Vortex Identification Criteria Research Articles

Two complementary eigen-based geometric properties of a vortex

In our previous paper [V. Kolář and J. Šístek, “Orbitally compact and loose vortex regions,” Phys. Fluids 35, 121708 (2023)], the eigenvalue-based measure of orbital compactness of particle motion inside a vortex for compressible flows has been proposed. Here, a complementary eigenvector-based geometric property of cylindricity (three-dimensional /3D/ aspect) is introduced. This property is closely related to the local flow axisymmetry in the swirl plane (two-dimensional /2D/ aspect) which explains the positive response of the vortex-identification Δ-criterion, and closely related criteria swirling strength and Rortex (Liutex), for almost no vorticity and a large (without any limitation) rate-of-strain magnitude. A relatively high correlation between orbital compactness, cylindricity, and widely used vortex-identification criteria has been found for several flow examples.

Scaling of coherent structures in compressible wall-bounded turbulence

Semi-local scales have been widely used in compressible wall-bounded turbulence, but it is still unclear whether they are applicable to the scaling of coherent structures, especially under conditions of high Mach number and cold wall temperature. By scrutinizing the direct numerical simulation dataset at different Mach numbers and wall temperatures, this paper demonstrates that the coherent structures normalized by semi-local scales are universal in size. In addition to this, we find that the ratios of Kolmogorov scales to semi-local scales are independent of Mach number and wall temperature. Thus, Kolmogorov scales can achieve the same scaling effect as the semi-local scales. The velocity spectra are also compared to verify the current scaling method quantitatively. A method to determine the threshold for the vortex identification criterion is proposed, allowing the same threshold for different cases to obtain vortices of similar size. The scaling of other statistics including turbulent kinetic energy, streamwise Reynolds normal stress, and root mean square of fluctuating vorticity is also investigated. A new velocity scale is proposed based on the total-stress-based transformation for mean streamwise velocity, which can collapse the profiles of these statistics more accurately than the semi-local velocity scale. The present paper demonstrates that through appropriate normalization, the structures and statistics of compressible turbulence become universal, reaffirming the validity of Morkovin's hypothesis even for the present high Mach number and cold wall cases.

Numerical simulation on the pressure, turbulence, and λ2$$ {\lambda}_2 $$ vortex characteristics within the annular symmetric jet process under different vacuum degrees

AbstractThe jet impingement flash technology represents a paramount research subject in the domain of heat and mass transfer. To augment its commercial potential, the conjunction of annular multi‐aperture jet impingement with negative pressure flash evaporation is introduced in this study. The employment of an annular nozzle array is integral to the enhancement of the heat and mass transfer efficiency between the phases. The Realizable k‐ε model is used in this study. The negative pressure flash vaporization model was also developed by introducing a mass source term and an energy source term based on the Mixture model. The flow characteristics are characterized using numerical simulation. Additionally, the λ2 vortex identification criterion is investigated the vortex structure. The simulation results exhibit good agreement with experimental findings, demonstrating that a higher initial vacuum leads to a stronger flashing effect and a more chaotic movement of the flow group within the flow field. Thus, this study provides a reference method for the structural design and optimization of annular symmetric jet impingement negative pressure deammonia chemical equipment for engineering applications.

Numerical Characterization of Prestall Disturbances in a Compressor Stage

Abstract Compared to the subject of rotating stall, less attention has been given to prestall flow disturbances in turbomachinery. This is mostly due to the fact that these phenomena, often referred to as Rotating Instabilities, do not necessarily or distinctly occur in every compressor and usually last for a long period without posing serious threats to stable operation. The present study aims at numerically characterizing prestall disturbances in detail in a compressor stage in which they have been experimentally observed. Full-annulus computational fluid dynamics (CFD) computations employing a hybrid scale-resolving turbulence model are performed and compared against unsteady experimental data. Assessment of specific prestall disturbance metrics, including power spectral density, coherence, and circumferential mode distribution at the rotor clearance, shows that the numerical model is successful in reproducing the unsteady phenomena close to stall inception. Moreover, dynamic mode decomposition is employed to directly link each peak of the unique prestall disturbance spectral signature to spatial structures with a different circumferential order. This procedure is done for both 1D circumferential modes, based on flush-mounted pressure probes, and for 2D surfaces exposing the tip clearance dynamics. The high-resolution numerical model, supplemented with vortex identification criteria and data-driven decompositions, enhances the understanding of prestall disturbances and their associated coherent flow structures.

Orbitally compact and loose vortex regions

The measure of orbital compactness of the motion of swirling material points inside a vortex is formulated without the assumption of incompressibility. Orbitally compact and loose vortex regions are distinguished. Their boundary is set very permissively and expressed through the introduced measure of orbital compactness. The present analysis is associated with the vortex-identification local trace criterion and explains its limited applicability. The comparison of compact and loose volumetric ratios for selected vortex-identification methods employs numerical data of four flow situations. The investigation shows that some vortex-identification criteria are too permissive, more or less ignoring the inherent vortex property of orbital compactness.

Vortex characteristics inside profile reed channel of an air-jet loom based on large eddy simulation

In the process of jet weaving, airflow plays a primary role by carrying the weft yarns and interlacing them with the warp yarns to form the fabric. The vortex characteristics within the weft insertion channel of an air-jet loom directly affect the motion of the weft yarns, thus impacting the quality of the fabric. In this study, the large eddy simulation (LES) method was employed, and the Omega vortex identification criterion was used to analyze the vortex characteristics within the profile reed channel. The effects of different positions of relay nozzles, nozzle spacing, and reed gap ratio on the airflow characteristics were investigated. Additionally, the vortex volume ratio () and velocity fluctuation rate () were introduced as indicators to measure the proportion of vortices and the turbulence intensity of the airflow field. The numerical results indicated that the introduction of relay nozzles significantly reduced the intensity of airflow vortices and the proportion of vortices within the profile reed channel. When the inlet pressures of the main and relay nozzles were fixed, the minimum values of and were observed when the first relay nozzle was located at 105 mm, the nozzle spacing was 65 mm, and the gap ratio was 1:2. The findings of this study provide theoretical guidance for further improving the airflow characteristics within the profile reed channel of an air-jet looms.

A parameter-free LES model for anisotropic mesh adaptivity

Balancing accuracy and computational cost is a challenge in the modelling of turbulent flows. A widely used method for turbulence modelling is large–eddy simulation (LES). LES allows one to describe large scale flow features at a reasonable computational cost compared to the more accurate direct numerical simulation (DNS), making it a popular choice for engineering applications. One strategy to balance accuracy and cost with LES is through the use of mesh adaptivity, which allows the degrees of freedom in a problem to be reduced by changing spatial discretisation. However, mesh adaptivity can affect accuracy when using the standard Smagorinsky LES model with an implicit filter, considering that the parameter Cs is highly dependent on the filter width, which depends on mesh resolution. This work is aimed to develop an LES model that does not require any user–defined parameters and is suitable for mesh adaptivity with implicit filter. In this study we introduce a parameter–free LES model incorporating an anisotropic eddy–viscosity formulation combined with anisotropic mesh adaptivity. In our model, the parameter Cs in the eddy–viscosity formulation of the Smagorinsky model, is replaced by a function that evaluates the relative location of turbulence fluctuations in each element with respect to the turbulence spectrum inertial range. The anisotropic formulation of the eddy–viscosity allows for the application of an appropriate filter width in different directions, improving accuracy. Additionally, the mesh adaptivity algorithm assesses the local turbulence fluctuations via local Reynolds number and vortex identification criteria. This assessment leads to the refinement of regions with higher turbulence fluctuations down to the smallest scale limit in the inertial range in the corresponding direction, and also leads to the coarsening of regions without turbulence fluctuation up to largest scale limit in the inertial range. This method is tested using a flow past a sphere test case. The results are compared both qualitatively and quantitatively to results obtained with the standard Smagorinsky model, and demonstrate the better performance of our method with lower computational cost. This allows us to simulate large Reynolds number cases and compare our quantitative results to experimental results found in the literature, emphasising that our method produces good results at reasonable computational cost.

Effect of the yaw angle on the aerodynamics of two tandem wind turbines by considering a dual-rotor wind turbine in front

The innovative dual-rotor counter-rotating wind turbine (CRWT) shows great importance in the development of offshore wind farms. In this paper, the performance and wake characteristics of the independent CRWT and two tandem wind turbines equipped with a CRWT at different yaw angles were numerically studied using the open-source software SOWFA (Simulator fOr Wind Farm Applications). The actuator line model (ALM) and large-eddy simulation (LES) were used to model wind turbines and turbulent flows. The third generation of vortex identification criterion was used to analyze wake vortex characteristics. The results indicated the auxiliary rotor had a negligible effect on the main rotor in terms of the dominant frequency and fluctuations. In comparison with the rotational blade frequency (BF), it was found that one BF and double BF were equivalent to the dominant frequency of the SRWT and CRWT, respectively. The CRWT suffers a greater velocity deficit and has a faster velocity recovery. In the case of tandem wind turbines, the upstream wind turbine equipped with a CRWT performs minimal influence on the optimal yaw angle of 30°. In addition, the effects of the yaw angle on wake center deflection, wake width, and performance fluctuation for the downstream wind turbine were investigated.

Spatial-temporal evolution and pressure fluctuation characteristics of the combined submerged vortex in a closed pump sump

Following the retrofit of the pump sump, there is a high risk of inducing the Combined Submerged Vortex (CSV), which consists of the roof-attached vortex (RAV) and floor-attached vortex (FAV). This vortex formation can lead to irregular pressure fluctuations, adversely affecting the unit's performance and compromising the stability of energy conversion. This study aims to investigate the spatiotemporal evolution of the CSV and its associated pressure fluctuation characteristics in a closed pump sump. High-speed visualization and pressure fluctuation tests are conducted on a transparent closed-loop test rig. The findings demonstrate that the spatiotemporal evolution of the CSV can be divided into three stages: developing, competing, and collapsing. The competing stage, in particular, has a significant impact on the FAV. During the CSV period, the dominant low frequencies induced by the RAV and FAV are 0.24 and 0.13 Hz, respectively, with the FAV exhibiting higher intensity than the RAV. The regions of high coherence between the RAV and FAV are primarily concentrated within the low-frequency range of 0.25–2 Hz, and the signals exhibit multiple phase differences. Furthermore, a vortex identification criterion for a closed sump is proposed based on Continuous Wavelet Transform.

Computational turbulent flow characteristics in a centrifugal pump

This investigation provides the 3D numerical simulations of a six-blade centrifugal pump that is commonly applied in agriculture and food processing sectors. The simulations were carried out using the unsteady Reynolds averaged Navier–Stokes equations. The k-omega turbulence model was used as a closure for the equations. The velocity and pressure flow fields were used to predict the turbulent flows in the pump under three different operating conditions (part-load 0.8Qd, design 1.0 Qd, and overload 1.2 Qd). The omega vortex identification criterion was further applied to visualize the coherent vortex structures in the impeller and volute at the investigated flow conditions. The impeller eye was characterized with the lowest static pressure fields causing this region to be highly susceptible to cavitation under all flow conditions. At the design point, the velocity vectors were orderly patterned along the blade flow curvature. However, flow separation occurred around the leading edge mainly due to the fact that the flow is non-tangential to the leading edge of the blade as a result of the unsteady effect developed upstream. In conclusion, it can be confirmed that the volute geometry is highly sensitive to the evolution and formation of vortices as revealed by the omega vortex criterion. This work reveals that the design of the volute geometry should be further improved to mitigate unsteady flow losses. Again, this kind of study helps reduce the required experimental measurements for the improvement and design of hydraulic machines.

Vortex identification methods applied to wind turbine tip vortices

Abstract. This study describes the impact of postprocessing methods on the calculated parameters of tip vortices of a wind turbine model when tested using particle image velocimetry (PIV). Several vortex identification methods and differentiation schemes are compared. The chosen methods are based on two components of the velocity field and their derivatives. They are applied to each instantaneous velocity field from the dataset and also to the calculated average velocity field. The methodologies are compared through the vortex center location, vortex core radius and jittering zone. Results show that the tip vortex center locations and radius have good comparability and can vary only a few grid spacings between methods. Conversely, the convection velocity and the jittering surface, defined as the area where the instantaneous vortex centers are located, vary between identification methods. Overall, the examined parameters depend significantly on the postprocessing method and selected vortex identification criteria. Therefore, this study proves that the selection of the most suitable postprocessing methods of PIV data is pivotal to ensure robust results.

On the effectiveness of local vortex identification criteria in the vortex representation of wall-bounded turbulence

On the effectiveness of local vortex identification criteria in the vortex representation of wall-bounded turbulence

Investigation on the Flow Behavior of Side Channel Pumps Based on Vortex Identification

The momentum flow exchange between the impeller and side channel produces highly turbulent flows in side channel pumps. The turbulent flows feature complex patterns of vortex structures that are partly responsible for the dissipation of energy losses and unsteady pressure pulsations. The concept of turbulent flows in side channel pumps requires a reliable vortex identification criterion to capture and predict the effects of the vortex structures on the performance. For this reason, the current study presents the application of the new Ω-criterion to a side channel pump model in comparison with other traditional methods such as Q and λ2 criteria. The 3D flow fields of the pump were obtained through unsteady Reynolds-averaged Navier-Stokes (RANS) simulations. Comparative studies showed that the Ω-criterion identifies the vortex of different intensities with a standard threshold, Ω=0.52. The Q and λ2 criteria required different thresholds to capture vortex of different intensities thus leads to subjective errors. Comparing the Ω-criterion intensity on different planes with the entropy losses and pressure pulsation, the longitudinal vortex plays an important role in the momentum exchange development which increases the head performance of the pump. However, the rate of exchange is impeded by the axial and radial vortices restricted in the impeller. Therefore, the impeller generates the highest entropy loss and pressure pulsation intensities which lower the output efficiency. Finally, the findings provide a fundamental background to the morphology of the vortex structures in the turbulent flows which can be dependent upon for efficiency improvement of side channel pumps.

Image-based flow decomposition using empirical wavelet transform

Abstract

Vortices evolution in the solar atmosphere

Aims. We study vortex dynamics in the solar atmosphere by employing and deriving the analytical evolution equations of two vortex identification criteria. Methods. The two criteria used are vorticity and the swirling strength. Vorticity can be biased in the presence of shear flows, but its dynamical equation is well known; the swirling strength is a more precise criterion for the identification of vortical flows, but its evolution equation is not known yet. Therefore, we explore the possibility of deriving a dynamical equation for the swirling strength. We then apply the two equations to analyze radiative magneto-hydrodynamical simulations of the solar atmosphere produced with the CO5BOLD code. Results. We present a detailed review of the swirling strength criterion and the mathematical derivation of its evolution equation. This equation did not exist in the literature before and it constitutes a novel tool that is suitable for the analysis of a wide range of problems in (magneto-)hydrodynamics. By applying this equation to numerical models, we find that hydrodynamical and magnetic baroclinicities are the driving physical processes responsible for vortex generation in the convection zone and the photosphere. Higher up in the chromosphere, the magnetic terms alone dominate. Moreover, we find that the swirling strength is produced at small scales in a chaotic fashion, especially inside magnetic flux concentrations. Conclusions. The swirling strength represents an appropriate criterion for the identification of vortices in turbulent flows, such as those in the solar atmosphere. Moreover, its evolution equation, which is derived in this paper, is pivotal for obtaining precise information about the dynamics of these vortices and the physical mechanisms responsible for their production and evolution. Since this equation is available, the swirling strength is now the ideal quantity to study the dynamics of vortices in (magneto-)hydrodynamics.

The role of flow rotation in the adult right atrium: a 4D flow cardiovascular magnetic resonance study

Objective: In healthy adults, the right atrium (RA) serves as a reservoir for the systemic flow return from the superior vena cava (SVC) and inferior vena cava (IVC), preparing the two flows to be transferred to the right ventricle (RV) and pulmonary circulation. This study aims to quantify the haemodynamics of the RA and the associated SVC and IVC inflows, which have not been fully understood to date. Approach: Eighteen adults with structurally normal hearts underwent 4D flow magnetic resonance imaging. The cardiac cycle was resolved to 20 temporal phases with a spatial resolution of 3 × 3 × 3 mm3. Analysis included objective visualisation of the flow structures in the RA identified by three different vortex identification criteria, kinetic energy (KE), enstrophy and dissipation. KE and helicity flux were also assessed in both caval veins. Main results: Vortex identification methods confirmed that in the majority of participants the blood flow from the caval veins filling the RA during ventricular systole is not chaotic, but rather forms an organised pattern of a single coherent forward turning vortex structure. Thirteen participants displayed a single vortex flow structure, four showed multiple vortices and one had a helical flow pattern without a clear vortex structure. A strong positive correlation exists between the flow KE and enstrophy density. Significance: This suggests that flow energy in the RA is mainly rotational, part of which is convected by the highly helical SVC and IVC inflows. Multiple vortices tend to be associated with higher dissipation rates in the central RA region due to turbulence. The rotational nature of the flow in the RA maintains KE better than non-rotational flow. RA flow characteristics are highly related to the helicity content in the caval veins, as well as the KE flux intensity. Lower caval helicity or IVC KE flux dominance tends to favour single vortex formation while the opposite tends to lead to multiple vortices or the rare helical flow patterns. Atria lacking single vortex flow are inclined to have a larger energy input from atrial contraction.

Theory and applications of the vortex-surface field

We review the progress on the theory and applications of the vortex-surface field (VSF). The VSF provides a systematic Lagrangian-based framework for the identification, characterization, and modeling of flow structures. From the theoretical perspective, the vorticity is simplified to a scalar field as the VSF. The VSF isosurface is a vortex surface consisting of vortex lines. By introducing the virtual circulation-preserving velocity, the Helmholtz theorem and the Ertel theorem are extended to some non-ideal flows, so that the VSF evolution equation can be expressed in a Lagrangian conservation form. Thus the VSF isosurfaces of the same threshold at different times have strong coherence, facilitating the tracking of vortex surfaces. As a general flow diagnostic tool, the numerical VSF solution can be constructed in arbitrary flow fields by solving a pseudo-transport equation driven by the frozen, instantaneous vorticity. In addition, the local optimization method and the boundary-constraint method can further improve the smoothness and convergence of VSF solutions. Then the two-time method is developed for calculating the temporal evolution of VSFs. From post-processing of large-scale database of numerical simulations, the VSF elucidates mechanisms in the flows with essential vortex dynamics, such as turbulence and transition. For example, the VSF reveals the complex network of tangling vortex tubes in isotropic turbulence, consistent with the vorticity equation and dynamics. In addition, Eulerian vortex-identification criteria cannot identify complete vortex tubes, so the visual “breakdown” of worm-like structures were often reported in the literature. The universal framework of the VSF evolution illustrates an ordered evolution process of coherence structures in transitional flows, in which it is no need to ad hoc change the structure-identification method and isocontour threshold. Moreover, the quantitative VSF study elucidates the interaction between the vortex surface and the shock wave, flame, or electromagnetic field in multi-physics coupled flows. Based on the characterization of VSFs, we seek robust statistical features, and then determine and model correlations between the features and critical quantities to be predicted in engineering applications. For example, we develop a predictive model of the skin-friction coefficient in boundary-layer transition based on the small-scale inclination angle in experimental images. Some open problems in the VSF study are discussed, including the regularization for the breakdown of virtual conservation theorems at vorticity nulls and the speedup of the numerical construction and evolution of VSFs.

The effects of flexible vortex generator on the wake structures for improving turbulence

Turbulence is a very useful flow characteristic that is used in many engineering devices to facilitate mixing, heat transfer in heat exchanger and improving aerodynamics in propeller. This paper has numerically studied the spatial characteristics of the wake behind a free-oscillating flexible vortex generator (FVG) in order to evaluate its turbulence generation ability. As the wake is playing as the effective turbulence region, the spatial characteristics can reflect the ability of the FVG in turbulence generation when a larger wake size indicates a greater turbulence region. Two VGs are considered in this study; circular and flat plate cantilever. Each VG was submerged individually in a subcritical flow (102 <ReD < 105) and the generated wake was studied. The wake behind the FVG was visualized via the lambda2 vortex identification criterion and it was compared with its respective rigid counterpart. From the comparison, it is found that the FVG has a larger wake compared to its rigid counterpart. The result demonstrates that the FVG can generate a larger turbulence region. The cause of the increasing wake size was found to be the weakening of downwash behind the FVG when it bends. The downwash becomes weaker as the deflection of the FVG increases.

Vortex statistics in two-dimensional turbulence based on IB-LBM

In this paper, the two-dimensional (2D) turbulence perturbed by arrays of cylinders placed both horizontally and vertically is investigated by Immersed Boundary Lattice Boltzmann Method (IB-LBM). The energy spectrum reveals the coexistence of the inverse and direct cascades in 2D grid turbulence. By observing at the distribution of fluxes in space, the energy and enstrophy fluxes have explained the physical mechanism of the double cascades where the two Kolmogorov laws for structure functions are simultaneously observed. The results of vortex statistics by the conditional analysis, which are based on a new and accurate vortex identification criteria called Liutex, show that the algebraic number density [Formula: see text], where [Formula: see text] is vortex area. The time-evolving vortex number density distribution constructs a theoretical framework involving a three-part: [Formula: see text]; [Formula: see text]; [Formula: see text], which is satisfied with the prediction well. The relationship between the vortex circulation [Formula: see text] and vortex area [Formula: see text] is [Formula: see text] and the one between the kinetic energy of vortex [Formula: see text] and [Formula: see text] is [Formula: see text] in the range where [Formula: see text]. Moreover, it has been found that vortices contain about 30% of the total energy of the flow by studying the energy ratio of all vortices to the entire flow field. What is more, it is an interesting phenomenon is that there is only a range where [Formula: see text] in the energy spectrum for the coherent structure field which is obtained by using Liutex as the extraction of vortices. The probability density function (PDF) of the fluctuations of longitudinal velocity shows that an indication of small intermittency in the direct cascade and the absence of intermittency in the inverse cascade range. On the other hand, the scaling exponents [Formula: see text] of the structure function for the inverse cascade are consistent with Kr67 model, which shows the absence of intermittency. While the measured intermittency parameters are [Formula: see text] and [Formula: see text], which explains that there is a very weak intermittent correction in the direct cascade, and ESS has verified the existence of intermittency in our 2D turbulence.

Vortex statistics of a cylinder wake flow close to the wall based on IB-LBM

In this paper, statistical behaviors of vortex in the wake flow of a circular cylinder placed near a plane wall in the two-dimensional (2D) channel are investigated by Immersed Boundary Lattice Boltzmann Method. Although vortices shed from the cylinder periodically, there are very complicated interactions between vortices and the solid wall. The gap ratios [Formula: see text] are considered in three cases [Formula: see text] to study vortex statistic behaviors when flow is in steady state. It can be seen that a single row of coherent structures in the same sign varies to dipole vortex shedding as [Formula: see text] increases. The results of vortex statistics by the conditional analysis, which are based on a new and accurate vortex identification criteria called Liutex, show the algebraic number density [Formula: see text], where [Formula: see text] is vortex area. The relationship between the vortex circulation [Formula: see text] and vortex area [Formula: see text] is [Formula: see text] and the one between the kinetic energy of vortex [Formula: see text] and [Formula: see text] is [Formula: see text] in the range where [Formula: see text]. Moreover, it has been found that vortices contain about 30% of the total energy of the flow which is almost conserved as Re varies by studying the energy ratio [Formula: see text] of all vortices to the entire flow field. The statistic behaviors of energy spectrums show that the spectrums contain an inertial range in which [Formula: see text] not only in the coherent structure field but also in the background field. More features of the vortex structure in the wake flow have been described by the empirical mode decomposition (EMD). There is a linear relationship between the frequency and the mode of the form [Formula: see text] e[Formula: see text] in the semi-log coordinates. The period of each mode [Formula: see text] e[Formula: see text] in the semi-log coordinates. The time-dependent intrinsic correlation (TDIC) shows that there is a strong negative correlation relationship between the pressure and the flow velocity in the complex attachment vortex.