Atmospheric turbulent velocity fluctuations are known to increase wind turbine structural loading and accelerate wake recovery, but the impact of vortical coherent structures in the atmosphere on wind turbines has not yet been evaluated. The current study uses flow imaging with natural snowfall with a field of view spanning the inflow and near wake. Vortical coherent structures with diameters of the order of 1 m are identified and characterized in the flow approaching a 2.5 MW wind turbine in the region spanning the bottom blade tip elevation to hub height. Their impact on turbine structural loading, power generation and wake behaviour are evaluated. Long coherent structure packets $(\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }200\;\textrm{m)}$ are shown to increase fluctuating stresses on the turbine support tower. Large inflow vortices interact with the turbine blades, leading to deviations from the expected power generation. The sign of these deviations is related to the rotation direction of the vortices, with rotation in the same direction as the circulation on the blades leading to periods of power surplus, and the opposite rotation causing power deficit. Periods of power deficit coincide with wake contraction events. These findings highlight the importance of considering coherent structure properties when making turbine design and siting decisions.

Аtmospheric wind flow around the mountain landscape in the vicinity of Danang airport and flight safety issues

Wind boundary layer flow over the mountain landscape and large structures located around runways (RWs) creates coherent vortex structures (CVSs) that can cross a glideslope and airspace in the vicinity of an airport. The aircraft, encountering a vortex structure, experiences significant changes of the aerodynamic forces and moments, what is especially hazardous due to proximity to terrain. From a mathematical point of view, the solution of this problem presents a challenge due to extremely large space – time scale of the phenomenon, the lack of relevant atmospheric models, as well as comprehensive initial – boundary conditions in numerical modeling. In this paper, a composite solution is constructed: the CVSs area generation is computed in sufficient details within the framework of the grid method. Based on the data obtained in the approximation of analytical functions, an initial vortex structure is formed, the evolution and stochastics of which are modeled within the potential approximation by means of Rankine vortices. The evaluation of the forces and moments increment from the impact of vortex structures on the aircraft was carried out by the panel method using the engineering approach. As an example, the CVSs, resulting from wind flow around the mountainous area of the Son Tra Peninsula, that is located short of RWs 35R-17L and 35L-17R of Da Nang airport, are investigated. To improve the computational grids quality and verify the method of solving the boundary value problem for the Reynolds-averaged Navier-Stokes equations, we used the criteria based on the principle of maximum pressure, requiring Q-parameter positivity property in the vortices cores and flow separation regions. A CVS related aviation event, involving a passenger aircraft MC-21, is studied. The aircraft, after takeoff from RW 35R-17L setting the course close to the direction of the vortex wind structure axis from the Son Tra Peninsula, encountered the mountainous area CVS.

Performance Enhancement Analysis of a Horizontal Axis Wind Turbine by Vortex Trapping Cavity

Abstract A wind turbine blade has the particularity of containing twisted and tapered thick airfoils. The challenge with this configuration is the highly separated flow in the region of high twist. This research presents a numerical investigation of the effectiveness of a vortex trapping cavity (VTC) on the aerodynamics of the National Renewable Energy Laboratory phase VI wind turbine. First, simulations are conducted on the S809 profile to study the fluid flow compared to the airfoil with the redesigned VTC. Second, the blade is simulated with and without VTC to assess its effect on the torque and the flow patterns. The results show that for high angles of incidence at Rec = 106, the lift coefficient increases by 10% and the wake region appears smaller for the case with VTC. For wind speeds larger than 10 m/s, the VTC improves the torque by 3.9%. This is due to the separation that takes place in the vicinity of the VTC and leads to trapping early separation eddies inside the cell. These eddies roll up forming a coherent laminar vortex structure, which in turn sheds periodically out of the cell. This phenomenon favorably reshapes excessive flow separation, reenergizes the boundary layer, and globally improves blade torque.

Large-eddy simulations of a swirling flow in a model Francis turbine

We performed Large-eddy simulations of the flow in a model air Francis turbine in a range of low-load regimes with a swirler rotating at fixed frequency. All investigated regimes revealed the presence of coherent helical vortex structure in the draft tube: the precessing vortex core. We identified the frequency of this instability and obtained mean flow velocity fields to be utilized in further works.

Analysis of spontaneous longitudinal combustion instability in an O2/CH4 single-injector rocket combustor

Self-excited longitudinal combustion instabilities were analyzed in a sub-scale combustor operating with a propellant combination of O2/CH4. Couplings between acoustics, hydrodynamics, and heat release were investigated numerically based on an experimental setup. The numerical results were in good agreement with the experimental data. Various post-processing methods have been adopted to explain the thermoacoustic behavior and reveal the underlying unstable combustion mechanisms. The classical longitudinal acoustic characteristics of the combustion chamber were identified by the pressure mode shape and dynamic mode decomposition (DMD) analysis. It was found that the incoming streams along the injector were periodically hindered by the traveling pressure wave originating from the chamber, thus, resulting in an oscillatory propellant supply and a pulsating heat release. This, in turn, feeds energy into the acoustic pressure oscillations, and maintains the combustion instability. Meanwhile, the coherent vortex structures in the reacting mixing-shear layer were found to be the principal reason for sustaining combustion instabilities. Besides, a positive feedback closed-loop system associated with periodic vortex shedding and merging is believed to sustain combustion instabilities. The plot of the Rayleigh index further confirmed that the shear layer region drives thermoacoustic instabilities.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

A vorticity wave packet breaking within a rapidly rotating vortex. Part II: wave/mean flow interaction

AbstractIn Part I, the author analyzed the asymmetric structure of a critical layer embedded in a linearly stable, columnar, and axisymmetric vortex on the ‐plane. This structure is the result of the long time asymptotic and slowly varying interaction between a vorticity wave packet and the vortex. He showed that the presence of a critical layer‐induced mean radial velocity led to the formation of a spiraling helical critical layer. Through matched asymptotic expansions, he found an analytical solution of the leading‐order motion equations inside the critical layer. In this paper, he derives the system of the coupled evolution equations of the wave amplitude and the low‐order CL‐induced mean flow on the critical radius in the quasi‐steady regime. The knowledge of the wave amplitude, the leading‐order mean axial and azimuthal velocity, and axial vorticity evolutions can be simply determined from three first‐order differential equations. The main outcome of the first‐order mean flow truncated system resolution is that the wave packet/vortex interaction leads to a fast vorticity wave breaking. The wave amplitude equation contains a coupling term, involving the vertical gradient of the mean axial vorticity located inside the separatrices, and accelerating the breaking. The leading‐order mean rotational and vertical momenta are conserved within the envelope as time proceeds. Numerical simulations nevertheless show that the wave packet and vortex kinetic energies slightly grow inside the envelope before the breaking onset in most of the cases, whereas the vortex was intensifying at the expense of the wave packet in the previous and unsteady interaction. The vertical wind shear strength has the highest effect on the wave/mean flow interaction. When the shear is moderate, it enhances intensification but when it is very large, it prohibits it in both the unsteady and slowly evolving stages. Including the second‐order mean flow in this system could, however, avoid the breaking and would permit the interaction to generate an asymptotic constant‐speed travelling coherent vortical structure.

Influence of Ekman friction on the velocity profile of a coherent vortex in a three-dimensional rotating turbulent flow

In the presence of strong background rotation, the velocity field tends to become quasi-two-dimensional, which leads to the inverse energy cascade. If the damping is small enough, then the energy is accumulated at the largest scales of the system, forming coherent columnar vortex structures known as condensates. Recently, it was found that the radial velocity profiles of axisymmetric cyclones and anticyclones are described by the dependence UGφ(r)=±ϵ/ν r ln (R/r), where ϵ is statistically stationary turbulent forcing power per unit mass, ν is the kinematic viscosity of a fluid, and R is the transverse size of the vortex. However, the corresponding theory did not take into account the boundary effects and, therefore, was mainly applicable to numerical simulations with periodic boundary conditions. Here, we demonstrate that for typical experimental conditions, the damping of the condensate far enough from the symmetry axis is determined by the linear Ekman friction α=2Ω0E1/2 associated with the no-slip conditions at the lower and upper boundaries of the system, where Ω0 is the angular velocity of the background rotation and E is the Ekman number. In this case, the azimuthal velocity of the coherent vortex does not depend on the distance to the vortex center and is determined by the expression UGφ=±3ϵ/α. We discuss the structure of the coherent vortex in this case and compare the results with velocity profiles of condensates in two-dimensional systems.

Flow Separation Control over an Airfoil Using Plasma Co-Flow Jet

A NACA0025 coflow jet airfoil model, including the inner and outer airfoils, was designed and manufactured through 3D printing technology. Using the duct connecting the leading- and trailing-edge slots formed by the inner and outer airfoils, eight plasma actuators are arranged in the duct and synchronously driven by two high-voltage alternating-current sources to realize the plasma coflow jet (PCFJ) flow control technique. The test angle of attack range is 8–30°, and the Reynolds number is 68,000. The induced airflow characteristics were studied, and the flow control mechanism of the PCFJ airfoil was explored using the detailed two-component particle image velocimetry technique. The results in the quiescent air show that in addition to the injection at the leading-edge slot and the suction at the trailing-edge slot, the actuators on the upper surface of the inner airfoil provide local flow acceleration and momentum injection. The results in the wind tunnel show that the PCFJ airfoil has a better performance in delaying flow separation, and its time-averaged flow separation position is delayed by 46% compared with the baseline airfoil. The mixing shear layer that becomes turbulent in advance and the subsequent coherent vortex structures, the injection at the leading edge and suction at the trailing edge, and local flow acceleration and momentum injection of the plasma actuators are the key factors for the mechanism of separation delaying of the PCFJ flow control technique.

Self-amplifying hetons in vertically sheared geostrophic turbulence

This paper examines baroclinic turbulence in the local approximation using a quasi-geostrophic beta-plane numerical model with bottom friction. New coherent vortex structures are found to emerge and self-amplify in a horizontally homogeneous mean flow directed westward in the upper layer where the potential vorticity gradient (PVG) is negative. Opposite sign eddies shifted eastward are formed in the lower layer with positive PVG owing to the Rossby wave radiation. Such baroclinic structures can be viewed as self-amplifying hetons supported by the energy transfer from the mean flow. Their growth and saturation are controlled by the competition between vortex amplification associated with the crossflow drift and viscous decay enhanced by core deformations. The presented numerical simulations indicate that subtropical regions with westward flows in the upper layer favor eddy growth and long-distance propagation.

Predicting rocker shoe parameters for reducing plantar pressure using machine learning methods

The formation and evolution of quadruple synthetic jets issuing into quiescent air are experimentally investigated. Four different configurations (monopole-like, dipole-like, quadrupole-like and 90-degrees-circularly-shifted-jets) have been studied by varying the phase lags between the ejection strokes of the four jets, at constant values of the source Reynolds and Strouhal numbers, equal to 4000 and 0.2, respectively. For each configuration instantaneous three-component in-plane velocity fields in the most relevant streamwise planes are measured with stereoscopic particle image velocimetry. The evolution of the turbulent jet flow is analyzed by the velocity field triple decomposition, thus separating the time-averaged component from the forced periodic oscillation and the turbulent fluctuation. It is observed that the near region of the flow domain is dominated by the formation and advection of large-scale coherent vortex structures, which are originated by the interaction of the vortex rings inherent to the single synthetic jets. The vortex dynamics is captured by phase-averaged measurements and its role in determining the flow field structure of each of the investigated configurations is widely discussed. The vortex structures are observed to lose their coherence and break down into turbulence while propagating downstream. The decay of the large-scale coherent motions is accompanied by the establishment of a self-preserving behavior of both the mean flow and turbulent quantities. Nevertheless, it is shown that the far-field topology depends critically on the source conditions and near-field evolution.

Delayed-Detached Eddy Simulations of Film Cooling Effect on Trailing Edge Cutback With Land Extensions

Abstract Film cooling effect on trailing edge cutback with land extensions (i.e., landed case) was numerically investigated with the delayed-detached eddy simulation (DDES) method. At three rib geometries (i.e., inline rib arrays, six-row pin-fin arrays, and five-row pin-fin arrays) and five blowing ratios (i.e., M = 0.5, 0.8, 1.1, 1.5, and 2.0), film cooing effectiveness, coherent vortex structures, and discharge coefficients for the landed cases were analyzed and compared with baseline cases (i.e., cutback without land extensions). The results show that land extensions have significant influences on coherent flow structures, vortex energy levels, film cooling effectiveness, and discharge coefficients in cutback region. Different from the baseline cases, the dominant vortex structures in landed cases exhibit the “double helix” (for cutback with inline rib array) or “strip” pattern (for cutback with pin-fin arrays), and the thickness of mixing region in landed cases is decreased. Among three rib geometries, the trailing edge cutback with six-row pin-fin arrays has the worst cooling effect for both baseline and landed cases. Compared with the baseline cases, the discharge coefficients for the landed cases are decreased by about 21.4%. With land extensions, the overall film cooling effectiveness on cutback is decreased first and then increased with increasing blowing ratio. Among all investigated cases, cutback with five-row pin-fin arrays for the landed case performs the best film cooling effect at M = 0.5.

Vortex Shedding Frequency Scaling of Coherent Structures Induced by a Plasma Actuator

The spatial–temporal evolution of coherent structures generated by an asymmetrical dielectric barrier discharge (DBD) plasma actuator is an intriguing unsteady process with profound implications for revealing the controlling mechanism of the plasma actuator and promoting the control effect of the DBD plasma actuator at high wind speed and high Reynolds number. In this study, the induced coherent structures of the plasma actuator are studied systematically with a particle image velocimetry for a range of force coefficients (). Results indicate that the vortices that shed periodically from the downstream edge of the exposed electrode are a result of the amplification of natural disturbances in the jet shear layer. During later evolution, the adjacent vortices pair up to form a new vortex, leading to a reduction of the dominant frequency in the velocity spectra. Further downstream, the coherent vortical structures decay considerably, correlating with the shear-layer transition process in the plasma wall jet. The vortex shedding frequency is observed to scale with the force coefficient according to , which is of importance to the selection of the dominant frequency by adjusting the actuation parameters of the plasma actuator based on the characteristic frequency of the controlled flowfield and improving the control effect of the plasma actuator. With increasing force coefficient, the propagation speed of the roll-up vortices increases linearly, whereas the streamwise vortex spacing decreases monotonically. It is of great significance that the nondimensional Strouhal number based on the vortex shedding frequency, vortex propagation speed, and streamwise vortex spacing is proposed and varies slightly between 0.045 and 0.065, for all the tested cases, which lays a foundation for promoting the numerical simulation model of the plasma actuator and revealing the controlling mechanism of the flow control using the plasma actuator.

Direct 3D observation and unraveling of electroconvection phenomena during concentration polarization at ion-exchange membranes

A decade ago, two-dimensional microscopic flow visualization proved the theoretically predicted existence of electroconvection roles as well as their decisive role in destabilizing the concentration polarization layer at ion-selective fluid/membrane interfaces. Electroconvection induces chaotic flow vortices injecting volume having bulk concentration into the ion-depleted diffusion layer at the interface. Experimental quantification of these important flow patterns have so far only been carried out in 2D. Numerical direct simulations suggest 3D features, yet experimental proof is lacking. 3D simulations are also limited in covering extended spacial and temporal scales.This study presents a new comprehensive experimental method for the time-resolved recording of the 3D electroconvective velocity field near a cation-exchange membrane. For the first time, the spatio-temporal velocity field can be visualized in 3D at multiples of the overlimiting current density. In contrast to today’s simulations, these experiments cover length and time scales typical for actual electrodialytic membrane processes.We visualize coherent vortex structures and reveal the changes in the velocity field and its statistics during the transition from vortex rolls to vortex rings with increasing current density. The transition is characterized by changes in the rotational direction, mean square velocity, and temporal energy spectrum with only little influence on the spatial spectrum. These findings indicate a more significant impact of EC’s structural change on the mean square velocities and temporal spectra than on the spatial spectra. This knowledge is a prerequisite for engineering ion-selective surfaces that will enable the operation of electrically driven processes beyond the diffusion-limited Nernst regime.

Enhancement of wake vortex decay by air blowing from the ground

It is well-known that the long-lasted aircraft wake vortex above the airport runway jeopardizes flight safety. Therefore, the research on the enhancement of wake vortex decay is pretty much essential. The previous studies suggest that the wake decay process can be improved by introducing artificial perturbations [1]. For example, the plate lines on the ground can trigger the helical secondary vortex structures (SVS), propagating along with the primary vortices. As a result, the vortex decay will be enhanced. In the present research, active flow control methods on wake vortex decay, like air blowing or suction, are studied. Blowing/suction zones are embedded on the ground to generate airflow below the wake vortex tubes. Different sizes and shapes of the blowing/suction zones are tested. The large eddy simulation (LES) method is used to quantitatively investigate the blowing/suction effects on wake vortex decay. Furthermore, the coherent vortex structures observed and the acceleration mechanism on wake decay caused by active flow control are studied carefully. According to the present research, it is found that with a small blowing velocity (1.79 m/s) and a short blowing duration (13.15 s), the aircraft wake strength can be roughly reduced by 50% at t⁎=1. Based on the simulation results, it is revealed that the apparent effect on the wake vortex development is due to the detached vortex generated near the blowing zone rather than the blowing flow itself. Besides, a detached vortex with a scale of 0.2b0 is needed to achieve a better wake decay enhancement.

Forced flow response analysis of a turbulent swirling annular jet flame

This study of an externally forced, amplifier-type turbulent reacting swirling annular jet presents a low-order model for the flow response to transverse acoustic excitation and compares the model's predictions with experimental measurements. The model is formulated based on linear stability calculations about the turbulent mean flow and eddy viscosity fields obtained from separate measurements of the unforced flow. The stability calculations yield weakly global spatial modes associated with the forcing frequency, which serve as a basis upon which to project the forcing input. Thus, the model constitutes a hydrodynamic transfer function connecting the input forcing to the output coherent flow response through the linearized low Mach number compressible Navier–Stokes equations. Following a detailed presentation of the stability analysis underlying the model, the response predictions are evaluated against previously reported experiments where the jet was transversely excited at both an acoustic pressure node and an antinode. The results reveal excellent agreement between the predicted response and the measured fluctuating fields, suggesting that the low-order linear model based on the turbulent mean flow field captures the essential physics of the mode selection process in this forced configuration. This work provides further evidence that linear hydrodynamics govern the growth and decay of spatiotemporally coherent vortical structures in the swirling, turbulent jet flame, and, in particular, explains the dominance of co-rotating spiral structures.

Detecting vortical structures in time-resolved volumetric flow fields

The detection of three-dimensional coherent vortical structures that get advected as well as deformed with time is a challenge. However, it is critical for the statistical analysis of these vortices, for example, the quasi-streamwise vortices (QSVs) in the near field of a turbulent shear layer, where cavitation inception typically occurs. These structures exhibit underlying correlations among different properties that can be derived from the velocity gradients. Exploiting these correlations, a pseudo-Lagrangian vortex detection method is proposed that uses k-means clustering based on vorticity magnitude and direction, values of λ2, strain rate structure, axial stretching, and location. The method facilitates the finding that QSVs have pressure minima that are lower than those in the surrounding flow, including the primary spanwise vortices. These minima typically appear after a period of axial stretching and before contraction events.